Finite Group Databasebeta

← #32157509

Subgroups — #32157509

Order 18176.

2806 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×C4⋊C4×D71C211yesmaximal, characteristic
2#22591219C211yesmaximal, characteristic, complemented
3#22591218C212yesmaximal, complemented
4#22591217C211yesmaximal, characteristic, complemented
5#22591215C211yesmaximal, characteristic, complemented
6#22591212C212yesmaximal, complemented
7#22591208C212yesmaximal, complemented
8#22591206C214yesmaximal, complemented
9#22591205C212yesmaximal, complemented
10#22590955C212yesmaximal, complemented
11#22590939C214yesmaximal, complemented
12#22590722C211yesmaximal, characteristic
13#22590722C212yesmaximal
14#22590721C211yesmaximal, characteristic
15#22590721C212yesmaximal
16#22590694C212yesmaximal, complemented
17C71×#2345C211yesmaximal, characteristic, complemented
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2212yes—
20C2×#14556086C2212yes—
21C2×#14556086C2214yes—
22C2×#14556085C2212yes—
23C2×#14556085C2214yes—
24C22×C4⋊Dic71C2211yescharacteristic
25C22×Dic71⋊C4C2212yes—
26C2×C4⋊C4×D71C4116yescomplemented
27C2×C4⋊C4×D71C2212yes—
28C2×C4⋊C4×D71C2211yescharacteristic
29C2×C4⋊C4×D71C2211yescharacteristic
30C2×C4⋊C4×D71C2212yes—
31C2×C4⋊C4×D71C2211yescharacteristic
32C2×C4⋊C4×D71C2211yescharacteristic
33#17985898C2212yescomplemented
34#17985897C2212yescomplemented
35#17985896C2214yescomplemented
36#17985895C2212yescomplemented
37#17985894C2214yescomplemented
38#17985886C2214yescomplemented
39#17985885C2214yescomplemented
40#17985884C2214yescomplemented
41#17985883C2214yescomplemented
42#17985882C2214yescomplemented
43#17985881C2214yescomplemented
44#17985880C2214yescomplemented
45#17985861C2212yes—
46#17985861C2214yes—
47#17985861C2212yes—
48#17985861C2214yes—
49#17985859C2211yescharacteristic
50#17985859C2212yes—
51#17985858C2214yes—
52#17985858C2212yes—
53#17985857C2211yescharacteristic
54#17985857C2212yes—
55#17985857C2212yes—
56#17985857C2211yescharacteristic
57#17985856C2214yes—
58#17985856C2212yes—
59#17985854C2211yescharacteristic
60#17985854C2211yescharacteristic
61#17985854C2212yes—
62C4⋊C4×Dic71C2212yescomplemented
63C4⋊C4×Dic71C2212yescomplemented
64C4×Dic71⋊C4C2214yescomplemented
65C4×C4⋊Dic71C2212yescomplemented
66#17985850C2214yescomplemented
67C22⋊C4×Dic71C2212yes—
68C22⋊C4×Dic71C2212yes—
69C22⋊C4×Dic71C2212yes—
70C4×(C2×D71)⋊C4C2214yes—
71C4×(C2×D71)⋊C4C2212yes—
72C4×C22⋊Dic71C2212yes—
73C4×C22⋊Dic71C2211yescharacteristic
74#17985846C2214yes—
75#17985846C2212yes—
76C22×C4⋊C4×C71C2211yescharacteristic
77#389×C71C2212yescomplemented
78#387×C71C2214yescomplemented
79#380×C71C2212yes—
80#380×C71C2211yescharacteristic
81C4×C4⋊C4×C71C2212yescomplemented
82C4×C22⋊C4×C71C2211yescharacteristic
83C4×C22⋊C4×C71C2212yes—
