Finite Group Databasebeta

← C2×#22592167 #32165199

Subgroups — C2×#22592167 #32165199

Order 18176.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556106C211yesmaximal, characteristic, complemented
2C22×#14556090C211yesmaximal, characteristic
3#22592167C2116yesmaximal, direct product factor
4C2×#17985932C211yesmaximal, characteristic, complemented
5C2×#17985923C211yesmaximal, characteristic, complemented
6C2×#17985912C211yesmaximal, characteristic, complemented
7C2×#17985903C211yesmaximal, characteristic, complemented
8C2×#17985882C211yesmaximal, characteristic, complemented
9C2×#17985877C211yesmaximal, characteristic
10C2×#17985877C211yesmaximal, characteristic
11C2×#17985873C211yesmaximal, characteristic, complemented
12C2×#17985873C211yesmaximal, characteristic, complemented
13C2×#17985873C211yesmaximal, characteristic, complemented
14C2×#17985856C211yesmaximal, characteristic, complemented
15C2×#95×D71C211yesmaximal, characteristic, complemented
16C2×#400×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C2×#14556106—28no—
24C2×#14556106C2218yescomplemented
25C2×#14556090—28no—
26C2×#14556090C2218yes—
27C22×C4⋊Dic71C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42#17985932C2218yescomplemented
43#17985923C2218yescomplemented
44#17985912C2218yescomplemented
45#17985903C2218yescomplemented
46#17985882C2218yescomplemented
47#17985877C2218yes—
48#17985877C2218yes—
49#17985873C2218yescomplemented
50#17985873C2218yescomplemented
51#17985873C2218yescomplemented
52#17985856C2218yescomplemented
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60#95×D71C2218yescomplemented
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63#400×C71C2218yescomplemented
64C2×#95×C71C2211yescharacteristic
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C24×D71C2311yescharacteristic
71C22×Dic142—24no—
72C22×Dic142—24no—
73C22×Dic142—42no—
74C22×Dic142C2314yes—
75C22×D284—24no—
76C22×D284—24no—
77C22×D284Q818yescomplemented
78C22×D284C2314yes—
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C22×C4×D71—24no—
86C22×C4×D71—24no—
87C22×C4×D71—24no—
88C22×C4×D71—24no—
89C22×C4×D71—24no—
90C22×C4×D71—24no—
91C22×C4×D71—24no—
92C22×C4×D71—42no—
93C22×C4×D71—42no—
94C22×C4×D71—42no—
95C22×C4×D71—42no—
96C22×C4×D71—42no—
97C22×C4×D71C2314yes—
98C22×C4×D71C2314yes—
99C22×C4×D71C2314yes—
100C22×C4×D71C2314yes—
101#14556106—232no—
102#14556090—232no—
103C2×C4⋊Dic71—24no—
104C2×C4⋊Dic71—42no—
105C2×C4⋊Dic71C2314yes—
106C2×C4⋊Dic71C2314yes—
107C2×Dic71⋊C4—24no—
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4—42no—
110C2×Dic71⋊C4—42no—
111C2×Dic71⋊C4C2314yes—
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4—42no—
120C2×(C2×D71)⋊C4—42no—
121C2×(C2×D71)⋊C4—42no—
122C2×(C2×D71)⋊C4D418yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×C4×Dic71—24no—
132C2×C4×Dic71C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C2×C4⋊C4×C71—24no—
148C2×C4⋊C4×C71—24no—
149C2×C4⋊C4×C71C2314yes—
150C2×C4⋊C4×C71C2314yes—
151#95×C71C2314yes—
152#95×C71C2314yes—
153#95×C71C2314yes—
154#95×C71C2314yes—
