Finite Group Databasebeta

← #17199686

Subgroups — #17199686

Order 4352.

2636 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763453C211yesmaximal, characteristic
2#14531947C211yesmaximal, characteristic, complemented
3#14531936C211yesmaximal, characteristic, complemented
4#14531934C211yesmaximal, characteristic, complemented
5#14531923C211yesmaximal, characteristic, complemented
6#14531893C211yesmaximal, characteristic, complemented
7#14531829C211yesmaximal, characteristic, complemented
8#14531819C211yesmaximal, characteristic, complemented
9#14531770C211yesmaximal, characteristic, complemented
10#14531763C211yesmaximal, characteristic, complemented
11#14531727C211yesmaximal, characteristic, complemented
12#14531722C211yesmaximal, characteristic, complemented
13#14531635C211yesmaximal, characteristic, complemented
14#14531629C211yesmaximal, characteristic, complemented
15#14531610C211yesmaximal, characteristic, complemented
16#14531593C211yesmaximal, characteristic, complemented
17#14531571C211yesmaximal, characteristic, complemented
18#14531543C211yesmaximal, characteristic, complemented
19#14531540C211yesmaximal, characteristic, complemented
20#14531486C211yesmaximal, characteristic, complemented
21#14531449C211yesmaximal, characteristic, complemented
22#14531442C211yesmaximal, characteristic, complemented
23#14531439C211yesmaximal, characteristic, complemented
24#14531426C211yesmaximal, characteristic, complemented
25#14531380C211yesmaximal, characteristic, complemented
26#14531371C211yesmaximal, characteristic, complemented
27#14531362C211yesmaximal, characteristic, complemented
28C4×#10587625C211yesmaximal, characteristic, complemented
29#14531224C211yesmaximal, characteristic, complemented
30C2×#11762697C211yesmaximal, characteristic, complemented
31D4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33#11763453C4116yescomplemented
34C2×#10587622C2211yescharacteristic
35C2×#10587621C2211yescharacteristic
36C2×#10587621C2211yescharacteristic
37C2×#10587610C2211yescharacteristic
38C2×#10587625C2211yescharacteristic
39C2×#10587625C2211yescharacteristic
40C2×#10587624C2211yescharacteristic
41C2×#10587639C2211yescharacteristic
42C2×#10587639C2211yescharacteristic
43C2×D4×Dic17C2211yescharacteristic
44C2×C4×C22⋊D17C2211yescharacteristic
45C2×C4×C22⋊D17C2211yescharacteristic, complemented
46C2×C4×C22⋊D17C2211yescharacteristic, complemented
47C2×#10587567C2211yescharacteristic, complemented
48C2×#10587567C2211yescharacteristic, complemented
49C2×#10587563C2211yescharacteristic, complemented
50C2×#10587563C2211yescharacteristic, complemented
51C22×#63225C2211yescharacteristic, complemented
52C22×C22⋊Dic17C2211yescharacteristic
53C22×C22⋊Dic17C2211yescharacteristic
54C22×C22⋊Dic17C2211yescharacteristic
55C22×C22⋊Dic17C2211yescharacteristic
56C22×C4×Dic17C2211yescharacteristic, complemented
57#11762713C2211yescharacteristic, complemented
58#11762713C2211yescharacteristic, complemented
59#11762713C2211yescharacteristic, complemented
60#11762713C2211yescharacteristic, complemented
61#11762709C2211yescharacteristic
62#11762709C2211yescharacteristic
63#11762709C2211yescharacteristic, complemented
64#11762709C2211yescharacteristic, complemented
65#11762709C2211yescharacteristic, complemented
66#11762709C2211yescharacteristic, complemented
67#11762704C2211yescharacteristic, complemented
68#11762704C2211yescharacteristic, complemented
69#11762704C2211yescharacteristic, complemented
70#11762704C2211yescharacteristic, complemented
71#11762703C2211yescharacteristic
72#11762703C2211yescharacteristic
73#11762703C2211yescharacteristic
74#11762703C2211yescharacteristic
75#11762703C2211yescharacteristic, complemented
76#11762703C2211yescharacteristic, complemented
77#11762703C2211yescharacteristic, complemented
78#11762703C2211yescharacteristic, complemented
