Finite Group Databasebeta

← #17194207

Subgroups — #17194207

Order 4352.

2732 conjugacy classes of subgroups.

The subgroup lattice has 1560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763485C211yesmaximal, characteristic
2#14531912C211yesmaximal, characteristic, complemented
3#14531902C211yesmaximal, characteristic, complemented
4#14531901C211yesmaximal, characteristic, complemented
5#14531891C211yesmaximal, characteristic, complemented
6#14531867C211yesmaximal, characteristic, complemented
7#14531865C211yesmaximal, characteristic, complemented
8#14531776C211yesmaximal, characteristic, complemented
9#14531774C211yesmaximal, characteristic, complemented
10#14531763C211yesmaximal, characteristic
11#14531726C211yesmaximal, characteristic, complemented
12#14531718C211yesmaximal, characteristic, complemented
13#14531646C211yesmaximal, characteristic, complemented
14#14531638C211yesmaximal, characteristic, complemented
15#14531635C211yesmaximal, characteristic, complemented
16#14531338C211yesmaximal, characteristic, complemented
17#14531338C211yesmaximal, characteristic, complemented
18#14531325C211yesmaximal, characteristic, complemented
19#14531316C211yesmaximal, characteristic, complemented
20#14531312C211yesmaximal, characteristic, complemented
21#14531311C211yesmaximal, characteristic, complemented
22#14531303C211yesmaximal, characteristic, complemented
23#14531301C211yesmaximal, characteristic, complemented
24#14531283C211yesmaximal, characteristic
25C4×#10587567C211yesmaximal, characteristic, complemented
26C4×#10587567C211yesmaximal, characteristic, complemented
27#117×Dic17C211yesmaximal, characteristic, complemented
28C4×#10587563C211yesmaximal, characteristic, complemented
29C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
31C17×#2342C211yesmaximal, characteristic, complemented
32C24×Dic17C2211yescharacteristic
33#11763485C4116yescomplemented
34C2×#10587565C2211yescharacteristic
35C2×#10587565C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587572C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587569C2211yescharacteristic
40C2×#10587610C2211yescharacteristic
41C2×#10587564C2211yescharacteristic
42C2×#10587639C2211yescharacteristic
43C2×#10587573C2211yescharacteristic, complemented
44C2×C4×C22⋊D17C2211yescharacteristic
45C2×C4×C22⋊D17C2211yescharacteristic
46C2×#10587567C2211yescharacteristic
47C2×#10587567C2211yescharacteristic
48C2×#10587567C2211yescharacteristic
49C2×#10587567C2211yescharacteristic
50C2×#10587567C2211yescharacteristic
51C2×#10587612C2211yescharacteristic
52C2×#10587563C2211yescharacteristic
53C2×#10587563C2211yescharacteristic
54C22×C22⋊Dic17C2211yescharacteristic
55C22×C22⋊Dic17C2211yescharacteristic
56C22×C4×Dic17C2211yescharacteristic
57C22×C4×Dic17C2211yescharacteristic
58C22×C4×Dic17C2211yescharacteristic
59C22×C4×Dic17C2211yescharacteristic
60C2×C42×D17C2211yescharacteristic, complemented
61#11762714C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762713C2211yescharacteristic, complemented
64#11762709C2211yescharacteristic
65#11762705C2211yescharacteristic, complemented
66#11762704C2211yescharacteristic, complemented
67#11762703C2211yescharacteristic
68#11762703C2211yescharacteristic
69#11762703C2211yescharacteristic
70#11762700C2211yescharacteristic, complemented
71#11762699C2211yescharacteristic, complemented
72#11762699C2211yescharacteristic, complemented
73#11762699C2211yescharacteristic, complemented
74#11762698C2211yescharacteristic, complemented
75#11762698C2211yescharacteristic, complemented
76#11762697C2211yescharacteristic
77#11762697C2211yescharacteristic
78#11762697C2211yescharacteristic
79#11762694C2211yescharacteristic, complemented
80#11762694C2211yescharacteristic, complemented
81#11762693C2211yescharacteristic, complemented
82#11762693C2211yescharacteristic, complemented
83#11762693C2211yescharacteristic, complemented
84#11762692C2211yescharacteristic, complemented
85#11762692C2211yescharacteristic, complemented
86#11762692C2211yescharacteristic, complemented
87#11762692C2211yescharacteristic, complemented
88#11762691C2211yescharacteristic, complemented
89#11762691C2211yescharacteristic, complemented
90#11762691C2211yescharacteristic, complemented
91#11762691C2211yescharacteristic, complemented
