Finite Group Databasebeta

← #32157635

Subgroups — #32157635

Order 18176.

2470 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11765866C211yesmaximal, characteristic
2#22591297C211yesmaximal, characteristic, complemented
3#22591272C212yesmaximal, complemented
4#22591266C212yesmaximal, complemented
5C4⋊C4×D284C211yesmaximal, characteristic, complemented
6#22591240C211yesmaximal, characteristic, complemented
7#22591221C212yesmaximal, complemented
8#22591195C214yesmaximal, complemented
9#22591169C212yesmaximal
10#22590985C212yesmaximal, complemented
11#22590972C214yesmaximal, complemented
12#22590745C211yesmaximal, characteristic, complemented
13#22590736C211yesmaximal, characteristic, complemented
14#22590736C212yesmaximal, complemented
15#382×D71C212yesmaximal, complemented
16#22590700C212yesmaximal, complemented
17C71×#2355C211yesmaximal, characteristic, complemented
18C22×#11765866C2211yescharacteristic
19C4×#11765866C4116yescomplemented
20C2×Q8×Dic71C2211yescharacteristic
21C2×C4×D284C2212yes—
22C2×C4×D284C2211yescharacteristic
23C2×C4×D284C2212yes—
24C2×#14556090C2212yes—
25C2×#14556090C2211yescharacteristic
26C2×#14556090C2212yes—
27C2×#14556086C2212yes—
28C2×#14556086C2212yes—
29C2×#14556086C2211yescharacteristic
30C2×C4⋊C4×D71C2212yes—
31C2×C4⋊C4×D71C2212yes—
32C2×C42×D71C2212yes—
33C2×C42×D71C2211yescharacteristic
34#17985906C2212yes—
35#17985897C2212yes—
36#17985895C2212yes—
37#17985890C2214yes—
38#17985888C2214yes—
39#17985885C2214yes—
40#17985884C2214yes—
41#17985882C2214yes—
42#17985877C2214yes—
43#17985877C2214yes—
44#17985873C2214yes—
45#17985870C2214yes—
46#17985869C2211yescharacteristic
47#17985866C2214yes—
48#17985866C2212yes—
49#17985865C2212yes—
50#17985864C2211yescharacteristic
51#17985864C2212yes—
52#17985864C2211yescharacteristic
53#17985863C2214yes—
54#17985863C2214yes—
55#17985861C2214yes—
56#17985861C2212yes—
57#17985856C2212yes—
58#17985856C2212yes—
59#17985856C2211yescharacteristic
60#17985856C2211yescharacteristic
61#17985856C2212yes—
62#17985856C2212yes—
63C4⋊C4×Dic71C2212yes—
64C4⋊C4×Dic71C2212yes—
65C4⋊C4×Dic71C2212yes—
66C4×C4⋊Dic71C2211yescharacteristic
67C4×C4⋊Dic71C2212yes—
68C4×(C2×D71)⋊C4C2212yes—
69C4×(C2×D71)⋊C4C2214yes—
70C4×(C2×D71)⋊C4C2214yes—
71#17985846C2214yes—
72#17985845C2212yes—
73#17985845C2214yes—
74#95×D71C2214yes—
75#95×D71C2214yes—
76C2×C4×Q8×C71C2211yescharacteristic
77#391×C71C2212yes—
78#387×C71C2214yes—
79#384×C71C2211yescharacteristic
80#382×C71C2212yes—
81C4×C4⋊C4×C71C2211yescharacteristic
82C4×C4⋊C4×C71C2212yes—
83C4×C4⋊C4×C71C2212yes—
84C2×#11765866—24no—
85C2×#11765866—24no—
86C2×#11765866C2×C418yes—
87C22×D284C2312yes—
88C22×D284C2311yescharacteristic
89C22×C4×D71C2312yes—
90C22×C4×D71C2311yescharacteristic
91C22×C4×D71C2312yes—
92C22×C4×D71C2311yescharacteristic
93C22×C4×D71C2314yes—
