Finite Group Databasebeta

← #32160323

Subgroups — #32160323

Order 18176.

2378 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556108C211yesmaximal, characteristic
2#22591504C214yesmaximal, complemented
3#22591369C212yesmaximal, complemented
4#22591366C212yesmaximal, complemented
5#22591219C212yesmaximal, complemented
6#22591217C211yesmaximal, characteristic, complemented
7#22591215C212yesmaximal, complemented
8C22⋊C4×Dic142C211yesmaximal, characteristic, complemented
9#22591172C211yesmaximal, characteristic, complemented
10#22591092C214yesmaximal, complemented
11#22591023C212yesmaximal, complemented
12#22591020C212yesmaximal, complemented
13#22590937C212yesmaximal
14#22590935C212yesmaximal
15#22590722C211yesmaximal, characteristic
16#22590721C211yesmaximal, characteristic
17C71×#2345C211yesmaximal, characteristic, complemented
18C23×Dic142C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556108C4116yescomplemented
21C2×#14556108C2212yes—
22C2×#14556108C2211yescharacteristic
23C2×#14556108C2211yescharacteristic
24C2×#14556108C2212yes—
25C2×#14556108C2211yescharacteristic
26C2×#14556108C2211yescharacteristic
27C2×C4×Dic142C2212yescomplemented
28C2×#14556093C2212yescomplemented
29C2×#14556086C2212yes—
30C2×#14556085C2212yes—
31C22×C4⋊Dic71C2212yes—
32C22×(C2×D71)⋊C4C2212yes—
33#17985905C2212yescomplemented
34#17985904C2212yescomplemented
35#17985903C2214yescomplemented
36#17985903C2214yescomplemented
37#17985898C2212yescomplemented
38#17985897C2214yescomplemented
39#17985895C2214yescomplemented
40#17985891C2214yes—
41#17985891C2214yes—
42#17985890C2214yes—
43#17985890C2214yes—
44#17985889C2214yes—
45#17985889C2214yes—
46#17985888C2214yes—
47#17985888C2214yes—
48#17985885C2214yescomplemented
49#17985884C2214yescomplemented
50#17985884C2214yescomplemented
51#17985882C2214yescomplemented
52#17985882C2214yescomplemented
53#17985861C2212yes—
54#17985861C2212yes—
55#17985859C2211yescharacteristic
56#17985859C2212yes—
57#17985858C2212yes—
58#17985857C2211yescharacteristic
59#17985857C2211yescharacteristic
60#17985857C2212yes—
61#17985857C2212yes—
62#17985856C2212yes—
63#17985854C2211yescharacteristic
64#17985854C2211yescharacteristic
65#17985854C2212yes—
66C4⋊C4×Dic71C2212yescomplemented
67C4⋊C4×Dic71C2214yescomplemented
68C4×C4⋊Dic71C2214yescomplemented
69C22⋊C4×Dic71C2212yes—
70C22⋊C4×Dic71C2212yes—
71C22⋊C4×Dic71C2212yes—
72C4×(C2×D71)⋊C4C2212yes—
73C4×C22⋊Dic71C2211yescharacteristic
74C4×C22⋊Dic71C2212yes—
75#17985846C2212yes—
76C22×C4⋊C4×C71C2211yescharacteristic
77#389×C71C2212yescomplemented
78#387×C71C2214yescomplemented
79#380×C71C2211yescharacteristic
80#380×C71C2212yes—
81C4×C4⋊C4×C71C2212yescomplemented
82C4×C22⋊C4×C71C2211yescharacteristic
83C4×C22⋊C4×C71C2212yes—
84C24×D71C2311yescharacteristic
85C22×Dic142—44no—
86C22×Dic142C2×C418yes—
