Finite Group Databasebeta

← #17197866

Subgroups — #17197866

Order 4352.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763397C211yesmaximal, characteristic
2#14531972C211yesmaximal, characteristic, complemented
3#14531957C211yesmaximal, characteristic, complemented
4#14531940C211yesmaximal, characteristic, complemented
5#14531933C211yesmaximal, characteristic, complemented
6#14531899C211yesmaximal, characteristic, complemented
7#14531864C211yesmaximal, characteristic, complemented
8#14531852C211yesmaximal, characteristic, complemented
9#14531831C211yesmaximal, characteristic, complemented
10#14531803C211yesmaximal, characteristic, complemented
11#14531800C211yesmaximal, characteristic, complemented
12#14531789C211yesmaximal, characteristic, complemented
13#14531779C211yesmaximal, characteristic, complemented
14#14531720C211yesmaximal, characteristic, complemented
15#14531709C211yesmaximal, characteristic, complemented
16#14531691C211yesmaximal, characteristic, complemented
17C4⋊C4×C22⋊D17C211yesmaximal, characteristic, complemented
18#14531598C211yesmaximal, characteristic, complemented
19#14531569C211yesmaximal, characteristic, complemented
20#14531560C211yesmaximal, characteristic, complemented
21#14531554C211yesmaximal, characteristic, complemented
22#14531490C211yesmaximal, characteristic, complemented
23#14531481C211yesmaximal, characteristic, complemented
24#14531476C211yesmaximal, characteristic, complemented
25#14531451C211yesmaximal, characteristic, complemented
26#14531442C211yesmaximal, characteristic, complemented
27#14531442C211yesmaximal, characteristic, complemented
28#14531382C211yesmaximal, characteristic, complemented
29C4×#10587639C211yesmaximal, characteristic, complemented
30C4×#10587639C211yesmaximal, characteristic, complemented
31C2×C17×#385C211yesmaximal, characteristic, complemented
32#11763397C4116yescomplemented
33C2×#10587565C2211yescharacteristic
34C2×#10587565C2211yescharacteristic
35C2×#10587571C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587610C2211yescharacteristic
40C2×#10587616C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587639C2211yescharacteristic
44C2×#10587639C2211yescharacteristic
45C2×#10587573C2211yescharacteristic, complemented
46C2×#10587579C2211yescharacteristic, complemented
47C2×C4×C22⋊D17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic
54C2×C4×C22⋊D17C2211yescharacteristic
55C2×C4×C22⋊D17C2211yescharacteristic
56C2×C4×C22⋊D17C2211yescharacteristic
57C2×#10587578C2211yescharacteristic, complemented
58C2×C4⋊C4×D17C2211yescharacteristic, complemented
59#11762714C2211yescharacteristic, complemented
60#11762713C2211yescharacteristic, complemented
61#11762713C2211yescharacteristic, complemented
62#11762710C2211yescharacteristic, complemented
63#11762709C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762706C2211yescharacteristic, complemented
68#11762706C2211yescharacteristic, complemented
69#11762705C2211yescharacteristic, complemented
70#11762705C2211yescharacteristic, complemented
71#11762704C2211yescharacteristic, complemented
72#11762704C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762702C2211yescharacteristic
80#11762702C2211yescharacteristic
81#11762702C2211yescharacteristic
82#11762702C2211yescharacteristic
83#11762702C2211yescharacteristic
84#11762702C2211yescharacteristic
85#11762702C2211yescharacteristic
86#11762702C2211yescharacteristic
87#11762701C2211yescharacteristic, complemented
88#11762701C2211yescharacteristic, complemented
89#11762699C2211yescharacteristic, complemented