94C22×C4×D71C2314yes—
95C22×C4×D71C2312yes—
96C22×C4×D71C2311yescharacteristic
97Q8×Dic71C2×C418yescomplemented
98C4×D284—28no—
99C4×D284C2×C418yes—
100C4×D284C2×C4116yescomplemented
101#14556090—28no—
102#14556090C2×C418yes—
103#14556090C2×C4116yescomplemented
104#14556086—44no—
105#14556086C2×C418yescomplemented
106#14556086C2×C4116yescomplemented
107C2×C4⋊Dic71C2311yescharacteristic
108C2×C4⋊Dic71C2311yescharacteristic
109C2×C4⋊Dic71C2312yes—
110C2×C4⋊Dic71C2312yes—
111C2×C4⋊Dic71C2312yes—
112C2×C4⋊Dic71C2312yes—
113C2×C4⋊Dic71C2311yescharacteristic
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2314yes—
116C4⋊C4×D71—44no—
117C4⋊C4×D71—44no—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2312yes—
121C2×(C2×D71)⋊C4C2312yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2312yes—
124C2×(C2×D71)⋊C4C2312yes—
125C2×(C2×D71)⋊C4C2312yes—
126C2×C4×Dic71C2312yes—
127C2×C4×Dic71C2314yes—
128C2×C4×Dic71C2314yes—
129C2×C4×Dic71C2311yescharacteristic
130C2×C4×Dic71C2312yes—
131C2×C4×Dic71C2311yescharacteristic
132C2×C4×Dic71C2312yes—
133C2×C4×Dic71C2311yescharacteristic
134C42×D71C2×C418yescomplemented
135C42×D71C2×C4116yescomplemented
136C71⋊#95C2312yes—
137C71⋊#95C2312yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C71⋊#95C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2312yes—
143C71⋊#95C2312yes—
144C71⋊#95C2312yes—
145C71⋊#95C2312yes—
146C71⋊#95C2314yes—
147C71⋊#95C2314yes—
148C71⋊#95C2312yes—
149C71⋊#95C2314yes—
150C22×Q8×C71C2311yescharacteristic
151C4×Q8×C71C2×C418yescomplemented
152C2×C4⋊C4×C71C2312yes—
153C2×C4⋊C4×C71C2311yescharacteristic
154C2×C4⋊C4×C71C2311yescharacteristic
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2312yes—
157C2×C4⋊C4×C71C2311yescharacteristic
158C2×C4⋊C4×C71C2312yes—
159C2×C42×C71C2312yes—
160C2×C42×C71C2314yes—
161C2×C42×C71C2312yes—
162C2×C42×C71C2311yescharacteristic
163#95×C71C2314yes—
164#95×C71C2314yes—
165#95×C71C2312yes—
166#95×C71C2314yes—
167C23×D71C2411yescharacteristic
168C23×D71C2412yes—
169#11765866—232no—
170C2×D284—24no—
171C2×D284—24no—
172C2×D284C22×C418yes—
173C2×D284C22×C414yes—
174C2×D284#4114yes—
175C2×D284#4114yes—
176C22×Dic71C2412yes—
177C22×Dic71C2414yes—
178C22×Dic71C2412yes—
179C22×Dic71C2411yescharacteristic
180C22×Dic71C2411yescharacteristic
181C22×Dic71C2411yescharacteristic
182C22×Dic71C2412yes—
183C2×C4×D71—24no—
184C2×C4×D71—24no—
185C2×C4×D71—22no—
186C2×C4×D71—22no—
187C2×C4×D71—24no—
188C2×C4×D71—22no—
189C2×C4×D71—24no—
190C2×C4×D71—22no—
191C2×C4×D71—28no—
192C2×C4×D71—28no—
193C2×C4×D71—42no—
194C2×C4×D71—41no—
195C2×C4×D71—42no—
196C2×C4×D71—41no—
197C2×C4×D71—44no—
198C2×C4×D71—44no—
199C2×C4×D71—44no—
200C2×C4×D71—44no—
201C2×C4×D71C22×C418yes—
202C2×C4×D71C22×C414yes—
203C2×C4×D71C22×C418yes—
204C2×C4×D71C22×C414yes—
205C2×C4×D71C22×C418yes—