87C22×Dic142C2311yescharacteristic
88C22×Dic142C2311yescharacteristic
89C22×Dic142C2312yes—
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2312yes—
92C22×C4×D71—44no—
93C22×C4×D71C2×C418yes—
94C22×C4×D71C2311yescharacteristic
95C22×C4×D71C2311yescharacteristic
96C22×C4×D71C2311yescharacteristic
97C22×C4×D71C2311yescharacteristic
98#14556108C2×C418yes—
99#14556108C2×C418yes—
100#14556108C2×C418yes—
101#14556108C2×C418yes—
102#14556108C2×C4116yes—
103#14556108C2×C4116yes—
104C4×Dic142—44no—
105#14556093—44no—
106#14556086—44no—
107#14556085—44no—
108C2×C4⋊Dic71C2×C4116yes—
109C2×C4⋊Dic71C2312yes—
110C2×C4⋊Dic71C2314yes—
111C2×C4⋊Dic71C2312yes—
112C2×C4⋊Dic71C2312yes—
113C2×C4⋊Dic71C2312yes—
114C2×C4⋊Dic71C2312yes—
115C2×Dic71⋊C4C2312yes—
116C2×Dic71⋊C4C2312yes—
117C2×Dic71⋊C4C2314yes—
118C2×Dic71⋊C4C2314yes—
119C2×C22⋊Dic71C2311yescharacteristic
120C2×C22⋊Dic71C2311yescharacteristic
121C2×C22⋊Dic71C2312yes—
122C2×(C2×D71)⋊C4C2×C4116yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2312yes—
125C2×(C2×D71)⋊C4C2312yes—
126C2×(C2×D71)⋊C4C2312yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2312yes—
129C2×(C2×D71)⋊C4C2312yes—
130C2×(C2×D71)⋊C4C2312yes—
131C2×(C2×D71)⋊C4C2312yes—
132C2×(C2×D71)⋊C4C2312yes—
133C2×C4×Dic71C2312yes—
134C2×C4×Dic71C2314yes—
135C2×C4×Dic71C2314yes—
136C2×C4×Dic71C2314yes—
137C2×C4×Dic71C2314yes—
138C71⋊#95C2312yes—
139C71⋊#95C2312yes—
140C71⋊#95C2314yes—
141C71⋊#95C2312yes—
142C71⋊#95C2312yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2314yes—
147C71⋊#95C2314yes—
148C71⋊#95C2314yes—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2312yes—
151C2×C4⋊C4×C71C2×C418yes—
152C2×C4⋊C4×C71C2312yes—
153C2×C4⋊C4×C71C2314yes—
154C2×C4⋊C4×C71C2311yescharacteristic
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2311yescharacteristic
157C2×C22⋊C4×C71C2312yes—
158C2×C22⋊C4×C71C2311yescharacteristic
159C2×C22⋊C4×C71C2311yescharacteristic
160C2×C42×C71C2312yes—
161C2×C42×C71C2314yes—
162#95×C71C2312yes—
163#95×C71C2312yes—
164#95×C71C2314yes—
165#95×C71C2314yes—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—42no—
169C23×D71—42no—
170C23×D71C22×C414yes—
171C23×D71C2411yescharacteristic
172C23×D71C2411yescharacteristic
173C2×Dic142—24no—
174C2×Dic142—24no—
175C2×Dic142—416no—
176C2×Dic142—44no—
177C2×Dic142C22×C414yes—
178C2×Dic142C22×C414yes—
179C2×Dic142C22×C418yes—
180C22×Dic71—42no—
181C22×Dic71—44no—
182C22×Dic71C22×C414yes—
183C22×Dic71C22×C418yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2414yes—
187C22×Dic71C2411yescharacteristic
188C22×Dic71C2411yescharacteristic
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C2×C4×D71—24no—
192C2×C4×D71—24no—
193C2×C4×D71—416no—
194C2×C4×D71—42no—
195C2×C4×D71—42no—
196C2×C4×D71C22×C414yes—
197C2×C4×D71C22×C414yes—
198C2×C4×D71C22×C414yes—
