Finite Group Databasebeta

← C2×#22599171 #32868071

Subgroups — C2×#22599171 #32868071

Order 18176.

2342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986512C211yesmaximal, characteristic
2C2×C22⋊Q8×D71C211yesmaximal, characteristic, complemented
3#22599171C2116yesmaximal, direct product factor
4C2×#17986333C211yesmaximal, characteristic, complemented
5C2×#17986319C211yesmaximal, characteristic, complemented
6C2×#17986343C211yesmaximal, characteristic, complemented
7C2×#17986339C211yesmaximal, characteristic, complemented
8C2×#17986255C211yesmaximal, characteristic, complemented
9C2×#17986247C211yesmaximal, characteristic, complemented
10C2×#17986245C211yesmaximal, characteristic, complemented
11C2×#17986164C211yesmaximal, characteristic, complemented
12C2×#17986160C211yesmaximal, characteristic, complemented
13C2×#17986153C211yesmaximal, characteristic, complemented
14C2×#17986139C211yesmaximal, characteristic, complemented
15C2×#17985962C211yesmaximal, characteristic, complemented
16C2×#470×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×Q8×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C22×#11765855C2211yescharacteristic, complemented
21C22×#11765854C2211yescharacteristic, complemented
22C22×#11765852C2211yescharacteristic, complemented
23C22×#11765849C2211yescharacteristic
24#17986512—24no—
25#17986512C2218yes—
26C2×#14556113—21no—
27C2×#14556108C2211yescharacteristic
28C2×#14556107C2211yescharacteristic
29C2×#14556106—21no—
30C2×#14556105—21no—
31C2×#14556104C2211yescharacteristic
32C2×#14556104C2211yescharacteristic
33C22⋊Q8×D71—24no—
34C22⋊Q8×D71C2218yescomplemented
35C2×#14556103C2211yescharacteristic
36C2×#14556102C2211yescharacteristic
37C2×#14556098—21no—
38C2×#14556090—21no—
39C2×(C22⋊D71)⋊C4—21no—
40C2×#14556086C2211yescharacteristic
41C2×C4⋊C4×D71—21no—
42C2×C4⋊C4×D71C2211yescharacteristic
43C2×C22⋊C4×D71—21no—
44#17986343C2218yescomplemented
45#17986339C2218yescomplemented
46#17986333C2218yescomplemented
47#17986319C2218yescomplemented
48#17986255C2218yescomplemented
49#17986247C2218yescomplemented
50#17986245C2218yescomplemented
51#17986164C2218yescomplemented
52#17986160C2218yescomplemented
53#17986153C2218yescomplemented
54#17986139C2218yescomplemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×#14556053C2211yescharacteristic, complemented
59C2×#14556052C2211yescharacteristic, complemented
60C2×#14556052C2211yescharacteristic, complemented
61C2×#14556051C2211yescharacteristic, complemented
62C2×#14556050C2211yescharacteristic, complemented
63C2×#14556048C2211yescharacteristic, complemented
64#17985962C2218yescomplemented
65C2×(C2×D71)⋊C8C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×(C2×D71)⋊C8C2211yescharacteristic
69C22×Q16×C71C2211yescharacteristic, complemented
70C22×M16×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73#470×C71C2218yescomplemented
74C2×#106×C71C2211yescharacteristic, complemented
