Finite Group Databasebeta

← #32160479

Subgroups — #32160479

Order 18176.

2190 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
1C2×#17986533C211yesmaximal, characteristic
2#22591484C214yesmaximal, complemented
3#22591436C212yesmaximal, complemented
4#22591411C212yesmaximal, complemented
5#22591299C211yesmaximal, characteristic, complemented
6#22591291C211yesmaximal, characteristic, complemented
7#22591290C212yesmaximal, complemented
8#22591270C212yesmaximal, complemented
9#22591252C211yesmaximal, characteristic, complemented
10#22591240C211yesmaximal, characteristic, complemented
11#22591115C214yesmaximal, complemented
12#22591029C212yesmaximal
13#22591018C212yesmaximal, complemented
14#22590965C212yesmaximal, complemented
15#22590950C212yesmaximal, complemented
16#22590747C211yesmaximal, characteristic, complemented
17C71×#2285C211yesmaximal, characteristic, complemented
18#17986533C4116yescomplemented
19C2×#14556122C2212yes—
20C2×#14556120C2211yescharacteristic
21C2×#14556116C2211yescharacteristic
22C2×#14556111C2212yes—
23C2×#14556107C2211yescharacteristic
24C2×#14556102C2211yescharacteristic
25C2×C4×Dic142C2211yescharacteristic
26C2×#14556093C2212yes—
27C2×C4×D284C2211yescharacteristic
28C2×#14556090C2212yes—
29C2×C4×C22⋊D71C2212yes—
30C2×#14556087C2212yes—
31C2×#14556086C2212yes—
32C2×#14556085C2212yes—
33C2×C4⋊C4×D71C2212yes—
34#17985904C2212yes—
35#17985900C2212yes—
36#17985899C2214yes—
37#17985896C2214yes—
38#17985896C2214yes—
39#17985895C2212yes—
40#17985895C2212yes—
41#17985894C2214yes—
42#17985893C2214yes—
43#17985891C2214yes—
44#17985891C2214yes—
45#17985890C2214yes—
46#17985889C2214yes—
47#17985887C2214yes—
48#17985886C2214yes—
49#17985886C2214yes—
50#17985883C2214yes—
51#17985880C2214yes—
52#17985875C2214yes—
53#17985873C2214yes—
54#17985873C2214yes—
55#17985870C2214yes—
56#17985869C2211yescharacteristic
57#17985869C2211yescharacteristic
58#17985868C2212yes—
59#17985865C2212yes—
60#17985864C2212yes—
61#17985859C2211yescharacteristic
62#17985859C2211yescharacteristic
63#17985859C2212yes—
64#17985856C2212yes—
65#17985856C2212yes—
66C4⋊C4×Dic71C2212yes—
67C4⋊C4×Dic71C2212yes—
68C4⋊C4×Dic71C2212yes—
69C4⋊C4×Dic71C2212yes—
70C4×Dic71⋊C4C2214yes—
71C4×C4⋊Dic71C2211yescharacteristic
72C4×C4⋊Dic71C2211yescharacteristic
73C4×C4⋊Dic71C2212yes—
74C4×(C2×D71)⋊C4C2214yes—
75C2×#117×C71C2212yes—
76C22×C42×C71C2211yescharacteristic
77#384×C71C2211yescharacteristic
78#384×C71C2211yescharacteristic
79#382×C71C2212yes—
80#380×C71C2212yes—
81#380×C71C2212yes—
82C4×C4⋊C4×C71C2212yes—
83C4×C4⋊C4×C71C2212yes—
84C22×Dic142C2311yescharacteristic
85C22×D284C2311yescharacteristic
86C22×C22⋊D71C2312yes—
87C22×C4×D71C2312yes—