199C2×C4×D71C22×C414yes—
200C4⋊Dic71—24no—
201C4⋊Dic71—44no—
202C4⋊Dic71C22×C418yes—
203C4⋊Dic71C22×C418yes—
204C4⋊Dic71C22×C418yes—
205C4⋊Dic71C22×C418yes—
206Dic71⋊C4—42no—
207Dic71⋊C4—42no—
208Dic71⋊C4—44no—
209Dic71⋊C4—44no—
210C22⋊Dic71—22no—
211C22⋊Dic71—22no—
212C22⋊Dic71—24no—
213(C2×D71)⋊C4—42no—
214(C2×D71)⋊C4—44no—
215(C2×D71)⋊C4—42no—
216(C2×D71)⋊C4—42no—
217(C2×D71)⋊C4—42no—
218(C2×D71)⋊C4—44no—
219(C2×D71)⋊C4C22×C418yes—
220(C2×D71)⋊C4C22×C418yes—
221(C2×D71)⋊C4C22×C418yes—
222(C2×D71)⋊C4C22×C418yes—
223C4×Dic71—24no—
224C4×Dic71—44no—
225C4×Dic71—44no—
226C4×Dic71—44no—
227C4×Dic71—44no—
228C24×C71C2411yescharacteristic
229C22×C4×C71—24no—
230C22×C4×C71—44no—
231C22×C4×C71C22×C414yes—
232C22×C4×C71C22×C418yes—
233C22×C4×C71C2412yes—
234C22×C4×C71C2412yes—
235C22×C4×C71C2414yes—
236C22×C4×C71C2411yescharacteristic
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2411yescharacteristic
240C4⋊C4×C71—24no—
241C4⋊C4×C71—44no—
242C4⋊C4×C71C22×C418yes—
243C4⋊C4×C71C22×C414yes—
244C4⋊C4×C71C22×C414yes—
245C22⋊C4×C71—24no—
246C22⋊C4×C71—22no—
247C22⋊C4×C71—22no—
248C42×C71—24no—
249C42×C71—44no—
250C23×C71—22no—
251C23×C71—22no—
252C23×C71C23×C412yes—
253C23×C712−1+412yes—
254C23×C712−1+412yes—
255C23×C71C2511yescharacteristic
256C22×D71—28no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—21no—
262C22×D71—21no—
263C22×D71—22no—
264C22×D71—22no—
265C22×D71—44no—
266C22×D71—44no—
267C22×D71—48no—
268C22×D71—48no—
269C22×D71C23×C412yes—
270C22×D71C23×C412yes—
271C2×C4×C71—22no—
272C2×C4×C71—24no—
273C2×C4×C71—24no—
274C2×C4×C71—28no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—24no—
278C2×C4×C71—22no—
279C2×C4×C71—24no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—24no—
283C2×C4×C71—22no—
284C2×C4×C71—48no—
285C2×C4×C71C23×C414yes—
286C2×C4×C71C23×C414yes—
287C2×C4×C71C23×C412yes—
288C2×C4×C71C23×C412yes—
289C2×C4×C71H(5,𝔽2)14yes—
290C2×Dic71—22no—
291C2×Dic71—24no—
292C2×Dic71—24no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—24no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—24no—
300C2×Dic71—22no—
301C2×Dic71—24no—
302C2×Dic71—22no—
303C2×Dic71—44no—
304C2×Dic71—48no—
305C2×Dic71C23×C414yes—
306C2×Dic71C23×C414yes—
307C2×Dic71C23×C412yes—
308C2×Dic71C23×C412yes—
309C4×D71—28no—
310C4×D71—28no—
311C4×D71—44no—
312C4×D71—44no—
313Dic142—28no—
314Dic142—28no—
315Dic142—48no—
316C22×C71—22no—
317C22×C71—22no—
318C22×C71—24no—
319C22×C71—24no—
320C22×C71#51914yes—
321C22×C71C24×C411yescharacteristic
322C22×C71C2×H(5,𝔽2)12yes—
323C22×C71C2×2−1+411yescharacteristic
324C22×C71C2×2−1+411yescharacteristic
325C22×C71#58512yes—
326C2×D71—22no—
327C2×D71—22no—
328C2×D71—22no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—416no—
333C2×D71—42no—
334C2×D71—42no—
335C2×D71—42no—
336C2×D71—42no—
337C4×C71—22no—
338C4×C71—24no—
