Finite Group Databasebeta

← C2×#22592625 #32167267

Subgroups — C2×#22592625 #32167267

Order 18176.

2918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556085C211yesmaximal, characteristic
2C22×C4⋊C4×D71C211yesmaximal, characteristic
3#22592625C2116yesmaximal, direct product factor
4C2×#17985941C211yesmaximal, characteristic, complemented
5C2×#17985940C211yesmaximal, characteristic, complemented
6C2×#17985933C211yesmaximal, characteristic, complemented
7C2×#17985932C211yesmaximal, characteristic, complemented
8C2×#17985884C211yesmaximal, characteristic, complemented
9C2×#17985883C211yesmaximal, characteristic, complemented
10C2×#17985880C211yesmaximal, characteristic, complemented
11C2×#17985873C211yesmaximal, characteristic
12C2×#17985870C211yesmaximal, characteristic
13C2×#17985861C211yesmaximal, characteristic
14C2×#17985861C211yesmaximal, characteristic
15C2×#17985861C211yesmaximal, characteristic
16C2×#387×C71C211yesmaximal, characteristic, complemented
17C23×C4×D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556085—28no—
21C2×#14556085C2218yes—
22C22×C4⋊Dic71C2211yescharacteristic
23C22×C4⋊Dic71C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C2×C4⋊C4×D71—28no—
31C2×C4⋊C4×D71C2218yes—
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37#17985941C2218yescomplemented
38#17985940C2218yescomplemented
39#17985933C2218yescomplemented
40#17985932C2218yescomplemented
41#17985884C2218yescomplemented
42#17985883C2218yescomplemented
43#17985880C2218yescomplemented
44#17985873C2218yes—
45#17985870C2218yes—
46#17985861C2218yes—
47#17985861C2218yes—
48#17985861C2218yes—
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⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C42×C71C2211yescharacteristic
64#387×C71C2218yescomplemented
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C22×C4×D71—24no—
78C22×C4×D71—24no—
79C22×C4×D71—24no—
80C22×C4×D71—24no—
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71D418yes—
86C22×C4×D71C2314yes—
87C22×C4×D71C2314yes—
88C22×C4×D71C2314yes—
89#14556085—232no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71—24no—
92C2×C4⋊Dic71C2314yes—
93C2×C4⋊Dic71C2314yes—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4C2314yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C4⋊C4×D71—232no—
107C2×(C2×D71)⋊C4—24no—
108C2×(C2×D71)⋊C4—24no—
109C2×(C2×D71)⋊C4—24no—
110C2×(C2×D71)⋊C4—24no—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×C4×Dic71—24no—
116C2×C4×Dic71C2314yes—
117C71⋊#95C2314yes—
118C71⋊#95C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C23×C4×C71C2311yescharacteristic
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C2×C4⋊C4×C71—24no—
137C2×C4⋊C4×C71—24no—
138C2×C4⋊C4×C71C2314yes—
139C2×C4⋊C4×C71C2314yes—
140C2×C42×C71—24no—
141C2×C42×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×D71C2×D414yes—
151C23×D71#4114yes—
152C23×D71#4114yes—
153C23×D71C2412yes—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
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×Dic71C2×D414yes—
174C22×Dic71#4114yes—
175C22×Dic71C2412yes—
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C22×Dic71C2412yes—
179C22×Dic71C2412yes—
180C22×Dic71C2412yes—
181C22×Dic71C2412yes—
182C2×C4×D71—232no—
183C2×C4×D71—232no—
184C2×C4×D71—28no—
185C2×C4×D71—28no—
186C2×C4×D71—28no—
187C2×C4×D71—28no—
188C2×C4×D71—28no—
