Finite Group Databasebeta

← #32157666

Subgroups — #32157666

Order 18176.

3014 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D71C211yesmaximal, characteristic
2#22591288C212yesmaximal, complemented
3#22591268C214yesmaximal, complemented
4#22591241C212yesmaximal, complemented
5#22591216C212yesmaximal, complemented
6#22591184C214yesmaximal, complemented
7#22591161C212yesmaximal
8#22590983C211yesmaximal, characteristic, complemented
9#22590975C212yesmaximal, complemented
10#22590969C212yesmaximal, complemented
11#22590744C211yesmaximal, characteristic, complemented
12#22590732C211yesmaximal, characteristic, complemented
13#22590720C212yesmaximal, complemented
14#380×D71C212yesmaximal, complemented
15#22590702C211yesmaximal, characteristic, complemented
16#22590700C211yesmaximal, characteristic, complemented
17C71×#2319C211yesmaximal, characteristic, complemented
18C22×D4×D71C2211yescharacteristic
19C23×C4×D71C2212yes—
20C2×C4×D284C2212yes—
21C2×C4×D284C2211yescharacteristic
22C2×D4×Dic71C2211yescharacteristic
23C2×#14556090C2212yes—
24C2×#14556090C2211yescharacteristic
25C2×C4×C22⋊D71C2212yes—
26C2×(C22⋊D71)⋊C4C2212yes—
27C4×D4×D71C4116yescomplemented
28C2×#14556085C2212yes—
29C2×#14556084C2214yescomplemented
30C2×C4⋊C4×D71C2211yescharacteristic
31C2×C4⋊C4×D71C2214yescomplemented
32C2×C22⋊C4×D71C2214yes—
33C2×C22⋊C4×D71C2212yes—
34C2×C42×D71C2211yescharacteristic
35#17985902C2212yes—
36#17985898C2212yescomplemented
37#17985893C2214yescomplemented
38#17985892C2214yescomplemented
39#17985887C2214yescomplemented
40#17985886C2214yescomplemented
41#17985880C2214yescomplemented
42#17985875C2214yes—
43#17985875C2214yes—
44#17985873C2214yescomplemented
45#17985870C2214yescomplemented
46#17985868C2212yescomplemented
47#17985866C2211yescharacteristic, complemented
48#17985866C2211yescharacteristic, complemented
49#17985863C2212yescomplemented
50#17985863C2212yescomplemented
51#17985862C2212yescomplemented
52#17985861C2212yes—
53#17985859C2212yescomplemented
54#17985858C2211yescharacteristic
55#17985858C2212yes—
56#17985858C2211yescharacteristic
57#17985858C2214yescomplemented
58#17985857C2214yescomplemented
59#17985856C2212yes—
60#17985856C2214yes—
61#17985854C2214yes—
62C4⋊C4×Dic71C2212yescomplemented
63C4×Dic71⋊C4C2212yescomplemented
64C4×Dic71⋊C4C2212yescomplemented
65C4×C4⋊Dic71C2211yescharacteristic, complemented
66C4×C4⋊Dic71C2212yescomplemented
67C4×(C2×D71)⋊C4C2212yes—
68C4×(C2×D71)⋊C4C2214yescomplemented
69#17985846C2214yes—
70#17985846C2212yescomplemented
71#17985846C2212yescomplemented
72#17985846C2214yescomplemented
73#17985845C2211yescharacteristic, complemented
74#95×D71C2212yescomplemented
75#95×D71C2212yescomplemented
76C2×C4×D4×C71C2211yescharacteristic
77#390×C71C2212yes—
78#389×C71C2212yescomplemented
79#388×C71C2214yescomplemented
80#381×C71C2212yescomplemented
81#380×C71C2212yescomplemented
82C4×C4⋊C4×C71C2211yescharacteristic, complemented
83#376×C71C2211yescharacteristic, complemented
84C24×D71C2312yes—
85C22×D284C2311yescharacteristic
86C22×C22⋊D71C2312yes—
87C2×D4×D71—28no—