88C22×C4×D71C2314yes—
89#14556122C2×C4116yescomplemented
90#14556120C2×C418yescomplemented
91#14556116C2×C418yes—
92#14556111C2×C4116yescomplemented
93#14556107C2×C418yescomplemented
94#14556102C2×C418yes—
95C4×Dic142C2×C418yescomplemented
96#14556093—44no—
97C4×D284C2×C418yes—
98#14556090—44no—
99C4×C22⋊D71C2×C4116yescomplemented
100#14556087—44no—
101#14556086—44no—
102#14556085C2×C4116yescomplemented
103C2×C4⋊Dic71C2311yescharacteristic
104C2×C4⋊Dic71C2311yescharacteristic
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2311yescharacteristic
107C2×C4⋊Dic71C2312yes—
108C2×C4⋊Dic71C2312yes—
109C2×C4⋊Dic71C2312yes—
110C2×C4⋊Dic71C2312yes—
111C2×C4⋊Dic71C2311yescharacteristic
112C2×C4⋊Dic71C2311yescharacteristic
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2314yes—
116C2×Dic71⋊C4C2312yes—
117C2×Dic71⋊C4C2312yes—
118C2×Dic71⋊C4C2312yes—
119C2×Dic71⋊C4C2312yes—
120C4⋊C4×D71—44no—
121C2×C22⋊Dic71C2312yes—
122C2×C22⋊Dic71C2312yes—
123C2×C22⋊Dic71C2312yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2312yes—
128C2×(C2×D71)⋊C4C2312yes—
129C2×(C2×D71)⋊C4C2312yes—
130C2×(C2×D71)⋊C4C2312yes—
131C2×C4×Dic71C2312yes—
132C2×C4×Dic71C2312yes—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2314yes—
135C2×C4×Dic71C2314yes—
136C2×C4×Dic71C2312yes—
137C71⋊#95C2312yes—
138C71⋊#95C2314yes—
139C71⋊#95C2312yes—
140C71⋊#95C2312yes—
141C71⋊#95C2312yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2314yes—
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150#117×C71—44no—
151C2×C4⋊C4×C71C2312yes—
152C2×C4⋊C4×C71C2312yes—
153C2×C4⋊C4×C71C2312yes—
154C2×C4⋊C4×C71C2312yes—
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2312yes—
157C2×C22⋊C4×C71C2314yes—
158C2×C42×C71C2×C418yescomplemented
159C2×C42×C71C2314yes—
160C2×C42×C71C2311yescharacteristic
161C2×C42×C71C2311yescharacteristic
162C2×C42×C71C2311yescharacteristic
163C2×C42×C71C2311yescharacteristic
164#95×C71C2314yes—
165#95×C71C2314yes—
166C23×D71C2412yes—
167C2×Dic142—22no—
168C2×Dic142—22no—
169C2×Dic142C22×C414yes—
170C2×D284—22no—
171C2×D284—22no—
172C2×D284C22×C414yes—
173C2×C22⋊D71—42no—
174C2×C22⋊D71—42no—
175C2×C22⋊D71C22×C418yes—
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C22×Dic71C2412yes—
179C22×Dic71C2412yes—
180C22×Dic71C2412yes—
181C22×Dic71C2412yes—
182C22×Dic71C2412yes—
183C2×C4×D71—24no—
184C2×C4×D71—24no—
185C2×C4×D71—44no—
186C2×C4×D71—44no—
187C2×C4×D71—44no—
188C2×C4×D71C22×C418yes—
189C4⋊Dic71—22no—
190C4⋊Dic71—22no—
191C4⋊Dic71—22no—
192C4⋊Dic71—22no—
193C4⋊Dic71—42no—
194C4⋊Dic71—42no—
195C4⋊Dic71—42no—
196C4⋊Dic71—42no—
197C4⋊Dic71C22×C414yes—
198C4⋊Dic71C22×C414yes—
199Dic71⋊C4—44no—
200Dic71⋊C4—44no—
201Dic71⋊C4—44no—
202Dic71⋊C4C22×C418yes—