206C2×C4×D71C22×C414yes—
207C4⋊Dic71—24no—
208C4⋊Dic71—22no—
209C4⋊Dic71—24no—
210C4⋊Dic71—22no—
211C4⋊Dic71—42no—
212C4⋊Dic71C22×C414yes—
213C4⋊Dic71C22×C418yes—
214Dic71⋊C4—44no—
215Dic71⋊C4—44no—
216(C2×D71)⋊C4—28no—
217(C2×D71)⋊C4—28no—
218(C2×D71)⋊C4—42no—
219(C2×D71)⋊C4—42no—
220(C2×D71)⋊C4—44no—
221(C2×D71)⋊C4C22×C418yes—
222(C2×D71)⋊C4C22×C418yes—
223(C2×D71)⋊C4C22×C418yes—
224C4×Dic71—24no—
225C4×Dic71—44no—
226C4×Dic71—44no—
227C4×Dic71C22×C414yes—
228C4×Dic71C22×C418yes—
229C4×Dic71C22×C414yes—
230C4×Dic71C22×C414yes—
231C4×Dic71C22×C418yes—
232C2×Q8×C71—22no—
233C2×Q8×C71—22no—
234C2×Q8×C71C22×C414yes—
235C22×C4×C71C2412yes—
236C22×C4×C71C2414yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2411yescharacteristic
241C22×C4×C71C2411yescharacteristic
242C22×C4×C71C2411yescharacteristic
243C4⋊C4×C71—24no—
244C4⋊C4×C71—22no—
245C4⋊C4×C71—24no—
246C4⋊C4×C71—22no—
247C4⋊C4×C71—42no—
248C4⋊C4×C71C22×C414yes—
249C4⋊C4×C71C22×C418yes—
250C42×C71—24no—
251C42×C71—44no—
252C42×C71C22×C414yes—
253C42×C71C22×C418yes—
254C23×C71C2511yescharacteristic
255C22×D71—22no—
256C22×D71—22no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—21no—
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71C23×C412yes—
266C22×D71C23×C414yes—
267C22×D71C2×#4114yes—
268C22×D71C2×#4114yes—
269Q8×C71—28no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—21no—
274C2×C4×C71—22no—
275C2×C4×C71—21no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—24no—
279C2×C4×C71—24no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—24no—
284C2×C4×C71—22no—
285C2×C4×C71C23×C412yes—
286C2×C4×C71C23×C414yes—
287C2×C4×C71C23×C414yes—
288C2×C4×C71C23×C412yes—
289C2×C4×C71C23×C412yes—
290C2×C4×C71C2×#4112yes—
291C2×C4×C71C2×#4112yes—
292C2×C4×C71H(5,𝔽2)12yes—
293C2×C4×C712−1+412yes—
294C2×Dic71—21no—
295C2×Dic71—21no—
296C2×Dic71—21no—
297C2×Dic71—22no—
298C2×Dic71—21no—
299C2×Dic71—22no—
300C2×Dic71—21no—
301C2×Dic71—21no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—24no—
305C2×Dic71—24no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—24no—
310C2×Dic71—22no—
311C2×Dic71C23×C412yes—
312C2×Dic71C23×C412yes—
313C2×Dic71C23×C412yes—
314C2×Dic71C23×C414yes—
315D284—216no—
316D284#117116yescomplemented
317C4×D71—216no—
318C4×D71—28no—
319C4×D71—216no—
320C4×D71—28no—
321C4×D71—48no—
322C4×D71—44no—
323C4×D71—88no—
324C4×D71—88no—
325C22×C71C24×C411yescharacteristic
326C22×C71C22×#4111yescharacteristic
327C22×C71C22×#4111yescharacteristic
328C22×C71C2×H(5,𝔽2)11yescharacteristic
329C22×C71C2×2−1+411yescharacteristic
330C22×C71#58511yescharacteristic
331C22×C71#58511yescharacteristic
332C2×D71—24no—
333C2×D71—24no—
334C2×D71—24no—
335C2×D71—24no—
336C2×D71—24no—
337C2×D71—24no—
338C2×D71—22no—
339C2×D71—22no—
340C2×D71—22no—
341C2×D71—41no—
342C2×D71—41no—
343C2×D71—41no—
344C2×D71—41no—
