Finite Group Databasebeta

← C2×#22592907 #32166429

Subgroups — C2×#22592907 #32166429

Order 18176.

2658 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22592907C2116yesmaximal, direct product factor
2C2×C71⋊#401C211yesmaximal, characteristic, complemented
3C2×#17985940C211yesmaximal, characteristic, complemented
4C2×#17985928C211yesmaximal, characteristic, complemented
5C2×#17985926C211yesmaximal, characteristic, complemented
6C2×#17985890C211yesmaximal, characteristic, complemented
7C2×#17985888C211yesmaximal, characteristic, complemented
8C2×#17985886C211yesmaximal, characteristic, complemented
9C2×#17985877C211yesmaximal, characteristic
10C2×#17985877C211yesmaximal, characteristic
11C2×#17985877C211yesmaximal, characteristic
12C2×#17985873C211yesmaximal, characteristic, complemented
13C2×#17985858C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
15C2×#95×D71C211yesmaximal, characteristic, complemented
16C2×#383×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C22×C4⋊Dic71C2211yescharacteristic
22C22×Dic71⋊C4C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×(C2×D71)⋊C4C2211yescharacteristic
26C22×(C2×D71)⋊C4C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35C71⋊#401C2218yescomplemented
36#17985940C2218yescomplemented
37#17985928C2218yescomplemented
38#17985926C2218yescomplemented
39#17985890C2218yescomplemented
40#17985888C2218yescomplemented
41#17985886C2218yescomplemented
42#17985877C2218yes—
43#17985877C2218yes—
44#17985877C2218yes—
45#17985873C2218yescomplemented
46#17985858C2218yescomplemented
47C4×(C2×D71)⋊C4C2218yescomplemented
48C2×C71⋊#95C2211yescharacteristic
49C2×C71⋊#95C2211yescharacteristic
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58#95×D71C2218yescomplemented
59C22×C42×C71C2211yescharacteristic
60#383×C71C2218yescomplemented
61C2×#95×C71C2211yescharacteristic
62C2×#95×C71C2211yescharacteristic
63C2×#95×C71C2211yescharacteristic
64C2×#95×C71C2211yescharacteristic
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C24×D71C2311yescharacteristic
68C24×D71C2311yescharacteristic
69C22×D284—24no—
70C22×D284—24no—
71C22×D284—24no—
72C22×D284C2314yes—
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C22×C4×D71—24no—
80C22×C4×D71—24no—
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71—42no—
85C22×C4×D71—42no—
86C22×C4×D71—42no—
87C22×C4×D71—42no—
88C22×C4×D71C2314yes—
89C22×C4×D71C2314yes—
90C22×C4×D71C2314yes—
91C2×C4⋊Dic71—42no—
92C2×C4⋊Dic71C2314yes—
93C2×Dic71⋊C4—24no—
94C2×Dic71⋊C4—42no—
95C2×Dic71⋊C4—42no—
96C2×Dic71⋊C4C2314yes—
97C2×Dic71⋊C4C2314yes—
98C2×Dic71⋊C4C2314yes—
99C2×(C2×D71)⋊C4—24no—
100C2×(C2×D71)⋊C4—24no—
101C2×(C2×D71)⋊C4—24no—
102C2×(C2×D71)⋊C4—24no—
103C2×(C2×D71)⋊C4—24no—
104C2×(C2×D71)⋊C4—42no—
105C2×(C2×D71)⋊C4—42no—
106C2×(C2×D71)⋊C4—42no—
107C2×(C2×D71)⋊C4—42no—
108C2×(C2×D71)⋊C4C2314yes—
109C2×(C2×D71)⋊C4C2314yes—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×C4×Dic71—42no—
118C2×C4×Dic71C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C23×C4×C71C2311yescharacteristic
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C2×C42×C71—24no—
137C2×C42×C71C2314yes—
138#95×C71C2314yes—
139#95×C71C2314yes—
140#95×C71C2314yes—
141#95×C71C2314yes—
142#95×C71C2314yes—
143#95×C71C2314yes—
144C23×D71—22no—
145C23×D71—22no—
146C23×D71—22no—
147C23×D71—22no—
148C23×D71—22no—
149C23×D71—22no—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71#4114yes—
156C23×D71#4114yes—
157C23×D71#4114yes—
158C23×D71C2412yes—
159C23×D71C2412yes—
160C2×D284—28no—
161C2×D284—28no—
162C2×D284—28no—
163C2×D284—416no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71#4114yes—
182C22×Dic71C2412yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C2×C4×D71—28no—
189C2×C4×D71—28no—
190C2×C4×D71—28no—
191C2×C4×D71—28no—
192C2×C4×D71—28no—
193C2×C4×D71—44no—
194C2×C4×D71—44no—