79#11762703C2211yescharacteristic, complemented
80#11762703C2211yescharacteristic, complemented
81#11762703C2211yescharacteristic, complemented
82#11762703C2211yescharacteristic, complemented
83#11762699C2211yescharacteristic, complemented
84#11762699C2211yescharacteristic, complemented
85#11762697C2211yescharacteristic
86#11762697C2211yescharacteristic
87#11762697C2211yescharacteristic
88#11762697C2211yescharacteristic
89#11762697C2211yescharacteristic
90#11762697C2211yescharacteristic
91#11762697C2211yescharacteristic
92#11762697C2211yescharacteristic
93#11762697C2211yescharacteristic, complemented
94#11762697C2211yescharacteristic, complemented
95#11762697C2211yescharacteristic, complemented
96#11762697C2211yescharacteristic, complemented
97#11762697C2211yescharacteristic, complemented
98#11762697C2211yescharacteristic, complemented
99#11762697C2211yescharacteristic, complemented
100#11762697C2211yescharacteristic, complemented
101#11762694C2211yescharacteristic, complemented
102#11762694C2211yescharacteristic, complemented
103#11762693C2211yescharacteristic, complemented
104#11762693C2211yescharacteristic, complemented
105#11762693C2211yescharacteristic, complemented
106#11762693C2211yescharacteristic, complemented
107#11762692C2211yescharacteristic, complemented
108#11762692C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762690C2211yescharacteristic, complemented
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762689C2211yescharacteristic
114#11762689C2211yescharacteristic
115#11762689C2211yescharacteristic
116#11762689C2211yescharacteristic
117#11762689C2211yescharacteristic
118#11762689C2211yescharacteristic
119#11762688C2211yescharacteristic, complemented
120#11762688C2211yescharacteristic, complemented
121#11762686C2211yescharacteristic, complemented
122#11762686C2211yescharacteristic, complemented
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic, complemented
126#11762685C2211yescharacteristic, complemented
127#11762685C2211yescharacteristic, complemented
128#11762685C2211yescharacteristic, complemented
129#11762682C2211yescharacteristic, complemented
130#11762682C2211yescharacteristic, complemented
131#11762682C2211yescharacteristic, complemented
132#11762682C2211yescharacteristic, complemented
133#11762681C2211yescharacteristic, complemented
134#11762681C2211yescharacteristic, complemented
135#11762681C2211yescharacteristic, complemented
136#11762681C2211yescharacteristic, complemented
137#11762676C2211yescharacteristic, complemented
138#11762672C2211yescharacteristic
139#11762672C2211yescharacteristic
140#11762671C2211yescharacteristic, complemented
141#11762670C2211yescharacteristic, complemented
142#11762670C2211yescharacteristic, complemented
143#11762668C2211yescharacteristic, complemented
144#11762668C2211yescharacteristic, complemented
145#11762667C2211yescharacteristic, complemented
146#11762667C2211yescharacteristic, complemented
147#11762667C2211yescharacteristic, complemented
148#11762667C2211yescharacteristic, complemented
149#11762665C2211yescharacteristic
150#11762665C2211yescharacteristic
151C4×#63225C2211yescharacteristic, complemented
152C4×#63225C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic, complemented
155C22⋊C4×Dic17C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic, complemented
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166C4×C22⋊Dic17C2211yescharacteristic, complemented
167C4×C22⋊Dic17C2211yescharacteristic, complemented
168#11762654C2211yescharacteristic, complemented
169#11762654C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C23×D4×C17C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C4×D4×C17C2211yescharacteristic
176C22×C22⋊C4×C17C2211yescharacteristic
177C22×C22⋊C4×C17C2211yescharacteristic
178C17×#390C2211yescharacteristic
179C17×#390C2211yescharacteristic