155#95×C71C2314yes—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—22no—
163C23×D71—22no—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71C2×D414yes—
167C23×D71C2×Q814yes—
168C23×D71C2×Q814yes—
169C23×D71#4114yes—
170C23×D71C2412yes—
171C23×D71C2412yes—
172C2×Dic142—28no—
173C2×Dic142—28no—
174C2×Dic142—44no—
175C2×Dic142—416no—
176C2×D284—232no—
177C2×D284—28no—
178C2×D284—28no—
179C2×D284C2×Q8116yescomplemented
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—22no—
192C22×Dic71—22no—
193C22×Dic71—22no—
194C22×Dic71—22no—
195C22×Dic71C2×D414yes—
196C22×Dic71#4114yes—
197C22×Dic71#4114yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C22×Dic71C2412yes—
201C22×Dic71C2412yes—
202C22×Dic71C2412yes—
203C22×Dic71C2412yes—
204C2×C4×D71—28no—
205C2×C4×D71—28no—
206C2×C4×D71—28no—
207C2×C4×D71—28no—
208C2×C4×D71—28no—
209C2×C4×D71—28no—
210C2×C4×D71—28no—
211C2×C4×D71—44no—
212C2×C4×D71—44no—
213C2×C4×D71—44no—
214C2×C4×D71—44no—
215C2×C4×D71—44no—
216C2×C4×D71—416no—
217C2×C4×D71—416no—
218C2×C4×D71—416no—
219C2×C4×D71—416no—
220C4⋊Dic71—28no—
221C4⋊Dic71—44no—
222Dic71⋊C4—28no—
223Dic71⋊C4—28no—
224Dic71⋊C4—44no—
225Dic71⋊C4—44no—
226(C2×D71)⋊C4—28no—
227(C2×D71)⋊C4—28no—
228(C2×D71)⋊C4—28no—
229(C2×D71)⋊C4—28no—
230(C2×D71)⋊C4—44no—
231(C2×D71)⋊C4—44no—
232(C2×D71)⋊C4—44no—
233(C2×D71)⋊C4C2×D4116yes—
234C4×Dic71—28no—
235C24×C71C2411yescharacteristic
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71C2×D414yes—
256C22×C4×C71C2×Q814yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2412yes—
262C22×C4×C71C2412yes—
263C22×C4×C71C2412yes—
264C4⋊C4×C71—28no—
265C4⋊C4×C71—28no—
266C23×C71C22×D412yes—
267C23×C71C22×Q812yes—
268C23×C71C2×#4112yes—
269C23×C71C2×#4112yes—
270C23×C71C2×#4112yes—
271C23×C71H(5,𝔽2)12yes—
272C23×C71H(5,𝔽2)12yes—
273C23×C71C2511yescharacteristic
274C22×D71—28no—
275C22×D71—28no—
276C22×D71—28no—
277C22×D71—28no—
278C22×D71—28no—
279C22×D71—28no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—22no—
284C22×D71—28no—
285C22×D71—28no—
286C22×D71—28no—
287C22×D71—22no—
288C22×D71—22no—
289C22×D71—22no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—22no—
293C22×D71—44no—
294C22×D71—44no—
295C22×D71—44no—
296C22×D71—44no—
297C22×D71C22⋊Q8116yes—
298C22×D71C22×D414yes—
299C22×D71C22×Q814yes—
300C22×D71C22×Q814yes—
301C22×D71C2×#4114yes—
302C2×C4×C71—28no—
303C2×C4×C71—28no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—44no—
324C2×C4×C71—44no—
325C2×C4×C71—44no—
326C2×C4×C71—44no—
327C2×C4×C71—44no—
328C2×C4×C71C22×D414yes—
329C2×C4×C71C22×Q814yes—
330C2×Dic71—28no—
331C2×Dic71—28no—
332C2×Dic71—28no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—44no—
349C2×Dic71—44no—
350C2×Dic71—44no—
351C2×Dic71C22×D414yes—
352C2×Dic71C2×#4114yes—
353C2×Dic71C2×#4114yes—
354D284—232no—
355C4×D71—416no—
356C4×D71—416no—
357C4×D71—416no—
358C4×D71—416no—
359Dic142—416no—
360C22×C71C2×C22⋊Q814yes—
361C22×C71#52914yes—
362C22×C71#53814yes—
363C22×C71#54614yes—
364C22×C71#54614yes—
365C22×C71#55414yes—
366C22×C71#55414yes—
367C22×C71C23×D411yescharacteristic
368C22×C71C23×Q811yescharacteristic
369C22×C71C22×#4111yescharacteristic