88C2×D4×D71C2×C418yes—
89C23×Dic71C2312yes—
90C22×C4×D71—48no—
91C22×C4×D71C2×C4116yescomplemented
92C22×C4×D71C2311yescharacteristic
93C22×C4×D71C2312yes—
94C22×C4×D71C2311yescharacteristic
95C22×C4×D71C2311yescharacteristic
96C22×C4×D71C2314yes—
97C22×C4×D71C2314yes—
98C22×C4×D71C2312yes—
99C22×C4×D71C2312yes—
100C4×D284—28no—
101C4×D284C2×C418yes—
102D4×Dic71C2×C418yescomplemented
103#14556090—28no—
104#14556090C2×C418yes—
105C4×C22⋊D71C2×C4116yescomplemented
106(C22⋊D71)⋊C4C2×C4116yescomplemented
107#14556085—44no—
108#14556084—48no—
109C2×C4⋊Dic71C2312yes—
110C2×C4⋊Dic71C2314yes—
111C2×C4⋊Dic71C2311yescharacteristic
112C2×Dic71⋊C4C2312yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2312yes—
115C2×Dic71⋊C4C2314yes—
116C2×Dic71⋊C4C2312yes—
117C4⋊C4×D71—48no—
118C4⋊C4×D71C2×C418yescomplemented
119C2×C22⋊Dic71C2314yes—
120C2×C22⋊Dic71C2314yes—
121C2×C22⋊Dic71C2312yes—
122C2×(C2×D71)⋊C4C2312yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2312yes—
127C2×(C2×D71)⋊C4C2312yes—
128C2×(C2×D71)⋊C4C2312yes—
129C22⋊C4×D71—48no—
130C22⋊C4×D71C2×C4116yescomplemented
131C2×C4×Dic71C2312yes—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2312yes—
135C2×C4×Dic71C2311yescharacteristic
136C2×C4×Dic71C2311yescharacteristic
137C2×C4×Dic71C2311yescharacteristic
138C42×D71C2×C418yescomplemented
139C71⋊#95C2311yescharacteristic
140C71⋊#95C2314yes—
141C71⋊#95C2312yes—
142C71⋊#95C2314yes—
143C71⋊#95C2311yescharacteristic
144C71⋊#95C2312yes—
145C71⋊#95C2314yes—
146C71⋊#95C2312yes—
147C71⋊#95C2312yes—
148C71⋊#95C2314yes—
149C71⋊#95C2312yes—
150C71⋊#95C2312yes—
151C22×D4×C71C2311yescharacteristic
152C23×C4×C71C2312yes—
153C4×D4×C71C2×C418yescomplemented
154C2×C4⋊C4×C71C2312yes—
155C2×C4⋊C4×C71C2314yes—
156C2×C4⋊C4×C71C2311yescharacteristic
157C2×C22⋊C4×C71C2314yes—
158C2×C22⋊C4×C71C2314yes—
159C2×C22⋊C4×C71C2312yes—
160C2×C42×C71C2312yes—
161C2×C42×C71C2312yes—
162C2×C42×C71C2311yescharacteristic
163#95×C71C2311yescharacteristic
164#95×C71C2312yes—
165#95×C71C2314yes—
166#95×C71C2311yescharacteristic
167#95×C71C2312yes—
168C23×D71—28no—
169C23×D71—24no—
170C23×D71—24no—
171C23×D71—44no—
172C23×D71C22×C418yes—
173C23×D71C2412yes—
174C23×D71C2411yescharacteristic
175C2×D284C22×C414yes—
176C2×D284#4118yes—
177C2×C22⋊D71—28no—
178C2×C22⋊D71C22×C418yes—
179D4×D71—232no—
180C22×Dic71—28no—
181C22×Dic71C22×C418yes—
182C22×Dic71C2412yes—
183C22×Dic71C2414yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2411yescharacteristic
187C22×Dic71C2411yescharacteristic
188C22×Dic71C2411yescharacteristic
189C2×C4×D71—22no—
190C2×C4×D71—22no—
191C2×C4×D71—24no—
192C2×C4×D71—24no—
193C2×C4×D71—28no—
194C2×C4×D71—28no—
195C2×C4×D71—28no—
196C2×C4×D71—432no—
197C2×C4×D71—44no—
198C2×C4×D71—44no—
199C2×C4×D71—44no—
200C2×C4×D71—44no—
201C2×C4×D71—44no—
202C2×C4×D71—44no—
203C2×C4×D71C22×C414yes—
204C2×C4×D71C22×C418yes—
205C2×C4×D71C22×C414yes—
206C2×C4×D71C22×C414yes—
207C2×C4×D71C22×C418yes—
208C2×C4×D71C22×C418yes—
209C4⋊Dic71—24no—
210C4⋊Dic71—44no—
211C4⋊Dic71C22×C414yes—
212Dic71⋊C4—24no—
213Dic71⋊C4—28no—
214Dic71⋊C4—24no—
215Dic71⋊C4—44no—