339C4×C71—24no—
340C4×C71—42no—
341C4×C71—44no—
342C4×C71—42no—
343C4×C71#51814yes—
344Dic71—24no—
345Dic71—24no—
346Dic71—22no—
347Dic71—22no—
348Dic71—42no—
349Dic71—42no—
350Dic71—44no—
351#34370—711nomaximal, Sylow
352C2×C71—24no—
353C2×C71C2×#51811yescharacteristic
354C2×C71C2×#51911yescharacteristic
355C2×C71#342811yescharacteristic
356C2×C71#354112yes—
357C2×C71#354112yes—
358D71—42no—
359D71—42no—
360C22×C22⋊Q8—711no—
361#2378—714no—
362#2362—712no—
363#2362—712no—
364#2345—712no—
365#2345—712no—
366#2345—711no—
367#2345D7111yescharacteristic, complemented
368Q8×C22⋊C4—711no—
369Q8×C22⋊C4—711no—
370#2332—714no—
371#2323—712no—
372#2323—712no—
373#2312—712no—
374#2312—712no—
375#2280—711no—
376#2280—711no—
377C71#3437011yescharacteristic, complemented, Sylow
378C23×Q8—711no—
379C24×C4—711no—
380C2×C22⋊Q8—7116no—
381C2×C22⋊Q8—711no—
382C2×C22⋊Q8—711no—
383C2×C22⋊Q8—712no—
384C2×C22⋊Q8—711no—
385C2×C22⋊Q8—711no—
386C2×C22⋊Q8—712no—
387C2×C4×Q8—712no—
388C2×C4×Q8—712no—
389C2×#117—712no—
390C2×#117—712no—
391C22×C4⋊C4—712no—
392C22×C4⋊C4C2×D7111yescharacteristic
393C22×C22⋊C4—712no—
394#391—712no—
395#391—712no—
396#391—714no—
397#391—714no—
398#389—712no—
399#389—714no—
400#389—714no—
401#389C2×D7112yescomplemented
402#388—714no—
403#388—714no—
404#388—714no—
405#388—714no—
406#388—714no—
407#388—714no—
408#388—714no—
409#388—714no—
410#387—714no—
411#387—714no—
412#387—714no—
413#387—714no—
414#387—714no—
415#387C2×D7114yescomplemented
416#381—712no—
417#381—712no—
418#380—712no—
419#380—711no—
420#380—712no—
421#380—712no—
422#380—712no—
423#380—711no—
424#380—711no—
425#380—712no—
426#380C2×D7112yes—
427#380C2×D7111yescharacteristic
428#379—711no—
429#379—712no—
430#379—711no—
431C4×C4⋊C4—712no—
432C4×C4⋊C4—714no—
433C4×C4⋊C4—714no—
434C4×C4⋊C4C2×D7112yescomplemented
435C4×C22⋊C4—712no—
436C4×C22⋊C4—711no—
437C4×C22⋊C4—712no—
438C4×C22⋊C4—712no—
439C4×C22⋊C4—712no—
440C4×C22⋊C4—712no—
441C4×C22⋊C4—712no—
442C4×C22⋊C4C2×D7112yes—
443C4×C22⋊C4C2×D7111yescharacteristic
444C25—711no—
445C22×Q8—2844no—
446C22×Q8—718no—
447C22×Q8—712no—
448C22×Q8—711no—
449C22×Q8—711no—
450C23×C4—2844no—
451C23×C4—712no—
452C23×C4—711no—
453C23×C4—718no—
454C23×C4—711no—
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—711no—
458C23×C4C22×D7111yescharacteristic
459C23×C4C22×D7112yes—
460C22⋊Q8—7116no—
461C22⋊Q8—7116no—
462C22⋊Q8—718no—
463C22⋊Q8—718no—
464C22⋊Q8—718no—
465C22⋊Q8—718no—
466C4×Q8—2844no—
467C4×Q8—2844no—
468#117—2844no—
469#117—2844no—
470C2×C4⋊C4—712no—
471C2×C4⋊C4—712no—
472C2×C4⋊C4—714no—
473C2×C4⋊C4—714no—
474C2×C4⋊C4—714no—
475C2×C4⋊C4—7116no—
476C2×C4⋊C4—712no—
477C2×C4⋊C4—712no—
478C2×C4⋊C4—712no—
479C2×C4⋊C4—712no—
480C2×C4⋊C4—712no—
481C2×C4⋊C4C4×D7118yes—
482C2×C4⋊C4C22×D7112yes—
483C2×C4⋊C4C22×D7114yes—
484C2×C4⋊C4C22×D7111yescharacteristic