84C24×D71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2312yes—
87C22×C4×D71—28no—
88C22×C4×D71—48no—
89C22×C4×D71C2×C418yes—
90C22×C4×D71C2×C4116yes—
91C22×C4×D71C2311yescharacteristic
92C22×C4×D71C2311yescharacteristic
93C22×C4×D71C2311yescharacteristic
94C22×C4×D71C2312yes—
95C22×C4×D71C2312yes—
96C22×C4×D71C2312yes—
97C22×C4×D71C2312yes—
98C22×C4×D71C2311yescharacteristic
99#14556086—28no—
100#14556086—48no—
101#14556085—28no—
102#14556085—48no—
103C2×C4⋊Dic71C2×C418yes—
104C2×C4⋊Dic71C2312yes—
105C2×C4⋊Dic71C2314yes—
106C2×C4⋊Dic71C2311yescharacteristic
107C2×C4⋊Dic71C2312yes—
108C2×C4⋊Dic71C2311yescharacteristic
109C2×Dic71⋊C4C2×C4116yes—
110C2×Dic71⋊C4C2312yes—
111C2×Dic71⋊C4C2312yes—
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2312yes—
115C2×Dic71⋊C4C2312yes—
116C2×Dic71⋊C4C2312yes—
117C2×Dic71⋊C4C2312yes—
118C4⋊C4×D71C2×C418yes—
119C4⋊C4×D71C2×C4116yes—
120C4⋊C4×D71C2×C418yes—
121C4⋊C4×D71C2×C4116yes—
122C4⋊C4×D71C2×C418yes—
123C4⋊C4×D71C2×C418yes—
124C2×C22⋊Dic71C2311yescharacteristic
125C2×C22⋊Dic71C2312yes—
126C2×C22⋊Dic71C2311yescharacteristic
127C2×(C2×D71)⋊C4C2312yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2312yes—
131C2×(C2×D71)⋊C4C2312yes—
132C2×(C2×D71)⋊C4C2312yes—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2312yes—
135C2×C4×Dic71C2314yes—
136C2×C4×Dic71C2314yes—
137C2×C4×Dic71C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2312yes—
140C71⋊#95C2314yes—
141C71⋊#95C2312yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2312yes—
145C71⋊#95C2312yes—
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×C71C2311yescharacteristic
158C2×C22⋊C4×C71C2312yes—
159C2×C22⋊C4×C71C2311yescharacteristic
160C2×C42×C71C2312yes—
161C2×C42×C71C2314yes—
162#95×C71C2314yes—
163#95×C71C2312yes—
164#95×C71C2312yes—
165#95×C71C2314yes—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—24no—
169C23×D71—24no—
170C23×D71C22×C414yes—
171C23×D71C2411yescharacteristic
172C23×D71C2411yescharacteristic
173C22×Dic71—24no—
174C22×Dic71—44no—
175C22×Dic71C22×C414yes—
176C22×Dic71C22×C418yes—
177C22×Dic71C2412yes—
178C22×Dic71C2412yes—
179C22×Dic71C2414yes—
180C22×Dic71C2411yescharacteristic
181C22×Dic71C2412yes—
182C22×Dic71C2412yes—
183C22×Dic71C2411yescharacteristic
184C2×C4×D71—24no—
185C2×C4×D71—28no—
186C2×C4×D71—28no—
187C2×C4×D71—24no—
188C2×C4×D71—24no—
189C2×C4×D71—232no—
190C2×C4×D71—432no—
191C2×C4×D71—44no—
192C2×C4×D71—44no—
193C2×C4×D71C22×C414yes—
194C2×C4×D71C22×C418yes—
195C2×C4×D71C22×C418yes—
196C2×C4×D71C22×C414yes—
197C2×C4×D71C22×C414yes—
198C2×C4×D71C22×C418yes—
199C2×C4×D71C22×C418yes—
200C2×C4×D71C22×C414yes—
201C2×C4×D71#4118yes—
202C4⋊Dic71—24no—
203C4⋊Dic71—44no—
204C4⋊Dic71C22×C418yes—
205C4⋊Dic71C22×C414yes—
206C4⋊Dic71C22×C414yes—