189C2×C4×D71—28no—
190C2×C4×D71—28no—
191C2×C4×D71—28no—
192C2×C4×D71—416no—
193C2×C4×D71C2×D4116yes—
194C4⋊Dic71—28no—
195C4⋊Dic71—28no—
196Dic71⋊C4—28no—
197Dic71⋊C4—28no—
198Dic71⋊C4—28no—
199Dic71⋊C4—28no—
200Dic71⋊C4—28no—
201Dic71⋊C4—28no—
202(C2×D71)⋊C4—28no—
203(C2×D71)⋊C4—28no—
204(C2×D71)⋊C4—28no—
205(C2×D71)⋊C4—28no—
206C4×Dic71—28no—
207C24×C71C2411yescharacteristic
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×C71—22no—
227C22×C4×C71C2×D414yes—
228C22×C4×C71#4114yes—
229C22×C4×C71C2412yes—
230C22×C4×C71C2412yes—
231C22×C4×C71C2412yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2412yes—
234C22×C4×C71C2412yes—
235C22×C4×C71C2412yes—
236C4⋊C4×C71—28no—
237C4⋊C4×C71—28no—
238C42×C71—28no—
239C23×C71C22×D412yes—
240C23×C71C2×#4112yes—
241C23×C71C2×#4112yes—
242C23×C71C2×#4112yes—
243C23×C71C2×#4112yes—
244C23×C712−1+412yes—
245C23×C712−1+412yes—
246C23×C71C2511yescharacteristic
247C22×D71—28no—
248C22×D71—28no—
249C22×D71—28no—
250C22×D71—28no—
251C22×D71—28no—
252C22×D71—28no—
253C22×D71—22no—
254C22×D71—22no—
255C22×D71—22no—
256C22×D71—22no—
257C22×D71#123116yes—
258C22×D71C22×D414yes—
259C22×D71C2×#4114yes—
260C22×D71C2×#4114yes—
261C2×C4×C71—28no—
262C2×C4×C71—28no—
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—22no—
281C2×C4×C71—22no—
282C2×C4×C71—44no—
283C2×C4×C71—44no—
284C2×C4×C71—44no—
285C2×C4×C71—44no—
286C2×C4×C71—44no—
287C2×C4×C71C22×D414yes—
288C2×C4×C71C2×#4114yes—
289C2×Dic71—28no—
290C2×Dic71—28no—
291C2×Dic71—22no—
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—22no—
309C2×Dic71—22no—
310C2×Dic71—44no—
311C2×Dic71—44no—
312C2×Dic71—44no—
313C2×Dic71—44no—
314C2×Dic71—44no—
315C2×Dic71C22×D414yes—
316C2×Dic71C2×#4114yes—
317C4×D71—232no—
318C4×D71—232no—
319C4×D71—416no—
320C22×C71C2×#12314yes—
321C22×C71#52514yes—
322C22×C71#53614yes—
323C22×C71#55214yes—
324C22×C71#55214yes—
325C22×C71#55214yes—
326C22×C71#55214yes—
327C22×C71C23×D411yescharacteristic
328C22×C71C22×#4111yescharacteristic
329C22×C71C22×#4111yescharacteristic
330C22×C71C22×#4111yescharacteristic
331C22×C71C22×#4111yescharacteristic
332C22×C71C2×2−1+411yescharacteristic
333C22×C71C2×2−1+411yescharacteristic
334C2×D71—24no—
335C2×D71—24no—
336C2×D71—24no—
337C2×D71—24no—
338C2×D71—24no—
339C2×D71—24no—
340C2×D71—232no—
341C2×D71C2×#12318yes—
342C4×C71—24no—
343C4×C71—24no—
344C4×C71—42no—
345C4×C71—42no—
346C4×C71—42no—
347C4×C71—42no—
348C4×C71—42no—
349Dic71—24no—
350Dic71—24no—
351Dic71—42no—
352Dic71—42no—
353Dic71—42no—
354Dic71—42no—
355Dic71—42no—
356C2×#2484—711nomaximal, Sylow
357C2×C71#248418yescomplemented
358C2×C71C22×#12311yescharacteristic
359C2×C71C2×#52511yescharacteristic
360C2×C71C2×#53611yescharacteristic
361C2×C71C2×#55211yescharacteristic
362C2×C71C2×#55211yescharacteristic
363C2×C71C2×#55211yescharacteristic
364C2×C71C2×#55211yescharacteristic
365D71—28no—
366C22×#117—711no—
367C23×C4⋊C4—711no—
368#2484—7116no—
369C2×#400—711no—
370C2×#400—711no—
371C2×#398—711no—
372C2×#398—711no—
373C2×#387—711no—
374C2×#387—711no—
375C2×#387—711no—
376C2×#387D7111yescharacteristic, complemented
377C2×#385—711no—
378C2×#385—711no—
379C2×#381—711no—
380C2×#381—711no—
381C2×#381—711no—
382C71C2×#248411yescharacteristic, complemented, Sylow
383C24×C4—711no—
384C24×C4—711no—
385C24×C4—711no—
386C2×#117—718no—
387C2×#117—1428no—
388C22×C4⋊C4—711no—
