Finite Group Databasebeta

← C2×#22592672 #32166392

Subgroups — C2×#22592672 #32166392

Order 18176.

3114 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556112C211yesmaximal, characteristic
2#22592672C2116yesmaximal, direct product factor
3C2×#17985938C211yesmaximal, characteristic, complemented
4C2×#17985938C211yesmaximal, characteristic, complemented
5C2×#17985925C211yesmaximal, characteristic, complemented
6C2×#17985910C211yesmaximal, characteristic, complemented
7C2×#17985906C211yesmaximal, characteristic, complemented
8C2×#17985889C211yesmaximal, characteristic, complemented
9C2×#17985889C211yesmaximal, characteristic, complemented
10C2×#17985878C211yesmaximal, characteristic
11C2×#17985876C211yesmaximal, characteristic
12C2×#17985864C211yesmaximal, characteristic, complemented
13C2×#17985860C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
15C22×C71⋊#95C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C2×#14556112—28no—
21C2×#14556112C2218yes—
22C22×C4⋊Dic71C2211yescharacteristic
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C22⋊Dic71C2211yescharacteristic
25C22×(C2×D71)⋊C4C2211yescharacteristic
26C22×(C2×D71)⋊C4C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×C4×Dic71C2211yescharacteristic
32C22×C4×Dic71C2211yescharacteristic
33#17985938C2218yescomplemented
34#17985938C2218yescomplemented
35#17985925C2218yescomplemented
36#17985910C2218yescomplemented
37#17985906C2218yescomplemented
38#17985889C2218yescomplemented
39#17985889C2218yescomplemented
40#17985878C2218yes—
41#17985876C2218yes—
42#17985864C2218yescomplemented
43#17985860C2218yescomplemented
44C22⋊C4×Dic71C2218yescomplemented
45C2×C71⋊#95C2211yescharacteristic
46C2×C71⋊#95C2211yescharacteristic
47C2×C71⋊#95C2211yescharacteristic
48C2×C71⋊#95C2211yescharacteristic
49C2×C71⋊#95C2211yescharacteristic
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2218yescomplemented
60C23×Q8×C71C2211yescharacteristic
61C24×C4×C71C2211yescharacteristic
62C2×C22⋊Q8×C71—28no—
63C2×C22⋊Q8×C71C2218yescomplemented
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×C22⋊D71—24no—
71C22×C22⋊D71—24no—
72C22×C22⋊D71—24no—
73C22×C22⋊D71C2314yes—
74C23×Dic71—24no—
75C23×Dic71—24no—
76C23×Dic71—24no—
77C23×Dic71—24no—
78C23×Dic71—24no—
79C23×Dic71—42no—
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2314yes—
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2314yes—
88C23×Dic71C2311yescharacteristic
89#14556112—232no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71—24no—
92C2×C4⋊Dic71C2314yes—
93C2×C4⋊Dic71C2314yes—
94C2×C22⋊Dic71—24no—
95C2×C22⋊Dic71C2314yes—
96C2×(C2×D71)⋊C4—24no—
97C2×(C2×D71)⋊C4—24no—
98C2×(C2×D71)⋊C4—24no—
99C2×(C2×D71)⋊C4—24no—
100C2×(C2×D71)⋊C4—42no—
101C2×(C2×D71)⋊C4—42no—
102C2×(C2×D71)⋊C4C2314yes—
103C2×(C2×D71)⋊C4C2314yes—
104C2×(C2×D71)⋊C4C2314yes—
105C2×(C2×D71)⋊C4C2314yes—
106C2×(C2×D71)⋊C4C2314yes—
107C2×(C2×D71)⋊C4C2314yes—
108C2×C4×Dic71—24no—
109C2×C4×Dic71—42no—
110C2×C4×Dic71C2314yes—
111C2×C4×Dic71C2314yes—
112C71⋊#95C2314yes—
113C71⋊#95C2314yes—
114C71⋊#95C2314yes—
115C71⋊#95C2314yes—
116C71⋊#95C2314yes—
117C71⋊#95C2314yes—