75C2×#103×C71C2211yescharacteristic, complemented
76C2×#103×C71C2211yescharacteristic, complemented
77C24×D71D411yescharacteristic
78C2×#11765866—22no—
79C2×#11765866—42no—
80C2×#11765866—42no—
81C2×#11765866C2314yes—
82C22×Dic142—21no—
83C22×Dic142C2311yescharacteristic
84C2×Q8×D71—22no—
85C2×Q8×D71—42no—
86C2×Q8×D71—42no—
87C2×Q8×D71C2314yes—
88C22×D284—21no—
89C22×D284—21no—
90C22×D284C2311yescharacteristic
91C22×C22⋊D71—21no—
92C23×Dic71D411yescharacteristic
93C22×C4×D71—21no—
94C22×C4×D71—21no—
95C22×C4×D71—21no—
96C22×C4×D71—42no—
97C22×C4×D71—42no—
98C22×C4×D71D411yescharacteristic
99C22×C4×D71D414yes—
100C22×C4×D71D411yescharacteristic
101C22×C4×D71C2311yescharacteristic
102C22×C4×D71C2311yescharacteristic
103C22×C4×D71C2314yes—
104C2×#11765855—42no—
105C2×#11765855C2314yescomplemented
106C2×#11765854—42no—
107C2×#11765854C2314yescomplemented
108C2×#11765852—42no—
109C2×#11765852C2314yescomplemented
110C2×#11765849—42no—
111C2×#11765849C2314yes—
112C22×C71⋊C8C2311yescharacteristic
113C22×C71⋊C8C2311yescharacteristic
114#14556113—28no—
115#14556108—22no—
116#14556108C2314yes—
117#14556107—22no—
118#14556107C2314yes—
119#14556106—28no—
120#14556105—28no—
121#14556104—22no—
122#14556104—22no—
123#14556104C2314yes—
124#14556104C2314yes—
125#14556103—22no—
126#14556103C2314yes—
127#14556102—22no—
128#14556102C2314yes—
129#14556098—28no—
130#14556090—28no—
131(C22⋊D71)⋊C4—28no—
132#14556086—22no—
133#14556086C2314yes—
134C2×C4⋊Dic71—21no—
135C2×C4⋊Dic71C2311yescharacteristic
136C2×C4⋊Dic71C2311yescharacteristic
137C2×Dic71⋊C4—21no—
138C2×Dic71⋊C4—21no—
139C2×Dic71⋊C4—21no—
140C2×Dic71⋊C4—21no—
141C4⋊C4×D71—28no—
142C4⋊C4×D71—22no—
143C4⋊C4×D71C2314yes—
144C2×C22⋊Dic71—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—21no—
147C2×(C2×D71)⋊C4—21no—
148C2×(C2×D71)⋊C4—21no—
149C2×(C2×D71)⋊C4—21no—
150C2×(C2×D71)⋊C4—21no—
151C22⋊C4×D71—28no—
152C2×C4×Dic71—21no—
153#14556062C2314yescomplemented
154#14556061C2314yescomplemented
155#14556059C2314yescomplemented
156#14556053C2314yescomplemented
157#14556052C2314yescomplemented
158#14556052C2314yescomplemented
159#14556051C2314yescomplemented
160#14556050C2314yescomplemented
161#14556048C2314yescomplemented
162(C2×D71)⋊C8C2314yes—
163(C2×D71)⋊C8C2314yes—
164(C2×D71)⋊C8C2314yes—
165(C2×D71)⋊C8C2314yes—
166C22×Q8×C71C2311yescharacteristic
167C22×Q8×C71C2311yescharacteristic
168C23×C4×C71C2311yescharacteristic
169C2×Q16×C71—42no—
170C2×Q16×C71C2314yescomplemented
171C2×M16×C71—42no—
172C2×M16×C71C2314yes—
173C22×C8×C71C2311yescharacteristic
174C22×C8×C71C2311yescharacteristic
175C22⋊Q8×C71—22no—
176C22⋊Q8×C71—22no—
177C22⋊Q8×C71C2314yes—
178C22⋊Q8×C71C2314yes—
179C2×C4⋊C4×C71—21no—
180C2×C4⋊C4×C71—21no—
181C2×C4⋊C4×C71C2311yescharacteristic
182C2×C4⋊C4×C71C2311yescharacteristic
183C2×C22⋊C4×C71—21no—
184C2×C22⋊C4×C71—21no—
185#106×C71C2314yescomplemented
186#103×C71C2314yescomplemented
187#103×C71C2314yescomplemented
188C23×D71—24no—
189C23×D71—21no—