389C22×C4⋊C4—711no—
390C22×C4⋊C4—711no—
391C22×C4⋊C4—711no—
392C22×C4⋊C4—711no—
393C22×C4⋊C4—711no—
394C22×C4⋊C4—711no—
395C22×C4⋊C4—711no—
396C22×C4⋊C4—718no—
397C22×C4⋊C4—1428no—
398C22×C4⋊C4C2×D7111yescharacteristic
399C22×C4⋊C4C2×D7111yescharacteristic
400C22×C22⋊C4—711no—
401C22×C22⋊C4—711no—
402C22×C22⋊C4—711no—
403C22×C22⋊C4—711no—
404C22×C42—711no—
405C22×C42C2×D7111yescharacteristic
406#400—718no—
407#400—718no—
408#398—718no—
409#398—718no—
410#387—718no—
411#387—718no—
412#387—718no—
413#387C2×D7118yescomplemented
414#385—718no—
415#385—718no—
416#381—718no—
417#381—718no—
418#381—718no—
419C2×#95—711no—
420C2×#95—711no—
421C2×#95—711no—
422C2×#95—711no—
423C2×#95—711no—
424C2×#95—711no—
425C2×#95—711no—
426C2×#95—711no—
427C2×#95—711no—
428C2×#95—711no—
429C2×#95—711no—
430C2×#95—711no—
431C2×#95C2×D7111yescharacteristic
432C2×#95C2×D7111yescharacteristic
433C2×#95C2×D7111yescharacteristic
434C2×#95C2×D7111yescharacteristic
435C25—711no—
436C23×C4—711no—
437C23×C4—711no—
438C23×C4—718no—
439C23×C4—714no—
440C23×C4—711no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4—711no—
444C23×C4—711no—
445C23×C4—714no—
446C23×C4—714no—
447C23×C4—1424no—
448C23×C4—1424no—
449C23×C4—1424no—
450C23×C4—1424no—
451C23×C4—1424no—
452C23×C4—1424no—
453C23×C4—1424no—
454C23×C4—1424no—
455C23×C4C22×D7111yescharacteristic
456C23×C4C22×D7111yescharacteristic
457C23×C4C22×D7111yescharacteristic
458C23×C4C22×D7111yescharacteristic
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C23×C4C22×D7111yescharacteristic
462#117—14232no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—714no—
466C2×C4⋊C4—714no—
467C2×C4⋊C4—714no—
468C2×C4⋊C4—714no—
469C2×C4⋊C4—714no—
470C2×C4⋊C4—714no—
471C2×C4⋊C4—714no—
472C2×C4⋊C4—714no—
473C2×C4⋊C4—14232no—
474C2×C4⋊C4—1424no—
475C2×C4⋊C4—1424no—
476C2×C4⋊C4—1424no—
477C2×C4⋊C4—1424no—
478C2×C4⋊C4—1424no—
479C2×C4⋊C4—1424no—
480C2×C4⋊C4—1424no—
481C2×C4⋊C4—1424no—
482C2×C4⋊C4C22×D7114yes—
483C2×C4⋊C4C22×D7114yes—
484C2×C22⋊C4—714no—
485C2×C22⋊C4—714no—
486C2×C22⋊C4—714no—
487C2×C22⋊C4—714no—
488C2×C22⋊C4—1424no—
489C2×C22⋊C4—1424no—
490C2×C22⋊C4—1424no—
491C2×C22⋊C4—1424no—
492C2×C42—24no—
493C2×C42—714no—
494C2×C42—1424no—
495C2×C42C22×D7114yes—
496#95—714no—
497#95—714no—
498#95—714no—
499#95—714no—
500#95—714no—
501#95—714no—
502#95—714no—
503#95—714no—
504#95—714no—
505#95—714no—
506#95—714no—
507#95—714no—
508#95C22×D7114yes—
509#95C22×D7114yes—
510#95C22×D7114yes—
511#95C22×D7114yes—
512C24—714no—
513C24—714no—
514C24—714no—
515C24—712no—
516C24—1422no—
517C24—1422no—
518C24—1422no—
519C24—1422no—
520C24C23×D7111yescharacteristic
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—28416no—
541C22×C4—714no—
542C22×C4—714no—
543C22×C4—712no—
544C22×C4—712no—
545C22×C4—7116no—
546C22×C4—712no—
547C22×C4—712no—
548C22×C4—712no—
549C22×C4—712no—
550C22×C4—712no—
551C22×C4—1428no—
552C22×C4—1428no—
553C22×C4—1428no—
554C22×C4—1428no—
555C22×C4—1428no—
556C22×C4—1428no—
557C22×C4—1428no—
558C22×C4—14232no—
559C22×C4—14232no—
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×C4—1422no—
569C22×C4—1422no—
570C22×C4—1422no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1428no—
580C22×C4D4×D7114yes—
581C22×C4#1176586514yes—
582C22×C4C23×D7112yes—
583C22×C4C23×D7112yes—
584C22×C4C23×D7112yes—
585C22×C4C23×D7112yes—
586C22×C4C23×D7112yes—