485C2×C4⋊C4C22×D7111yescharacteristic
486C2×C4⋊C4C22×D7112yes—
487C2×C22⋊C4—714no—
488C2×C22⋊C4—712no—
489C2×C22⋊C4—712no—
490C2×C22⋊C4—712no—
491C2×C22⋊C4—714no—
492C2×C22⋊C4—712no—
493C2×C22⋊C4—7116no—
494C2×C22⋊C4—712no—
495C2×C22⋊C4—712no—
496C2×C22⋊C4—712no—
497C2×C22⋊C4—712no—
498C2×C22⋊C4—711no—
499C2×C22⋊C4—712no—
500C2×C22⋊C4—711no—
501C2×C22⋊C4C22×D7111yescharacteristic
502C2×C22⋊C4C22×D7112yes—
503C2×C22⋊C4C22×D7111yescharacteristic
504C2×C42—714no—
505C2×C42—714no—
506C2×C42—714no—
507C2×C42—714no—
508C2×C42—712no—
509C2×C42C22×D7112yes—
510C2×C42C22×D7114yes—
511#95—712no—
512#95—712no—
513#95—714no—
514#95—712no—
515#95—712no—
516#95—714no—
517#95—714no—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95C22×D7112yes—
523#95C22×D7112yes—
524#95C22×D7114yes—
525#95C22×D7114yes—
526C24—2842no—
527C24—2842no—
528C24—714no—
529C24—711no—
530C24—711no—
531C24—1422no—
532C24—1422no—
533C24C23×D7111yescharacteristic
534C2×Q8—28416no—
535C2×Q8—2844no—
536C2×Q8—718no—
537C2×Q8—714no—
538C2×Q8—714no—
539C2×Q8—1424no—
540C2×Q8—1424no—
541C22×C4—24no—
542C22×C4—44no—
543C22×C4—2842no—
544C22×C4—2842no—
545C22×C4—28416no—
546C22×C4—2842no—
547C22×C4—2844no—
548C22×C4—718no—
549C22×C4—714no—
550C22×C4—714no—
551C22×C4—714no—
552C22×C4—711no—
553C22×C4—712no—
554C22×C4—712no—
555C22×C4—711no—
556C22×C4—714no—
557C22×C4—714no—
558C22×C4—712no—
559C22×C4—714no—
560C22×C4—712no—
561C22×C4—1424no—
562C22×C4—1424no—
563C22×C4C2×C4×D7114yes—
564C22×C4C2×C4×D7118yes—
565C22×C4C23×D7112yes—
566C22×C4C23×D7114yes—
567C22×C4C23×D7112yes—
568C22×C4C23×D7111yescharacteristic
569C22×C4C23×D7112yes—
570C22×C4C23×D7112yes—
571C22×C4C23×D7111yescharacteristic
572C4⋊C4—24no—
573C4⋊C4—44no—
574C4⋊C4—2842no—
575C4⋊C4—2842no—
576C4⋊C4—2844no—
577C4⋊C4—2844no—
578C4⋊C4—2844no—
579C4⋊C4—718no—
580C4⋊C4—718no—
581C4⋊C4—718no—
582C4⋊C4—718no—
583C4⋊C4—1424no—
584C4⋊C4C2×C4×D7118yes—
585C4⋊C4C2×C4×D7114yes—
586C4⋊C4C2×C4×D7114yes—
587C22⋊C4—22no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—2842no—
591C22⋊C4—2844no—
592C22⋊C4—2842no—
593C22⋊C4—2842no—
594C22⋊C4—2842no—
595C22⋊C4—2844no—
596C22⋊C4—718no—
597C22⋊C4—718no—
598C22⋊C4—718no—
599C22⋊C4—718no—
600C22⋊C4—1422no—
601C22⋊C4—1424no—
602C22⋊C4—1422no—
603C42—24no—
604C42—44no—
605C42—2844no—
606C42—2844no—
607C42—2844no—
608C42—2844no—
609C42—1424no—
610C23—22no—
611C23—22no—
612C23—2848no—
613C23—2848no—
614C23—2844no—
615C23—2844no—
616C23—712no—
617C23—712no—
618C23—1422no—
619C23—1422no—
620C23—1421no—
621C23—1421no—
622C23—1421no—
623C23—1421no—
624C23—1422no—
625C23—1422no—
626C23—1428no—
627C23C22×C4×D7112yes—
628C23#1455617512yes—
629C23#1455617612yes—
630C23C24×D7111yescharacteristic
631Q8—2848no—
632Q8—1428no—
633Q8—1428no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—48no—
648C2×C4—2844no—