118C71⋊#95C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C25×C71C2311yescharacteristic
127C22×Q8×C71—24no—
128C22×Q8×C71—24no—
129C22×Q8×C71—42no—
130C22×Q8×C71C2314yes—
131C23×C4×C71—24no—
132C23×C4×C71—24no—
133C23×C4×C71—42no—
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2314yes—
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C22⋊Q8×C71—232no—
142C2×C4⋊C4×C71—24no—
143C2×C4⋊C4×C71—24no—
144C2×C4⋊C4×C71—24no—
145C2×C4⋊C4×C71C2314yes—
146C2×C4⋊C4×C71C2314yes—
147C2×C4⋊C4×C71C2314yes—
148C2×C22⋊C4×C71—24no—
149C2×C22⋊C4×C71D418yes—
150C2×C22⋊C4×C71C2314yes—
151C2×C22⋊C4×C71C2314yes—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71—22no—
159C23×D71C2412yes—
160C2×C22⋊D71—28no—
161C2×C22⋊D71—28no—
162C2×C22⋊D71—28no—
163C2×C22⋊D71—416no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—28no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—28no—
172C22×Dic71—28no—
173C22×Dic71—28no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
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—28no—
189C22×Dic71—44no—
190C22×Dic71—416no—
191C22×Dic71—416no—
192C22×Dic71#4114yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C4⋊Dic71—28no—
201C4⋊Dic71—28no—
202C22⋊Dic71—28no—
203(C2×D71)⋊C4—28no—
204(C2×D71)⋊C4—28no—
205(C2×D71)⋊C4—28no—
206(C2×D71)⋊C4—28no—
207(C2×D71)⋊C4—44no—
208(C2×D71)⋊C4—44no—
209C4×Dic71—28no—
210C4×Dic71—44no—
211C24×C71—22no—
212C24×C71—22no—
213C24×C71—22no—
214C24×C71—22no—
215C24×C71C2×D414yes—
216C24×C71#4114yes—
217C24×C71#4114yes—
218C24×C71C2412yes—
219C24×C71C2411yescharacteristic
220C2×Q8×C71—28no—
221C2×Q8×C71—28no—
222C2×Q8×C71—44no—
223C2×Q8×C71—416no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—28no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—28no—
241C22×C4×C71—44no—
242C22×C4×C71—416no—
243C22×C4×C71C2×D414yes—
244C22×C4×C71C2×D414yes—
245C22×C4×C71#4114yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2412yes—
252C4⋊C4×C71—28no—
253C4⋊C4×C71—28no—
254C4⋊C4×C71—28no—
255C22⋊C4×C71—28no—
256C22⋊C4×C71C2×D4116yes—
257C23×C71—28no—
258C23×C71—28no—
259C23×C71—28no—
260C23×C71—28no—
261C23×C71—28no—
262C23×C71—28no—
263C23×C71—22no—
264C23×C71—22no—
265C23×C71—22no—
266C23×C71—22no—
267C23×C71#124116yes—
268C23×C71C22×D414yes—
269C23×C71C22×D412yes—
270C23×C71C2×#4112yes—
271C23×C71C2×#4112yes—
272C23×C71C2×#4114yes—
273C23×C71C2×#4114yes—
274C23×C71C2×#4112yes—
275C23×C71C2×#4112yes—
276C23×C71H(5,𝔽2)12yes—
277C23×C712−1+412yes—
278C23×C71C2511yescharacteristic
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—22no—
284C22×D71—22no—
285C22×D71—22no—
286C22×D71—44no—
287C22×D71—44no—
288C22×D71—44no—
289C22×D71—44no—
290C22×D71—44no—
291C22×D71—44no—
292C22×D71—44no—
293Q8×C71—416no—
294C2×C4×C71—28no—
295C2×C4×C71—28no—
296C2×C4×C71—28no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
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—416no—
313C2×C4×C71—44no—
314C2×C4×C71—44no—
315C2×C4×C71—44no—
316C2×C4×C71C22×D414yes—
317C2×C4×C71C22×D414yes—
318C2×C4×C71C2×#4114yes—
319C22⋊D71—416no—
320C2×Dic71—28no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
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—416no—