587C22×C4C23×D7112yes—
588C22×C4C23×D7112yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—1428no—
592C4⋊C4—1428no—
593C4⋊C4—1428no—
594C4⋊C4—1428no—
595C4⋊C4—1428no—
596C4⋊C4—1428no—
597C4⋊C4—1428no—
598C4⋊C4—1428no—
599C22⋊C4—1428no—
600C22⋊C4—1428no—
601C22⋊C4—1428no—
602C22⋊C4—1428no—
603C42—28no—
604C42—1428no—
605C23—714no—
606C23—714no—
607C23—714no—
608C23—7116no—
609C23—1422no—
610C23—1422no—
611C23—1428no—
612C23—1422no—
613C23—1422no—
614C23—1428no—
615C23—1428no—
616C23—1428no—
617C23—1428no—
618C23—1428no—
619C23C2×D4×D7112yes—
620C23#41×D7112yes—
621C23#41×D7112yes—
622C23#41×D7112yes—
623C23C2×#1176586512yes—
624C23#1455617512yes—
625C23#1455617612yes—
626C23C24×D7111yescharacteristic
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—28no—
632C2×C4—28no—
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—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—28416no—
654C2×C4—2844no—
655C2×C4—2844no—
656C2×C4—2844no—
657C2×C4—2844no—
658C2×C4—2844no—
659C2×C4—714no—
660C2×C4—714no—
661C2×C4—14232no—
662C2×C4—14232no—
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—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4—1422no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1428no—
683C2×C4—1428no—
684C2×C4C2×D4×D7114yes—
685C2×C4C2×#1176586514yes—
686C22—718no—
687C22—1424no—
688C22—14232no—
689C22—1424no—
690C22—1424no—
691C22—1424no—
692C22—1424no—
693C22—1424no—
694C22#123×D7114yes—
695C22#1798650814yes—
696C22#1798657214yes—
697C22#1798668114yes—
698C22#1798668514yes—
699C22#1798668814yes—
700C22#1798669014yes—
701C22C22×D4×D7111yescharacteristic
702C22C2×#41×D7111yescharacteristic
703C22C2×#41×D7111yescharacteristic
704C22C2×#41×D7111yescharacteristic
705C22C22×#1176586511yescharacteristic
706C22C2×#1455617511yescharacteristic
707C22C2×#1455617611yescharacteristic
708C4—24no—
709C4—24no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—2842no—
716C4—2842no—
717C4—2842no—
718C4—2842no—
719C4—2842no—
720C4—1424no—
721C4—1424no—
722C2—1428no—
723C2#2259262518yesdirect product factor
724C2C2×#123×D7111yescharacteristic
725C2C2×#1798650811yescharacteristic
726C2C2×#1798657211yescharacteristic
727C2C2×#1798668111yescharacteristic
728C2C2×#1798668511yescharacteristic
729C2C2×#1798668811yescharacteristic
730C2C2×#1798669011yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#387×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#387D71
hypocenterC71C2×#2484
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #22592625C2direct (N × H)
4. C2×#17985941C2semidirect
5. C2×#17985940C2semidirect
6. C2×#17985933C2semidirect
7. C2×#17985932C2semidirect
8. C2×#17985884C2semidirect
9. C2×#17985883C2semidirect
10. C2×#17985880C2semidirect
16. C2×#387×C71C2semidirect
37. #17985941C22semidirect
38. #17985940C22semidirect
39. #17985933C22semidirect
40. #17985932C22semidirect
41. #17985884C22semidirect
42. #17985883C22semidirect
43. #17985880C22semidirect
64. #387×C71C22semidirect
357. C2×C71#2484semidirect
376. C2×#387D71semidirect
382. C71C2×#2484semidirect
413. #387C2×D71semidirect
723. C2#22592625direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560852
C22×C4⋊C4×D712
#225926252
C2×#179859412
C2×#179859402
C2×#179859332
C2×#179859322
C2×#179858842
C2×#179858832
C2×#179858802
C2×#179858732
C2×#179858702
C2×#179858612
C2×#387×C712
C2×#248471