90#11762699C2211yescharacteristic, complemented
91#11762699C2211yescharacteristic, complemented
92#11762699C2211yescharacteristic, complemented
93#11762698C2211yescharacteristic, complemented
94#11762698C2211yescharacteristic, complemented
95#11762697C2211yescharacteristic
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic
98#11762697C2211yescharacteristic
99#11762696C2211yescharacteristic, complemented
100#11762696C2211yescharacteristic, complemented
101#11762694C2211yescharacteristic, complemented
102#11762694C2211yescharacteristic, complemented
103#11762692C2211yescharacteristic, complemented
104#11762692C2211yescharacteristic, complemented
105#11762691C2211yescharacteristic, complemented
106#11762691C2211yescharacteristic, complemented
107#11762690C2211yescharacteristic, complemented
108#11762690C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762690C2211yescharacteristic, complemented
111#11762688C2211yescharacteristic
112#11762688C2211yescharacteristic
113#11762688C2211yescharacteristic
114#11762688C2211yescharacteristic
115#11762688C2211yescharacteristic
116#11762688C2211yescharacteristic
117#11762688C2211yescharacteristic
118#11762688C2211yescharacteristic
119#11762687C2211yescharacteristic, complemented
120#11762687C2211yescharacteristic, complemented
121#11762685C2211yescharacteristic
122#11762685C2211yescharacteristic
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762683C2211yescharacteristic, complemented
126#11762683C2211yescharacteristic, complemented
127#11762682C2211yescharacteristic
128#11762682C2211yescharacteristic
129#11762682C2211yescharacteristic
130#11762682C2211yescharacteristic
131#11762682C2211yescharacteristic
132#11762682C2211yescharacteristic
133#11762682C2211yescharacteristic
134#11762682C2211yescharacteristic
135#11762680C2211yescharacteristic, complemented
136#11762680C2211yescharacteristic, complemented
137#11762680C2211yescharacteristic, complemented
138#11762680C2211yescharacteristic, complemented
139#11762678C2211yescharacteristic, complemented
140#11762676C2211yescharacteristic, complemented
141#11762674C2211yescharacteristic, complemented
142#11762673C2211yescharacteristic, complemented
143#11762671C2211yescharacteristic, complemented
144#11762669C2211yescharacteristic
145#11762669C2211yescharacteristic
146#11762668C2211yescharacteristic, complemented
147#11762666C2211yescharacteristic, complemented
148#11762666C2211yescharacteristic, complemented
149#11762665C2211yescharacteristic
150#11762665C2211yescharacteristic
151C4⋊C4×Dic17C2211yescharacteristic, complemented
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4⋊C4×Dic17C2211yescharacteristic, complemented
155#11762660C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157#11762660C2211yescharacteristic, complemented
158C4×C22⋊Dic17C2211yescharacteristic
159C4×C22⋊Dic17C2211yescharacteristic
160C4×C22⋊Dic17C2211yescharacteristic
161C4×C22⋊Dic17C2211yescharacteristic
162C4×C22⋊Dic17C2211yescharacteristic
163C4×C22⋊Dic17C2211yescharacteristic
164C4×C22⋊Dic17C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic
166C4×C22⋊Dic17C2211yescharacteristic
167C4×C22⋊Dic17C2211yescharacteristic
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic, complemented
171#11762654C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C24×C4×C17C2211yescharacteristic
174C22×C4⋊C4×C17C2211yescharacteristic
175C22×C4⋊C4×C17C2211yescharacteristic
176C22×C22⋊C4×C17C2211yescharacteristic
177C22×C22⋊C4×C17C2211yescharacteristic
178C17×#385C2211yescharacteristic