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#380C2211yescharacteristic
185C17×#379C2211yescharacteristic
186C17×#379C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C25×C17C2311yescharacteristic
190C22×D4×C17—42no—
191C22×D4×C17—42no—
192C22×D4×C17C2×C418yescomplemented
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C2×#63254—42no—
216C2×#63254—42no—
217C2×#63254C2×C418yescomplemented
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C4×D4×C17—42no—
223C4×D4×C17—42no—
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17—42no—
227C2×C22⋊C4×C17—42no—
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246#10587639C2×C418yescomplemented
247#10587639C2×C418yescomplemented
248C2×C22⋊Dic17—42no—
249C2×C22⋊Dic17—42no—
250C2×C22⋊Dic17C2×C418yescomplemented
251C2×C22⋊Dic17C2×C418yescomplemented
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277C2×C22⋊Dic17C2311yescharacteristic
278C2×C22⋊Dic17C2311yescharacteristic
279#10587625C2×C418yescomplemented
280#10587625C2×C418yescomplemented
281#10587624C2×C418yescomplemented
282#10587622C2×C418yescomplemented
283#10587621C2×C418yescomplemented
284#10587621C2×C418yescomplemented
285D4×Dic17C2×C418yescomplemented
286C4×C22⋊D17—42no—
287C4×C22⋊D17—42no—
288C4×C22⋊D17C2×C418yescomplemented
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297#10587610C2×C418yescomplemented
298C2×#63225—42no—
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×C4×Dic17—42no—
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332#10587567—42no—
333#10587567—42no—
334#10587563—42no—
335#10587563—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17—22no—
377C24×C17—22no—
378C24×C17—41no—
379C24×C17—41no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17—41no—
383C24×C17—41no—
384C24×C17—41no—
385C24×C17—41no—
386C24×C17—41no—
387C24×C17—41no—
388C24×C17C22×C414yes—
389C24×C17C22×C414yes—
390C24×C17C2411yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C24×C17C2411yescharacteristic
395C23×D17C2411yescharacteristic
396C2×D4×C17—22no—
397C2×D4×C17—22no—
398C2×D4×C17—22no—
399C2×D4×C17—22no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17—41no—
403C2×D4×C17—41no—
404C2×D4×C17—416no—
405C2×D4×C17C22×C414yes—
406C2×D4×C17C22×C414yes—
407C2×D4×C17C22×C414yes—
408C2×D4×C17C22×C414yes—
409C22×C4×C17—22no—
410C22×C4×C17—22no—
411C22×C4×C17—22no—
412C22×C4×C17—22no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17—41no—
418C22×C4×C17—41no—
419C22×C4×C17—41no—
420C22×C4×C17—41no—
421C22×C4×C17—41no—
422C22×C4×C17—41no—
423C22×C4×C17C22×C414yes—
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17C22×C414yes—
445C2×C22⋊D17C22×C414yes—
446C2×C22⋊D17C22×C414yes—
447C2×C22⋊D17C22×C414yes—
448C2×C22⋊D17C22×C414yes—
449C22×Dic17—22no—
450C22×Dic17—22no—
451C22×Dic17—22no—
452C22×Dic17—22no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17—41no—
463C22×Dic17—41no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17—41no—
467C22×Dic17—41no—
468C22×Dic17—41no—
469C22×Dic17C22×C414yes—
470C22×Dic17C22×C414yes—
471C22×Dic17C22×C414yes—
472C22×Dic17C22×C414yes—
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488#63254—416no—
489C2×C4×D17—22no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×C4×D17—41no—
495C2×C4×D17—41no—
496C2×C4×D17—41no—
497C2×C4×D17C22×C414yes—
498C2×Dic34—41no—
499C2×Dic34—41no—
500C2×Dic34C22×C414yes—
501C4⋊C4×C17—41no—
502C4⋊C4×C17—41no—
503C22⋊C4×C17—22no—
504C22⋊C4×C17—22no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17—22no—
507C22⋊C4×C17—22no—
508C22⋊C4×C17—41no—
509C22⋊C4×C17—41no—
510C22⋊C4×C17—41no—
511C22⋊C4×C17—41no—
512C22⋊C4×C17—41no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17—41no—
515C22⋊C4×C17—41no—
516C22⋊C4×C17—41no—
517C22⋊C4×C17—41no—
518C22⋊C4×C17—41no—
519C42×C17—41no—
520C42×C17—41no—
521C22⋊Dic17—22no—