370C22×C71C22×#4111yescharacteristic
371C22×C71C22×#4111yescharacteristic
372C22×C71C2×H(5,𝔽2)11yescharacteristic
373C22×C71C2×H(5,𝔽2)11yescharacteristic
374C2×D71—24no—
375C2×D71—24no—
376C2×D71—24no—
377C2×D71—24no—
378C2×D71—24no—
379C2×D71—24no—
380C2×D71—232no—
381C2×D71—24no—
382C2×D71—24no—
383C2×D71—24no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C2×D71—416no—
389C2×D71C2×C22⋊Q818yes—
390C4×C71—24no—
391C4×C71—24no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71—42no—
396C4×C71—42no—
397Dic71—24no—
398Dic71—24no—
399Dic71—24no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#2450—711nomaximal, Sylow
404C2×C71#245018yescomplemented
405C2×C71C22×C22⋊Q811yescharacteristic
406C2×C71C2×#52911yescharacteristic
407C2×C71C2×#53811yescharacteristic
408C2×C71C2×#54611yescharacteristic
409C2×C71C2×#54611yescharacteristic
410C2×C71C2×#55411yescharacteristic
411C2×C71C2×#55411yescharacteristic
412D71—28no—
413D71—44no—
414C22×C22⋊Q8—711no—
415C22×C4×D4—711no—
416#2450—7116no—
417C2×#400D7111yescharacteristic, complemented
418C2×#398—711no—
419C2×#396—711no—
420C2×#393—711no—
421C2×#391—711no—
422C2×#387—711no—
423C2×#386—711no—
424C2×#386—711no—
425C2×#385—711no—
426C2×#385—711no—
427C2×#385—711no—
428C2×#380—711no—
429C22×#95—711no—
430C71C2×#245011yescharacteristic, complemented, Sylow
431C23×Q8—711no—
432C23×D4—711no—
433C24×C4—711no—
434C24×C4—711no—
435C24×C4—711no—
436C24×C4—711no—
437C2×C22⋊Q8—718no—
438C2×C22⋊Q8—1428no—
439C2×C4×D4—718no—
440C2×C4×D4—1428no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4—711no—
443C22×C4⋊C4—711no—
444C22×C4⋊C4—711no—
445C22×C4⋊C4—711no—
446C22×C4⋊C4—711no—
447C22×C4⋊C4C2×D7111yescharacteristic
448C22×C4⋊C4C2×D7111yescharacteristic
449C22×C22⋊C4—711no—
450C22×C22⋊C4—711no—
451C22×C22⋊C4—711no—
452C22×C22⋊C4—711no—
453C22×C22⋊C4—711no—
454C22×C22⋊C4—711no—
455C22×C22⋊C4—711no—
456C22×C22⋊C4—711no—
457C22×C42—711no—
458#400C2×D7118yescomplemented
459#398—718no—
460#396—718no—
461#393—718no—
462#391—718no—
463#387—718no—
464#386—718no—
465#386—718no—
466#385—718no—
467#385—718no—
468#385—718no—
469#380—718no—
470C2×#95—711no—
471C2×#95—711no—
472C2×#95—711no—
473C2×#95—711no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95—718no—
478C2×#95C2×D7111yescharacteristic
479C2×#95C2×D7111yescharacteristic
480C2×#95C2×D7111yescharacteristic
481C2×#95C2×D7111yescharacteristic
482C2×#95C2×D7111yescharacteristic
483C25—711no—
484C25—711no—
485C22×Q8—2842no—
486C22×Q8—714no—
487C22×Q8—1424no—
488C22×Q8—1424no—
489C22×D4—718no—
490C22×D4—714no—
491C22×D4—1424no—
492C22×D4—1424no—
493C23×C4—2842no—
494C23×C4—2842no—
495C23×C4—2842no—
496C23×C4—2842no—
497C23×C4—2842no—
498C23×C4—714no—
499C23×C4—714no—
500C23×C4—714no—
501C23×C4—714no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—711no—
505C23×C4—711no—
506C23×C4—711no—
507C23×C4—711no—
508C23×C4—1424no—
509C23×C4—1424no—
510C23×C4—1424no—
511C23×C4—1424no—
512C23×C4—1424no—
513C23×C4—1424no—
514C23×C4—1424no—
515C23×C4C22×D7111yescharacteristic
516C23×C4C22×D7111yescharacteristic