179C17×#385C2211yescharacteristic
180C17×#385C2211yescharacteristic
181C17×#385C2211yescharacteristic
182C17×#385C2211yescharacteristic
183C17×#385C2211yescharacteristic
184C17×#385C2211yescharacteristic
185C17×#385C2211yescharacteristic
186C2×C17×#95C2211yescharacteristic
187C2×C17×#95C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C23×C4×C17—42no—
190C23×C4×C17—42no—
191C23×C4×C17—42no—
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×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
207C22×C22⋊D17C2311yescharacteristic
208C22×D68C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×Dic34C2311yescharacteristic
216C2×C4⋊C4×C17—42no—
217C2×C4⋊C4×C17—42no—
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17—42no—
227C2×C22⋊C4×C17C2×C418yescomplemented
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
236#10587639C2×C418yescomplemented
237#10587639C2×C418yescomplemented
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
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
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256#10587616C2×C418yescomplemented
257C4×C22⋊D17—42no—
258C4×C22⋊D17—42no—
259C4×C22⋊D17—42no—
260C4×C22⋊D17—42no—
261C4×C22⋊D17—42no—
262C4×C22⋊D17—42no—
263C4×C22⋊D17—42no—
264C4×C22⋊D17—42no—
265C4×C22⋊D17C2×C418yescomplemented
266C4×C22⋊D17C2×C418yescomplemented
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289#10587610C2×C418yescomplemented
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
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
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324#10587579—42no—
325#10587578—42no—
326C4⋊C4×D17—42no—
327#10587573—42no—
328#10587571C2×C418yescomplemented
329#10587571C2×C418yescomplemented
330#10587570C2×C418yescomplemented
331#10587570C2×C418yescomplemented
332#10587569C2×C418yescomplemented
333#10587569C2×C418yescomplemented
334#10587565C2×C418yescomplemented
335#10587565C2×C418yescomplemented
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
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×C17C22×C414yes—
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C24×C17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C22×C4×C17—22no—
389C22×C4×C17—22no—
390C22×C4×C17—22no—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—22no—
394C22×C4×C17—22no—
395C22×C4×C17—22no—
396C22×C4×C17—22no—
397C22×C4×C17—22no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—416no—
417C22×C4×C17C22×C414yes—
418C22×C4×C17C22×C414yes—
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—41no—
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⋊D17C22×C414yes—
444C2×C22⋊D17C22×C414yes—
445C2×C22⋊D17C22×C414yes—
446C2×C22⋊D17C22×C414yes—
447C2×C22⋊D17C22×C414yes—
448C2×C22⋊D17C22×C414yes—
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C2×D68—41no—
464C2×D68—41no—
465C2×D68C22×C414yescomplemented
466C2×C4×D17—22no—
467C2×C4×D17—22no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17C22×C414yescomplemented
483C2×C4×D17C22×C414yescomplemented
484C2×Dic34—41no—
485C2×Dic34—41no—
486C2×Dic34C22×C414yescomplemented
487C4⋊C4×C17—22no—
488C4⋊C4×C17—22no—
489C4⋊C4×C17—22no—
490C4⋊C4×C17—22no—
491C4⋊C4×C17—41no—
492C4⋊C4×C17—41no—
493C4⋊C4×C17—41no—
494C4⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17C22×C414yes—
500C22⋊C4×C17C22×C414yes—
501C22⋊C4×C17C22×C414yes—
502C22⋊C4×C17C22×C414yes—
503C22⋊Dic17—22no—
504C22⋊Dic17—22no—
505C22⋊Dic17—22no—
506C22⋊Dic17—22no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509C22⋊Dic17—41no—