203Dic71⋊C4C22×C418yes—
204Dic71⋊C4C22×C418yes—
205Dic71⋊C4C22×C418yes—
206C22⋊Dic71—42no—
207C22⋊Dic71—42no—
208C22⋊Dic71C22×C418yes—
209(C2×D71)⋊C4—44no—
210(C2×D71)⋊C4—44no—
211(C2×D71)⋊C4—44no—
212(C2×D71)⋊C4C22×C418yes—
213(C2×D71)⋊C4C22×C418yes—
214(C2×D71)⋊C4C22×C418yes—
215(C2×D71)⋊C4C22×C418yes—
216C4×Dic71—24no—
217C4×Dic71—24no—
218C4×Dic71—44no—
219C4×Dic71—44no—
220C4×Dic71—44no—
221C4×Dic71C22×C418yes—
222C24×C71C2411yescharacteristic
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—41no—
228C22×C4×C71—41no—
229C22×C4×C71C22×C414yes—
230C22×C4×C71C22×C414yes—
231C22×C4×C71C22×C414yes—
232C22×C4×C71C2414yes—
233C22×C4×C71C2414yes—
234C22×C4×C71C2411yescharacteristic
235C22×C4×C71C2411yescharacteristic
236C22×C4×C71C2411yescharacteristic
237C22×C4×C71C2411yescharacteristic
238C22×C4×C71C2411yescharacteristic
239C22×C4×C71C2411yescharacteristic
240C4⋊C4×C71—24no—
241C4⋊C4×C71—24no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—24no—
244C4⋊C4×C71—42no—
245C4⋊C4×C71—42no—
246C22⋊C4×C71—44no—
247C42×C71—44no—
248C42×C71C22×C414yes—
249C42×C71C22×C414yes—
250C42×C71C22×C414yes—
251C42×C71C22×C414yes—
252C23×C71—21no—
253C23×C71—21no—
254C23×C71—21no—
255C23×C71—21no—
256C23×C71—21no—
257C23×C71—21no—
258C23×C71C23×C412yes—
259C23×C71C2511yescharacteristic
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—22no—
264C22×D71—22no—
265C22×D71—22no—
266C22×D71C23×C414yes—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—28no—
276C2×C4×C71—28no—
277C2×C4×C71—24no—
278C2×C4×C71—24no—
279C2×C4×C71—24no—
280C2×C4×C71—24no—
281C2×C4×C71—24no—
282C2×C4×C71—24no—
283C2×C4×C71—44no—
284C2×C4×C71C23×C412yes—
285C2×C4×C71C23×C412yes—
286C2×C4×C71C23×C412yes—
287C2×C4×C71C23×C412yes—
288C2×C4×C71C23×C412yes—
289C2×C4×C71C23×C412yes—
290C2×C4×C71H(5,𝔽2)12yes—
291C2×C4×C71H(5,𝔽2)12yes—
292C2×C4×C712−1+412yes—
293C2×C4×C712−1+412yes—
294C22⋊D71—48no—
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—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71C23×C414yes—
314C2×Dic71C23×C414yes—
315C2×Dic71C23×C414yes—
316D284—28no—
317C4×D71—216no—
318C4×D71—88no—
319Dic142—28no—
320C22×C71—22no—
321C22×C71—22no—
322C22×C71—22no—
323C22×C71—41no—
324C22×C71—41no—
325C22×C71—41no—
326C22×C71—41no—
327C22×C71C24×C411yescharacteristic
328C22×C71C2×H(5,𝔽2)11yescharacteristic
329C22×C71C2×H(5,𝔽2)11yescharacteristic
330C22×C71C2×2−1+411yescharacteristic
331C22×C71C2×2−1+411yescharacteristic
332C22×C71#58511yescharacteristic
333C22×C71#58511yescharacteristic
334C2×D71—24no—
335C2×D71—24no—
336C2×D71—24no—
337C2×D71—42no—
338C2×D71—42no—
339C2×D71—42no—
340C2×D71—42no—
341C4×C71—22no—
342C4×C71—22no—
343C4×C71—22no—