207Dic71⋊C4—24no—
208Dic71⋊C4—24no—
209Dic71⋊C4—44no—
210Dic71⋊C4—44no—
211Dic71⋊C4C22×C418yes—
212Dic71⋊C4C22×C418yes—
213Dic71⋊C4C22×C418yes—
214Dic71⋊C4C22×C418yes—
215C22⋊Dic71—22no—
216C22⋊Dic71—24no—
217C22⋊Dic71—22no—
218(C2×D71)⋊C4—24no—
219(C2×D71)⋊C4—24no—
220(C2×D71)⋊C4—28no—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—28no—
223(C2×D71)⋊C4—24no—
224C4×Dic71—24no—
225C4×Dic71—28no—
226C4×Dic71—44no—
227C4×Dic71—44no—
228C4×Dic71—44no—
229C24×C71C2411yescharacteristic
230C22×C4×C71—24no—
231C22×C4×C71—44no—
232C22×C4×C71C22×C414yes—
233C22×C4×C71C22×C418yes—
234C22×C4×C71C2412yes—
235C22×C4×C71C2412yes—
236C22×C4×C71C2414yes—
237C22×C4×C71C2411yescharacteristic
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2411yescharacteristic
241C4⋊C4×C71—24no—
242C4⋊C4×C71—44no—
243C4⋊C4×C71C22×C418yes—
244C4⋊C4×C71C22×C414yes—
245C4⋊C4×C71C22×C414yes—
246C22⋊C4×C71—22no—
247C22⋊C4×C71—24no—
248C22⋊C4×C71—22no—
249C42×C71—24no—
250C42×C71—44no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71C23×C412yes—
254C23×C712−1+412yes—
255C23×C712−1+412yes—
256C23×C71C2511yescharacteristic
257C22×D71—216no—
258C22×D71—216no—
259C22×D71—28no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71—28no—
267C22×D71—28no—
268C22×D71C23×C412yes—
269C22×D71C23×C412yes—
270C22×D71C2×#4114yes—
271C22×D71H(5,𝔽2)14yes—
272C2×C4×C71—22no—
273C2×C4×C71—24no—
274C2×C4×C71—24no—
275C2×C4×C71—28no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—24no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—24no—
284C2×C4×C71—22no—
285C2×C4×C71—48no—
286C2×C4×C71C23×C414yes—
287C2×C4×C71C23×C414yes—
288C2×C4×C71C23×C412yes—
289C2×C4×C71C23×C412yes—
290C2×C4×C71C2×#4114yes—
291C2×Dic71—22no—
292C2×Dic71—24no—
293C2×Dic71—24no—
294C2×Dic71—28no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—24no—
298C2×Dic71—22no—
299C2×Dic71—24no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—24no—
304C2×Dic71—48no—
305C2×Dic71C23×C412yes—
306C2×Dic71C23×C414yes—
307C2×Dic71C23×C414yes—
308C2×Dic71C23×C412yes—
309C2×Dic71C2×#4114yes—
310C4×D71—28no—
311C4×D71—216no—
312C4×D71—216no—
313C4×D71—28no—
314C4×D71—28no—
315C4×D71—48no—
316C4×D71—48no—
317C4×D71#117116yescomplemented
318C22×C71—22no—
319C22×C71—22no—
320C22×C71—24no—
321C22×C71—24no—
322C22×C71#51914yes—
323C22×C71C24×C411yescharacteristic
324C22×C71C22×#4112yes—
325C22×C71C2×H(5,𝔽2)12yes—
326C22×C71C2×2−1+411yescharacteristic
327C22×C71C2×2−1+411yescharacteristic
328C2×D71—232no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—24no—
334C2×D71—24no—
335C2×D71—24no—
336C2×D71—24no—
337C2×D71C2×#11714yes—
338C2×D71#51814yes—
339C4×C71—22no—
340C4×C71—24no—
341C4×C71—24no—
342C4×C71—42no—
343C4×C71—44no—
344C4×C71—42no—
345C4×C71C2×#11714yes—
346Dic71—22no—