216Dic71⋊C4C22×C418yes—
217C22⋊Dic71—44no—
218C22⋊Dic71—44no—
219C22⋊Dic71C22×C418yes—
220(C2×D71)⋊C4—28no—
221(C2×D71)⋊C4—28no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—28no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4C22×C418yes—
226(C2×D71)⋊C4C22×C418yes—
227C4×Dic71—24no—
228C4×Dic71—44no—
229C4×Dic71—44no—
230C4×Dic71—42no—
231C4×Dic71C22×C414yes—
232C4×Dic71C22×C414yes—
233C4×Dic71C22×C414yes—
234C24×C71C2412yes—
235C2×D4×C71—24no—
236C2×D4×C71C22×C414yes—
237C22×C4×C71—44no—
238C22×C4×C71C22×C418yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2414yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2411yescharacteristic
243C22×C4×C71C2412yes—
244C22×C4×C71C2411yescharacteristic
245C22×C4×C71C2411yescharacteristic
246C4⋊C4×C71—24no—
247C4⋊C4×C71—44no—
248C4⋊C4×C71C22×C414yes—
249C22⋊C4×C71—44no—
250C22⋊C4×C71—44no—
251C22⋊C4×C71C22×C418yes—
252C42×C71—24no—
253C42×C71—42no—
254C42×C71C22×C414yes—
255C23×C71—24no—
256C23×C71—22no—
257C23×C71—24no—
258C23×C71—22no—
259C23×C71C23×C414yes—
260C23×C71C2511yescharacteristic
261C22×D71—22no—
262C22×D71—24no—
263C22×D71—22no—
264C22×D71—22no—
265C22×D71—22no—
266C22×D71—216no—
267C22×D71—216no—
268C22×D71—48no—
269C22×D71—416no—
270C22×D71—416no—
271C22×D71C23×C414yes—
272C22×D71C23×C412yes—
273C22×D71C2×#4118yes—
274C22×D71H(5,𝔽2)12yes—
275C22×D712−1+412yes—
276D4×C71—28no—
277C2×C4×C71—21no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—21no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—24no—
284C2×C4×C71—24no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—24no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—48no—
291C2×C4×C71C23×C412yes—
292C2×C4×C71C23×C412yes—
293C2×C4×C71C23×C414yes—
294C2×C4×C71C23×C412yes—
295C2×C4×C71C2×#4114yes—
296C22⋊D71—216no—
297C2×Dic71—22no—
298C2×Dic71—24no—
299C2×Dic71—21no—
300C2×Dic71—21no—
301C2×Dic71—216no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—24no—
305C2×Dic71—22no—
306C2×Dic71—24no—
307C2×Dic71—24no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71C23×C412yes—
312C2×Dic71C23×C412yes—
313C2×Dic71C23×C414yes—
314C2×Dic71C23×C412yes—
315C2×Dic71H(5,𝔽2)14yes—
316D284#117116yescomplemented
317C4×D71—28no—
318C4×D71—28no—
319C4×D71—28no—
320C4×D71—216no—
321C4×D71—48no—
322C4×D71—48no—
323C4×D71—88no—
324C4×D71—88no—
325C22×C71—24no—
326C22×C71—24no—
327C22×C71—24no—
328C22×C71—44no—
329C22×C71—44no—
330C22×C71C24×C411yescharacteristic
331C22×C71C22×#4112yes—
332C22×C71C2×H(5,𝔽2)12yes—
333C22×C71C2×H(5,𝔽2)11yescharacteristic
334C22×C71C2×2−1+411yescharacteristic
335C2×D71—22no—
336C2×D71—22no—
337C2×D71—24no—
338C2×D71—24no—
339C2×D71—28no—
340C2×D71—24no—
341C2×D71—24no—
342C2×D71—28no—
343C2×D71—432no—
344C2×D71C2×#11718yes—
345C2×D71#52014yes—
346C4×C71—22no—
347C4×C71—24no—
348C4×C71—22no—
349C4×C71—42no—
350C4×C71—44no—
351C4×C71—42no—
352C4×C71C2×#11714yes—
353Dic71—22no—
354Dic71—24no—
355Dic71—22no—
356Dic71—42no—
357Dic71—44no—
358Dic71—42no—
359Dic71#51814yes—
360#34194—711nomaximal, Sylow
361C2×C71—44no—
362C2×C71C22×#11711yescharacteristic