344C4×C71—22no—
345C4×C71—44no—
346C4×C71—44no—
347C4×C71#52014yes—
348C4×C71#52014yes—
349Dic71—24no—
350Dic71—24no—
351Dic71—24no—
352Dic71—42no—
353Dic71—42no—
354Dic71—42no—
355Dic71—42no—
356#34383—711nomaximal, Sylow
357C2×C71—42no—
358C2×C71C2×#52011yescharacteristic
359C2×C71C2×#52011yescharacteristic
360C2×C71#342811yescharacteristic
361C2×C71#354611yescharacteristic
362C2×C71#354711yescharacteristic
363C2×C71#355411yescharacteristic
364C2×C71#355511yescharacteristic
365D71—44no—
366C2×#529—711no—
367#2376—714no—
368#2370—712no—
369#2367—712no—
370#2355—711no—
371#2354—711no—
372#2354—712no—
373#2352—712no—
374Q8×C4⋊C4—711no—
375D4×C4⋊C4—711no—
376#2334—714no—
377#2324—712no—
378#2323—712no—
379#2317—712no—
380#2314—712no—
381#2285—711no—
382#2285D7111yescharacteristic, complemented
383C71#3438311yescharacteristic, complemented, Sylow
384#529—7116no—
385C2×#126—712no—
386C2×#125—711no—
387C2×#124—711no—
388C2×#123—712no—
389C2×C22⋊Q8—711no—
390C2×#121—711no—
391C2×C4×Q8—712no—
392C2×C4×Q8—711no—
393C2×C4×D4—712no—
394C2×C4×D4—712no—
395C2×C4×D4—711no—
396C2×#117—712no—
397C2×#117—712no—
398C2×#117—712no—
399C2×#117C2×D7112yes—
400C22×C4⋊C4—712no—
401C22×C42C2×D7111yescharacteristic
402#391—712no—
403#390—712no—
404#390—714no—
405#389—712no—
406#389—712no—
407#389—714no—
408#389—714no—
409#389—714no—
410#388—714no—
411#388—714no—
412#388—714no—
413#388—714no—
414#388—714no—
415#388—714no—
416#387—714no—
417#387—714no—
418#387—714no—
419#387—714no—
420#386—714no—
421#385—714no—
422#385—714no—
423#385—714no—
424#384—712no—
425#384—711no—
426#384—711no—
427#384C2×D7111yescharacteristic
428#384C2×D7111yescharacteristic
429#382—712no—
430#382—712no—
431#382C2×D7112yes—
432#380—711no—
433#380—711no—
434#380—712no—
435#380—712no—
436#380—712no—
437#380C2×D7112yes—
438#380C2×D7112yes—
439C4×C4⋊C4—712no—
440C4×C4⋊C4—712no—
441C4×C4⋊C4—712no—
442C4×C4⋊C4—712no—
443C4×C4⋊C4—714no—
444C4×C4⋊C4—711no—
445C4×C4⋊C4—711no—
446C4×C4⋊C4—712no—
447C4×C4⋊C4C2×D7112yes—
448C4×C4⋊C4C2×D7112yes—
449C4×C22⋊C4—714no—
450C22×Q8—711no—
451C22×D4—712no—
452C22×D4—711no—
453C23×C4—714no—
454C23×C4—712no—
455C23×C4C22×D7111yescharacteristic
456C23×C4C22×D7111yescharacteristic
457C23×C4C22×D7111yescharacteristic
458#126—7116no—
459#125—718no—
460#124—718no—
461#123—7116no—
462C22⋊Q8—718no—
463#121—718no—
464C4×Q8—2844no—
465C4×Q8—718no—
466C4×D4—2844no—
467C4×D4—7116no—
468C4×D4—718no—
469#117—44no—
470#117—2844no—
471#117—2844no—
472#117—7116no—
473C2×C4⋊C4—2844no—
474C2×C4⋊C4—714no—
475C2×C4⋊C4—712no—
476C2×C4⋊C4—712no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—712no—
479C2×C4⋊C4—712no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—712no—