510C22⋊Dic17—41no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17C22×C414yes—
516C22⋊Dic17C22×C414yes—
517C22⋊Dic17C22×C414yes—
518C22⋊Dic17C22×C414yes—
519C22⋊Dic17C22×C414yes—
520C22⋊Dic17C22×C414yes—
521#63227—22no—
522#63227—22no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227C22×C414yescomplemented
534#63227C22×C414yescomplemented
535#63227C22×C414yescomplemented
536#63227C22×C414yescomplemented
537C4⋊Dic17—41no—
538C4⋊Dic17—41no—
539C4⋊Dic17—41no—
540C4⋊Dic17—41no—
541C4⋊Dic17C22×C414yescomplemented
542C4⋊Dic17C22×C414yescomplemented
543#63225—22no—
544#63225—22no—
545#63225—41no—
546#63225—41no—
547#63225—41no—
548#63225—41no—
549#63225—41no—
550#63225—41no—
551#63225—41no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225C22×C414yescomplemented
556#63225C22×C414yescomplemented
557#63225C22×C414yescomplemented
558#63225C22×C414yescomplemented
559C4×Dic17—22no—
560C4×Dic17—22no—
561C4×Dic17—41no—
562C4×Dic17—41no—
563C4×Dic17—41no—
564C4×Dic17—41no—
565C4×Dic17—41no—
566C4×Dic17—41no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17C22×C414yescomplemented
576C4×Dic17C22×C414yescomplemented
577#34416—171nomaximal, Sylow
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—28no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—44no—
596C23×C17—44no—
597C23×C17—44no—
598C23×C17—44no—
599C23×C17—44no—
600C23×C17—44no—
601C23×C17C23×C412yes—
602C23×C17C23×C412yes—
603C23×C17C23×C412yes—
604C23×C17H(5,𝔽2)12yes—
605C23×C172−1+412yes—
606C23×C17C2511yescharacteristic
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17C23×C412yes—
620C22×D17C23×C412yes—
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—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—44no—
652C2×C4×C17—44no—
653C2×C4×C17—44no—
654C2×C4×C17—44no—
655C2×C4×C17—44no—
656C2×C4×C17—44no—
657C2×C4×C17—44no—
658C2×C4×C17—44no—
659C2×C4×C17—82no—
660C2×C4×C17—82no—
661C2×C4×C17C23×C412yes—
662C2×C4×C17C23×C412yes—
663C2×C4×C17C23×C412yes—
664C2×C4×C17C23×C412yes—
665C2×C4×C17H(5,𝔽2)12yes—
666C2×C4×C17H(5,𝔽2)12yes—
667C22⋊D17—28no—
668C22⋊D17—28no—
669C22⋊D17—44no—
670C22⋊D17—44no—
671C22⋊D17—44no—
672C22⋊D17—44no—
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—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
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×Dic17C23×C412yes—
710C2×Dic17C23×C412yes—
711C2×Dic17C23×C412yes—
712C2×Dic17C23×C412yes—
713C2×Dic17C23×C412yes—
714C2×Dic17C23×C412yes—
715D68—44no—
716C4×D17—44no—
717C4×D17—44no—
718C4×D17—82no—
719C4×D17—82no—
720C4×D17—82no—
721C4×D17—82no—
722Dic34—44no—
723C2×#538—171no—
724#2383—171no—
725#2379—171no—
726#2377—171no—
727#2376—171no—
728#2373—171no—
729#2368—171no—
730#2367—171no—
731#2364—171no—
732#2361—171no—
733#2361—171no—
734#2360—171no—
735#2359—171no—
736#2353—171no—
737#2352—171no—
738#2349—171no—
739D4×C4⋊C4—171no—
740#2337—171no—
741#2335—171no—
742#2334—171no—
743#2334—171no—
744#2326—171no—
745#2325—171no—
746#2324—171no—
747#2322—171no—
748#2321—171no—
749#2321—171no—
750#2312—171no—
751C4×#120—171no—
752C4×#120—171no—
753C2×#385D1711yescharacteristic, complemented
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—416no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17#52014yes—
776C22×C17C24×C411yescharacteristic
777C22×C17C2×H(5,𝔽2)11yescharacteristic
778C22×C17C2×H(5,𝔽2)11yescharacteristic
779C22×C17C2×H(5,𝔽2)11yescharacteristic
780C22×C17C2×2−1+411yescharacteristic
781C22×C17#58511yescharacteristic
782C22×C17#58511yescharacteristic
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—22no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C4×C17—22no—