92#11762690C2211yescharacteristic, complemented
93#11762690C2211yescharacteristic, complemented
94#11762690C2211yescharacteristic, complemented
95#11762688C2211yescharacteristic
96#11762686C2211yescharacteristic
97#11762686C2211yescharacteristic
98#11762686C2211yescharacteristic
99#11762686C2211yescharacteristic
100#11762685C2211yescharacteristic
101#11762682C2211yescharacteristic
102#11762681C2211yescharacteristic
103#11762681C2211yescharacteristic
104#11762681C2211yescharacteristic
105#11762681C2211yescharacteristic
106#11762681C2211yescharacteristic
107#11762681C2211yescharacteristic
108#11762680C2211yescharacteristic, complemented
109#11762676C2211yescharacteristic, complemented
110#11762676C2211yescharacteristic, complemented
111#11762673C2211yescharacteristic, complemented
112#11762671C2211yescharacteristic, complemented
113#11762670C2211yescharacteristic
114#11762667C2211yescharacteristic
115C4⋊C4×Dic17C2211yescharacteristic, complemented
116C4⋊C4×Dic17C2211yescharacteristic, complemented
117C4⋊C4×Dic17C2211yescharacteristic, complemented
118C4⋊C4×Dic17C2211yescharacteristic, complemented
119C4⋊C4×Dic17C2211yescharacteristic, complemented
120C4×#63225C2211yescharacteristic, complemented
121C4×#63225C2211yescharacteristic, complemented
122C4×#63225C2211yescharacteristic, complemented
123C4×#63225C2211yescharacteristic, complemented
124#11762660C2211yescharacteristic, complemented
125#11762660C2211yescharacteristic, complemented
126#11762660C2211yescharacteristic, complemented
127#11762660C2211yescharacteristic, complemented
128#11762660C2211yescharacteristic, complemented
129#11762660C2211yescharacteristic, complemented
130#11762660C2211yescharacteristic, complemented
131C22⋊C4×Dic17C2211yescharacteristic
132C22⋊C4×Dic17C2211yescharacteristic
133C22⋊C4×Dic17C2211yescharacteristic
134C22⋊C4×Dic17C2211yescharacteristic
135C22⋊C4×Dic17C2211yescharacteristic
136C22⋊C4×Dic17C2211yescharacteristic
137C22⋊C4×Dic17C2211yescharacteristic
138C22⋊C4×Dic17C2211yescharacteristic
139C22⋊C4×Dic17C2211yescharacteristic
140C22⋊C4×Dic17C2211yescharacteristic
141C22⋊C4×Dic17C2211yescharacteristic
142C22⋊C4×Dic17C2211yescharacteristic
143C22⋊C4×Dic17C2211yescharacteristic
144C22⋊C4×Dic17C2211yescharacteristic
145C22⋊C4×Dic17C2211yescharacteristic
146C22⋊C4×Dic17C2211yescharacteristic
147C22⋊C4×Dic17C2211yescharacteristic
148C22⋊C4×Dic17C2211yescharacteristic
149C22⋊C4×Dic17C2211yescharacteristic
150C22⋊C4×Dic17C2211yescharacteristic
151C22⋊C4×Dic17C2211yescharacteristic
152C22⋊C4×Dic17C2211yescharacteristic
153C22⋊C4×Dic17C2211yescharacteristic
154C4×#63227C2211yescharacteristic, complemented
155C4×#63227C2211yescharacteristic, complemented
156C4×C22⋊Dic17C2211yescharacteristic
157#11762656C2211yescharacteristic, complemented
158#11762656C2211yescharacteristic, complemented
159#11762656C2211yescharacteristic, complemented
160#11762656C2211yescharacteristic, complemented
161#11762656C2211yescharacteristic, complemented
162#11762655C2211yescharacteristic, complemented
163#11762655C2211yescharacteristic, complemented
164#11762654C2211yescharacteristic, complemented
165#11762654C2211yescharacteristic, complemented
166C2×#10587502C2211yescharacteristic
167C2×#10587502C2211yescharacteristic
168C2×#10587502C2211yescharacteristic
169C2×#10587502C2211yescharacteristic
170C42×Dic17C2211yescharacteristic, complemented
171C42×Dic17C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C17×#117C2211yescharacteristic
174C22×C22⋊C4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#385C2211yescharacteristic
181C17×#385C2211yescharacteristic
182C17×#381C2211yescharacteristic
183C17×#380C2211yescharacteristic
184C17×#379C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C23×C4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C23×Dic17—24no—
197C23×Dic17—24no—
198C23×Dic17—42no—
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×Dic34C2311yescharacteristic
213C17×#117—24no—
214C2×C4⋊C4×C17C2311yescharacteristic
215C2×C4⋊C4×C17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C22⋊C4×C17—24no—
219C2×C22⋊C4×C17C2×C418yescomplemented
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
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×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238#10587639C2×C418yes—