363C2×C71C2×#51811yescharacteristic
364C2×C71C2×#52011yescharacteristic
365C2×C71#351912yes—
366C2×C71#352012yes—
367D71—24no—
368D71—28no—
369C22×C4×D4—711no—
370#2354—712no—
371#2352—714no—
372D4×C4⋊C4—712no—
373#2345—712no—
374#2342—714no—
375D4×C22⋊C4—712no—
376#2319—711no—
377#2319D7111yescharacteristic, complemented
378#2318—712no—
379#2318—712no—
380#2285—711no—
381#2283—711no—
382#2280—712no—
383C2×#380—712no—
384#2275—711no—
385#2275—711no—
386C71#3419411yescharacteristic, complemented, Sylow
387C23×D4—711no—
388C24×C4—712no—
389C2×C4×D4—711no—
390C2×C4×D4—712no—
391C2×C4×D4—7116no—
392C2×C4×D4—711no—
393C2×C4×D4—712no—
394C2×C4×D4—712no—
395C2×C4×D4—711no—
396C2×C4×D4—712no—
397C2×C4×D4C2×D7111yescharacteristic
398C2×#117—714no—
399C2×#117—712no—
400C22×C4⋊C4—714no—
401C22×C4⋊C4—711no—
402C22×C22⋊C4—714no—
403C22×C22⋊C4—712no—
404C22×C42—711no—
405#390—712no—
406#390C2×D7112yes—
407#389—712no—
408#389C2×D7112yescomplemented
409#388—714no—
410#388—714no—
411#388—714no—
412#388C2×D7114yescomplemented
413#387—714no—
414#387—714no—
415#386—714no—
416#386—714no—
417#385—714no—
418#385—714no—
419#384—712no—
420#383—711no—
421#383—711no—
422#382—712no—
423#382—712no—
424#381—712no—
425#381—712no—
426#381C2×D7112yescomplemented
427#380—712no—
428#380—712no—
429#380—714no—
430#380—714no—
431#380—714no—
432#380—711no—
433#380—712no—
434#380—711no—
435#380C2×D7112yescomplemented
436#379—714no—
437C4×C4⋊C4—712no—
438C4×C4⋊C4—711no—
439C4×C4⋊C4—712no—
440C4×C4⋊C4—712no—
441C4×C4⋊C4—712no—
442C4×C4⋊C4C2×D7111yescharacteristic, complemented
443C4×C22⋊C4—712no—
444C4×C22⋊C4—714no—
445C4×C22⋊C4—712no—
446C4×C22⋊C4—712no—
447C4×C22⋊C4—714no—
448C4×C22⋊C4—714no—
449#376—711no—
450#376C2×D7111yescharacteristic, complemented
451C2×#95—712no—
452C2×#95—712no—
453C25—712no—
454C22×D4—712no—
455C22×D4—718no—
456C22×D4—711no—
457C22×D4—1428no—
458C22×D4C22×D7111yescharacteristic
459C23×C4—2848no—
460C23×C4—7116no—
461C23×C4—712no—
462C23×C4—712no—
463C23×C4—714no—
464C23×C4—714no—
465C23×C4—712no—
466C23×C4—711no—
467C23×C4—712no—
468C23×C4—711no—
469C23×C4—711no—
470C23×C4C22×D7112yes—
471C4×D4—718no—
472C4×D4—7116no—
473C4×D4—718no—
474C4×D4—7116no—
475C4×D4—718no—
476C4×D4—1428no—
477C4×D4—1428no—
478C4×D4C4×D7118yescomplemented
479#117—2844no—
480#117—2848no—
481C2×C4⋊C4—2848no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—714no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—712no—
486C2×C4⋊C4—718no—
487C2×C4⋊C4—712no—
488C2×C4⋊C4—714no—
489C2×C4⋊C4—712no—
490C2×C4⋊C4—712no—
491C2×C4⋊C4C22×D7112yes—
492C2×C4⋊C4C22×D7114yes—
493C2×C4⋊C4C22×D7111yescharacteristic
494C2×C22⋊C4—2848no—
495C2×C22⋊C4—714no—
496C2×C22⋊C4—714no—
497C2×C22⋊C4—712no—
498C2×C22⋊C4—712no—
499C2×C22⋊C4—712no—
500C2×C22⋊C4—7116no—
501C2×C22⋊C4—712no—
502C2×C22⋊C4—714no—
503C2×C22⋊C4—714no—
504C2×C22⋊C4—714no—
505C2×C22⋊C4—712no—
506C2×C22⋊C4C22×D7114yes—
507C2×C22⋊C4C22×D7114yes—
508C2×C22⋊C4C22×D7112yes—
509C2×C42—714no—
510C2×C42—714no—
511C2×C42—712no—
512C2×C42—711no—
513C2×C42—711no—
514C2×C42—711no—
515C2×C42—718no—
516C2×C42—712no—