347Dic71—24no—
348Dic71—24no—
349Dic71—42no—
350Dic71—42no—
351Dic71—44no—
352Dic71C2×#11714yes—
353#34178—711nomaximal, Sylow
354C2×C71—24no—
355C2×C71C22×#11711yescharacteristic
356C2×C71C2×#51811yescharacteristic
357C2×C71C2×#51911yescharacteristic
358C2×C71#349212yes—
359C2×C71#349212yes—
360D71—24no—
361D71—24no—
362C23×C4⋊C4—711no—
363#2345—712no—
364#2345—711no—
365#2345—711no—
366#2345—712no—
367#2345—711no—
368#2345D7111yescharacteristic, complemented
369#2344—712no—
370#2344—714no—
371#2344—712no—
372#2316—712no—
373#2313—714no—
374#2280—712no—
375#2280—711no—
376#2280—712no—
377#2280—711no—
378#2274—712no—
379C71#3417811yescharacteristic, complemented, Sylow
380C24×C4—712no—
381C24×C4—711no—
382C2×#117—714no—
383C2×#117—712no—
384C2×#117—714no—
385C2×#117—712no—
386C22×C4⋊C4—712no—
387C22×C4⋊C4—711no—
388C22×C4⋊C4—7116no—
389C22×C4⋊C4—712no—
390C22×C4⋊C4—711no—
391C22×C4⋊C4—712no—
392C22×C4⋊C4—711no—
393C22×C4⋊C4—711no—
394C22×C4⋊C4—711no—
395C22×C4⋊C4C2×D7111yescharacteristic
396#389—714no—
397#389—712no—
398#389—712no—
399#389—712no—
400#389—714no—
401#389C2×D7112yescomplemented
402#387—714no—
403#387—714no—
404#387—714no—
405#387—714no—
406#387—714no—
407#387—714no—
408#387—714no—
409#387C2×D7114yescomplemented
410#381—712no—
411#381—712no—
412#381—714no—
413#381—714no—
414#380—712no—
415#380—711no—
416#380—714no—
417#380—712no—
418#380—712no—
419#380—712no—
420#380—711no—
421#380—711no—
422#380—714no—
423#380—712no—
424#380C2×D7112yes—
425#380C2×D7111yescharacteristic
426#379—711no—
427#379—712no—
428#379—711no—
429C4×C4⋊C4—712no—
430C4×C4⋊C4—712no—
431C4×C4⋊C4—712no—
432C4×C4⋊C4—714no—
433C4×C4⋊C4—714no—
434C4×C4⋊C4C2×D7112yescomplemented
435C4×C22⋊C4—711no—
436C4×C22⋊C4—712no—
437C4×C22⋊C4—712no—
438C4×C22⋊C4—712no—
439C4×C22⋊C4—712no—
440C4×C22⋊C4—714no—
441C4×C22⋊C4—712no—
442C4×C22⋊C4—714no—
443C4×C22⋊C4—712no—
444C4×C22⋊C4C2×D7111yescharacteristic
445C4×C22⋊C4C2×D7112yes—
446C25—711no—
447C23×C4—2848no—
448C23×C4—712no—
449C23×C4—7116no—
450C23×C4—712no—
451C23×C4—712no—
452C23×C4—711no—
453C23×C4—711no—
454C23×C4—718no—
455C23×C4—712no—
456C23×C4—712no—
457C23×C4—711no—
458C23×C4—711no—
459C23×C4—711no—
460C23×C4—1428no—
461C23×C4C22×D7111yescharacteristic
462C23×C4C22×D7112yes—
463#117—2848no—
464#117—2848no—
465#117—1428no—
466#117—1428no—
467C2×C4⋊C4—714no—
468C2×C4⋊C4—714no—
469C2×C4⋊C4—714no—
470C2×C4⋊C4—7116no—
471C2×C4⋊C4—718no—
472C2×C4⋊C4—712no—
473C2×C4⋊C4—711no—
474C2×C4⋊C4—712no—
475C2×C4⋊C4—712no—
476C2×C4⋊C4—712no—
477C2×C4⋊C4—712no—
478C2×C4⋊C4—711no—
479C2×C4⋊C4—718no—
480C2×C4⋊C4—718no—
481C2×C4⋊C4—7116no—
482C2×C4⋊C4—7116no—
483C2×C4⋊C4—718no—
484C2×C4⋊C4—718no—
485C2×C4⋊C4—712no—
486C2×C4⋊C4—712no—
487C2×C4⋊C4—712no—
488C2×C4⋊C4C4×D7118yes—
489C2×C4⋊C4C22×D7112yes—