522C22⋊Dic17—22no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17—41no—
527C22⋊Dic17—41no—
528C22⋊Dic17—41no—
529C22⋊Dic17—41no—
530C22⋊Dic17—41no—
531C22⋊Dic17—41no—
532C22⋊Dic17—41no—
533C22⋊Dic17—41no—
534C22⋊Dic17—41no—
535C22⋊Dic17—41no—
536C22⋊Dic17—41no—
537C22⋊Dic17C22×C414yes—
538C22⋊Dic17C22×C414yes—
539C22⋊Dic17C22×C414yes—
540C22⋊Dic17C22×C414yes—
541C22⋊Dic17C22×C414yes—
542C22⋊Dic17C22×C414yes—
543C22⋊Dic17C22×C414yes—
544C22⋊Dic17C22×C414yes—
545C22⋊Dic17C22×C414yes—
546C22⋊Dic17C22×C414yes—
547C22⋊Dic17C22×C414yes—
548#63227—41no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227—41no—
554#63227C22×C414yes—
555C4⋊Dic17C22×C414yes—
556#63225—22no—
557#63225—41no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569#63225—41no—
570#63225C22×C414yes—
571#63225C22×C414yes—
572#63225C22×C414yes—
573C4×Dic17—22no—
574C4×Dic17—22no—
575C4×Dic17—41no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583C4×Dic17—41no—
584C4×Dic17—41no—
585C4×Dic17—41no—
586C4×Dic17—41no—
587C4×Dic17C22×C414yes—
588#34492—171nomaximal, Sylow
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—28no—
618C23×C17—44no—
619C23×C17—44no—
620C23×C17—44no—
621C23×C17—44no—
622C23×C17—44no—
623C23×C17—82no—
624C23×C17—82no—
625C23×C17—82no—
626C23×C17—82no—
627C23×C17—82no—
628C23×C17—82no—
629C23×C17—82no—
630C23×C17—82no—
631C23×C17C23×C412yes—
632C23×C17C23×C412yes—
633C23×C17C23×C412yes—
634C23×C17C23×C412yes—
635C23×C17C23×C412yes—
636C23×C17H(5,𝔽2)12yes—
637C23×C17H(5,𝔽2)12yes—
638C23×C17C2511yescharacteristic
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17C23×C412yes—
646D4×C17—28no—
647D4×C17—28no—
648D4×C17—44no—
649D4×C17—44no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—44no—
678C2×C4×C17—44no—
679C2×C4×C17—82no—
680C2×C4×C17—82no—
681C2×C4×C17—82no—
682C2×C4×C17C23×C412yes—
683C2×C4×C17C23×C412yes—
684C2×C4×C17H(5,𝔽2)12yes—
685C22⋊D17—28no—
686C22⋊D17—44no—
687C22⋊D17—44no—
688C22⋊D17—44no—
689C22⋊D17—44no—
690C2×Dic17—28no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—44no—
730C2×Dic17—44no—
731C2×Dic17—44no—
732C2×Dic17—44no—
733C2×Dic17—82no—
734C2×Dic17—82no—
735C2×Dic17—82no—
736C2×Dic17C23×C412yes—
737C2×Dic17C23×C412yes—
738C2×Dic17C23×C412yes—
739C2×Dic17C23×C412yes—
740C2×Dic17C23×C412yes—
741C2×Dic17C23×C412yes—
742C2×Dic17C23×C412yes—
743C4×D17—44no—
744C4×D17—82no—
745C4×D17—82no—
746Dic34—44no—
747C2×#546—171no—
748#2378—171no—
749#2377—171no—
750#2376—171no—
751#2375—171no—
752#2372—171no—
753#2364—171no—
754#2363—171no—
755#2359—171no—
756#2358—171no—
757#2353—171no—
758#2353—171no—
759#2342—171no—
760#2342—171no—
761#2339—171no—
762D4×C22⋊C4D1711yescharacteristic, complemented
763#2337—171no—
764#2335—171no—
765#2333—171no—
766#2332—171no—
767#2325—171no—
768#2322—171no—
769#2321—171no—
770#2321—171no—
771#2319—171no—
772#2312—171no—
773#2311—171no—
774#2308—171no—
775C4×#121—171no—
776#2290—171no—
777C2×#388—171no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
785C22×C17—22no—
786C22×C17—22no—
787C22×C17—22no—
788C22×C17—22no—
789C22×C17—22no—
790C22×C17—22no—
791C22×C17—22no—
792C22×C17—22no—
793C22×C17—22no—
794C22×C17—22no—
795C22×C17—22no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—41no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—88no—
813C22×C17—88no—
814C22×C17#51814yes—
815C22×C17C24×C411yescharacteristic
816C22×C17C2×H(5,𝔽2)11yescharacteristic
817C22×C17C2×H(5,𝔽2)11yescharacteristic
818C22×C17C2×H(5,𝔽2)11yescharacteristic
819C22×C17#58511yescharacteristic
820C22×C17#58511yescharacteristic
821C22×C17#58511yescharacteristic
822C2×D17—22no—
823C2×D17—22no—
824C2×D17—22no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C4×C17—22no—
830C4×C17—22no—
831C4×C17—22no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839Dic17—22no—
840Dic17—22no—
841Dic17—22no—
842Dic17—22no—
843Dic17—22no—