482C2×C4⋊C4—712no—
483C2×C4⋊C4—711no—
484C2×C4⋊C4—712no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—712no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—711no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4C22×D7112yes—
492C2×C4⋊C4C22×D7112yes—
493C2×C4⋊C4C22×D7112yes—
494C2×C4⋊C4C22×D7112yes—
495C2×C4⋊C4C22×D7112yes—
496C2×C4⋊C4C22×D7112yes—
497C2×C22⋊C4—712no—
498C2×C22⋊C4—712no—
499C2×C22⋊C4—714no—
500C2×C22⋊C4—714no—
501C2×C22⋊C4—714no—
502C2×C22⋊C4—712no—
503C2×C22⋊C4—712no—
504C2×C22⋊C4—712no—
505C2×C22⋊C4—712no—
506C2×C22⋊C4—712no—
507C2×C22⋊C4C22×D7114yes—
508C2×C42—714no—
509C2×C42—714no—
510C2×C42—714no—
511C2×C42—712no—
512C2×C42—712no—
513C2×C42—712no—
514C2×C42C4×D7118yescomplemented
515C2×C42C22×D7114yes—
516C2×C42C22×D7111yescharacteristic
517C2×C42C22×D7111yescharacteristic
518C2×C42C22×D7111yescharacteristic
519C2×C42C22×D7111yescharacteristic
520#95—712no—
521#95—714no—
522#95—712no—
523#95—712no—
524#95—712no—
525#95—714no—
526#95—714no—
527#95—714no—
528#95—714no—
529#95—714no—
530#95C22×D7114yes—
531#95C22×D7114yes—
532C24—712no—
533C24C23×D7111yescharacteristic
534C2×Q8—714no—
535C2×Q8—1422no—
536C2×Q8—1422no—
537C2×D4—2842no—
538C2×D4—2842no—
539C2×D4—718no—
540C2×D4—714no—
541C2×D4—1422no—
542C2×D4—1422no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—2844no—
550C22×C4—2844no—
551C22×C4—2844no—
552C22×C4—712no—
553C22×C4—712no—
554C22×C4—712no—
555C22×C4—718no—
556C22×C4—712no—
557C22×C4—712no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—1424no—
561C22×C4—1424no—
562C22×C4C2×C4×D7114yes—
563C22×C4C2×C4×D7114yes—
564C22×C4C2×C4×D7114yes—
565C22×C4C23×D7114yes—
566C22×C4C23×D7114yes—
567C22×C4C23×D7111yescharacteristic
568C22×C4C23×D7111yescharacteristic
569C22×C4C23×D7111yescharacteristic
570C22×C4C23×D7111yescharacteristic
571C22×C4C23×D7111yescharacteristic
572C22×C4C23×D7111yescharacteristic
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—2844no—
580C4⋊C4—2844no—
581C4⋊C4—2844no—
582C4⋊C4—2842no—
583C4⋊C4—2842no—
584C4⋊C4—2842no—
585C4⋊C4—2842no—
586C4⋊C4—718no—
587C4⋊C4—718no—
588C4⋊C4—718no—
589C4⋊C4—718no—
590C4⋊C4—714no—
591C4⋊C4—714no—
592C4⋊C4—1422no—
593C4⋊C4—1422no—
594C4⋊C4—1422no—
595C4⋊C4—1422no—
596C22⋊C4—44no—
597C22⋊C4—2844no—
598C22⋊C4—2844no—
599C22⋊C4—2844no—
600C22⋊C4—2842no—
601C22⋊C4—2842no—
602C22⋊C4—718no—
603C22⋊C4—718no—
604C22⋊C4—718no—
605C22⋊C4—718no—
606C22⋊C4—718no—
607C42—44no—
608C42—2844no—
609C42—2844no—
610C42—2844no—
611C42—718no—
612C42—1424no—
613C42—1424no—
614C42C2×C4×D7114yes—
615C42C2×C4×D7114yes—
616C42C2×C4×D7114yes—
617C42C2×C4×D7114yes—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—714no—
625C23—1422no—