798C4×C17—22no—
799C4×C17—22no—
800C4×C17—22no—
801C4×C17—22no—
802C4×C17—22no—
803C4×C17—41no—
804C4×C17—41no—
805C4×C17—41no—
806C4×C17—41no—
807C4×C17—41no—
808C4×C17—41no—
809Dic17—22no—
810Dic17—22no—
811Dic17—22no—
812Dic17—22no—
813Dic17—22no—
814Dic17—22no—
815Dic17—41no—
816Dic17—41no—
817Dic17—41no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823C24×C4C2×D1711yescharacteristic
824#538—1716no—
825C2×#126—171no—
826C2×#126—171no—
827C2×#124—171no—
828C2×#124—171no—
829C2×#123—171no—
830C2×#123—171no—
831C2×C22⋊Q8—171no—
832C2×#121—171no—
833C2×#121—171no—
834C2×#121—171no—
835C2×#120—171no—
836C2×#120—171no—
837C2×C4×Q8—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×C4×D4—171no—
845C2×C4×D4—171no—
846C2×C4×D4—171no—
847C2×C4×D4—171no—
848C2×C4×D4—171no—
849C2×#117—171no—
850C22×C4⋊C4—171no—
851C22×C4⋊C4C2×D1711yescharacteristic
852C22×C4⋊C4C2×D1711yescharacteristic
853C22×C22⋊C4C2×D1711yescharacteristic
854C22×C22⋊C4C2×D1711yescharacteristic
855#391—171no—
856#391—171no—
857#391—171no—
858#390—171no—
859#390—171no—
860#390—171no—
861#390—171no—
862#390—171no—
863#389—171no—
864#389—171no—
865#389—171no—
866#389—171no—
867#389—171no—
868#389—171no—
869#389—171no—
870#389—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388—171no—
888#388—171no—
889#388—171no—
890#388—171no—
891#388—171no—
892#388—171no—
893#388—171no—
894#388—171no—
895#387—171no—
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387—171no—
901#387—171no—
902#387—171no—
903#387—171no—
904#387—171no—
905#387—171no—
906#387—171no—
907#386—171no—
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386—171no—
914#386—171no—
915#386—171no—
916#386—171no—
917#386—171no—
918#386—171no—
919#386—171no—
920#386—171no—
921#385—171no—
922#385—171no—
923#385—171no—
924#385—171no—
925#385—171no—
926#385—171no—
927#385—171no—
928#385—171no—
929#385—171no—
930#385—171no—
931#385—171no—
932#385—171no—
933#385—171no—
934#385—171no—
935#385C2×D1711yescharacteristic
936#385C2×D1711yescharacteristic
937#385C2×D1711yescharacteristic
938#385C2×D1711yescharacteristic
939#385C2×D1711yescharacteristic
940#385C2×D1711yescharacteristic
941#385C2×D1711yescharacteristic
942#385C2×D1711yescharacteristic
943#384—171no—
944#383—171no—
945#382—171no—
946#382—171no—
947#381—171no—
948#380—171no—
949#380—171no—
950#380—171no—
951#380—171no—
952#380—171no—
953#379—171no—
954#379—171no—
955C4×C4⋊C4—171no—
956C4×C4⋊C4—171no—
957C4×C4⋊C4—171no—
958C4×C4⋊C4—171no—
959C4×C4⋊C4—171no—
960C4×C4⋊C4—171no—
961C4×C4⋊C4—171no—
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4—171no—
974C4×C22⋊C4—171no—
975#376—171no—
976C2×#95—171no—
977C2×#95C2×D1711yescharacteristic
978C2×#95C2×D1711yescharacteristic
979C2×C17—24no—
980C2×C17—42no—
981C2×C17—42no—
982C2×C17C2×#52011yescharacteristic
983C2×C17C4×H(5,𝔽2)11yescharacteristic
984C2×C17C4×H(5,𝔽2)11yescharacteristic
985C2×C17#353211yescharacteristic
986C2×C17#353311yescharacteristic
987C2×C17#354111yescharacteristic
988C2×C17#354111yescharacteristic
989D17—42no—
990D17—42no—
991C25C22×D1711yescharacteristic
992C22×Q8—171no—
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4—171no—
997C22×D4—171no—
998C22×D4—171no—
999C22×D4—171no—
1000C23×C4—42no—
1001C23×C4—42no—
1002C23×C4—42no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4C22×D1711yescharacteristic
1010C23×C4C22×D1711yescharacteristic
1011C23×C4C22×D1711yescharacteristic
1012C23×C4C22×D1711yescharacteristic
1013C23×C4C22×D1711yescharacteristic
1014C23×C4C22×D1711yescharacteristic