345C2×D71C2×#11718yes—
346C4×C71—24no—
347C4×C71—24no—
348C4×C71—22no—
349C4×C71—42no—
350C4×C71—44no—
351C4×C71—42no—
352C4×C71C2×#11714yes—
353C4×C71#52014yes—
354Dic71—22no—
355Dic71—22no—
356Dic71—24no—
357Dic71—22no—
358Dic71—42no—
359Dic71—44no—
360Dic71—42no—
361#34191—711nomaximal, Sylow
362C2×C71C22×#11711yescharacteristic
363C2×C71C2×#52011yescharacteristic
364C2×C71#342811yescharacteristic
365C2×C71#351411yescharacteristic
366C2×C71#351411yescharacteristic
367C2×C71#351511yescharacteristic
368C2×C71#351511yescharacteristic
369D71—28no—
370D71—42no—
371C2×C4×#41—711no—
372#2355—711no—
373#2355D7111yescharacteristic, complemented
374#2352—712no—
375#2352—712no—
376D4×C4⋊C4—711no—
377D4×C4⋊C4—711no—
378#2346—712no—
379#2343—714no—
380#2339—712no—
381#2320—712no—
382#2318—714no—
383#2285—711no—
384#2283—711no—
385#2283—712no—
386C2×#382—712no—
387#2275—712no—
388C71#3419111yescharacteristic, complemented, Sylow
389C22×#41—711no—
390C4×#41—7116no—
391C2×C4×Q8—711no—
392C2×C4×Q8C2×D7111yescharacteristic
393C2×C4×D4—712no—
394C2×C4×D4—711no—
395C2×C4×D4—712no—
396C2×C4×D4—711no—
397C2×C4×D4—712no—
398C2×C4×D4—712no—
399C2×#117—712no—
400C2×#117—712no—
401C2×#117—711no—
402C22×C4⋊C4—712no—
403C22×C4⋊C4—712no—
404C22×C42—712no—
405C22×C42—711no—
406#391—712no—
407#391C2×D7112yes—
408#389—712no—
409#389—712no—
410#388—714no—
411#388—714no—
412#387—714no—
413#387—714no—
414#387—714no—
415#387C2×D7114yes—
416#386—714no—
417#386—714no—
418#385—714no—
419#385—714no—
420#384—711no—
421#384C2×D7111yescharacteristic
422#383—714no—
423#383—712no—
424#382—711no—
425#382—712no—
426#382—711no—
427#382—712no—
428#382—714no—
429#382—714no—
430#382C2×D7112yes—
431#381—712no—
432#381—714no—
433#380—712no—
434#380—712no—
435#380—712no—
436#380—712no—
437#380—711no—
438#380—711no—
439C4×C4⋊C4—712no—
440C4×C4⋊C4—712no—
441C4×C4⋊C4—712no—
442C4×C4⋊C4—711no—
443C4×C4⋊C4—712no—
444C4×C4⋊C4C2×D7112yes—
445C4×C4⋊C4C2×D7111yescharacteristic
446C4×C4⋊C4C2×D7112yes—
447C4×C22⋊C4—714no—
448C4×C22⋊C4—712no—
449C4×C22⋊C4—714no—
450C4×C22⋊C4—714no—
451#376—712no—
452#376—714no—
453C2×#95—714no—
454C2×#95—714no—
455C2×#41—718no—
456C2×#41—1424no—
457C2×#41—1424no—
458C22×Q8C22×D7111yescharacteristic
459C22×D4—711no—
460C22×D4—712no—
461C23×C4—712no—
462C23×C4—711no—
463C23×C4—714no—
464C23×C4—714no—
465C23×C4—712no—
466C23×C4—711no—
467C23×C4—712no—
468C23×C4—711no—
469C4×Q8—718no—
470C4×Q8C4×D7118yescomplemented
471C4×D4—718no—
472C4×D4—7116no—
473C4×D4—718no—
474C4×D4—7116no—
475C4×D4—1428no—
476C4×D4—1428no—
477#117—2844no—
478#117—7116no—
479#117—718no—
480C2×C4⋊C4—2844no—
481C2×C4⋊C4—2844no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—714no—
484C2×C4⋊C4—712no—
485C2×C4⋊C4—712no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—712no—