626C23—1422no—
627C23—1422no—
628C23—1422no—
629C23—1422no—
630C23—1422no—
631C23C22×C4×D7112yes—
632C23C24×D7111yescharacteristic
633Q8—1428no—
634D4—2848no—
635D4—1428no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—44no—
653C2×C4—5688no—
654C2×C4—714no—
655C2×C4—714no—
656C2×C4—714no—
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—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4—14216no—
676C2×C4C22×C4×D7112yes—
677C2×C4C22×C4×D7112yes—
678C2×C4C22×C4×D7112yes—
679C2×C4C22×C4×D7112yes—
680C2×C4C22×C4×D7112yes—
681C2×C4C22×C4×D7112yes—
682C2×C4#1455617312yes—
683C2×C4#1455617412yes—
684C2×C4#1455617512yes—
685C2×C4#1455617612yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—2842no—
694C22—2842no—
695C22—2842no—
696C22—2842no—
697C22—1424no—
698C22—1424no—
699C22—1424no—
700C22C23×C4×D7111yescharacteristic
701C22C2×#1455617311yescharacteristic
702C22C2×#1455617411yescharacteristic
703C22C2×#1455617511yescharacteristic
704C22C2×#1455617611yescharacteristic
705C22#1798683511yescharacteristic
706C22#1798683511yescharacteristic
707C4—22no—
708C4—22no—
709C4—22no—
710C4—22no—
711C4—44no—
712C4—44no—
713C4—2842no—
714C4—2842no—
715C4—2842no—
716C4—2842no—
717C4—1424no—
718C4—1424no—
719C4—1424no—
720C4#1798647914yes—
721C4#1798648014yes—
722C2—42no—
723C2—2844no—
724C2C2×#1798647911yescharacteristic
725C2C2×#1798648011yescharacteristic
726C2#2260154111yescharacteristic
727C2#2260270611yescharacteristic
728C2#2260272311yescharacteristic
729C2#2260280511yescharacteristic
730C2#2260282211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2285C2
socle, cosocleC23×C71C25
prime radicalC2×#14556102C22
hypercenter#2285D71
hypocenterC71#34383
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #22591484C2semidirect
3. #22591436C2semidirect
4. #22591411C2semidirect
5. #22591299C2semidirect
6. #22591291C2semidirect
7. #22591290C2semidirect
8. #22591270C2semidirect
9. #22591252C2semidirect
10. #22591240C2semidirect
11. #22591115C2semidirect
13. #22591018C2semidirect
14. #22590965C2semidirect
15. #22590950C2semidirect
16. #22590747C2semidirect
17. C71×#2285C2semidirect
18. #17986533C4semidirect
89. #14556122C2×C4semidirect
90. #14556120C2×C4semidirect
92. #14556111C2×C4semidirect
93. #14556107C2×C4semidirect
95. C4×Dic142C2×C4semidirect
99. C4×C22⋊D71C2×C4semidirect
102. #14556085C2×C4semidirect
158. C2×C42×C71C2×C4semidirect
382. #2285D71semidirect
383. C71#34383semidirect
514. C2×C42C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865332
#225914842
#225914362
#225914112
#225912992
#225912912
#225912902
#225912702
#225912522
#225912402
#225911152
#225910292
#225910182
#225909652
#225909502
#225907472
C71×#22852
#3438371