190C23×D71—42no—
191C23×D71—42no—
192C23×D71C2×D411yescharacteristic
193C23×D71C2×D411yescharacteristic
194C23×D71C2×D414yes—
195#11765866—44no—
196#11765866—44no—
197#11765866—48no—
198C2×Dic142—22no—
199C2×Dic142—22no—
200C2×Dic142—21no—
201C2×Dic142—24no—
202C2×Dic142—44no—
203C2×Dic142C2412yes—
204Q8×D71—44no—
205Q8×D71—44no—
206Q8×D71—48no—
207C2×D284—22no—
208C2×D284—22no—
209C2×D284—24no—
210C2×D284—24no—
211C2×D284—21no—
212C2×D284—44no—
213C2×D284—44no—
214C2×D284C2412yes—
215C2×C22⋊D71—24no—
216C2×C22⋊D71—44no—
217C22×Dic71—21no—
218C22×Dic71—21no—
219C22×Dic71—21no—
220C22×Dic71—42no—
221C22×Dic71C2×D411yescharacteristic
222C22×Dic71C2×D411yescharacteristic
223C22×Dic71C2×D414yes—
224C2×C4×D71—22no—
225C2×C4×D71—22no—
226C2×C4×D71—22no—
227C2×C4×D71—22no—
228C2×C4×D71—24no—
229C2×C4×D71—24no—
230C2×C4×D71—24no—
231C2×C4×D71—48no—
232C2×C4×D71—44no—
233C2×C4×D71—44no—
234C2×C4×D71—42no—
235C2×C4×D71—42no—
236C2×C4×D71—44no—
237C2×C4×D71—44no—
238C2×C4×D71—44no—
239C2×C4×D71C2×D412yes—
240C2×C4×D71C2×D412yes—
241C2×C4×D71C2×D414yes—
242C2×C4×D71C2×D414yes—
243C2×C4×D71C2412yes—
244C2×C4×D71C2412yes—
245#11765855—44no—
246#11765854—44no—
247#11765852—44no—
248#11765849—44no—
249C2×C71⋊C8—22no—
250C2×C71⋊C8—22no—
251C2×C71⋊C8C2412yes—
252C2×C71⋊C8C2412yes—
253C4⋊Dic71—21no—
254C4⋊Dic71—21no—
255C4⋊Dic71—24no—
256C4⋊Dic71C2412yes—
257C4⋊Dic71C2412yes—
258Dic71⋊C4—24no—
259Dic71⋊C4—24no—
260Dic71⋊C4—24no—
261Dic71⋊C4—24no—
262C22⋊Dic71—24no—
263(C2×D71)⋊C4—24no—
264(C2×D71)⋊C4—24no—
265(C2×D71)⋊C4—24no—
266(C2×D71)⋊C4—24no—
267(C2×D71)⋊C4—24no—
268(C2×D71)⋊C4—24no—
269C4×Dic71—24no—
270C24×C71C2×D411yescharacteristic
271C2×Q8×C71—21no—
272C2×Q8×C71—21no—
273C2×Q8×C71—22no—
274C2×Q8×C71—22no—
275C2×Q8×C71—22no—
276C2×Q8×C71—22no—
277C2×Q8×C71C2412yes—
278C2×Q8×C71C2412yes—
279C22×C4×C71—22no—
280C22×C4×C71—22no—
281C22×C4×C71—21no—
282C22×C4×C71—21no—
283C22×C4×C71—21no—
284C22×C4×C71—21no—
285C22×C4×C71C2×D411yescharacteristic
286C22×C4×C71C2×D412yes—
287C22×C4×C71C2412yes—
288C22×C4×C71C2411yescharacteristic
289Q16×C71—44no—
290M16×C71—44no—
291C2×C8×C71—22no—
292C2×C8×C71—22no—
293C2×C8×C71C2412yes—
294C2×C8×C71C2412yes—
295C4⋊C4×C71—24no—
296C4⋊C4×C71—24no—
297C4⋊C4×C71—21no—
298C4⋊C4×C71—21no—
299C4⋊C4×C71C2412yes—
300C4⋊C4×C71C2412yes—
301C22⋊C4×C71—24no—
302C22⋊C4×C71—24no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71C22×D412yes—
307C23×C71C22×D411yescharacteristic
308C22×D71—22no—
309C22×D71—22no—
310C22×D71—22no—
311C22×D71—22no—
312C22×D71—22no—
313C22×D71—28no—
314C22×D71—22no—
315C22×D71—44no—
316C22×D71—44no—
317C22×D71—416no—
318C22×D71—42no—
319C22×D71—42no—
320C22×D71—42no—
321C22×D71#13714yes—
322C22×D71C22×D412yes—
323C22×D71C22×D412yes—
324Q8×C71—22no—
325Q8×C71—22no—
326Q8×C71—22no—
327Q8×C71—22no—
328Q8×C71—42no—
329Q8×C71—42no—
330C2×C4×C71—22no—
331C2×C4×C71—24no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—22no—
338C2×C4×C71—42no—
339C2×C4×C71—42no—