1015C23×C4C22×D1711yescharacteristic
1016C23×C4C22×D1711yescharacteristic
1017C23×C4C22×D1711yescharacteristic
1018C23×C4C22×D1711yescharacteristic
1019#126—178no—
1020#126—178no—
1021#124—178no—
1022#124—178no—
1023#123—178no—
1024#123—178no—
1025C22⋊Q8—178no—
1026#121—178no—
1027#121—178no—
1028#121—178no—
1029#120—178no—
1030#120—178no—
1031C4×Q8—682no—
1032C4×D4—178no—
1033C4×D4—178no—
1034C4×D4—682no—
1035C4×D4—682no—
1036C4×D4—682no—
1037C4×D4—682no—
1038C4×D4—682no—
1039C4×D4—682no—
1040C4×D4—682no—
1041C4×D4—682no—
1042C4×D4—682no—
1043#117—682no—
1044C2×C4⋊C4—42no—
1045C2×C4⋊C4—42no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—682no—
1069C2×C4⋊C4C22×D1711yescharacteristic
1070C2×C4⋊C4C22×D1711yescharacteristic
1071C2×C4⋊C4C22×D1711yescharacteristic
1072C2×C4⋊C4C22×D1711yescharacteristic
1073C2×C4⋊C4C22×D1711yescharacteristic
1074C2×C4⋊C4C22×D1711yescharacteristic
1075C2×C4⋊C4C22×D1711yescharacteristic
1076C2×C4⋊C4C22×D1711yescharacteristic
1077C2×C22⋊C4—42no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
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⋊C4C4×D1718yescomplemented
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C22⋊C4C22×D1711yescharacteristic
1119C2×C22⋊C4C22×D1711yescharacteristic
1120C2×C22⋊C4C22×D1711yescharacteristic
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42—171no—
1133C2×C42—171no—
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42—171no—
1137C2×C42—171no—
1138C2×C42—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#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95C22×D1711yescharacteristic
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179C17#3441611yescharacteristic, complemented, Sylow
1180C24—22no—
1181C24—22no—
1182C24—41no—
1183C24—41no—
1184C24—41no—
1185C24—41no—
1186C24—171no—
1187C24—171no—
1188C24C2×C4×D1714yes—
1189C24C23×D1711yescharacteristic
1190C24C23×D1711yescharacteristic
1191C24C23×D1711yescharacteristic
1192C2×Q8—174no—
1193C2×Q8—681no—
1194C2×Q8—681no—
1195C2×D4—174no—
1196C2×D4—174no—
1197C2×D4—174no—
1198C2×D4—174no—
1199C2×D4—174no—
1200C2×D4—174no—
1201C2×D4—174no—
1202C2×D4—342no—
1203C2×D4—342no—
1204C2×D4—342no—
1205C2×D4—342no—
1206C2×D4—681no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4—681no—
1214C2×D4—681no—
1215C2×D4—681no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—41no—
1236C22×C4—41no—
1237C22×C4—41no—
1238C22×C4—41no—
1239C22×C4—41no—
1240C22×C4—41no—
1241C22×C4—41no—
1242C22×C4—41no—
1243C22×C4—41no—
1244C22×C4—416no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—171no—
1249C22×C4—171no—
1250C22×C4—171no—
1251C22×C4—174no—
1252C22×C4—174no—
1253C22×C4—171no—
1254C22×C4—171no—
1255C22×C4—171no—
1256C22×C4—171no—
1257C22×C4—171no—
1258C22×C4—171no—
1259C22×C4—171no—
1260C22×C4—171no—
1261C22×C4—342no—
1262C22×C4—342no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4C2×C4×D1714yes—
1278C22×C4C2×C4×D1714yes—
1279C22×C4C23×D1711yescharacteristic
1280C22×C4C23×D1711yescharacteristic
1281C22×C4C23×D1711yescharacteristic
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C4⋊C4—22no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—22no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—174no—
1300C4⋊C4—174no—
1301C4⋊C4—174no—
1302C4⋊C4—174no—
1303C4⋊C4—174no—
1304C4⋊C4—174no—
1305C4⋊C4—342no—
1306C4⋊C4—342no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—174no—
1326C22⋊C4—174no—
1327C22⋊C4—174no—
1328C22⋊C4—174no—
1329C22⋊C4—174no—
1330C22⋊C4—174no—
1331C22⋊C4—174no—
1332C22⋊C4—174no—
1333C22⋊C4—174no—