490C2×C4⋊C4C22×D7114yes—
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7112yes—
493C2×C4⋊C4C22×D7111yescharacteristic
494C2×C22⋊C4—711no—
495C2×C22⋊C4—712no—
496C2×C22⋊C4—711no—
497C2×C22⋊C4—712no—
498C2×C22⋊C4—714no—
499C2×C22⋊C4—712no—
500C2×C22⋊C4—714no—
501C2×C22⋊C4—712no—
502C2×C22⋊C4—712no—
503C2×C22⋊C4C22×D7111yescharacteristic
504C2×C22⋊C4C22×D7112yes—
505C2×C22⋊C4C22×D7111yescharacteristic
506C2×C42—714no—
507C2×C42—714no—
508C2×C42—714no—
509C2×C42—714no—
510C2×C42—712no—
511C2×C42C22×D7112yes—
512C2×C42C22×D7114yes—
513#95—714no—
514#95—714no—
515#95—714no—
516#95—714no—
517#95—712no—
518#95—712no—
519#95—712no—
520#95—712no—
521#95—714no—
522#95—714no—
523#95—714no—
524#95C22×D7114yes—
525#95C22×D7112yes—
526#95C22×D7112yes—
527#95C22×D7114yes—
528C24—711no—
529C24—711no—
530C24—714no—
531C24—1424no—
532C24—1424no—
533C24—1422no—
534C24—1422no—
535C24C23×D7111yescharacteristic
536C22×C4—24no—
537C22×C4—44no—
538C22×C4—2844no—
539C22×C4—2844no—
540C22×C4—28432no—
541C22×C4—2844no—
542C22×C4—718no—
543C22×C4—718no—
544C22×C4—718no—
545C22×C4—711no—
546C22×C4—714no—
547C22×C4—718no—
548C22×C4—714no—
549C22×C4—711no—
550C22×C4—712no—
551C22×C4—712no—
552C22×C4—714no—
553C22×C4—718no—
554C22×C4—718no—
555C22×C4—714no—
556C22×C4—714no—
557C22×C4—712no—
558C22×C4—714no—
559C22×C4—712no—
560C22×C4—1424no—
561C22×C4—14232no—
562C22×C4—1428no—
563C22×C4—1428no—
564C22×C4—1424no—
565C22×C4—1424no—
566C22×C4—1424no—
567C22×C4C2×C4×D7114yes—
568C22×C4C2×C4×D7118yes—
569C22×C4C23×D7112yes—
570C22×C4C23×D7114yes—
571C22×C4C23×D7112yes—
572C22×C4C23×D7111yescharacteristic
573C22×C4C23×D7112yes—
574C22×C4C23×D7112yes—
575C22×C4C23×D7111yescharacteristic
576C4⋊C4—24no—
577C4⋊C4—44no—
578C4⋊C4—2844no—
579C4⋊C4—2844no—
580C4⋊C4—2844no—
581C4⋊C4—718no—
582C4⋊C4—718no—
583C4⋊C4—718no—
584C4⋊C4—718no—
585C4⋊C4—718no—
586C4⋊C4—714no—
587C4⋊C4—714no—
588C4⋊C4—1424no—
589C4⋊C4—1424no—
590C4⋊C4—1424no—
591C4⋊C4C2×C4×D7118yes—
592C4⋊C4C2×C4×D7114yes—
593C4⋊C4C2×C4×D7114yes—
594C22⋊C4—22no—
595C22⋊C4—24no—
596C22⋊C4—22no—
597C22⋊C4—1424no—
598C22⋊C4—1428no—
599C22⋊C4—1424no—
600C22⋊C4—1424no—
601C22⋊C4—1424no—
602C22⋊C4—1428no—
603C22⋊C4—1422no—
604C22⋊C4—1424no—
605C22⋊C4—1422no—
606C42—24no—
607C42—44no—
608C42—2844no—
609C42—2844no—
610C42—2844no—
611C42—1428no—
612C42—1424no—
613C23—22no—
614C23—22no—
615C23—712no—
616C23—712no—
617C23—714no—
618C23—714no—
619C23—1428no—
620C23—1428no—
621C23—14216no—
622C23—14216no—
623C23—1422no—
624C23—1422no—
625C23—1421no—
626C23—1421no—
627C23—1421no—
628C23—1421no—
629C23—1428no—
630C23C22×C4×D7112yes—
631C23#1455617512yes—
632C23#1455617612yes—
633C23C24×D7111yescharacteristic
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—2848no—
649C2×C4—2848no—