340C2×C4×C71—42no—
341C2×C4×C71—42no—
342C2×C4×C71C22×D412yes—
343C2×C4×C71C22×D411yescharacteristic
344C2×C4×C71H(5,𝔽2)12yes—
345C2×C4×C71H(5,𝔽2)12yes—
346C2×C4×C71C2511yescharacteristic
347C22⋊D71—48no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—22no—
353C2×Dic71—44no—
354C2×Dic71—42no—
355C2×Dic71—42no—
356C2×Dic71—42no—
357C2×Dic71C22×D412yes—
358C2×Dic71C22×D412yes—
359D284—22no—
360D284—22no—
361D284—48no—
362D284—48no—
363D284—42no—
364C4×D71—24no—
365C4×D71—24no—
366C4×D71—22no—
367C4×D71—22no—
368C4×D71—22no—
369C4×D71—22no—
370C4×D71—44no—
371C4×D71—44no—
372C4×D71—48no—
373C4×D71—48no—
374C4×D71—48no—
375Dic142—22no—
376Dic142—22no—
377Dic142—48no—
378Dic142—42no—
379C8×C71—22no—
380C8×C71—22no—
381C71⋊C8—22no—
382C71⋊C8—22no—
383C22×C71—22no—
384C22×C71—22no—
385C22×C71—22no—
386C22×C71—44no—
387C22×C71#53412yes—
388C22×C71C2×#13712yes—
389C22×C71#57512yes—
390C22×C71C23×D411yescharacteristic
391C2×D71—22no—
392C2×D71—28no—
393C2×D71—22no—
394C2×D71—22no—
395C2×D71—22no—
396C2×D71—22no—
397C2×D71—416no—
398C2×D71—44no—
399C2×D71—42no—
400C2×D71—42no—
401C2×D71—42no—
402C2×D71—84no—
403C2×D71C2×#13714yes—
404C4×C71—22no—
405C4×C71—42no—
406C4×C71—42no—
407C4×C71—42no—
408C4×C71—42no—
409C4×C71#53412yes—
410C4×C71C2×H(5,𝔽2)11yescharacteristic
411C4×C71C2×H(5,𝔽2)11yescharacteristic
412Dic71—22no—
413Dic71—22no—
414Dic71—42no—
415Dic71—42no—
416Dic71—42no—
417C2×#3196—711nomaximal, Sylow
418C2×C71—42no—
419C2×C71#319614yescomplemented
420C2×C71C2×#53411yescharacteristic
421C2×C71C22×#13711yescharacteristic
422C2×C71C2×#57511yescharacteristic
423D71—24no—
424D71—42no—
425D71—82no—
426C2×#525—711no—
427C22×C22⋊Q8—711no—
428#3196—7116no—
429C2×#484—711no—
430C2×#481—711no—
431C2×#485—711no—
432C2×#485—711no—
433C2×#470—711no—
434C2×#470D7111yescharacteristic, complemented
435C2×#468—711no—
436C2×#468—711no—
437C2×#452—711no—
438C2×#452—711no—
439C2×#451—711no—
440C2×#448—711no—
441C2×#407—711no—
442C71C2×#319611yescharacteristic, complemented, Sylow
443C22×#41—711no—
444C23×Q8—711no—
445C24×C4—711no—
446C22×Q16—711no—
447C22×Q16C2×D7111yescharacteristic, complemented
448C22×SD16—711no—
449C22×SD16—711no—
450C22×M16—711no—
451C22×M16C2×D7111yescharacteristic
452#525—718no—
453#525—1424no—
454C2×#123—1421no—
455C2×C22⋊Q8—711no—
456C2×C22⋊Q8—711no—
457C2×C22⋊Q8—711no—
458C2×C22⋊Q8—718no—
459C2×C22⋊Q8—711no—
460C2×C22⋊Q8—1421no—
461C2×C22⋊Q8—1421no—
462C2×C22⋊Q8—1424no—
463C2×C22⋊Q8C2×D7111yescharacteristic
464C2×C22⋊Q8C2×D7111yescharacteristic
465C2×#121—711no—
466C2×#121—711no—
467C2×#120—1421no—
468C2×C4×D4—1421no—
469C2×C4×D4—1421no—
470C2×#117—711no—
471C22×C4⋊C4—711no—
472C22×C4⋊C4—1421no—
473C22×C22⋊C4—1421no—
474#485—718no—
475#485—718no—
476#484—718no—
477#481—718no—
478#470—718no—
479#470C2×D7118yescomplemented
480#468—718no—
481#468—718no—
482#452—718no—
483#452—718no—
484#451—718no—
485#448—718no—
486C2×#107—711no—
487C2×#107—711no—
488C2×#106—711no—