517C2×C42C22×D7112yes—
518C2×C42C22×D7112yes—
519C2×C42C22×D7111yescharacteristic
520#95—711no—
521#95—712no—
522#95—714no—
523#95—714no—
524#95—711no—
525#95—712no—
526#95—714no—
527#95—712no—
528#95—712no—
529#95—714no—
530#95—712no—
531#95—712no—
532#95C22×D7111yescharacteristic
533#95C22×D7112yes—
534#95C22×D7111yescharacteristic
535#95C22×D7112yes—
536#95C22×D7114yes—
537C24—2844no—
538C24—718no—
539C24—711no—
540C24—712no—
541C24—1424no—
542C24—1428no—
543C24—1424no—
544C24C23×D7112yes—
545C2×D4—24no—
546C2×D4—718no—
547C2×D4—714no—
548C2×D4—718no—
549C2×D4—14232no—
550C2×D4—1428no—
551C2×D4C2×C4×D7114yes—
552C22×C4—44no—
553C22×C4—2844no—
554C22×C4—2844no—
555C22×C4—2844no—
556C22×C4—2844no—
557C22×C4—2844no—
558C22×C4—2844no—
559C22×C4—28432no—
560C22×C4—718no—
561C22×C4—718no—
562C22×C4—711no—
563C22×C4—718no—
564C22×C4—711no—
565C22×C4—712no—
566C22×C4—711no—
567C22×C4—714no—
568C22×C4—714no—
569C22×C4—714no—
570C22×C4—718no—
571C22×C4—712no—
572C22×C4—712no—
573C22×C4—714no—
574C22×C4—1428no—
575C22×C4—1428no—
576C22×C4—1428no—
577C22×C4—1424no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1428no—
581C22×C4—1424no—
582C22×C4C2×C4×D7118yes—
583C22×C4C23×D7112yes—
584C22×C4C23×D7112yes—
585C22×C4C23×D7114yes—
586C22×C4C23×D7111yescharacteristic
587C22×C4C23×D7111yescharacteristic
588C22×C4C23×D7112yes—
589C22×C4C23×D7111yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—44no—
592C4⋊C4—2844no—
593C4⋊C4—2844no—
594C4⋊C4—718no—
595C4⋊C4—714no—
596C4⋊C4—1424no—
597C4⋊C4—1428no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C4⋊C4C2×C4×D7114yes—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—2844no—
604C22⋊C4—2844no—
605C22⋊C4—718no—
606C22⋊C4—718no—
607C22⋊C4—718no—
608C22⋊C4—1424no—
609C22⋊C4—1428no—
610C22⋊C4—1424no—
611C22⋊C4—1428no—
612C22⋊C4—1428no—
613C22⋊C4C2×C4×D7118yes—
614C42—24no—
615C42—42no—
616C42—2842no—
617C42—2844no—
618C42—2844no—
619C42—714no—
620C42—714no—
621C42—714no—
622C42—1424no—
623C42C2×C4×D7114yes—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—2848no—
629C23—28416no—
630C23—28416no—
631C23—714no—
632C23—712no—
633C23—718no—
634C23—712no—
635C23—712no—
636C23—14216no—
637C23—14216no—
638C23—1422no—
639C23—1422no—
640C23—1424no—
641C23—1422no—
642C23—1422no—
643C23C22×C4×D7114yes—
644C23C24×D7111yescharacteristic
645D4—28no—
646D4—7116no—
647D4—14216no—
648C2×C4—21no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—48no—
662C2×C4—2848no—
663C2×C4—2848no—
664C2×C4—5688no—
665C2×C4—5688no—
666C2×C4—712no—
667C2×C4—714no—
668C2×C4—712no—
669C2×C4—712no—
670C2×C4—714no—
671C2×C4—1428no—
672C2×C4—14216no—
673C2×C4—1428no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4—1424no—
677C2×C4—1422no—
678C2×C4—1424no—
679C2×C4—1424no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—14216no—
684C2×C4—1422no—
685C2×C4—1424no—
686C2×C4—1421no—
687C2×C4—1421no—
688C2×C4—1428no—
689C2×C4C22×C4×D7112yes—
690C2×C4C22×C4×D7112yes—
691C2×C4C22×C4×D7114yes—
692C2×C4C22×C4×D7112yes—
693C2×C4#41×D7114yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—44no—