239C2×C22⋊Dic17—24no—
240C2×C22⋊Dic17C2×C418yescomplemented
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252#10587615C2×C418yescomplemented
253C4×C22⋊D17—24no—
254C4×C22⋊D17C2×C418yescomplemented
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264#10587612C2×C418yescomplemented
265C2×C4⋊Dic17C2311yescharacteristic
266C2×C4⋊Dic17C2311yescharacteristic
267C2×C4⋊Dic17C2311yescharacteristic
268#10587610C2×C418yescomplemented
269C2×#63225C2311yescharacteristic
270C2×#63225C2311yescharacteristic
271C2×#63225C2311yescharacteristic
272C2×#63225C2311yescharacteristic
273C2×#63225C2311yescharacteristic
274C2×#63225C2311yescharacteristic
275C2×#63225C2311yescharacteristic
276C2×#63225C2311yescharacteristic
277C2×#63225C2311yescharacteristic
278C2×#63225C2311yescharacteristic
279C2×#63225C2311yescharacteristic
280C2×#63225C2311yescharacteristic
281C2×#63225C2311yescharacteristic
282C2×#63225C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×C4×Dic17—24no—
285C2×C4×Dic17—24no—
286C2×C4×Dic17—42no—
287C2×C4×Dic17—42no—
288C2×C4×Dic17C2311yescharacteristic
289C2×C4×Dic17C2311yescharacteristic
290C2×C4×Dic17C2311yescharacteristic
291C2×C4×Dic17C2311yescharacteristic
292C2×C4×Dic17C2311yescharacteristic
293C2×C4×Dic17C2311yescharacteristic
294C2×C4×Dic17C2311yescharacteristic
295C2×C4×Dic17C2311yescharacteristic
296C2×C4×Dic17C2311yescharacteristic
297C2×C4×Dic17C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317#10587573—42no—
318#10587572C2×C418yescomplemented
319#10587571C2×C418yescomplemented
320#10587569C2×C418yescomplemented
321#10587567—24no—
322#10587567—24no—
323#10587567—24no—
324#10587567—42no—
325#10587567C2×C418yescomplemented
326#10587565C2×C418yescomplemented
327#10587565C2×C418yescomplemented
328#10587564C2×C418yescomplemented
329#10587563—24no—
330#10587563C2×C418yescomplemented
331C42×D17—42no—
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
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—22no—
379C24×C17—22no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17C22×C414yes—
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C24×C17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C22×C4×C17—22no—
388C22×C4×C17—22no—
389C22×C4×C17—22no—
390C22×C4×C17—22no—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17C22×C414yes—
398C22×C4×C17C22×C414yes—
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C2×C22⋊D17—22no—
412C2×C22⋊D17—22no—
413C2×C22⋊D17—22no—
414C2×C22⋊D17—22no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17C22×C414yes—
418C2×C22⋊D17C22×C414yes—
419C2×C22⋊D17C22×C414yes—
420C22×Dic17—22no—
421C22×Dic17—22no—
422C22×Dic17—22no—
423C22×Dic17—22no—
424C22×Dic17—22no—
425C22×Dic17—22no—
426C22×Dic17—22no—
427C22×Dic17—22no—
428C22×Dic17—22no—
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—22no—
432C22×Dic17—22no—
433C22×Dic17—22no—
434C22×Dic17—22no—
435C22×Dic17—22no—
436C22×Dic17—22no—
437C22×Dic17—22no—
438C22×Dic17—22no—
439C22×Dic17—41no—
440C22×Dic17—41no—
441C22×Dic17—41no—
442C22×Dic17—41no—
443C22×Dic17—41no—
444C22×Dic17—41no—
445C22×Dic17—41no—
446C22×Dic17—416no—
447C22×Dic17C22×C414yes—
448C22×Dic17C22×C414yes—
449C22×Dic17#4114yes—
450C22×Dic17#4114yes—
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C2×C4×D17—22no—
467C2×C4×D17—22no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17C22×C414yescomplemented
475C2×Dic34—41no—
476C2×Dic34—41no—
477C2×Dic34C22×C414yescomplemented
478C4⋊C4×C17—22no—
479C4⋊C4×C17—22no—
480C4⋊C4×C17—41no—
481C4⋊C4×C17—41no—
482C22⋊C4×C17—22no—
483C22⋊C4×C17—22no—
484C22⋊C4×C17—22no—
485C22⋊C4×C17—22no—
486C22⋊C4×C17—22no—
487C22⋊C4×C17—22no—
488C22⋊C4×C17—22no—
489C22⋊C4×C17—41no—
490C22⋊C4×C17—41no—
491C22⋊C4×C17C22×C414yes—
492C22⋊C4×C17C22×C414yes—
493C22⋊C4×C17C22×C414yes—
494C22⋊C4×C17C22×C414yes—
495C22⋊C4×C17#4114yes—
496C42×C17—22no—
497C42×C17—22no—
498C42×C17—41no—
499C42×C17—41no—
500C22⋊Dic17—22no—
501C22⋊Dic17—22no—
502C22⋊Dic17—22no—
503C22⋊Dic17C22×C414yes—
504C22⋊Dic17C22×C414yes—
505C22⋊Dic17C22×C414yes—
506C22⋊Dic17C22×C414yes—
507C22⋊Dic17C22×C414yes—
508C22⋊Dic17C22×C414yes—
509C22⋊Dic17C22×C414yes—
510C22⋊Dic17#4114yes—
511#63227—22no—
512#63227—22no—
513#63227—22no—
514#63227—22no—