650C2×C4—2848no—
651C2×C4—712no—
652C2×C4—714no—
653C2×C4—7116no—
654C2×C4—712no—
655C2×C4—714no—
656C2×C4—714no—
657C2×C4—1428no—
658C2×C4—14216no—
659C2×C4—14216no—
660C2×C4—1428no—
661C2×C4—1422no—
662C2×C4—1424no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1424no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1424no—
669C2×C4—1422no—
670C2×C4—1428no—
671C2×C4—1422no—
672C2×C4—1424no—
673C2×C4—1424no—
674C2×C4—1428no—
675C2×C4C22×C4×D7112yes—
676C2×C4C22×C4×D7114yes—
677C2×C4C22×C4×D7114yes—
678C2×C4C22×C4×D7112yes—
679C2×C4#41×D7114yes—
680C22—22no—
681C22—22no—
682C22—24no—
683C22—24no—
684C22—714no—
685C22—714no—
686C22—14232no—
687C22—1422no—
688C22—1422no—
689C22—1422no—
690C22—1422no—
691C22—1424no—
692C22—1424no—
693C22—1424no—
694C22—1424no—
695C22#1798647514yes—
696C22C23×C4×D7111yescharacteristic
697C22C2×#41×D7112yes—
698C22H(5,𝔽2)×D7112yes—
699C22C2×#1455617511yescharacteristic
700C22C2×#1455617611yescharacteristic
701C4—22no—
702C4—24no—
703C4—24no—
704C4—42no—
705C4—44no—
706C4—42no—
707C4—2842no—
708C4—2844no—
709C4—2842no—
710C4—714no—
711C4—1422no—
712C4—1424no—
713C4—1424no—
714C4#117×D7114yes—
715C2—24no—
716C2—1424no—
717C2—1424no—
718C2C2×#117×D7111yescharacteristic
719C2#518×D7111yescharacteristic
720C2C2×#1798647511yescharacteristic
721C2#2260204412yes—
722C2#2260204812yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2345C2
socle, cosocleC23×C71C25
prime radicalC24×D71C23
hypercenter#2345D71
hypocenterC71#34178
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #22591219C2semidirect
3. #22591218C2semidirect
4. #22591217C2semidirect
5. #22591215C2semidirect
6. #22591212C2semidirect
7. #22591208C2semidirect
8. #22591206C2semidirect
9. #22591205C2semidirect
10. #22590955C2semidirect
11. #22590939C2semidirect
16. #22590694C2semidirect
17. C71×#2345C2semidirect
26. C2×C4⋊C4×D71C4semidirect
33. #17985898C22semidirect
34. #17985897C22semidirect
35. #17985896C22semidirect
36. #17985895C22semidirect
37. #17985894C22semidirect
38. #17985886C22semidirect
39. #17985885C22semidirect
40. #17985884C22semidirect
41. #17985883C22semidirect
42. #17985882C22semidirect
43. #17985881C22semidirect
44. #17985880C22semidirect
62. C4⋊C4×Dic71C22semidirect
63. C4⋊C4×Dic71C22semidirect
64. C4×Dic71⋊C4C22semidirect
65. C4×C4⋊Dic71C22semidirect
66. #17985850C22semidirect
77. #389×C71C22semidirect
78. #387×C71C22semidirect
81. C4×C4⋊C4×C71C22semidirect
317. C4×D71#117semidirect
368. #2345D71semidirect
379. C71#34178semidirect
401. #389C2×D71semidirect
409. #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×C4⋊C4×D712
#225912192
#225912182
#225912172
#225912152
#225912122
#225912082
#225912062
#225912052
#225909552
#225909392
#225907222
#225907212
#225906942
C71×#23452
#3417871