517C23×C4C22×D7111yescharacteristic
518C23×C4C22×D7111yescharacteristic
519C23×C4C22×D7111yescharacteristic
520C23×C4C22×D7111yescharacteristic
521C23×C4C22×D7111yescharacteristic
522C22⋊Q8—14232no—
523C4×D4—14232no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—2842no—
527C2×C4⋊C4—2842no—
528C2×C4⋊C4—2842no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4—714no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—714no—
534C2×C4⋊C4—714no—
535C2×C4⋊C4—1424no—
536C2×C4⋊C4—1424no—
537C2×C4⋊C4—1424no—
538C2×C4⋊C4C22×D7114yes—
539C2×C4⋊C4C22×D7114yes—
540C2×C22⋊C4—2842no—
541C2×C22⋊C4—2842no—
542C2×C22⋊C4—2842no—
543C2×C22⋊C4—714no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—714no—
546C2×C22⋊C4—718no—
547C2×C22⋊C4—714no—
548C2×C22⋊C4—714no—
549C2×C22⋊C4—714no—
550C2×C22⋊C4—714no—
551C2×C22⋊C4—714no—
552C2×C22⋊C4—1424no—
553C2×C22⋊C4—1424no—
554C2×C22⋊C4—1424no—
555C2×C22⋊C4—1424no—
556C2×C42—714no—
557C2×C42—1424no—
558#95—714no—
559#95—714no—
560#95—714no—
561#95—714no—
562#95—714no—
563#95—714no—
564#95—714no—
565#95C22×D7114yes—
566#95C22×D7114yes—
567#95C22×D7114yes—
568#95C22×D7114yes—
569#95C22×D7114yes—
570C24—714no—
571C24—714no—
572C24—714no—
573C24—712no—
574C24—714no—
575C24—712no—
576C24—1422no—
577C24—1422no—
578C24—1422no—
579C24—1422no—
580C24—1422no—
581C24—1422no—
582C24—1422no—
583C24—1422no—
584C24—1422no—
585C24—1422no—
586C24C23×D7111yescharacteristic
587C2×Q8—2844no—
588C2×Q8—28416no—
589C2×Q8—1428no—
590C2×Q8—1428no—
591C2×D4—7116no—
592C2×D4—1428no—
593C2×D4—1428no—
594C2×D4—14232no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—28416no—
615C22×C4—2844no—
616C22×C4—2844no—
617C22×C4—2844no—
618C22×C4—2844no—
619C22×C4—2844no—
620C22×C4—28416no—
621C22×C4—28416no—
622C22×C4—28416no—
623C22×C4—714no—
624C22×C4—714no—
625C22×C4—714no—
626C22×C4—712no—
627C22×C4—712no—
628C22×C4—712no—
629C22×C4—712no—
630C22×C4—712no—
631C22×C4—712no—
632C22×C4—1428no—
633C22×C4—1428no—
634C22×C4—1428no—
635C22×C4—1428no—
636C22×C4—1428no—
637C22×C4—1428no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1422no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4—1422no—
645C22×C4—1422no—
646C22×C4—1422no—
647C22×C4—1428no—
648C22×C4—1422no—
649C22×C4—1422no—
650C22×C4—1422no—
651C22×C4—1422no—
652C22×C4—1422no—
653C22×C4—1422no—
654C22×C4D4×D7114yes—
655C22×C4Q8×D7114yes—
656C22×C4C23×D7112yes—
657C22×C4C23×D7112yes—
658C22×C4C23×D7112yes—
659C22×C4C23×D7112yes—
660C22×C4C23×D7112yes—
661C22×C4C23×D7112yes—
662C22×C4C23×D7112yes—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—2844no—
666C4⋊C4—2844no—
667C4⋊C4—2844no—
668C4⋊C4—1428no—
669C4⋊C4—1428no—
670C4⋊C4—1428no—
671C22⋊C4—2844no—
672C22⋊C4—2844no—
673C22⋊C4—2844no—
674C22⋊C4—7116no—
675C22⋊C4—1428no—
676C22⋊C4—1428no—
677C22⋊C4—1428no—
678C22⋊C4—1428no—
679C42—1428no—
680C23—2844no—
681C23—2844no—
682C23—2844no—
683C23—2844no—
684C23—714no—
685C23—714no—
686C23—714no—
687C23—7116no—
688C23—714no—
689C23—1422no—
690C23—1422no—
691C23—1422no—
692C23—1422no—
693C23—1422no—
694C23—1422no—
695C23—1428no—
696C23—1428no—
697C23—1428no—