515#63227—41no—
516#63227—41no—
517#63227C22×C414yescomplemented
518#63227C22×C414yescomplemented
519#63227C22×C414yescomplemented
520C4⋊Dic17C22×C414yescomplemented
521C4⋊Dic17C22×C414yescomplemented
522C4⋊Dic17C22×C414yescomplemented
523#63225—22no—
524#63225—22no—
525#63225—22no—
526#63225—22no—
527#63225—22no—
528#63225—22no—
529#63225—41no—
530#63225—41no—
531#63225—41no—
532#63225—41no—
533#63225C22×C414yescomplemented
534#63225C22×C414yescomplemented
535#63225C22×C414yescomplemented
536#63225C22×C414yescomplemented
537#63225C22×C414yescomplemented
538C4×Dic17—22no—
539C4×Dic17—22no—
540C4×Dic17—22no—
541C4×Dic17—22no—
542C4×Dic17—22no—
543C4×Dic17—22no—
544C4×Dic17—22no—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—22no—
548C4×Dic17—22no—
549C4×Dic17—22no—
550C4×Dic17—22no—
551C4×Dic17—22no—
552C4×Dic17—22no—
553C4×Dic17—22no—
554C4×Dic17—22no—
555C4×Dic17—22no—
556C4×Dic17—22no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17—41no—
561C4×Dic17—41no—
562C4×Dic17—41no—
563C4×Dic17—41no—
564C4×Dic17C22×C414yescomplemented
565C4×Dic17C22×C414yescomplemented
566C4×Dic17C22×C414yescomplemented
567C4×#551—171nomaximal, Sylow
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—28no—
577C23×C17—28no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—44no—
585C23×C17—44no—
586C23×C17—44no—
587C23×C17—44no—
588C23×C17—44no—
589C23×C17C23×C412yes—
590C23×C17C23×C412yes—
591C23×C17C23×C412yes—
592C23×C17C2×#4112yes—
593C23×C17C2×#4112yes—
594C23×C17C2×#4112yes—
595C23×C17C2×#4112yes—
596C23×C17C2511yescharacteristic
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17C23×C412yes—
604C2×C4×C17—28no—
605C2×C4×C17—21no—
606C2×C4×C17—21no—
607C2×C4×C17—21no—
608C2×C4×C17—21no—
609C2×C4×C17—21no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—44no—
636C2×C4×C17—44no—
637C2×C4×C17—44no—
638C2×C4×C17C23×C412yes—
639C2×C4×C17C23×C412yes—
640C2×C4×C17C23×C412yes—
641C2×C4×C17C23×C412yes—
642C2×C4×C17C2×#4112yes—
643C2×C4×C17C2×#4112yes—
644C22⋊D17—28no—
645C22⋊D17—28no—
646C22⋊D17—44no—
647C2×Dic17—28no—
648C2×Dic17—21no—
649C2×Dic17—21no—
650C2×Dic17—21no—
651C2×Dic17—21no—
652C2×Dic17—21no—
653C2×Dic17—21no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—28no—
671C2×Dic17—28no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—44no—
682C2×Dic17—44no—
683C2×Dic17—44no—
684C2×Dic17—44no—
685C2×Dic17—44no—
686C2×Dic17—44no—
687C2×Dic17—44no—
688C2×Dic17C23×C412yes—
689C2×Dic17C23×C412yes—
690C2×Dic17C23×C412yes—
691C2×Dic17C23×C412yes—
692C2×Dic17C23×C412yes—
693C2×Dic17C23×C412yes—
694C2×Dic17C23×C412yes—
695C2×Dic17C2×#4112yes—
696C2×Dic17C2×#4112yes—
697C2×Dic17C2×#4112yes—
698C2×Dic17C2×#4112yes—
699C2×Dic17C2×#4112yes—
700C2×Dic17C2×#4112yes—
701C2×Dic17H(5,𝔽2)12yes—
702C4×D17—44no—
703C4×D17—44no—
704C4×D17—44no—
705Dic34—44no—
706C2×#551—171no—
707#2374—171no—
708#2373—171no—
709#2373—171no—
710#2372—171no—
711#2368—171no—
712#2368—171no—
713#2359—171no—
714#2359—171no—
715#2358—171no—
716#2353—171no—
717#2353—171no—
718#2343—171no—
719#2343—171no—
720#2342—171no—
721#2342D1711yescharacteristic, complemented
722C4×#126—171no—
723C4×#126—171no—
724C4×#124—171no—
725C4×C22⋊Q8—171no—
726C4×C22⋊Q8—171no—
727C4×#123—171no—
728C4×#123—171no—
729C4×#123—171no—
730C4×#120—171no—
731C42×D4—171no—
732C42×D4—171no—
733C4×#117—171no—
734C4×#117—171no—
735C2×C4×C22⋊C4—171no—
736C2×C4×C22⋊C4—171no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—22no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—22no—
748C22×C17—22no—
749C22×C17—22no—
750C22×C17—22no—
751C22×C17—22no—
752C22×C17—416no—
753C22×C17—41no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17—41no—
757C22×C17C4×#4114yes—
758C22×C17C4×#4114yes—
759C22×C17C24×C411yescharacteristic
760C22×C17C22×#4111yescharacteristic
761C22×C17C22×#4111yescharacteristic
762C22×C17C22×#4111yescharacteristic
763C22×C17C22×#4111yescharacteristic
764C22×C17C2×H(5,𝔽2)11yescharacteristic
765C22×C17#58511yescharacteristic
766C2×D17—22no—
767C2×D17—22no—
768C2×D17—22no—
769C2×D17—41no—
770C2×D17—41no—
771C2×D17—41no—
772C2×D17—41no—
773C4×C17—22no—
774C4×C17—22no—
775C4×C17—22no—
776C4×C17—22no—
777C4×C17—22no—
778C4×C17—22no—
779C4×C17—41no—
780C4×C17—41no—
781C4×C17—41no—
782C4×C17—41no—
783C4×C17—41no—