489C2×#106C2×D7111yescharacteristic, complemented
490C2×#103—711no—
491C2×#103—711no—
492C2×#103—711no—
493C2×#103—711no—
494C2×#103C2×D7111yescharacteristic, complemented
495C2×#103C2×D7111yescharacteristic, complemented
496C2×#102—711no—
497C2×#102—711no—
498#407—718no—
499C2×C22⋊C8—711no—
500C2×C22⋊C8—711no—
501C2×C22⋊C8—711no—
502C2×C22⋊C8—711no—
503C25—711no—
504C2×#41—2842no—
505C2×#41—2842no—
506C2×#41—714no—
507C2×#41—1422no—
508C22×Q8—2842no—
509C22×Q8—2842no—
510C22×Q8—714no—
511C22×Q8—711no—
512C22×Q8—1421no—
513C22×Q8—1422no—
514C22×Q8C22×D7111yescharacteristic
515C22×Q8C22×D7111yescharacteristic
516C22×D4—711no—
517C22×D4—1421no—
518C22×D4—1421no—
519C22×D4—1421no—
520C23×C4—2842no—
521C23×C4—2842no—
522C23×C4—711no—
523C23×C4—711no—
524C23×C4—711no—
525C23×C4—714no—
526C23×C4—714no—
527C23×C4—711no—
528C23×C4—711no—
529C23×C4—1421no—
530C23×C4—1421no—
531C23×C4—1421no—
532C23×C4C22×D7111yescharacteristic
533C2×Q16—42no—
534C2×Q16—2842no—
535C2×Q16—714no—
536C2×Q16C22×D7114yescomplemented
537C2×SD16—2842no—
538C2×SD16—2842no—
539C2×SD16—714no—
540C2×SD16—714no—
541C2×M16—42no—
542C2×M16—2842no—
543C2×M16—714no—
544C2×M16C22×D7114yes—
545C22×C8—711no—
546C22×C8—711no—
547C22×C8C22×D7111yescharacteristic
548C22×C8C22×D7111yescharacteristic
549#123—1428no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—714no—
553C22⋊Q8—714no—
554C22⋊Q8—714no—
555C22⋊Q8—714no—
556C22⋊Q8—1428no—
557C22⋊Q8—1428no—
558C22⋊Q8—1422no—
559C22⋊Q8—1422no—
560C22⋊Q8—1422no—
561C22⋊Q8—1422no—
562C22⋊Q8C22×D7114yes—
563C22⋊Q8C22×D7114yes—
564#121—714no—
565#121—714no—
566#121—1422no—
567#121—1422no—
568#120—1428no—
569C4×D4—1428no—
570C4×D4—1428no—
571#117—714no—
572#117—1422no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—711no—
576C2×C4⋊C4—711no—
577C2×C4⋊C4—714no—
578C2×C4⋊C4—1422no—
579C2×C4⋊C4—1428no—
580C2×C4⋊C4—1421no—
581C2×C4⋊C4—1421no—
582C2×C4⋊C4—1421no—
583C2×C4⋊C4—1421no—
584C2×C4⋊C4—1421no—
585C2×C4⋊C4C22×D7111yescharacteristic
586C2×C4⋊C4C22×D7111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—1428no—
590C2×C22⋊C4—1421no—
591C2×C22⋊C4—1421no—
592C2×C22⋊C4—1421no—
593C2×C22⋊C4—1421no—
594C2×C22⋊C4—1421no—
595C2×C22⋊C4—1421no—
596C2×C22⋊C4—1421no—
597C2×C42—1421no—
598#107—714no—
599#107—714no—
600#106—714no—
601#106C22×D7114yescomplemented
602#103—714no—
603#103—714no—
604#103—714no—
605#103—714no—
606#103C22×D7114yescomplemented
607#103C22×D7114yescomplemented
608#102—714no—
609#102—714no—
610C22⋊C8—714no—
611C22⋊C8—714no—
612C22⋊C8—714no—
613C22⋊C8—714no—
614C24—2842no—
615C24—2842no—
616C24—714no—
617C24—711no—
618C24—711no—
619C24—1424no—
620C24—1421no—
621C24D4×D7111yescharacteristic
622#41—2848no—
623#41—2844no—
624#41—2844no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—2844no—
632C2×Q8—2844no—
633C2×Q8—2844no—
634C2×Q8—2848no—
635C2×Q8—712no—
636C2×Q8—1424no—
637C2×Q8—1422no—
638C2×Q8—1422no—
639C2×Q8—1421no—
640C2×Q8C23×D7112yes—
641C2×Q8C23×D7112yes—