698C23—1422no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1428no—
703C23—1428no—
704C23—1428no—
705C23—1428no—
706C23—1428no—
707C23—1428no—
708C23C2×D4×D7112yes—
709C23C2×Q8×D7112yes—
710C23#41×D7112yes—
711C23#41×D7112yes—
712C23#41×D7112yes—
713C23#1455617412yes—
714C23#1455617412yes—
715C23C24×D7111yescharacteristic
716Q8—28416no—
717D4—14232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—28416no—
745C2×C4—28416no—
746C2×C4—28416no—
747C2×C4—28416no—
748C2×C4—2844no—
749C2×C4—2844no—
750C2×C4—2844no—
751C2×C4—714no—
752C2×C4—714no—
753C2×C4—714no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1428no—
770C2×C4—1428no—
771C2×C4—1428no—
772C2×C4C2×D4×D7114yes—
773C2×C4C2×Q8×D7114yes—
774C22—2842no—
775C22—2842no—
776C22—2842no—
777C22—28416no—
778C22—2842no—
779C22—718no—
780C22—1424no—
781C22—1424no—
782C22—1424no—
783C22—1424no—
784C22—1424no—
785C22—1424no—
786C22—1424no—
787C22—1424no—
788C22—14232no—
789C22—1424no—
790C22C22⋊Q8×D7114yes—
791C22#1798653214yes—
792C22#1798658814yes—
793C22#1798664114yes—
794C22#1798664214yes—
795C22#1798670514yes—
796C22#1798670514yes—
797C22C22×D4×D7111yescharacteristic
798C22C22×Q8×D7111yescharacteristic
799C22C2×#41×D7111yescharacteristic
800C22C2×#41×D7111yescharacteristic
801C22C2×#41×D7111yescharacteristic
802C22C2×#1455617411yescharacteristic
803C22C2×#1455617411yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—2842no—
812C4—2842no—
813C4—2842no—
814C4—1424no—
815C4—1424no—
816C4—1424no—
817C2—2844no—
818C2—1428no—
819C2#2259216718yesdirect product factor
820C2C2×C22⋊Q8×D7111yescharacteristic
821C2C2×#1798653211yescharacteristic
822C2C2×#1798658811yescharacteristic
823C2C2×#1798664111yescharacteristic
824C2C2×#1798664211yescharacteristic
825C2C2×#1798670511yescharacteristic
826C2C2×#1798670511yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#400×C71C2
socleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#400D71
hypocenterC71C2×#2450
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#14556106C2semidirect
3. #22592167C2direct (N × H)
4. C2×#17985932C2semidirect
5. C2×#17985923C2semidirect
6. C2×#17985912C2semidirect
7. C2×#17985903C2semidirect
8. C2×#17985882C2semidirect
11. C2×#17985873C2semidirect
12. C2×#17985873C2semidirect
13. C2×#17985873C2semidirect
14. C2×#17985856C2semidirect
15. C2×#95×D71C2semidirect
16. C2×#400×C71C2semidirect
24. C2×#14556106C22semidirect
42. #17985932C22semidirect
43. #17985923C22semidirect
44. #17985912C22semidirect
45. #17985903C22semidirect
46. #17985882C22semidirect
49. #17985873C22semidirect
50. #17985873C22semidirect
51. #17985873C22semidirect
52. #17985856C22semidirect
60. #95×D71C22semidirect
63. #400×C71C22semidirect
77. C22×D284Q8semidirect
179. C2×D284C2×Q8semidirect
404. C2×C71#2450semidirect
417. C2×#400D71semidirect
430. C71C2×#2450semidirect
458. #400C2×D71semidirect
819. C2#22592167direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561062
C22×#145560902
#225921672
C2×#179859322
C2×#179859232
C2×#179859122
C2×#179859032
C2×#179858822
C2×#179858772
C2×#179858732
C2×#179858562
C2×#95×D712
C2×#400×C712
C2×#245071