784C4×C17—41no—
785Dic17—22no—
786Dic17—22no—
787Dic17—22no—
788Dic17—22no—
789Dic17—22no—
790Dic17—22no—
791Dic17—22no—
792Dic17—22no—
793Dic17—22no—
794Dic17—22no—
795Dic17—22no—
796Dic17—41no—
797Dic17—41no—
798Dic17—41no—
799Dic17#55114yescomplemented
800C24×C4—171no—
801#551—1716no—
802C2×#126—171no—
803C2×#126—171no—
804C2×#124—171no—
805C2×#123—171no—
806C2×#123—171no—
807C2×#123—171no—
808C2×C22⋊Q8—171no—
809C2×C22⋊Q8—171no—
810C2×#120—171no—
811C2×C4×Q8—171no—
812C2×C4×D4—171no—
813C2×C4×D4—171no—
814C2×C4×D4—171no—
815C2×C4×D4—171no—
816C2×C4×D4—171no—
817C2×C4×D4—171no—
818C2×C4×D4—171no—
819C2×#117—171no—
820C2×#117—171no—
821C2×#117—171no—
822C2×#117C2×D1711yescharacteristic
823C22×C22⋊C4—171no—
824C22×C22⋊C4—171no—
825C22×C22⋊C4C2×D1711yescharacteristic
826C22×C22⋊C4C2×D1711yescharacteristic
827C22×C42—171no—
828C22×C42—171no—
829C22×C42—171no—
830C22×C42—171no—
831C22×C42—171no—
832#391—171no—
833#391—171no—
834#391—171no—
835#390—171no—
836#389—171no—
837#389—171no—
838#388—171no—
839#388—171no—
840#388—171no—
841#388—171no—
842#388—171no—
843#388—171no—
844#388—171no—
845#388—171no—
846#388—171no—
847#388—171no—
848#388—171no—
849#388—171no—
850#388C2×D1711yescharacteristic
851#388C2×D1711yescharacteristic
852#388C2×D1711yescharacteristic
853#388C2×D1711yescharacteristic
854#387—171no—
855#387—171no—
856#387—171no—
857#387—171no—
858#387—171no—
859#387—171no—
860#387—171no—
861#387—171no—
862#387—171no—
863#387—171no—
864#387—171no—
865#387—171no—
866#387—171no—
867#387—171no—
868#387—171no—
869#387—171no—
870#386—171no—
871#386—171no—
872#386—171no—
873#386—171no—
874#386—171no—
875#386—171no—
876#385—171no—
877#385—171no—
878#385—171no—
879#385—171no—
880#385—171no—
881#385—171no—
882#385—171no—
883#385—171no—
884#385C2×D1711yescharacteristic
885#385C2×D1711yescharacteristic
886#383—171no—
887#383—171no—
888#382—171no—
889#381—171no—
890#381—171no—
891#381C2×D1711yescharacteristic
892#380—171no—
893#380C2×D1711yescharacteristic
894#379C2×D1711yescharacteristic
895C4×C4⋊C4—171no—
896C4×C4⋊C4—171no—
897C4×C4⋊C4—171no—
898C4×C4⋊C4—171no—
899C4×C4⋊C4—171no—
900C4×C4⋊C4—171no—
901C4×C4⋊C4—171no—
902C4×C4⋊C4—171no—
903C4×C4⋊C4—171no—
904C4×C4⋊C4—171no—
905C4×C4⋊C4—171no—
906C4×C4⋊C4—171no—
907C4×C4⋊C4—171no—
908C4×C4⋊C4—171no—
909C4×C4⋊C4—171no—
910C4×C4⋊C4—171no—
911C4×C22⋊C4—171no—
912C4×C22⋊C4—171no—
913C4×C22⋊C4—171no—
914C4×C22⋊C4—171no—
915C4×C22⋊C4—171no—
916C4×C22⋊C4—171no—
917C4×C22⋊C4—171no—
918C4×C22⋊C4—171no—
919C4×C22⋊C4—171no—
920C4×C22⋊C4—171no—
921C4×C22⋊C4—171no—
922C4×C22⋊C4—171no—
923C4×C22⋊C4—171no—
924C4×C22⋊C4—171no—
925C4×C22⋊C4—171no—
926C4×C22⋊C4—171no—
927C4×C22⋊C4—171no—
928C4×C22⋊C4—171no—
929C4×C22⋊C4—171no—
930C4×C22⋊C4—171no—
931C4×C22⋊C4—171no—
932C4×C22⋊C4—171no—
933C4×C22⋊C4—171no—
934C4×C22⋊C4—171no—
935C4×C22⋊C4—171no—
936C4×C22⋊C4—171no—
937C4×C22⋊C4—171no—
938C4×C22⋊C4—171no—
939C4×C22⋊C4—171no—
940C4×C22⋊C4—171no—
941C4×C22⋊C4—171no—
942C4×C22⋊C4C2×D1711yescharacteristic
943C4×C22⋊C4C2×D1711yescharacteristic
944C4×C22⋊C4C2×D1711yescharacteristic
945#376—171no—
946#376—171no—
947#376—171no—
948#376—171no—
949C2×#95—171no—
950C2×#95—171no—
951C2×#95—171no—
952C2×#95—171no—
953C43—171no—
954C43—171no—
955C43—171no—
956C2×C17—24no—
957C2×C17—24no—
958C2×C17—42no—
959C2×C17C2×C4×#4111yescharacteristic
960C2×C17C2×C4×#4111yescharacteristic
961C2×C17C4×H(5,𝔽2)11yescharacteristic
962C2×C17C2×#55111yescharacteristic
963C2×C17#347511yescharacteristic
964C2×C17#347511yescharacteristic
965C2×C17#348111yescharacteristic
966D17—42no—
967C25C22×D1711yescharacteristic
968C22×Q8—171no—
969C22×D4—171no—
970C22×D4—171no—
971C22×D4—171no—
972C23×C4—171no—
973C23×C4—171no—
974C23×C4—171no—
975C23×C4—171no—
976C23×C4—171no—
977C23×C4—171no—
978C23×C4—171no—
979C23×C4—171no—
980C23×C4—171no—
981C23×C4—171no—
982C23×C4—171no—
983C23×C4—171no—
984C23×C4—171no—
985C23×C4—344no—
986C23×C4—344no—
987C23×C4—682no—
988C23×C4C22×D1711yescharacteristic
989C23×C4C22×D1711yescharacteristic
990C23×C4C22×D1711yescharacteristic
991C23×C4C22×D1711yescharacteristic
992#126—178no—
993#126—178no—
994#124—178no—
995#123—178no—
996#123—178no—
997#123—178no—
998C22⋊Q8—178no—
999C22⋊Q8—178no—
1000#120—178no—
1001C4×Q8—682no—
1002C4×D4—178no—
