Finite Group Databasebeta

← C2×#22592424 #32165667

Subgroups — C2×#22592424 #32165667

Order 18176.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556123C211yesmaximal, characteristic
2C22×#14556093C211yesmaximal, characteristic, complemented
3#22592424C2116yesmaximal, direct product factor
4C2×#17985921C211yesmaximal, characteristic
5C2×#17985920C211yesmaximal, characteristic, complemented
6C2×#17985912C211yesmaximal, characteristic
7C2×#17985895C211yesmaximal, characteristic, complemented
8C2×#17985891C211yesmaximal, characteristic
9C2×#17985888C211yesmaximal, characteristic
10C2×#17985888C211yesmaximal, characteristic
11C2×#17985888C211yesmaximal, characteristic
12C2×#17985886C211yesmaximal, characteristic, complemented
13C2×#17985886C211yesmaximal, characteristic, complemented
14C2×#17985882C211yesmaximal, characteristic, complemented
15C2×#17985850C211yesmaximal, characteristic, complemented
16C2×#400×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C2×#14556123—28no—
19C2×#14556123C2218yes—
20C2×#14556093—28no—
21C2×#14556093C2218yescomplemented
22C22×C4⋊Dic71C2211yescharacteristic
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39C22×C4×Dic71C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42#17985921C2218yes—
43#17985920C2218yescomplemented
44#17985912C2218yes—
45#17985895C2218yescomplemented
46#17985891C2218yes—
47#17985888C2218yes—
48#17985888C2218yes—
49#17985888C2218yes—
50#17985886C2218yescomplemented
51#17985886C2218yescomplemented
52#17985882C2218yescomplemented
53#17985850C2218yescomplemented
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
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
70C22×Dic142—24no—
71C22×Dic142—24no—
72C22×Dic142—24no—
73C22×Dic142C2314yes—
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81#14556123—232no—
82#14556093—232no—
83C2×C4⋊Dic71—24no—
84C2×C4⋊Dic71—24no—
85C2×C4⋊Dic71—24no—
86C2×C4⋊Dic71C2314yes—
87C2×C4⋊Dic71C2314yes—
88C2×C4⋊Dic71C2314yes—
89C2×Dic71⋊C4—24no—
90C2×Dic71⋊C4—24no—
91C2×Dic71⋊C4—24no—
92C2×Dic71⋊C4—24no—
93C2×Dic71⋊C4D418yes—
94C2×Dic71⋊C4C2314yes—
95C2×Dic71⋊C4C2314yes—
96C2×Dic71⋊C4C2314yes—
97C2×Dic71⋊C4C2314yes—
98C2×Dic71⋊C4C2314yes—
99C2×(C2×D71)⋊C4—24no—
100C2×(C2×D71)⋊C4—24no—
101C2×(C2×D71)⋊C4—24no—
102C2×(C2×D71)⋊C4—24no—
103C2×(C2×D71)⋊C4—24no—
104C2×(C2×D71)⋊C4—24no—
105C2×(C2×D71)⋊C4—24no—
106C2×(C2×D71)⋊C4C2314yes—
107C2×(C2×D71)⋊C4C2314yes—
108C2×(C2×D71)⋊C4C2314yes—
109C2×(C2×D71)⋊C4C2314yes—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×C4×Dic71—24no—
114C2×C4×Dic71—24no—
115C2×C4×Dic71—24no—
116C2×C4×Dic71—24no—
117C2×C4×Dic71—24no—
118C2×C4×Dic71C2314yes—
119C2×C4×Dic71C2314yes—
120C2×C4×Dic71C2314yes—
121C2×C4×Dic71C2314yes—
122C2×C4×Dic71C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C2×C4⋊C4×C71—24no—
138C2×C4⋊C4×C71—24no—
139C2×C4⋊C4×C71C2314yes—
140C2×C4⋊C4×C71C2314yes—
141#95×C71C2314yes—
142#95×C71C2314yes—
143#95×C71C2314yes—
144#95×C71C2314yes—
145#95×C71C2314yes—
146C23×D71—22no—
147C23×D71—22no—
148C23×D71—22no—
149C23×D71—22no—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71C2412yes—
154C2×Dic142—232no—
155C2×Dic142—28no—
156C2×Dic142—28no—
157C2×Dic142—28no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71C2×D414yes—
175C22×Dic71C2×D414yes—
176C22×Dic71#4114yes—
177C22×Dic71#4114yes—
178C22×Dic71#4114yes—
179C22×Dic71C2412yes—