844Dic17—22no—
845Dic17—22no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854C22×#41—171no—
855C23×D4C2×D1711yescharacteristic
856#546—1716no—
857C2×#124—171no—
858C2×#123—171no—
859C2×#123—171no—
860C2×C22⋊Q8—171no—
861C2×#121—171no—
862C2×#121—171no—
863C2×#121—171no—
864C2×#120—171no—
865C2×#120—171no—
866C2×C4×D4—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×C4×D4—171no—
870C2×C4×D4—171no—
871C2×C4×D4—171no—
872C2×C4×D4C2×D1711yescharacteristic
873C2×C4×D4C2×D1711yescharacteristic
874C2×#117—171no—
875C2×#117—171no—
876C22×C4⋊C4—171no—
877C22×C22⋊C4—171no—
878C22×C22⋊C4—171no—
879C22×C22⋊C4—171no—
880C22×C22⋊C4—171no—
881C22×C22⋊C4C2×D1711yescharacteristic
882C22×C22⋊C4C2×D1711yescharacteristic
883C22×C42—171no—
884#391—171no—
885#391—171no—
886#391—171no—
887#391—171no—
888#390—171no—
889#390—171no—
890#390—171no—
891#390—171no—
892#390—171no—
893#390—171no—
894#390C2×D1711yescharacteristic
895#390C2×D1711yescharacteristic
896#389—171no—
897#389—171no—
898#389—171no—
899#389—171no—
900#388—171no—
901#388—171no—
902#388—171no—
903#388—171no—
904#388—171no—
905#388—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388—171no—
921#388—171no—
922#388—171no—
923#388—171no—
924#388—171no—
925#388—171no—
926#388—171no—
927#388—171no—
928#388—171no—
929#388—171no—
930#387—171no—
931#387—171no—
932#387—171no—
933#387—171no—
934#387—171no—
935#387—171no—
936#387—171no—
937#387—171no—
938#387—171no—
939#387—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386—171no—
954#386—171no—
955#386—171no—
956#386—171no—
957#386—171no—
958#386C2×D1711yescharacteristic
959#386C2×D1711yescharacteristic
960#386C2×D1711yescharacteristic
961#386C2×D1711yescharacteristic
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#385—171no—
969#385—171no—
970#383—171no—
971#381—171no—
972#381—171no—
973#381—171no—
974#381—171no—
975#381—171no—
976#380—171no—
977#380—171no—
978#380—171no—
979#380—171no—
980#380—171no—
981#380—171no—
982#380C2×D1711yescharacteristic
983#379—171no—
984#379—171no—
985#379C2×D1711yescharacteristic
986#379C2×D1711yescharacteristic
987C4×C4⋊C4—171no—
988C4×C4⋊C4—171no—
989C4×C4⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992C4×C22⋊C4—171no—
993C4×C22⋊C4—171no—
994C4×C22⋊C4—171no—
995C4×C22⋊C4—171no—
996C4×C22⋊C4—171no—
997C4×C22⋊C4—171no—
998C4×C22⋊C4—171no—
999C4×C22⋊C4—171no—
1000C4×C22⋊C4—171no—
1001C4×C22⋊C4—171no—
1002C4×C22⋊C4—171no—
1003C4×C22⋊C4—171no—
1004C4×C22⋊C4C2×D1711yescharacteristic
1005#376—171no—
1006#376—171no—
1007C2×#95—171no—
1008C2×#95—171no—
1009C2×#95—171no—
1010C2×C17—24no—
1011C2×C17—42no—
1012C2×C17—42no—
1013C2×C17—42no—
1014C2×C17—42no—
1015C2×C17C2×#51811yescharacteristic
1016C2×C17#342811yescharacteristic
1017C2×C17C4×H(5,𝔽2)11yescharacteristic
1018C2×C17#353411yescharacteristic
1019C2×C17#354211yescharacteristic
1020C2×C17#354511yescharacteristic
1021C2×C17#356011yescharacteristic
1022D17—42no—
1023C25C22×D1711yescharacteristic
1024C25C22×D1711yescharacteristic
1025C2×#41—178no—
1026C2×#41—682no—
1027C2×#41—682no—
1028C22×Q8—171no—
1029C22×D4—42no—
1030C22×D4—42no—
1031C22×D4—171no—
1032C22×D4—171no—
1033C22×D4—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4C4×D1718yescomplemented
1037C22×D4C22×D1711yescharacteristic
1038C22×D4C22×D1711yescharacteristic
1039C22×D4C22×D1711yescharacteristic
1040C22×D4C22×D1711yescharacteristic
1041C23×C4—171no—
1042C23×C4—171no—
1043C23×C4—171no—
1044C23×C4—171no—
1045C23×C4—171no—
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4C22×D1711yescharacteristic
1053C23×C4C22×D1711yescharacteristic
1054C23×C4C22×D1711yescharacteristic
1055C23×C4C22×D1711yescharacteristic
1056C23×C4C22×D1711yescharacteristic
1057#124—178no—
1058#123—178no—
1059#123—178no—
1060C22⋊Q8—178no—
1061#121—178no—
1062#121—178no—
1063#121—178no—
1064#120—178no—
1065#120—178no—
1066C4×D4—42no—