1334C22⋊C4—174no—
1335C22⋊C4—342no—
1336C22⋊C4—342no—
1337C22⋊C4—342no—
1338C22⋊C4—342no—
1339C22⋊C4—342no—
1340C22⋊C4—342no—
1341C22⋊C4—681no—
1342C22⋊C4—681no—
1343C22⋊C4—681no—
1344C22⋊C4—681no—
1345C22⋊C4—681no—
1346C22⋊C4—681no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4C2×C4×D1714yes—
1360C22⋊C4C2×C4×D1714yes—
1361C22⋊C4C2×C4×D1714yes—
1362C22⋊C4C2×C4×D1714yes—
1363C42—174no—
1364C42—174no—
1365C42—342no—
1366C42—342no—
1367C42—681no—
1368C42—681no—
1369C42—681no—
1370C42—681no—
1371C42—681no—
1372C42—681no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42—681no—
1379C42—681no—
1380C42—681no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—28no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—44no—
1399C23—44no—
1400C23—44no—
1401C23—44no—
1402C23—44no—
1403C23—44no—
1404C23—172no—
1405C23—172no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23C22×C4×D1712yes—
1419C23C22×C4×D1712yes—
1420C23C22×C4×D1712yes—
1421C23#1058769112yes—
1422C23#1058769412yes—
1423C23C24×D1711yescharacteristic
1424Q8—684no—
1425D4—348no—
1426D4—348no—
1427D4—684no—
1428D4—684no—
1429D4—684no—
1430D4—684no—
1431D4—684no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—44no—
1463C2×C4—44no—
1464C2×C4—44no—
1465C2×C4—44no—
1466C2×C4—44no—
1467C2×C4—44no—
1468C2×C4—44no—
1469C2×C4—44no—
1470C2×C4—82no—
1471C2×C4—82no—
1472C2×C4—172no—
1473C2×C4—172no—
1474C2×C4—172no—
1475C2×C4—172no—
1476C2×C4—172no—
1477C2×C4—172no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—684no—
1515C2×C4—684no—
1516C2×C4—1362no—
1517C2×C4—1362no—
1518C2×C4—1362no—
1519C2×C4—1362no—
1520C2×C4C22×C4×D1712yes—
1521C2×C4C22×C4×D1712yes—
1522C2×C4C22×C4×D1712yes—
1523C2×C4C22×C4×D1712yes—
1524C2×C4#1058769112yes—
1525C2×C4#1058769112yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—416no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—342no—
1548C22—342no—
1549C22—342no—
1550C22—342no—
1551C22—342no—
1552C22—342no—
1553C22—681no—
1554C22—681no—
1555C22—681no—
1556C22—681no—
1557C22—681no—
1558C22—681no—
1559C22—681no—
1560C22—681no—
1561C22#1176329014yes—
1562C22C23×C4×D1711yescharacteristic
1563C22C2×#1058769111yescharacteristic
1564C22C2×#1058769111yescharacteristic
1565C22C2×#1058769111yescharacteristic
1566C22C2×#1058769411yescharacteristic
1567C22#1176364511yescharacteristic
1568C22#1176364511yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—342no—
1582C4—342no—
1583C4—342no—
1584C4—342no—
1585C4—342no—
1586C4—342no—
1587C4—681no—
1588C4—681no—
1589C4—681no—
1590C4—681no—
1591C4—681no—
1592C4—681no—
1593C4—681no—
1594C4—681no—
1595C2—24no—
1596C2—42no—
1597C2—42no—
1598C2—682no—
1599C2—682no—
1600C2C2×#1176329011yescharacteristic
1601C2C4×#1058769111yescharacteristic
1602C2C4×#1058769111yescharacteristic
1603C2#1454293911yescharacteristic
1604C2#1454295511yescharacteristic
1605C2#1454308111yescharacteristic
1606C2#1454308111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC2×C17×#385C2
socle, cosocleC23×C17C25
prime radicalC2×#11763397C2
hypercenterC2×#385D17
hypocenterC17#34416
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #14531972C2semidirect
3. #14531957C2semidirect
4. #14531940C2semidirect
5. #14531933C2semidirect
6. #14531899C2semidirect
7. #14531864C2semidirect
8. #14531852C2semidirect
9. #14531831C2semidirect
10. #14531803C2semidirect
11. #14531800C2semidirect
12. #14531789C2semidirect
13. #14531779C2semidirect
14. #14531720C2semidirect
15. #14531709C2semidirect
16. #14531691C2semidirect
17. C4⋊C4×C22⋊D17C2semidirect
18. #14531598C2semidirect