642C2×D4—2844no—
643C2×D4—2844no—
644C2×D4—2844no—
645C2×D4—712no—
646C2×D4—1424no—
647C2×D4—1424no—
648C2×D4—1424no—
649C2×D4—1421no—
650C2×D4—1422no—
651C2×D4—1422no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—2842no—
659C22×C4—2842no—
660C22×C4—2844no—
661C22×C4—2844no—
662C22×C4—2848no—
663C22×C4—2844no—
664C22×C4—2844no—
665C22×C4—2844no—
666C22×C4—2842no—
667C22×C4—714no—
668C22×C4—714no—
669C22×C4—714no—
670C22×C4—711no—
671C22×C4—711no—
672C22×C4—712no—
673C22×C4—712no—
674C22×C4—712no—
675C22×C4—712no—
676C22×C4—1424no—
677C22×C4—1424no—
678C22×C4—1424no—
679C22×C4—1421no—
680C22×C4—1421no—
681C22×C4—1421no—
682C22×C4—1422no—
683C22×C4—1422no—
684C22×C4—1422no—
685C22×C4—1422no—
686C22×C4D4×D7112yes—
687C22×C4D4×D7111yescharacteristic
688C22×C4C23×D7112yes—
689C22×C4C23×D7111yescharacteristic
690Q16—44no—
691Q16—2844no—
692SD16—2844no—
693SD16—2844no—
694M16—44no—
695M16—2844no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—712no—
699C2×C8—712no—
700C2×C8—1422no—
701C2×C8—1422no—
702C2×C8C23×D7112yes—
703C2×C8C23×D7112yes—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—712no—
709C4⋊C4—712no—
710C4⋊C4—1424no—
711C4⋊C4—1424no—
712C4⋊C4—1424no—
713C4⋊C4—1424no—
714C4⋊C4—1424no—
715C4⋊C4—1421no—
716C4⋊C4—1421no—
717C4⋊C4C23×D7112yes—
718C4⋊C4C23×D7112yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—1424no—
722C22⋊C4—1424no—
723C22⋊C4—1424no—
724C22⋊C4—1424no—
725C22⋊C4—1424no—
726C22⋊C4—1424no—
727C22⋊C4—1424no—
728C42—1424no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—2844no—
733C23—2844no—
734C23—28416no—
735C23—2842no—
736C23—2842no—
737C23—2842no—
738C23—712no—
739C23—714no—
740C23—712no—
741C23—1428no—
742C23—1422no—
743C23—1422no—
744C23—1422no—
745C23—1422no—
746C23—1422no—
747C23—1422no—
748C23C2×D4×D7112yes—
749C23C2×D4×D7111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—2848no—
757Q8—2842no—
758Q8—1422no—
759Q8—1422no—
760D4—2848no—
761D4—2848no—
762D4—2848no—
763D4—2842no—
764D4—1422no—
765D4—1422no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—2844no—
779C2×C4—2844no—
780C2×C4—2848no—
781C2×C4—2848no—
782C2×C4—2848no—
783C2×C4—2842no—
784C2×C4—2842no—
785C2×C4—2842no—
786C2×C4—2844no—
787C2×C4—712no—
788C2×C4—712no—
789C2×C4—1422no—
790C2×C4—1422no—
791C2×C4—1422no—
792C2×C4—1422no—
793C2×C4—1422no—
794C2×C4—1422no—
795C2×C4—1422no—
796C2×C4—1422no—
797C2×C4—1422no—
798C2×C4—1424no—
799C2×C4—1424no—
800C2×C4C2×D4×D7112yes—
801C2×C4C2×D4×D7111yescharacteristic
802C2×C4#1455617312yes—
803C2×C4#1455617412yes—
804C2×C4C24×D7111yescharacteristic
805C8—22no—
806C8—22no—
807C8—1422no—
808C8—1422no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—28416no—
814C22—2844no—
815C22—2842no—
816C22—2842no—
817C22—2842no—
818C22—5684no—
819C22—714no—
820C22—1422no—
821C22—1422no—
822C22—1422no—
823C22—1428no—
824C22—1422no—
825C22—1422no—
826C22#1798655712yes—
827C22#137×D7112yes—
828C22#1798679812yes—