1003C4×D4—178no—
1004C4×D4—344no—
1005C4×D4—344no—
1006C4×D4—344no—
1007C4×D4—344no—
1008C4×D4—682no—
1009#117—24no—
1010#117—178no—
1011#117—178no—
1012#117—344no—
1013C2×C4⋊C4—171no—
1014C2×C4⋊C4—171no—
1015C2×C4⋊C4—171no—
1016C2×C4⋊C4—171no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—171no—
1020C2×C4⋊C4—171no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4C22×D1711yescharacteristic
1032C2×C4⋊C4C22×D1711yescharacteristic
1033C2×C4⋊C4C22×D1711yescharacteristic
1034C2×C4⋊C4C22×D1711yescharacteristic
1035C2×C22⋊C4—24no—
1036C2×C22⋊C4—178no—
1037C2×C22⋊C4—171no—
1038C2×C22⋊C4—171no—
1039C2×C22⋊C4—171no—
1040C2×C22⋊C4—171no—
1041C2×C22⋊C4—171no—
1042C2×C22⋊C4—171no—
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—171no—
1045C2×C22⋊C4—171no—
1046C2×C22⋊C4—171no—
1047C2×C22⋊C4—171no—
1048C2×C22⋊C4—171no—
1049C2×C22⋊C4—171no—
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—344no—
1058C2×C22⋊C4C4×D1718yescomplemented
1059C2×C22⋊C4C22×D1711yescharacteristic
1060C2×C22⋊C4C22×D1711yescharacteristic
1061C2×C22⋊C4C22×D1711yescharacteristic
1062C2×C22⋊C4C22×D1711yescharacteristic
1063C2×C22⋊C4C22×D1711yescharacteristic
1064C2×C22⋊C4C22×D1711yescharacteristic
1065C2×C22⋊C4C22×D1711yescharacteristic
1066C2×C22⋊C4C22×D1711yescharacteristic
1067C2×C22⋊C4C22×D1711yescharacteristic
1068C2×C22⋊C4C22×D1711yescharacteristic
1069C2×C22⋊C4C22×D1711yescharacteristic
1070C2×C22⋊C4C22×D1711yescharacteristic
1071C2×C22⋊C4C22×D1711yescharacteristic
1072C2×C22⋊C4C22×D1711yescharacteristic
1073C2×C42—171no—
1074C2×C42—171no—
1075C2×C42—171no—
1076C2×C42—171no—
1077C2×C42—171no—
1078C2×C42—171no—
1079C2×C42—171no—
1080C2×C42—171no—
1081C2×C42—171no—
1082C2×C42—171no—
1083C2×C42—171no—
1084C2×C42—171no—
1085C2×C42—171no—
1086C2×C42—171no—
1087C2×C42—171no—
1088C2×C42—171no—
1089C2×C42—171no—
1090C2×C42—171no—
1091C2×C42—171no—
1092C2×C42—171no—
1093C2×C42—171no—
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—171no—
1102C2×C42—344no—
1103C2×C42—344no—
1104C2×C42—682no—
1105C2×C42—682no—
1106C2×C42—682no—
1107C2×C42C22×D1711yescharacteristic
1108C2×C42C22×D1711yescharacteristic
1109C2×C42C22×D1711yescharacteristic
1110C2×C42C22×D1711yescharacteristic
1111#95—171no—
1112#95—171no—
1113#95—171no—
1114#95—171no—
1115#95—171no—
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95C22×D1711yescharacteristic
1148#95C22×D1711yescharacteristic
1149#95C22×D1711yescharacteristic
1150#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154#95C22×D1711yescharacteristic
1155C17C4×#55111yescharacteristic, complemented, Sylow
1156C24—22no—
1157C24—22no—
1158C24—22no—
1159C24—22no—
1160C24—41no—
1161C24—41no—
1162C24—171no—
1163C24C2×C4×D1714yes—
1164C24C23×D1711yescharacteristic
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C2×Q8—174no—
1168C2×Q8—681no—
1169C2×Q8—681no—
1170C2×D4—174no—
1171C2×D4—174no—
1172C2×D4—174no—
1173C2×D4—342no—
1174C2×D4—342no—
1175C2×D4—342no—
1176C2×D4—342no—
1177C2×D4—681no—
1178C2×D4—681no—
1179C22×C4—22no—
1180C22×C4—22no—
1181C22×C4—22no—
1182C22×C4—22no—
1183C22×C4—22no—
1184C22×C4—22no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—171no—
1190C22×C4—174no—
1191C22×C4—174no—
1192C22×C4—174no—
1193C22×C4—171no—
1194C22×C4—171no—
1195C22×C4—171no—
1196C22×C4—171no—
1197C22×C4—171no—
1198C22×C4—171no—
1199C22×C4—171no—
1200C22×C4—171no—
1201C22×C4—171no—
1202C22×C4—171no—
1203C22×C4—171no—
1204C22×C4—174no—
1205C22×C4—174no—
1206C22×C4—171no—
1207C22×C4—171no—
1208C22×C4—171no—
1209C22×C4—342no—
1210C22×C4—342no—
1211C22×C4—342no—
1212C22×C4—342no—
1213C22×C4—342no—
1214C22×C4—342no—
1215C22×C4—342no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—342no—
1219C22×C4—342no—
1220C22×C4—342no—
1221C22×C4—342no—
1222C22×C4—342no—
1223C22×C4—342no—
1224C22×C4—342no—
1225C22×C4—342no—
1226C22×C4—342no—
1227C22×C4—342no—
1228C22×C4—342no—
1229C22×C4—342no—
1230C22×C4—342no—
1231C22×C4—342no—
1232C22×C4—342no—
1233C22×C4—681no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4—681no—
1240C22×C4—681no—
1241C22×C4—681no—
1242C22×C4—681no—
1243C22×C4—6816no—
1244C22×C4C2×C4×D1714yes—
1245C22×C4C2×C4×D1714yes—
1246C22×C4C23×D1711yescharacteristic
1247C22×C4C23×D1711yescharacteristic
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C22×C4C23×D1711yescharacteristic