342C2×Dic71—416no—
343C2×Dic71—44no—
344C2×Dic71—44no—
345C2×Dic71—44no—
346C2×Dic71—44no—
347C2×Dic71—44no—
348C2×Dic71—44no—
349C2×Dic71C2×#4114yes—
350C22×C71—24no—
351C22×C71—24no—
352C22×C71—24no—
353C22×C71—24no—
354C22×C71—24no—
355C22×C71—24no—
356C22×C71—232no—
357C22×C71C2×#12418yes—
358C22×C71C2×#12414yes—
359C22×C71#52914yes—
360C22×C71#53914yes—
361C22×C71#54614yes—
362C22×C71#54714yes—
363C22×C71#55114yes—
364C22×C71#55214yes—
365C22×C71C23×D411yescharacteristic
366C22×C71C22×#4111yescharacteristic
367C22×C71C22×#4111yescharacteristic
368C22×C71C22×#4111yescharacteristic
369C22×C71C22×#4111yescharacteristic
370C22×C71C2×H(5,𝔽2)11yescharacteristic
371C22×C71C2×2−1+411yescharacteristic
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—42no—
378C2×D71—42no—
379C2×D71—88no—
380C4×C71—24no—
381C4×C71—24no—
382C4×C71—24no—
383C4×C71—42no—
384C4×C71—42no—
385C4×C71—42no—
386Dic71—24no—
387Dic71—42no—
388Dic71—42no—
389Dic71—42no—
390Dic71—42no—
391Dic71—42no—
392Dic71—42no—
393C2×#2488—711nomaximal, Sylow
394C2×C71—28no—
395C2×C71#248818yescomplemented
396C2×C71C22×#12411yescharacteristic
397C2×C71C2×#52911yescharacteristic
398C2×C71C2×#53911yescharacteristic
399C2×C71C2×#54611yescharacteristic
400C2×C71C2×#54711yescharacteristic
401C2×C71C2×#55111yescharacteristic
402C2×C71C2×#55211yescharacteristic
403D71—82no—
404C22×#123—711no—
405C22×C22⋊Q8D7111yescharacteristic, complemented
406#2488—7116no—
407C2×#400—711no—
408C2×#400—711no—
409C2×#397—711no—
410C2×#393—711no—
411C2×#391—711no—
412C2×#388—711no—
413C2×#388—711no—
414C2×#386—711no—
415C2×#386—711no—
416C2×#382—711no—
417C2×#381—711no—
418C2×C4×C22⋊C4—711no—
419C22×#95—711no—
420C71C2×#248811yescharacteristic, complemented, Sylow
421C23×Q8C2×D7111yescharacteristic
422C23×D4—711no—
423C24×C4—711no—
424C24×C4—711no—
425C24×C4C2×D7111yescharacteristic
426C2×#123—718no—
427C2×#123—1428no—
428C2×C22⋊Q8—28no—
429C2×C22⋊Q8C2×D7118yescomplemented
430C22×C4⋊C4—711no—
431C22×C4⋊C4—711no—
432C22×C4⋊C4C2×D7111yescharacteristic
433C22×C4⋊C4C2×D7111yescharacteristic
434C22×C4⋊C4C2×D7111yescharacteristic
435C22×C22⋊C4—711no—
436C22×C22⋊C4—711no—
437C22×C22⋊C4—711no—
438C22×C22⋊C4—711no—
439C22×C22⋊C4—711no—
440C22×C22⋊C4—711no—
441C22×C22⋊C4—711no—
442C22×C22⋊C4C2×D7111yescharacteristic
443C22×C22⋊C4C2×D7111yescharacteristic
444C22×C42—711no—
445C22×C42—711no—
446#400—718no—
447#400—718no—
448#397—718no—
449#393—718no—
450#391—718no—
451#388—718no—
452#388—718no—
453#386—718no—
454#386—718no—
455#382—718no—
456#381—718no—
457C4×C22⋊C4—718no—
458C2×#95—711no—
459C2×#95—711no—
460C2×#95—711no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95—711no—
466C2×#95—711no—
467C2×#95—711no—
468C2×#95—711no—
469C2×#95—711no—
470C2×#95—711no—
471C2×#95—711no—
472C2×#95—718no—
473C25—711no—
474C25C22×D7111yescharacteristic
475C22×Q8—24no—
476C22×Q8—24no—
477C22×Q8—42no—
478C22×Q8C22×D7114yes—
479C22×D4—714no—
480C22×D4—1424no—
481C22×D4—1424no—
482C22×D4—1424no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—42no—
486C23×C4—2842no—
487C23×C4—714no—
488C23×C4—711no—
489C23×C4—714no—
490C23×C4—711no—
491C23×C4—711no—