1067C4×D4—42no—
1068C4×D4—178no—
1069C4×D4—178no—
1070C4×D4—682no—
1071C4×D4—682no—
1072C4×D4—682no—
1073C4×D4—682no—
1074#117—682no—
1075#117—682no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—171no—
1094C2×C4⋊C4—682no—
1095C2×C4⋊C4C22×D1711yescharacteristic
1096C2×C4⋊C4C22×D1711yescharacteristic
1097C2×C22⋊C4—42no—
1098C2×C22⋊C4—42no—
1099C2×C22⋊C4—178no—
1100C2×C22⋊C4—178no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—682no—
1136C2×C22⋊C4—682no—
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4C22×D1711yescharacteristic
1147C2×C22⋊C4C22×D1711yescharacteristic
1148C2×C22⋊C4C22×D1711yescharacteristic
1149C2×C22⋊C4C22×D1711yescharacteristic
1150C2×C22⋊C4C22×D1711yescharacteristic
1151C2×C22⋊C4C22×D1711yescharacteristic
1152C2×C22⋊C4C22×D1711yescharacteristic
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—171no—
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—171no—
1162C2×C42—171no—
1163C2×C42—171no—
1164C2×C42—171no—
1165C2×C42—171no—
1166C2×C42—171no—
1167C2×C42—171no—
1168C2×C42—682no—
1169C2×C42C22×D1711yescharacteristic
1170C2×C42C22×D1711yescharacteristic
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95C22×D1711yescharacteristic
1208#95C22×D1711yescharacteristic
1209#95C22×D1711yescharacteristic
1210#95C22×D1711yescharacteristic
1211C17#3449211yescharacteristic, complemented, Sylow
1212C24—22no—
1213C24—22no—
1214C24—41no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—41no—
1219C24—41no—
1220C24—41no—
1221C24—41no—
1222C24—41no—
1223C24—41no—
1224C24—171no—
1225C24C2×C4×D1714yes—
1226C24C2×C4×D1714yes—
1227C24C23×D1711yescharacteristic
1228C24C23×D1711yescharacteristic
1229C24C23×D1711yescharacteristic
1230C24C23×D1711yescharacteristic
1231C24C23×D1711yescharacteristic
1232#41—6816no—
1233C2×Q8—174no—
1234C2×Q8—681no—
1235C2×Q8—681no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—416no—
1245C2×D4—174no—
1246C2×D4—174no—
1247C2×D4—174no—
1248C2×D4—174no—
1249C2×D4—174no—
1250C2×D4—342no—
1251C2×D4—342no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4—681no—
1258C2×D4—681no—
1259C2×D4—681no—
1260C2×D4C2×C4×D1714yes—
1261C2×D4C2×C4×D1714yes—
1262C2×D4C2×C4×D1714yes—
1263C2×D4C2×C4×D1714yes—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—41no—
1272C22×C4—41no—
1273C22×C4—41no—
1274C22×C4—41no—
1275C22×C4—41no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—174no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—171no—
1282C22×C4—171no—
1283C22×C4—171no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—174no—
1287C22×C4—174no—
1288C22×C4—174no—
1289C22×C4—174no—
1290C22×C4—171no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—342no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4—681no—
1309C22×C4—681no—
1310C22×C4—681no—
1311C22×C4—681no—
1312C22×C4—681no—
1313C22×C4—681no—
1314C22×C4—681no—
1315C22×C4—681no—
1316C22×C4—681no—
1317C22×C4—681no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—681no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4C2×C4×D1714yes—
1327C22×C4C23×D1711yescharacteristic
1328C22×C4C23×D1711yescharacteristic
1329C22×C4C23×D1711yescharacteristic
1330C22×C4C23×D1711yescharacteristic
1331C22×C4C23×D1711yescharacteristic
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C4⋊C4—41no—
1338C4⋊C4—41no—
1339C4⋊C4—174no—
1340C4⋊C4—174no—
1341C4⋊C4—174no—
1342C4⋊C4—174no—
1343C4⋊C4—342no—
1344C4⋊C4—681no—
1345C4⋊C4—681no—
1346C4⋊C4—681no—
1347C4⋊C4—681no—
1348C4⋊C4—681no—
1349C4⋊C4—681no—
1350C4⋊C4—681no—
1351C4⋊C4—681no—
1352C4⋊C4—681no—
1353C4⋊C4—681no—
1354C4⋊C4—681no—
1355C4⋊C4—681no—
1356C4⋊C4—681no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—22no—
1361C22⋊C4—22no—
1362C22⋊C4—41no—
1363C22⋊C4—41no—
1364C22⋊C4—41no—
1365C22⋊C4—41no—
1366C22⋊C4—41no—
1367C22⋊C4—41no—
1368C22⋊C4—41no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—174no—