180C22×Dic71C2412yes—
181C22×Dic71C2412yes—
182C22×Dic71C2412yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C4⋊Dic71—28no—
187C4⋊Dic71—28no—
188C4⋊Dic71—28no—
189Dic71⋊C4—28no—
190Dic71⋊C4—28no—
191Dic71⋊C4—28no—
192Dic71⋊C4—28no—
193Dic71⋊C4C2×D4116yes—
194(C2×D71)⋊C4—28no—
195(C2×D71)⋊C4—28no—
196(C2×D71)⋊C4—28no—
197(C2×D71)⋊C4—28no—
198(C2×D71)⋊C4—28no—
199(C2×D71)⋊C4—28no—
200(C2×D71)⋊C4—28no—
201C4×Dic71—28no—
202C4×Dic71—28no—
203C4×Dic71—28no—
204C4×Dic71—28no—
205C4×Dic71—28no—
206C24×C71C2411yescharacteristic
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71C2×D414yes—
227C22×C4×C71#4114yes—
228C22×C4×C71C2412yes—
229C22×C4×C71C2412yes—
230C22×C4×C71C2412yes—
231C22×C4×C71C2412yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2412yes—
234C22×C4×C71C2412yes—
235C4⋊C4×C71—28no—
236C4⋊C4×C71—28no—
237C23×C71C22×D412yes—
238C23×C71C2×#4112yes—
239C23×C71C2×#4112yes—
240C23×C71C2×#4112yes—
241C23×C71C2×#4112yes—
242C23×C712−1+412yes—
243C23×C712−1+412yes—
244C23×C71C2511yescharacteristic
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—22no—
249C22×D71—22no—
250C22×D71—22no—
251C22×D71—22no—
252C22×D71—44no—
253C22×D71—44no—
254C22×D71—44no—
255C22×D71—44no—
256C22×D71—44no—
257C22×D71—44no—
258C22×D71—44no—
259C2×C4×C71—28no—
260C2×C4×C71—28no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—44no—
281C2×C4×C71—44no—
282C2×C4×C71—44no—
283C2×C4×C71—44no—
284C2×C4×C71—44no—
285C2×C4×C71C22×D414yes—
286C2×C4×C71C2×#4114yes—
287C2×Dic71—28no—
288C2×Dic71—28no—
289C2×Dic71—28no—
290C2×Dic71—28no—
291C2×Dic71—28no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—44no—
309C2×Dic71—44no—
310C2×Dic71C22×D414yes—
311C2×Dic71C22×D414yes—
312C2×Dic71C2×#4114yes—
313C2×Dic71C2×#4114yes—
314C2×Dic71C2×#4114yes—
315Dic142—232no—
316C22×C71#52514yes—
317C22×C71#52914yes—
318C22×C71#54114yes—
319C22×C71#54714yes—
320C22×C71#54814yes—
321C22×C71#55614yes—
322C22×C71#55614yes—
323C22×C71C23×D411yescharacteristic
324C22×C71C22×#4111yescharacteristic
325C22×C71C22×#4111yescharacteristic
326C22×C71C22×#4111yescharacteristic
327C22×C71C22×#4111yescharacteristic
328C22×C71C2×2−1+411yescharacteristic
329C22×C71C2×2−1+411yescharacteristic
330C2×D71—42no—
331C2×D71—42no—
332C2×D71—42no—
333C2×D71—42no—
334C2×D71—42no—
335C2×D71—42no—
336C2×D71—42no—
337C2×D71—88no—
338C4×C71—24no—
339C4×C71—24no—
340C4×C71—42no—
341C4×C71—42no—
342C4×C71—42no—
343C4×C71—42no—
344C4×C71—42no—
345Dic71—24no—
346Dic71—24no—
347Dic71—24no—
348Dic71—24no—
349Dic71—24no—
350Dic71—42no—
351Dic71—42no—
352C2×#2469—711nomaximal, Sylow
353C2×C71#246918yescomplemented
354C2×C71C2×#52511yescharacteristic
355C2×C71C2×#52911yescharacteristic
356C2×C71C2×#54111yescharacteristic
357C2×C71C2×#54711yescharacteristic
358C2×C71C2×#54811yescharacteristic
359C2×C71C2×#55611yescharacteristic
360C2×C71C2×#55611yescharacteristic
361D71—82no—
362C22×#126—711no—
363C22×C4×Q8—711no—
364#2469—7116no—
365C2×#400D7111yescharacteristic, complemented
366C2×#396—711no—
367C2×#395—711no—
368C2×#393—711no—
369C2×#389—711no—
370C2×#388—711no—
371C2×#388—711no—
372C2×#388—711no—
373C2×#388—711no—
374C2×#387—711no—
375C2×#387—711no—
376C2×#387—711no—
377C2×C4×C4⋊C4—711no—
378C71C2×#246911yescharacteristic, complemented, Sylow
379C23×Q8—711no—
380C2×#126—718no—
381C2×#126—1428no—
382C2×C4×Q8—718no—
383C2×C4×Q8—1428no—