492C23×C4—711no—
493C23×C4—711no—
494C23×C4—711no—
495C23×C4—711no—
496C23×C4—1424no—
497C23×C4—1424no—
498C23×C4—1424no—
499C23×C4—1424no—
500C23×C4—1424no—
501C23×C4C22×D7111yescharacteristic
502C23×C4C22×D7111yescharacteristic
503C23×C4C22×D7111yescharacteristic
504C23×C4C22×D7114yes—
505C23×C4C22×D7111yescharacteristic
506C23×C4C22×D7111yescharacteristic
507C23×C4C22×D7111yescharacteristic
508#123—14232no—
509C22⋊Q8—232no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—714no—
514C2×C4⋊C4—714no—
515C2×C4⋊C4—1424no—
516C2×C4⋊C4—1424no—
517C2×C4⋊C4C22×D7114yes—
518C2×C4⋊C4C22×D7114yes—
519C2×C4⋊C4C22×D7114yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—2842no—
522C2×C22⋊C4—2842no—
523C2×C22⋊C4—714no—
524C2×C22⋊C4—714no—
525C2×C22⋊C4—714no—
526C2×C22⋊C4—714no—
527C2×C22⋊C4—714no—
528C2×C22⋊C4—714no—
529C2×C22⋊C4—714no—
530C2×C22⋊C4—1424no—
531C2×C22⋊C4—1424no—
532C2×C22⋊C4—1424no—
533C2×C22⋊C4—1424no—
534C2×C22⋊C4—1424no—
535C2×C22⋊C4C22⋊D7118yes—
536C2×C22⋊C4C22×D7114yes—
537C2×C22⋊C4C22×D7114yes—
538C2×C42—2842no—
539C2×C42—714no—
540C2×C42—714no—
541C2×C42—1424no—
542#95—714no—
543#95—714no—
544#95—714no—
545#95—714no—
546#95—714no—
547#95—714no—
548#95—714no—
549#95—714no—
550#95—714no—
551#95—714no—
552#95—714no—
553#95—714no—
554#95—714no—
555#95—714no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—712no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24—1422no—
565C24—1422no—
566C24—1422no—
567C24—1422no—
568C24C2×C22⋊D7114yes—
569C24#1176586614yes—
570C24#1176586614yes—
571C24C23×D7112yes—
572C24C23×D7111yescharacteristic
573C2×Q8—28no—
574C2×Q8—28no—
575C2×Q8—44no—
576C2×Q8—416no—
577C2×D4—28416no—
578C2×D4—1428no—
579C2×D4—1428no—
580C2×D4—1428no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—28no—
598C22×C4—44no—
599C22×C4—416no—
600C22×C4—28416no—
601C22×C4—28416no—
602C22×C4—2844no—
603C22×C4—714no—
604C22×C4—712no—
605C22×C4—712no—
606C22×C4—712no—
607C22×C4—712no—
608C22×C4—712no—
609C22×C4—712no—
610C22×C4—712no—
611C22×C4—1428no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4—1422no—
615C22×C4—1428no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4—1422no—
620C22×C4—1422no—
621C22×C4—1422no—
622C22×C4—1428no—
623C22×C4—1428no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1428no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4C2×C22⋊D7114yes—
637C22×C4C2×C22⋊D7114yes—
638C22×C4#1176586414yes—
639C22×C4C23×D7112yes—
640C22×C4C23×D7112yes—
641C22×C4C23×D7112yes—
642C22×C4C23×D7112yes—
643C22×C4C23×D7112yes—
644C22×C4C23×D7112yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—1428no—
649C4⋊C4—1428no—
650C22⋊C4—28no—
651C22⋊C4—2844no—
652C22⋊C4—2844no—
653C22⋊C4—1428no—
654C22⋊C4—1428no—
655C22⋊C4—1428no—
656C22⋊C4—1428no—
657C22⋊C4—1428no—
658C22⋊C4C2×C22⋊D71116yes—
659C42—2844no—
660C42—1428no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—28no—
666C23—28no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—2844no—
672C23—2844no—
673C23—2844no—
674C23—2844no—
675C23—2844no—
676C23—2844no—
677C23—2844no—
678C23—1422no—
679C23—1422no—
680C23—1422no—
681C23—1422no—
682C23—1422no—
683C23—1422no—
684C23—1422no—