19. #14531569C2semidirect
20. #14531560C2semidirect
21. #14531554C2semidirect
22. #14531490C2semidirect
23. #14531481C2semidirect
24. #14531476C2semidirect
25. #14531451C2semidirect
26. #14531442C2semidirect
27. #14531442C2semidirect
28. #14531382C2semidirect
29. C4×#10587639C2semidirect
30. C4×#10587639C2semidirect
31. C2×C17×#385C2semidirect
32. #11763397C4semidirect
45. C2×#10587573C22semidirect
46. C2×#10587579C22semidirect
57. C2×#10587578C22semidirect
58. C2×C4⋊C4×D17C22semidirect
59. #11762714C22semidirect
60. #11762713C22semidirect
61. #11762713C22semidirect
62. #11762710C22semidirect
67. #11762706C22semidirect
68. #11762706C22semidirect
69. #11762705C22semidirect
70. #11762705C22semidirect
71. #11762704C22semidirect
72. #11762704C22semidirect
73. #11762704C22semidirect
74. #11762704C22semidirect
87. #11762701C22semidirect
88. #11762701C22semidirect
89. #11762699C22semidirect
90. #11762699C22semidirect
91. #11762699C22semidirect
92. #11762699C22semidirect
93. #11762698C22semidirect
94. #11762698C22semidirect
99. #11762696C22semidirect
100. #11762696C22semidirect
101. #11762694C22semidirect
102. #11762694C22semidirect
103. #11762692C22semidirect
104. #11762692C22semidirect
105. #11762691C22semidirect
106. #11762691C22semidirect
107. #11762690C22semidirect
108. #11762690C22semidirect
109. #11762690C22semidirect
110. #11762690C22semidirect
119. #11762687C22semidirect
120. #11762687C22semidirect
125. #11762683C22semidirect
126. #11762683C22semidirect
135. #11762680C22semidirect
136. #11762680C22semidirect
137. #11762680C22semidirect
138. #11762680C22semidirect
139. #11762678C22semidirect
140. #11762676C22semidirect
141. #11762674C22semidirect
142. #11762673C22semidirect
143. #11762671C22semidirect
146. #11762668C22semidirect
147. #11762666C22semidirect
148. #11762666C22semidirect
151. C4⋊C4×Dic17C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4⋊C4×Dic17C22semidirect
155. #11762660C22semidirect
156. #11762660C22semidirect
157. #11762660C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762656C22semidirect
171. #11762654C22semidirect
172. #95×D17C22semidirect
227. C2×C22⋊C4×C17C2×C4semidirect
236. #10587639C2×C4semidirect
237. #10587639C2×C4semidirect
256. #10587616C2×C4semidirect
265. C4×C22⋊D17C2×C4semidirect
266. C4×C22⋊D17C2×C4semidirect
289. #10587610C2×C4semidirect
328. #10587571C2×C4semidirect
329. #10587571C2×C4semidirect
330. #10587570C2×C4semidirect
331. #10587570C2×C4semidirect
332. #10587569C2×C4semidirect
333. #10587569C2×C4semidirect
334. #10587565C2×C4semidirect
335. #10587565C2×C4semidirect
465. C2×D68C22×C4semidirect
482. C2×C4×D17C22×C4semidirect
483. C2×C4×D17C22×C4semidirect
486. C2×Dic34C22×C4semidirect
533. #63227C22×C4semidirect
534. #63227C22×C4semidirect
535. #63227C22×C4semidirect
536. #63227C22×C4semidirect
541. C4⋊Dic17C22×C4semidirect
542. C4⋊Dic17C22×C4semidirect
555. #63225C22×C4semidirect
556. #63225C22×C4semidirect
557. #63225C22×C4semidirect
558. #63225C22×C4semidirect
575. C4×Dic17C22×C4semidirect
576. C4×Dic17C22×C4semidirect
753. C2×#385D17semidirect
1112. C2×C22⋊C4C4×D17semidirect
1179. C17#34416semidirect

Maximal subgroups

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

subgroupindex
C2×#117633972
#145319722
#145319572
#145319402
#145319332
#145318992
#145318642
#145318522
#145318312
#145318032
#145318002
#145317892
#145317792
#145317202
#145317092
#145316912
C4⋊C4×C22⋊D172
#145315982
#145315692
#145315602
#145315542
#145314902
#145314812
#145314762
#145314512
#145314422
#145313822
C4×#105876392
C2×C17×#3852
#3441617