384C22×C4⋊C4—711no—
385C22×C4⋊C4—711no—
386C22×C4⋊C4—711no—
387C22×C4⋊C4—711no—
388C22×C4⋊C4—711no—
389C22×C4⋊C4—711no—
390C22×C4⋊C4—711no—
391C22×C4⋊C4—711no—
392C22×C4⋊C4C2×D7111yescharacteristic
393C22×C4⋊C4C2×D7111yescharacteristic
394C22×C22⋊C4—711no—
395C22×C22⋊C4—711no—
396C22×C22⋊C4—711no—
397C22×C22⋊C4—711no—
398C22×C22⋊C4—711no—
399C22×C22⋊C4—711no—
400C22×C22⋊C4—711no—
401C22×C42—711no—
402C22×C42—711no—
403C22×C42—711no—
404C22×C42—711no—
405C22×C42—711no—
406#400C2×D7118yescomplemented
407#396—718no—
408#395—718no—
409#393—718no—
410#389—718no—
411#388—718no—
412#388—718no—
413#388—718no—
414#388—718no—
415#387—718no—
416#387—718no—
417#387—718no—
418C4×C4⋊C4—718no—
419C2×#95—711no—
420C2×#95—711no—
421C2×#95—711no—
422C2×#95—711no—
423C2×#95—711no—
424C2×#95—711no—
425C2×#95—711no—
426C2×#95C2×D7111yescharacteristic
427C2×#95C2×D7111yescharacteristic
428C2×#95C2×D7111yescharacteristic
429C2×#95C2×D7111yescharacteristic
430C2×#95C2×D7111yescharacteristic
431C25—711no—
432C22×Q8—714no—
433C22×Q8—1424no—
434C22×Q8—1424no—
435C22×Q8—1424no—
436C23×C4—711no—
437C23×C4—711no—
438C23×C4—711no—
439C23×C4—711no—
440C23×C4—711no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4C22×D7111yescharacteristic
444C23×C4C22×D7111yescharacteristic
445C23×C4C22×D7111yescharacteristic
446C23×C4C22×D7111yescharacteristic
447C23×C4C22×D7111yescharacteristic
448C23×C4C22×D7111yescharacteristic
449C23×C4C22×D7111yescharacteristic
450#126—14232no—
451C4×Q8—14232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—718no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—714no—
457C2×C4⋊C4—714no—
458C2×C4⋊C4—714no—
459C2×C4⋊C4—714no—
460C2×C4⋊C4—714no—
461C2×C4⋊C4—714no—
462C2×C4⋊C4—714no—
463C2×C4⋊C4—1424no—
464C2×C4⋊C4—1424no—
465C2×C4⋊C4—1424no—
466C2×C4⋊C4—1424no—
467C2×C4⋊C4—1424no—
468C2×C4⋊C4—1424no—
469C2×C4⋊C4—1424no—
470C2×C4⋊C4C22×D7114yes—
471C2×C4⋊C4C22×D7114yes—
472C2×C22⋊C4—714no—
473C2×C22⋊C4—714no—
474C2×C22⋊C4—714no—
475C2×C22⋊C4—714no—
476C2×C22⋊C4—714no—
477C2×C22⋊C4—714no—
478C2×C22⋊C4—714no—
479C2×C22⋊C4—1424no—
480C2×C22⋊C4—1424no—
481C2×C22⋊C4—1424no—
482C2×C22⋊C4—1424no—
483C2×C22⋊C4—1424no—
484C2×C22⋊C4—1424no—
485C2×C22⋊C4—1424no—
486C2×C42—714no—
487C2×C42—714no—
488C2×C42—714no—
489C2×C42—714no—
490C2×C42—714no—
491C2×C42—1424no—
492C2×C42—1424no—
493C2×C42—1424no—
494C2×C42—1424no—
495C2×C42—1424no—
496#95—714no—
497#95—714no—
498#95—714no—
499#95—714no—
500#95—714no—
501#95—714no—
502#95—714no—
503#95C22×D7114yes—
504#95C22×D7114yes—
505#95C22×D7114yes—
506#95C22×D7114yes—
507#95C22×D7114yes—
508C24—712no—
509C24—1422no—
510C24—1422no—
511C24—1422no—
512C24—1422no—
513C24—1422no—
514C24—1422no—
515C24—1422no—
516C24C23×D7111yescharacteristic
517C2×Q8—1428no—
518C2×Q8—1428no—
519C2×Q8—14232no—
520C2×Q8—1428no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—714no—
541C22×C4—714no—
542C22×C4—714no—
543C22×C4—714no—
544C22×C4—714no—
545C22×C4—712no—
546C22×C4—712no—
547C22×C4—712no—
548C22×C4—712no—
549C22×C4—712no—
550C22×C4—712no—
551C22×C4—712no—
552C22×C4—1422no—
553C22×C4—1422no—
554C22×C4—1422no—
555C22×C4—1422no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4—1422no—
562C22×C4—1422no—
563C22×C4—1422no—
564C22×C4—1422no—
565C22×C4—1422no—
566C22×C4—1422no—
567C22×C4—1422no—
568C22×C4D4×D7114yes—
569C22×C4#1176586614yes—
570C22×C4C23×D7112yes—