489C2×C4⋊C4—712no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7112yes—
493C2×C4⋊C4C22×D7112yes—
494C2×C4⋊C4C22×D7111yescharacteristic
495C2×C4⋊C4C22×D7112yes—
496C2×C4⋊C4C22×D7111yescharacteristic
497C2×C4⋊C4C22×D7112yes—
498C2×C22⋊C4—714no—
499C2×C22⋊C4—712no—
500C2×C22⋊C4—712no—
501C2×C22⋊C4—712no—
502C2×C22⋊C4—712no—
503C2×C22⋊C4—712no—
504C2×C22⋊C4—714no—
505C2×C22⋊C4—714no—
506C2×C42—714no—
507C2×C42—714no—
508C2×C42—712no—
509C2×C42—711no—
510C2×C42—711no—
511C2×C42—712no—
512C2×C42—711no—
513C2×C42—7116no—
514C2×C42—718no—
515C2×C42—712no—
516C2×C42C22×D7112yes—
517C2×C42C22×D7114yes—
518C2×C42C22×D7112yes—
519C2×C42C22×D7111yescharacteristic
520#95—712no—
521#95—712no—
522#95—714no—
523#95—714no—
524#95—714no—
525#95—714no—
526#95—712no—
527#95—712no—
528#95—712no—
529#95—712no—
530#95—714no—
531#95—714no—
532#95—712no—
533#95—714no—
534#95C22×D7114yes—
535#95C22×D7114yes—
536#95C22×D7112yes—
537#95C22×D7114yes—
538C24—712no—
539C24—711no—
540#41—14232no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C2×C4×D7114yes—
544C2×D4—714no—
545C2×D4—718no—
546C2×D4—714no—
547C2×D4—714no—
548C2×D4—1424no—
549C2×D4—1424no—
550C22×C4—2842no—
551C22×C4—2841no—
552C22×C4—2842no—
553C22×C4—2841no—
554C22×C4—2844no—
555C22×C4—2844no—
556C22×C4—2844no—
557C22×C4—2844no—
558C22×C4—718no—
559C22×C4—714no—
560C22×C4—711no—
561C22×C4—711no—
562C22×C4—711no—
563C22×C4—712no—
564C22×C4—718no—
565C22×C4—714no—
566C22×C4—718no—
567C22×C4—714no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—714no—
571C22×C4—1428no—
572C22×C4—1428no—
573C22×C4—1424no—
574C22×C4—1424no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1424no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1424no—
581C22×C4C23×D7112yes—
582C22×C4C23×D7112yes—
583C22×C4C23×D7114yes—
584C22×C4C23×D7112yes—
585C22×C4C23×D7112yes—
586C22×C4C23×D7111yescharacteristic
587C22×C4C23×D7111yescharacteristic
588C22×C4C23×D7111yescharacteristic
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—42no—
594C4⋊C4—2844no—
595C4⋊C4—2844no—
596C4⋊C4—2842no—
597C4⋊C4—718no—
598C4⋊C4—714no—
599C4⋊C4—1424no—
600C4⋊C4—1422no—
601C4⋊C4—1424no—
602C4⋊C4—1422no—
603C4⋊C4C2×C4×D7118yes—
604C4⋊C4C2×C4×D7114yes—
605C22⋊C4—2842no—
606C22⋊C4—2842no—
607C22⋊C4—2844no—
608C22⋊C4—718no—
609C22⋊C4—718no—
610C22⋊C4—718no—
611C22⋊C4—1428no—
612C22⋊C4—1428no—
613C42—24no—
614C42—44no—
615C42—2844no—
616C42—2844no—
617C42—714no—
618C42—718no—
619C42—714no—
620C42—718no—
621C42—714no—
622C42—1424no—
623C42C2×C4×D7118yes—
624C42C2×C4×D7114yes—
625C23—714no—
626C23—714no—
627C23—714no—
628C23—712no—
629C23—1421no—
630C23—1421no—
631C23—1421no—
632C23—1421no—
633C23—1421no—
634C23—1421no—
635C23—1422no—
636C23—1422no—
637C23—1422no—
638C23—1422no—
639C23C24×D7111yescharacteristic
640Q8—28no—
641D4—7116no—
642D4—14216no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—2844no—