1374C22⋊C4—174no—
1375C22⋊C4—174no—
1376C22⋊C4—174no—
1377C22⋊C4—174no—
1378C22⋊C4—174no—
1379C22⋊C4—174no—
1380C22⋊C4—174no—
1381C22⋊C4—174no—
1382C22⋊C4—174no—
1383C22⋊C4—174no—
1384C22⋊C4—174no—
1385C22⋊C4—342no—
1386C22⋊C4—342no—
1387C22⋊C4—681no—
1388C22⋊C4—681no—
1389C22⋊C4—681no—
1390C22⋊C4—681no—
1391C22⋊C4—681no—
1392C22⋊C4—681no—
1393C22⋊C4—681no—
1394C22⋊C4—681no—
1395C22⋊C4—681no—
1396C22⋊C4—681no—
1397C22⋊C4—681no—
1398C22⋊C4—681no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4—681no—
1402C22⋊C4—681no—
1403C22⋊C4—681no—
1404C22⋊C4—681no—
1405C22⋊C4—681no—
1406C22⋊C4—681no—
1407C42—41no—
1408C42—41no—
1409C42—174no—
1410C42—342no—
1411C42—342no—
1412C42—681no—
1413C42—681no—
1414C42—681no—
1415C42—681no—
1416C42—681no—
1417C42—681no—
1418C42—681no—
1419C42—681no—
1420C42—681no—
1421C42—681no—
1422C42—681no—
1423C42—681no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—28no—
1453C23—44no—
1454C23—44no—
1455C23—44no—
1456C23—44no—
1457C23—44no—
1458C23—82no—
1459C23—82no—
1460C23—82no—
1461C23—82no—
1462C23—82no—
1463C23—82no—
1464C23—82no—
1465C23—82no—
1466C23—172no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—341no—
1473C23C22×C4×D1712yes—
1474C23C22×C4×D1712yes—
1475C23C22×C4×D1712yes—
1476C23C22×C4×D1712yes—
1477C23C22×C4×D1712yes—
1478C23#1058769112yes—
1479C23#1058769112yes—
1480C23C24×D1711yescharacteristic
1481Q8—684no—
1482D4—28no—
1483D4—28no—
1484D4—44no—
1485D4—44no—
1486D4—348no—
1487D4—684no—
1488D4—684no—
1489D4—684no—
1490D4—684no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—44no—
1519C2×C4—44no—
1520C2×C4—82no—
1521C2×C4—82no—
1522C2×C4—82no—
1523C2×C4—172no—
1524C2×C4—172no—
1525C2×C4—172no—
1526C2×C4—172no—
1527C2×C4—172no—
1528C2×C4—172no—
1529C2×C4—172no—
1530C2×C4—348no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—684no—
1570C2×C4—684no—
1571C2×C4—684no—
1572C2×C4—684no—
1573C2×C4—684no—
1574C2×C4—1362no—
1575C2×C4—1362no—
1576C2×C4—1362no—
1577C2×C4—1362no—
1578C2×C4—1362no—
1579C2×C4C22×C4×D1712yes—
1580C2×C4C22×C4×D1712yes—
1581C2×C4#1058769112yes—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—22no—
1595C22—22no—
1596C22—22no—
1597C22—22no—
1598C22—22no—
1599C22—22no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—88no—
1617C22—88no—
1618C22—342no—
1619C22—342no—
1620C22—342no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—681no—
1625C22#1176328214yes—
1626C22C23×C4×D1711yescharacteristic
1627C22C2×#1058769111yescharacteristic
1628C22C2×#1058769111yescharacteristic
1629C22C2×#1058769111yescharacteristic
1630C22#1176364411yescharacteristic
1631C22#1176364411yescharacteristic
1632C22#1176364511yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—342no—
1644C4—342no—
1645C4—342no—
1646C4—342no—
1647C4—342no—
1648C4—342no—
1649C4—342no—
1650C4—681no—
1651C4—681no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C2—24no—
1659C2—42no—
1660C2—42no—
1661C2—42no—
1662C2—42no—
1663C2—682no—
1664C2C2×#1176328211yescharacteristic
1665C2#1454198211yescharacteristic
1666C2C4×#1058769111yescharacteristic
1667C2#1454296211yescharacteristic
1668C2#1454310511yescharacteristic
1669C2#1454313111yescharacteristic
1670C2#1454332411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingD4×C22⋊C4×C17C2
socle, cosocleC23×C17C25
prime radicalC2×#11763453C2
hypercenterD4×C22⋊C4D17
hypocenterC17#34492
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531947C2semidirect
3. #14531936C2semidirect
4. #14531934C2semidirect
5. #14531923C2semidirect
6. #14531893C2semidirect
7. #14531829C2semidirect
8. #14531819C2semidirect
9. #14531770C2semidirect
10. #14531763C2semidirect
11. #14531727C2semidirect
12. #14531722C2semidirect
13. #14531635C2semidirect
14. #14531629C2semidirect
15. #14531610C2semidirect
16. #14531593C2semidirect
17. #14531571C2semidirect
18. #14531543C2semidirect