571C22×C4C23×D7112yes—
572C22×C4C23×D7112yes—
573C22×C4C23×D7112yes—
574C22×C4C23×D7112yes—
575C22×C4C23×D7112yes—
576C22×C4C23×D7112yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—7116no—
580C4⋊C4—1428no—
581C4⋊C4—1428no—
582C4⋊C4—1428no—
583C4⋊C4—1428no—
584C4⋊C4—1428no—
585C4⋊C4—1428no—
586C4⋊C4—1428no—
587C22⋊C4—1428no—
588C22⋊C4—1428no—
589C22⋊C4—1428no—
590C22⋊C4—1428no—
591C22⋊C4—1428no—
592C22⋊C4—1428no—
593C22⋊C4—1428no—
594C42—1428no—
595C42—1428no—
596C42—1428no—
597C42—1428no—
598C42—1428no—
599C23—2844no—
600C23—2844no—
601C23—2844no—
602C23—2844no—
603C23—2844no—
604C23—2844no—
605C23—2844no—
606C23—1422no—
607C23—1422no—
608C23—1422no—
609C23—1422no—
610C23—1422no—
611C23—1422no—
612C23—1422no—
613C23C2×D4×D7112yes—
614C23#41×D7112yes—
615C23#41×D7112yes—
616C23#41×D7112yes—
617C23C2×#1176586612yes—
618C23#1455617512yes—
619C23#1455617512yes—
620C23C24×D7111yescharacteristic
621Q8—14232no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—2844no—
649C2×C4—2844no—
650C2×C4—714no—
651C2×C4—714no—
652C2×C4—714no—
653C2×C4—714no—
654C2×C4—714no—
655C2×C4—1422no—
656C2×C4—1422no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1422no—
669C2×C4—1422no—
670C2×C4—1422no—
671C2×C4—1428no—
672C2×C4—1428no—
673C2×C4—1428no—
674C2×C4—1428no—
675C2×C4—1428no—
676C2×C4C2×D4×D7114yes—
677C2×C4C2×#1176586614yes—
678C22—2842no—
679C22—2842no—
680C22—2842no—
681C22—2842no—
682C22—2842no—
683C22—2842no—
684C22—2842no—
685C22—5688no—
686C22#1798651214yes—
687C22#1798653414yes—
688C22#1798661214yes—
689C22#1798664714yes—
690C22#1798665714yes—
691C22#1798671614yes—
692C22#1798671614yes—
693C22C22×D4×D7111yescharacteristic
694C22C2×#41×D7111yescharacteristic
695C22C2×#41×D7111yescharacteristic
696C22C2×#41×D7111yescharacteristic
697C22C22×#1176586611yescharacteristic
698C22C2×#1455617511yescharacteristic
699C22C2×#1455617511yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—2842no—
708C4—2842no—
709C4—1424no—
710C4—1424no—
711C4—1424no—
712C4—1424no—
713C4—1424no—
714C2—5682no—
715C2#2259242418yesdirect product factor
716C2C2×#1798651211yescharacteristic
717C2C2×#1798653411yescharacteristic
718C2C2×#1798661211yescharacteristic
719C2C2×#1798664711yescharacteristic
720C2C2×#1798665711yescharacteristic
721C2C2×#1798671611yescharacteristic
722C2C2×#1798671611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#400×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#400D71
hypocenterC71C2×#2469
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
2. C22×#14556093C2semidirect
3. #22592424C2direct (N × H)
5. C2×#17985920C2semidirect
7. C2×#17985895C2semidirect
12. C2×#17985886C2semidirect
13. C2×#17985886C2semidirect
14. C2×#17985882C2semidirect
15. C2×#17985850C2semidirect
16. C2×#400×C71C2semidirect
21. C2×#14556093C22semidirect
43. #17985920C22semidirect
45. #17985895C22semidirect
50. #17985886C22semidirect
51. #17985886C22semidirect
52. #17985882C22semidirect
53. #17985850C22semidirect
63. #400×C71C22semidirect
353. C2×C71#2469semidirect
365. C2×#400D71semidirect
378. C71C2×#2469semidirect
406. #400C2×D71semidirect
715. C2#22592424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561232
C22×#145560932
#225924242
C2×#179859212
C2×#179859202
C2×#179859122
C2×#179858952
C2×#179858912
C2×#179858882
C2×#179858862
C2×#179858822
C2×#179858502
C2×#400×C712
C2×#246971