829C22C22×D4×D7111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—2842no—
836C4—2842no—
837C4—2842no—
838C4—1422no—
839C4—1422no—
840C4#1798655712yes—
841C4C2×#1455617311yescharacteristic
842C4C2×#1455617411yescharacteristic
843C2—42no—
844C2—2842no—
845C2—5682no—
846C2—1424no—
847C2#2259917114yesdirect product factor
848C2C2×#1798655711yescharacteristic
849C2C2×#137×D7111yescharacteristic
850C2C2×#1798679811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#470×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986512C2
hypercenterC2×#470D71
hypocenterC71C2×#3196
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D71C2semidirect
3. #22599171C2direct (N × H)
4. C2×#17986333C2semidirect
5. C2×#17986319C2semidirect
6. C2×#17986343C2semidirect
7. C2×#17986339C2semidirect
8. C2×#17986255C2semidirect
9. C2×#17986247C2semidirect
10. C2×#17986245C2semidirect
11. C2×#17986164C2semidirect
12. C2×#17986160C2semidirect
13. C2×#17986153C2semidirect
14. C2×#17986139C2semidirect
15. C2×#17985962C2semidirect
16. C2×#470×C71C2semidirect
20. C22×#11765855C22semidirect
21. C22×#11765854C22semidirect
22. C22×#11765852C22semidirect
34. C22⋊Q8×D71C22semidirect
44. #17986343C22semidirect
45. #17986339C22semidirect
46. #17986333C22semidirect
47. #17986319C22semidirect
48. #17986255C22semidirect
49. #17986247C22semidirect
50. #17986245C22semidirect
51. #17986164C22semidirect
52. #17986160C22semidirect
53. #17986153C22semidirect
54. #17986139C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556059C22semidirect
58. C2×#14556053C22semidirect
59. C2×#14556052C22semidirect
60. C2×#14556052C22semidirect
61. C2×#14556051C22semidirect
62. C2×#14556050C22semidirect
63. C2×#14556048C22semidirect
64. #17985962C22semidirect
69. C22×Q16×C71C22semidirect
73. #470×C71C22semidirect
74. C2×#106×C71C22semidirect
75. C2×#103×C71C22semidirect
76. C2×#103×C71C22semidirect
105. C2×#11765855C23semidirect
107. C2×#11765854C23semidirect
109. C2×#11765852C23semidirect
153. #14556062C23semidirect
154. #14556061C23semidirect
155. #14556059C23semidirect
156. #14556053C23semidirect
157. #14556052C23semidirect
158. #14556052C23semidirect
159. #14556051C23semidirect
160. #14556050C23semidirect
161. #14556048C23semidirect
170. C2×Q16×C71C23semidirect
185. #106×C71C23semidirect
186. #103×C71C23semidirect
187. #103×C71C23semidirect
419. C2×C71#3196semidirect
434. C2×#470D71semidirect
442. C71C2×#3196semidirect
447. C22×Q16C2×D71semidirect
479. #470C2×D71semidirect
489. C2×#106C2×D71semidirect
494. C2×#103C2×D71semidirect
495. C2×#103C2×D71semidirect
536. C2×Q16C22×D71semidirect
601. #106C22×D71semidirect
606. #103C22×D71semidirect
607. #103C22×D71semidirect
847. C2#22599171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865122
C2×C22⋊Q8×D712
#225991712
C2×#179863332
C2×#179863192
C2×#179863432
C2×#179863392
C2×#179862552
C2×#179862472
C2×#179862452
C2×#179861642
C2×#179861602
C2×#179861532
C2×#179861392
C2×#179859622
C2×#470×C712
C2×#319671