1254C22×C4C23×D1711yescharacteristic
1255C22×C4C23×D1711yescharacteristic
1256C22×C4C23×D1711yescharacteristic
1257C22×C4C23×D1711yescharacteristic
1258C4⋊C4—22no—
1259C4⋊C4—22no—
1260C4⋊C4—41no—
1261C4⋊C4—41no—
1262C4⋊C4—174no—
1263C4⋊C4—174no—
1264C4⋊C4—174no—
1265C4⋊C4—174no—
1266C4⋊C4—174no—
1267C4⋊C4—174no—
1268C4⋊C4—174no—
1269C4⋊C4—174no—
1270C4⋊C4—342no—
1271C4⋊C4—342no—
1272C4⋊C4—342no—
1273C4⋊C4—342no—
1274C4⋊C4—342no—
1275C4⋊C4—342no—
1276C4⋊C4—681no—
1277C4⋊C4—681no—
1278C4⋊C4—681no—
1279C4⋊C4—681no—
1280C22⋊C4—22no—
1281C22⋊C4—22no—
1282C22⋊C4—22no—
1283C22⋊C4—22no—
1284C22⋊C4—22no—
1285C22⋊C4—22no—
1286C22⋊C4—22no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—174no—
1290C22⋊C4—174no—
1291C22⋊C4—174no—
1292C22⋊C4—174no—
1293C22⋊C4—174no—
1294C22⋊C4—174no—
1295C22⋊C4—174no—
1296C22⋊C4—174no—
1297C22⋊C4—174no—
1298C22⋊C4—174no—
1299C22⋊C4—174no—
1300C22⋊C4—342no—
1301C22⋊C4—342no—
1302C22⋊C4—342no—
1303C22⋊C4—342no—
1304C22⋊C4—342no—
1305C22⋊C4—342no—
1306C22⋊C4—342no—
1307C22⋊C4—681no—
1308C22⋊C4—681no—
1309C22⋊C4C2×C4×D1714yes—
1310C22⋊C4C2×C4×D1714yes—
1311C22⋊C4C2×C4×D1714yes—
1312C22⋊C4C2×C4×D1714yes—
1313C22⋊C4#6325414yes—
1314C42—22no—
1315C42—22no—
1316C42—41no—
1317C42—41no—
1318C42—174no—
1319C42—174no—
1320C42—174no—
1321C42—342no—
1322C42—342no—
1323C42—342no—
1324C42—342no—
1325C42—342no—
1326C42—342no—
1327C42—342no—
1328C42—342no—
1329C42—342no—
1330C42—342no—
1331C42—342no—
1332C42—342no—
1333C42—342no—
1334C42—342no—
1335C42—342no—
1336C42—342no—
1337C42—342no—
1338C42—342no—
1339C42—342no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42—681no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—28no—
1356C23—28no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—44no—
1364C23—44no—
1365C23—44no—
1366C23—44no—
1367C23—44no—
1368C23—172no—
1369C23—341no—
1370C23—341no—
1371C23—341no—
1372C23—341no—
1373C23—341no—
1374C23—341no—
1375C23C22×C4×D1712yes—
1376C23C22×C4×D1712yes—
1377C23C22×C4×D1712yes—
1378C23C2×#6325412yes—
1379C23#41×D1712yes—
1380C23#41×D1712yes—
1381C23#41×D1712yes—
1382C23C24×D1711yescharacteristic
1383Q8—684no—
1384D4—348no—
1385D4—348no—
1386D4—684no—
1387C2×C4—28no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—44no—
1419C2×C4—44no—
1420C2×C4—44no—
1421C2×C4—172no—
1422C2×C4—172no—
1423C2×C4—172no—
1424C2×C4—172no—
1425C2×C4—172no—
1426C2×C4—172no—
1427C2×C4—172no—
1428C2×C4—172no—
1429C2×C4—172no—
1430C2×C4—172no—
1431C2×C4—172no—
1432C2×C4—172no—
1433C2×C4—172no—
1434C2×C4—172no—
1435C2×C4—348no—
1436C2×C4—348no—
1437C2×C4—348no—
1438C2×C4—341no—
1439C2×C4—341no—
1440C2×C4—341no—
1441C2×C4—341no—
1442C2×C4—341no—
1443C2×C4—341no—
1444C2×C4—341no—
1445C2×C4—341no—
1446C2×C4—341no—
1447C2×C4—341no—
1448C2×C4—341no—
1449C2×C4—341no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—684no—
1470C2×C4—684no—
1471C2×C4—684no—
1472C2×C4—684no—
1473C2×C4—684no—
1474C2×C4—684no—
1475C2×C4—684no—
1476C2×C4—684no—
1477C2×C4—684no—
1478C2×C4—684no—
1479C2×C4C22×C4×D1712yes—
1480C2×C4C22×C4×D1712yes—
1481C2×C4C22×C4×D1712yes—
1482C2×C4C22×C4×D1712yes—
1483C2×C4C2×#6325412yes—
1484C2×C4C2×#6325412yes—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—416no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—342no—
1506C22—342no—
1507C22—342no—
1508C22—681no—
1509C22—681no—
1510C22—681no—
1511C22—681no—
1512C22C4×#6325414yes—
1513C22#1176327714yes—
1514C22C23×C4×D1711yescharacteristic
1515C22C2×#41×D1711yescharacteristic
1516C22C2×#41×D1711yescharacteristic
1517C22C2×#41×D1711yescharacteristic
1518C22C22×#6325411yescharacteristic
1519C22H(5,𝔽2)×D1711yescharacteristic
1520C22#1176364411yescharacteristic
1521C4—22no—
1522C4—22no—
1523C4—22no—
1524C4—22no—
1525C4—22no—
1526C4—22no—
1527C4—41no—
1528C4—41no—
1529C4—41no—
1530C4—41no—
1531C4—41no—
1532C4—41no—
1533C4—174no—
1534C4—342no—
1535C4—342no—
1536C4—342no—
1537C4—342no—
1538C4—342no—
1539C4—342no—
1540C4—342no—
1541C4—342no—
1542C4—342no—
1543C4—342no—
1544C4—342no—
1545C4—681no—
1546C4—681no—
1547C4—681no—
1548C2—24no—
1549C2—24no—
1550C2—42no—
1551C2—682no—
1552C2C2×C4×#6325411yescharacteristic
1553C2C2×#1176327711yescharacteristic
1554C2#1454198811yescharacteristic
1555C2D17×#55111yescharacteristic
1556C2#1454233511yescharacteristic