649C2×C4—2844no—
650C2×C4—2844no—
651C2×C4—2848no—
652C2×C4—714no—
653C2×C4—714no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—1422no—
657C2×C4—1424no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1424no—
662C2×C4—1422no—
663C2×C4—1424no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1424no—
667C2×C4—1424no—
668C2×C4—1422no—
669C2×C4—1428no—
670C2×C4—1428no—
671C2×C4C22×C4×D7114yes—
672C2×C4C22×C4×D7114yes—
673C2×C4C22×C4×D7112yes—
674C2×C4C22×C4×D7112yes—
675C2×C4#1455617414yes—
676C22—22no—
677C22—22no—
678C22—24no—
679C22—24no—
680C22—28416no—
681C22—2842no—
682C22—2842no—
683C22—2842no—
684C22—2842no—
685C22—1422no—
686C22—1422no—
687C22—1422no—
688C22—1422no—
689C22—1422no—
690C22—1422no—
691C22#1798647514yes—
692C22C23×C4×D7111yescharacteristic
693C22C2×#1455617412yes—
694C22C2×#1455617511yescharacteristic
695C22C2×#1455617611yescharacteristic
696C22#1798683412yes—
697C4—22no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—44no—
702C4—42no—
703C4—2842no—
704C4—2842no—
705C4—2844no—
706C4—1422no—
707C4—1422no—
708C4—1424no—
709C4—1424no—
710C4#1798647314yes—
711C2—24no—
712C2—2842no—
713C2—2842no—
714C2C2×#1798647311yescharacteristic
715C2C2×#1798647511yescharacteristic
716C2#2260153811yescharacteristic
717C2#2260262712yes—
718C2#2260263412yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2345C2
socle, cosocleC23×C71C25
prime radicalC24×D71C23
hypercenter#2345D71
hypocenterC71#34370
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #22591504C2semidirect
3. #22591369C2semidirect
4. #22591366C2semidirect
5. #22591219C2semidirect
6. #22591217C2semidirect
7. #22591215C2semidirect
8. C22⋊C4×Dic142C2semidirect
9. #22591172C2semidirect
10. #22591092C2semidirect
11. #22591023C2semidirect
12. #22591020C2semidirect
17. C71×#2345C2semidirect
20. C2×#14556108C4semidirect
27. C2×C4×Dic142C22semidirect
28. C2×#14556093C22semidirect
33. #17985905C22semidirect
34. #17985904C22semidirect
35. #17985903C22semidirect
36. #17985903C22semidirect
37. #17985898C22semidirect
38. #17985897C22semidirect
39. #17985895C22semidirect
48. #17985885C22semidirect
49. #17985884C22semidirect
50. #17985884C22semidirect
51. #17985882C22semidirect
52. #17985882C22semidirect
66. C4⋊C4×Dic71C22semidirect
67. C4⋊C4×Dic71C22semidirect
68. C4×C4⋊Dic71C22semidirect
77. #389×C71C22semidirect
78. #387×C71C22semidirect
81. C4×C4⋊C4×C71C22semidirect
367. #2345D71semidirect
377. C71#34370semidirect
401. #389C2×D71semidirect
415. #387C2×D71semidirect
434. C4×C4⋊C4C2×D71semidirect

Maximal subgroups

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

subgroupindex
C22×#145561082
#225915042
#225913692
#225913662
#225912192
#225912172
#225912152
C22⋊C4×Dic1422
#225911722
#225910922
#225910232
#225910202
#225909372
#225909352
#225907222
#225907212
C71×#23452
#3437071