698C22—44no—
699C22—28432no—
700C22—718no—
701C22—714no—
702C22—1422no—
703C22—1422no—
704C22—1424no—
705C22—1424no—
706C22—1428no—
707C22—1424no—
708C22—1424no—
709C22—1428no—
710C22C23×C4×D7111yescharacteristic
711C22C2×#41×D7112yes—
712C22H(5,𝔽2)×D7112yes—
713C22H(5,𝔽2)×D7111yescharacteristic
714C222−1+4×D7111yescharacteristic
715C4—22no—
716C4—24no—
717C4—22no—
718C4—42no—
719C4—44no—
720C4—42no—
721C4—2842no—
722C4—2844no—
723C4—2842no—
724C4—714no—
725C4—1422no—
726C4—1424no—
727C4—1422no—
728C4#117×D7114yes—
729C2—44no—
730C2—1424no—
731C2—1428no—
732C2C2×#117×D7111yescharacteristic
733C2#518×D7111yescharacteristic
734C2#520×D7111yescharacteristic
735C2#2260237012yes—
736C2#2260238712yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2319C2
socle, cosocleC23×C71C25
prime radicalC22×D4×D71C22
hypercenter#2319D71
hypocenterC71#34194
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #22591288C2semidirect
3. #22591268C2semidirect
4. #22591241C2semidirect
5. #22591216C2semidirect
6. #22591184C2semidirect
8. #22590983C2semidirect
9. #22590975C2semidirect
10. #22590969C2semidirect
11. #22590744C2semidirect
12. #22590732C2semidirect
13. #22590720C2semidirect
14. #380×D71C2semidirect
15. #22590702C2semidirect
16. #22590700C2semidirect
17. C71×#2319C2semidirect
27. C4×D4×D71C4semidirect
29. C2×#14556084C22semidirect
31. C2×C4⋊C4×D71C22semidirect
36. #17985898C22semidirect
37. #17985893C22semidirect
38. #17985892C22semidirect
39. #17985887C22semidirect
40. #17985886C22semidirect
41. #17985880C22semidirect
44. #17985873C22semidirect
45. #17985870C22semidirect
46. #17985868C22semidirect
47. #17985866C22semidirect
48. #17985866C22semidirect
49. #17985863C22semidirect
50. #17985863C22semidirect
51. #17985862C22semidirect
53. #17985859C22semidirect
57. #17985858C22semidirect
58. #17985857C22semidirect
62. C4⋊C4×Dic71C22semidirect
63. C4×Dic71⋊C4C22semidirect
64. C4×Dic71⋊C4C22semidirect
65. C4×C4⋊Dic71C22semidirect
66. C4×C4⋊Dic71C22semidirect
68. C4×(C2×D71)⋊C4C22semidirect
70. #17985846C22semidirect
71. #17985846C22semidirect
72. #17985846C22semidirect
73. #17985845C22semidirect
74. #95×D71C22semidirect
75. #95×D71C22semidirect
78. #389×C71C22semidirect
79. #388×C71C22semidirect
80. #381×C71C22semidirect
81. #380×C71C22semidirect
82. C4×C4⋊C4×C71C22semidirect
83. #376×C71C22semidirect
91. C22×C4×D71C2×C4semidirect
102. D4×Dic71C2×C4semidirect
105. C4×C22⋊D71C2×C4semidirect
106. (C22⋊D71)⋊C4C2×C4semidirect
118. C4⋊C4×D71C2×C4semidirect
130. C22⋊C4×D71C2×C4semidirect
138. C42×D71C2×C4semidirect
153. C4×D4×C71C2×C4semidirect
316. D284#117semidirect
377. #2319D71semidirect
386. C71#34194semidirect
408. #389C2×D71semidirect
412. #388C2×D71semidirect
426. #381C2×D71semidirect
435. #380C2×D71semidirect
442. C4×C4⋊C4C2×D71semidirect
450. #376C2×D71semidirect
478. C4×D4C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D712
#225912882
#225912682
#225912412
#225912162
#225911842
#225911612
#225909832
#225909752
#225909692
#225907442
#225907322
#225907202
#380×D712
#225907022
#225907002
C71×#23192
#3419471