1557C2#1454233911yescharacteristic
1558C2#1454238911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2342C2
socle, cosocleC23×C17C25
prime radicalC2×#10587639C22
hypercenter#2342D17
hypocenterC17C4×#551
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #14531912C2semidirect
3. #14531902C2semidirect
4. #14531901C2semidirect
5. #14531891C2semidirect
6. #14531867C2semidirect
7. #14531865C2semidirect
8. #14531776C2semidirect
9. #14531774C2semidirect
11. #14531726C2semidirect
12. #14531718C2semidirect
13. #14531646C2semidirect
14. #14531638C2semidirect
15. #14531635C2semidirect
16. #14531338C2semidirect
17. #14531338C2semidirect
18. #14531325C2semidirect
19. #14531316C2semidirect
20. #14531312C2semidirect
21. #14531311C2semidirect
22. #14531303C2semidirect
23. #14531301C2semidirect
25. C4×#10587567C2semidirect
26. C4×#10587567C2semidirect
27. #117×Dic17C2semidirect
28. C4×#10587563C2semidirect
29. C2×C22⋊C4×Dic17C2semidirect
30. C2×C22⋊C4×Dic17C2semidirect
31. C17×#2342C2semidirect
33. #11763485C4semidirect
43. C2×#10587573C22semidirect
60. C2×C42×D17C22semidirect
61. #11762714C22semidirect
62. #11762713C22semidirect
63. #11762713C22semidirect
65. #11762705C22semidirect
66. #11762704C22semidirect
70. #11762700C22semidirect
71. #11762699C22semidirect
72. #11762699C22semidirect
73. #11762699C22semidirect
74. #11762698C22semidirect
75. #11762698C22semidirect
79. #11762694C22semidirect
80. #11762694C22semidirect
81. #11762693C22semidirect
82. #11762693C22semidirect
83. #11762693C22semidirect
84. #11762692C22semidirect
85. #11762692C22semidirect
86. #11762692C22semidirect
87. #11762692C22semidirect
88. #11762691C22semidirect
89. #11762691C22semidirect
90. #11762691C22semidirect
91. #11762691C22semidirect
92. #11762690C22semidirect
93. #11762690C22semidirect
94. #11762690C22semidirect
108. #11762680C22semidirect
109. #11762676C22semidirect
110. #11762676C22semidirect
111. #11762673C22semidirect
112. #11762671C22semidirect
115. C4⋊C4×Dic17C22semidirect
116. C4⋊C4×Dic17C22semidirect
117. C4⋊C4×Dic17C22semidirect
118. C4⋊C4×Dic17C22semidirect
119. C4⋊C4×Dic17C22semidirect
120. C4×#63225C22semidirect
121. C4×#63225C22semidirect
122. C4×#63225C22semidirect
123. C4×#63225C22semidirect
124. #11762660C22semidirect
125. #11762660C22semidirect
126. #11762660C22semidirect
127. #11762660C22semidirect
128. #11762660C22semidirect
129. #11762660C22semidirect
130. #11762660C22semidirect
154. C4×#63227C22semidirect
155. C4×#63227C22semidirect
157. #11762656C22semidirect
158. #11762656C22semidirect
159. #11762656C22semidirect
160. #11762656C22semidirect
161. #11762656C22semidirect
162. #11762655C22semidirect
163. #11762655C22semidirect
164. #11762654C22semidirect
165. #11762654C22semidirect
170. C42×Dic17C22semidirect
171. C42×Dic17C22semidirect
172. C42×Dic17C22semidirect
219. C2×C22⋊C4×C17C2×C4semidirect
240. C2×C22⋊Dic17C2×C4semidirect
252. #10587615C2×C4semidirect
254. C4×C22⋊D17C2×C4semidirect
264. #10587612C2×C4semidirect
268. #10587610C2×C4semidirect
318. #10587572C2×C4semidirect
319. #10587571C2×C4semidirect
320. #10587569C2×C4semidirect
325. #10587567C2×C4semidirect
326. #10587565C2×C4semidirect
327. #10587565C2×C4semidirect
328. #10587564C2×C4semidirect
330. #10587563C2×C4semidirect
474. C2×C4×D17C22×C4semidirect
477. C2×Dic34C22×C4semidirect
517. #63227C22×C4semidirect
518. #63227C22×C4semidirect
519. #63227C22×C4semidirect
520. C4⋊Dic17C22×C4semidirect
521. C4⋊Dic17C22×C4semidirect
522. C4⋊Dic17C22×C4semidirect
533. #63225C22×C4semidirect
534. #63225C22×C4semidirect
535. #63225C22×C4semidirect
536. #63225C22×C4semidirect
537. #63225C22×C4semidirect
564. C4×Dic17C22×C4semidirect
565. C4×Dic17C22×C4semidirect
566. C4×Dic17C22×C4semidirect
721. #2342D17semidirect
799. Dic17#551semidirect
1058. C2×C22⋊C4C4×D17semidirect
1155. C17C4×#551semidirect

Maximal subgroups

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

subgroupindex
C2×#117634852
#145319122
#145319022
#145319012
#145318912
#145318672
#145318652
#145317762
#145317742
#145317632
#145317262
#145317182
#145316462
#145316382
#145316352
#145313382
#145313252
#145313162
#145313122
#145313112
#145313032
#145313012
#145312832
C4×#105875672
#117×Dic172
C4×#105875632
C2×C22⋊C4×Dic172
C17×#23422
C4×#55117