685C23#14556117116yes—
686C23C22×C22⋊D7114yes—
687C23C22×C22⋊D7112yes—
688C23#41×D7112yes—
689C23C2×#1176586412yes—
690C23C2×#1176586614yes—
691C23C2×#1176586614yes—
692C23C2×#1176586612yes—
693C23C2×#1176586612yes—
694C23#1455617312yes—
695C23#1455617512yes—
696C23C24×D7111yescharacteristic
697Q8—416no—
698D4—28416no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—416no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—2844no—
722C2×C4—2844no—
723C2×C4—28416no—
724C2×C4—2844no—
725C2×C4—2844no—
726C2×C4—2844no—
727C2×C4—2844no—
728C2×C4—28416no—
729C2×C4—714no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1422no—
745C2×C4—1422no—
746C2×C4—1422no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1428no—
751C2×C4C22×C22⋊D7114yes—
752C2×C4C22×C22⋊D7114yes—
753C2×C4C2×#1176586414yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—232no—
760C22—24no—
761C22—2842no—
762C22—2842no—
763C22—2842no—
764C22—2842no—
765C22—2842no—
766C22—2842no—
767C22—2842no—
768C22—5688no—
769C22C2×#1455611718yes—
770C22C2×#1455611714yes—
771C22#1798653514yes—
772C22#1798659814yes—
773C22#1798664314yes—
774C22#1798664814yes—
775C22#1798667614yes—
776C22#1798669114yes—
777C22C23×C22⋊D7111yescharacteristic
778C22C2×#41×D7111yescharacteristic
779C22C22×#1176586411yescharacteristic
780C22C22×#1176586611yescharacteristic
781C22C22×#1176586611yescharacteristic
782C22C2×#1455617311yescharacteristic
783C22C2×#1455617511yescharacteristic
784C4—24no—
785C4—24no—
786C4—24no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—2842no—
791C4—2842no—
792C4—2842no—
793C4—2842no—
794C4—2842no—
795C4—2842no—
796C4—1424no—
797C2—28no—
798C2—5682no—
799C2#2259267218yesdirect product factor
800C2C22×#1455611711yescharacteristic
801C2C2×#1798653511yescharacteristic
802C2C2×#1798659811yescharacteristic
803C2C2×#1798664311yescharacteristic
804C2C2×#1798664811yescharacteristic
805C2C2×#1798667611yescharacteristic
806C2C2×#1798669111yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2488
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22592672C2direct (N × H)
3. C2×#17985938C2semidirect
4. C2×#17985938C2semidirect
5. C2×#17985925C2semidirect
6. C2×#17985910C2semidirect
7. C2×#17985906C2semidirect
8. C2×#17985889C2semidirect
9. C2×#17985889C2semidirect
12. C2×#17985864C2semidirect
13. C2×#17985860C2semidirect
14. C2×C22⋊C4×Dic71C2semidirect
15. C22×C71⋊#95C2semidirect
16. C22×C22⋊Q8×C71C2semidirect
33. #17985938C22semidirect
34. #17985938C22semidirect
35. #17985925C22semidirect
36. #17985910C22semidirect
37. #17985906C22semidirect
38. #17985889C22semidirect
39. #17985889C22semidirect
42. #17985864C22semidirect
43. #17985860C22semidirect
44. C22⋊C4×Dic71C22semidirect
59. C2×C71⋊#95C22semidirect
63. C2×C22⋊Q8×C71C22semidirect
395. C2×C71#2488semidirect
405. C22×C22⋊Q8D71semidirect
420. C71C2×#2488semidirect
429. C2×C22⋊Q8C2×D71semidirect
799. C2#22592672direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561122
#225926722
C2×#179859382
C2×#179859252
C2×#179859102
C2×#179859062
C2×#179858892
C2×#179858782
C2×#179858762
C2×#179858642
C2×#179858602
C2×C22⋊C4×Dic712
C22×C71⋊#952
C22×C22⋊Q8×C712
C2×#248871