19. #14531540C2semidirect
20. #14531486C2semidirect
21. #14531449C2semidirect
22. #14531442C2semidirect
23. #14531439C2semidirect
24. #14531426C2semidirect
25. #14531380C2semidirect
26. #14531371C2semidirect
27. #14531362C2semidirect
28. C4×#10587625C2semidirect
29. #14531224C2semidirect
30. C2×#11762697C2semidirect
31. D4×C22⋊C4×C17C2semidirect
33. #11763453C4semidirect
45. C2×C4×C22⋊D17C22semidirect
46. C2×C4×C22⋊D17C22semidirect
47. C2×#10587567C22semidirect
48. C2×#10587567C22semidirect
49. C2×#10587563C22semidirect
50. C2×#10587563C22semidirect
51. C22×#63225C22semidirect
56. C22×C4×Dic17C22semidirect
57. #11762713C22semidirect
58. #11762713C22semidirect
59. #11762713C22semidirect
60. #11762713C22semidirect
63. #11762709C22semidirect
64. #11762709C22semidirect
65. #11762709C22semidirect
66. #11762709C22semidirect
67. #11762704C22semidirect
68. #11762704C22semidirect
69. #11762704C22semidirect
70. #11762704C22semidirect
75. #11762703C22semidirect
76. #11762703C22semidirect
77. #11762703C22semidirect
78. #11762703C22semidirect
79. #11762703C22semidirect
80. #11762703C22semidirect
81. #11762703C22semidirect
82. #11762703C22semidirect
83. #11762699C22semidirect
84. #11762699C22semidirect
93. #11762697C22semidirect
94. #11762697C22semidirect
95. #11762697C22semidirect
96. #11762697C22semidirect
97. #11762697C22semidirect
98. #11762697C22semidirect
99. #11762697C22semidirect
100. #11762697C22semidirect
101. #11762694C22semidirect
102. #11762694C22semidirect
103. #11762693C22semidirect
104. #11762693C22semidirect
105. #11762693C22semidirect
106. #11762693C22semidirect
107. #11762692C22semidirect
108. #11762692C22semidirect
109. #11762690C22semidirect
110. #11762690C22semidirect
119. #11762688C22semidirect
120. #11762688C22semidirect
121. #11762686C22semidirect
122. #11762686C22semidirect
125. #11762685C22semidirect
126. #11762685C22semidirect
127. #11762685C22semidirect
128. #11762685C22semidirect
129. #11762682C22semidirect
130. #11762682C22semidirect
131. #11762682C22semidirect
132. #11762682C22semidirect
133. #11762681C22semidirect
134. #11762681C22semidirect
135. #11762681C22semidirect
136. #11762681C22semidirect
137. #11762676C22semidirect
140. #11762671C22semidirect
141. #11762670C22semidirect
142. #11762670C22semidirect
143. #11762668C22semidirect
144. #11762668C22semidirect
145. #11762667C22semidirect
146. #11762667C22semidirect
147. #11762667C22semidirect
148. #11762667C22semidirect
151. C4×#63225C22semidirect
152. C4×#63225C22semidirect
153. #11762660C22semidirect
154. C22⋊C4×Dic17C22semidirect
155. C22⋊C4×Dic17C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
164. C4×C22⋊Dic17C22semidirect
165. C4×C22⋊Dic17C22semidirect
166. C4×C22⋊Dic17C22semidirect
167. C4×C22⋊Dic17C22semidirect
168. #11762654C22semidirect
169. #11762654C22semidirect
170. C2×#10587502C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
192. C22×D4×C17C2×C4semidirect
217. C2×#63254C2×C4semidirect
246. #10587639C2×C4semidirect
247. #10587639C2×C4semidirect
250. C2×C22⋊Dic17C2×C4semidirect
251. C2×C22⋊Dic17C2×C4semidirect
279. #10587625C2×C4semidirect
280. #10587625C2×C4semidirect
281. #10587624C2×C4semidirect
282. #10587622C2×C4semidirect
283. #10587621C2×C4semidirect
284. #10587621C2×C4semidirect
285. D4×Dic17C2×C4semidirect
288. C4×C22⋊D17C2×C4semidirect
297. #10587610C2×C4semidirect
762. D4×C22⋊C4D17semidirect
1036. C22×D4C4×D17semidirect
1211. C17#34492semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117634532
#145319472
#145319362
#145319342
#145319232
#145318932
#145318292
#145318192
#145317702
#145317632
#145317272
#145317222
#145316352
#145316292
#145316102
#145315932
#145315712
#145315432
#145315402
#145314862
#145314492
#145314422
#145314392
#145314262
#145313802
#145313712
#145313622
C4×#105876252
#145312242
C2×#117626972
D4×C22⋊C4×C172
#3449217