659C2×C4—2848no—
660C2×C4—5688no—
661C2×C4—5688no—
662C2×C4—712no—
663C2×C4—712no—
664C2×C4—712no—
665C2×C4—714no—
666C2×C4—14216no—
667C2×C4—1422no—
668C2×C4—1422no—
669C2×C4—1424no—
670C2×C4—1424no—
671C2×C4—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4—1424no—
676C2×C4—1421no—
677C2×C4—1421no—
678C2×C4—1421no—
679C2×C4—1422no—
680C2×C4—1421no—
681C2×C4—1422no—
682C2×C4—1421no—
683C2×C4—1421no—
684C2×C4—1428no—
685C2×C4—1428no—
686C2×C4—14216no—
687C2×C4C22×C4×D7114yes—
688C2×C4C22×C4×D7112yes—
689C2×C4C22×C4×D7114yes—
690C2×C4C22×C4×D7112yes—
691C2×C4C22×C4×D7112yes—
692C2×C4#41×D7112yes—
693C2×C4#41×D7112yes—
694C2×C4#1455617412yes—
695C2×C4#1455617612yes—
696C22—2841no—
697C22—2841no—
698C22—2841no—
699C22—2841no—
700C22—718no—
701C22—1422no—
702C22—1422no—
703C22—1422no—
704C22—1424no—
705C22—1424no—
706C22—1424no—
707C22—1424no—
708C22—1424no—
709C22—1424no—
710C22C23×C4×D7111yescharacteristic
711C22C2×#41×D7111yescharacteristic
712C22C2×#41×D7111yescharacteristic
713C22C2×#1455617411yescharacteristic
714C22C2×#1455617611yescharacteristic
715C22#1798683411yescharacteristic
716C22#1798683611yescharacteristic
717C4—24no—
718C4—24no—
719C4—22no—
720C4—44no—
721C4—42no—
722C4—42no—
723C4—2842no—
724C4—2844no—
725C4—2842no—
726C4—1422no—
727C4—1422no—
728C4—1424no—
729C4—1422no—
730C4#117×D7114yes—
731C4#1798648114yes—
732C2—2842no—
733C2—1428no—
734C2C2×#117×D7111yescharacteristic
735C2C2×#1798648111yescharacteristic
736C2#2260154011yescharacteristic
737C2#2260230011yescharacteristic
738C2#2260230411yescharacteristic
739C2#2260231711yescharacteristic
740C2#2260232111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2355C2
socle, cosocleC23×C71C25
prime radicalC22×#11765866C22
hypercenter#2355D71
hypocenterC71#34191
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #22591297C2semidirect
3. #22591272C2semidirect
4. #22591266C2semidirect
5. C4⋊C4×D284C2semidirect
6. #22591240C2semidirect
7. #22591221C2semidirect
8. #22591195C2semidirect
10. #22590985C2semidirect
11. #22590972C2semidirect
12. #22590745C2semidirect
13. #22590736C2semidirect
14. #22590736C2semidirect
15. #382×D71C2semidirect
16. #22590700C2semidirect
17. C71×#2355C2semidirect
19. C4×#11765866C4semidirect
97. Q8×Dic71C2×C4semidirect
100. C4×D284C2×C4semidirect
103. #14556090C2×C4semidirect
105. #14556086C2×C4semidirect
106. #14556086C2×C4semidirect
134. C42×D71C2×C4semidirect
135. C42×D71C2×C4semidirect
151. C4×Q8×C71C2×C4semidirect
316. D284#117semidirect
373. #2355D71semidirect
388. C71#34191semidirect
470. C4×Q8C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117658662
#225912972
#225912722
#225912662
C4⋊C4×D2842
#225912402
#225912212
#225911952
#225911692
#225909852
#225909722
#225907452
#225907362
#382×D712
#225907002
C71×#23552
#3419171