195C2×C4×D71—44no—
196C2×C4×D71—44no—
197C2×C4×D71—416no—
198C2×C4×D71—416no—
199C2×C4×D71—416no—
200C4⋊Dic71—44no—
201Dic71⋊C4—28no—
202Dic71⋊C4—44no—
203Dic71⋊C4—44no—
204(C2×D71)⋊C4—28no—
205(C2×D71)⋊C4—28no—
206(C2×D71)⋊C4—28no—
207(C2×D71)⋊C4—28no—
208(C2×D71)⋊C4—28no—
209(C2×D71)⋊C4—44no—
210(C2×D71)⋊C4—44no—
211(C2×D71)⋊C4—44no—
212(C2×D71)⋊C4—44no—
213C4×Dic71—44no—
214C24×C71C2411yescharacteristic
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71#4114yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C42×C71—28no—
244C23×C71C2×#4112yes—
245C23×C71C2×#4112yes—
246C23×C71C2×#4112yes—
247C23×C71C2×#4112yes—
248C23×C71C2×#4112yes—
249C23×C71H(5,𝔽2)12yes—
250C23×C71H(5,𝔽2)12yes—
251C23×C71C2511yescharacteristic
252C22×D71—28no—
253C22×D71—28no—
254C22×D71—28no—
255C22×D71—28no—
256C22×D71—28no—
257C22×D71—28no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—22no—
264C22×D71—22no—
265C22×D71—22no—
266C22×D71—22no—
267C22×D71—22no—
268C22×D71—22no—
269C22×D71—44no—
270C22×D71—44no—
271C22×D71—44no—
272C22×D71—44no—
273C22×D71—44no—
274C22×D71—44no—
275C22×D71—44no—
276C22×D71#126116yes—
277C22×D71C2×#4114yes—
278C22×D71C2×#4114yes—
279C22×D71C2×#4114yes—
280C2×C4×C71—28no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—44no—
302C2×C4×C71—44no—
303C2×C4×C71—44no—
304C2×C4×C71—44no—
305C2×C4×C71—44no—
306C2×C4×C71—44no—
307C2×C4×C71C2×#4114yes—
308C2×Dic71—28no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—44no—
327C2×Dic71—44no—
328C2×Dic71—44no—
329C2×Dic71—44no—
330C2×Dic71—44no—
331C2×Dic71C2×#4114yes—
332D284—416no—
333C4×D71—416no—
334C4×D71—416no—
335C4×D71—416no—
336C22×C71C2×#12614yes—
337C22×C71#52914yes—
338C22×C71#53814yes—
339C22×C71#55114yes—
340C22×C71#55114yes—
341C22×C71#55314yes—
342C22×C71#55314yes—
343C22×C71C22×#4111yescharacteristic
344C22×C71C22×#4111yescharacteristic
345C22×C71C22×#4111yescharacteristic
346C22×C71C22×#4111yescharacteristic
347C22×C71C22×#4111yescharacteristic
348C22×C71C2×H(5,𝔽2)11yescharacteristic
349C22×C71C2×H(5,𝔽2)11yescharacteristic
350C2×D71—24no—
351C2×D71—24no—
352C2×D71—24no—
353C2×D71—24no—
354C2×D71—24no—
355C2×D71—24no—
356C2×D71—232no—
357C2×D71—42no—
358C2×D71—42no—
359C2×D71—42no—
360C2×D71—42no—
361C2×D71—42no—
362C2×D71—42no—
363C2×D71—42no—
364C2×D71—88no—
365C2×D71C2×#12618yes—
366C4×C71—24no—
367C4×C71—42no—
368C4×C71—42no—
369C4×C71—42no—
370C4×C71—42no—
371C4×C71—42no—
372C4×C71—42no—
373Dic71—24no—
374Dic71—42no—
375Dic71—42no—
376Dic71—42no—
377Dic71—42no—
378Dic71—42no—
379C2×#2510—711nomaximal, Sylow
380C2×C71#251018yescomplemented
381C2×C71C22×#12611yescharacteristic
382C2×C71C2×#52911yescharacteristic
383C2×C71C2×#53811yescharacteristic
384C2×C71C2×#55111yescharacteristic
385C2×C71C2×#55111yescharacteristic
386C2×C71C2×#55311yescharacteristic
387C2×C71C2×#55311yescharacteristic
388D71—28no—
389D71—82no—
390#2510—7116no—
391C2×#401—711no—
392C2×#400—711no—
393C2×#397—711no—
394C2×#397—711no—
395C2×#388—711no—
396C2×#388—711no—
397C2×#387—711no—
398C2×#386—711no—
399C2×#386—711no—
400C2×#386—711no—
401C2×#385—711no—
402C2×#383D7111yescharacteristic, complemented
403C2×#380—711no—
404C2×C4×C22⋊C4—711no—
405C22×#95—711no—
406C71C2×#251011yescharacteristic, complemented, Sylow
407C23×D4—711no—
408C24×C4—711no—
409C24×C4—711no—
410C24×C4—711no—
411C22×C4⋊C4—711no—
412C22×C4⋊C4—711no—
413C22×C4⋊C4—711no—
414C22×C4⋊C4—711no—
415C22×C22⋊C4—711no—
416C22×C22⋊C4—711no—
417C22×C22⋊C4—711no—
418C22×C22⋊C4—711no—
419C22×C22⋊C4—711no—
420C22×C22⋊C4—711no—
421C22×C22⋊C4—711no—
422C22×C22⋊C4—711no—
423C22×C22⋊C4—711no—
424C22×C42—711no—
425C22×C42C2×D7111yescharacteristic
426#401—718no—
427#400—718no—
428#397—718no—
429#397—718no—
430#388—718no—
431#388—718no—
432#387—718no—
433#386—718no—
434#386—718no—
435#386—718no—
436#385—718no—
437#383C2×D7118yescomplemented
438#380—718no—
439C4×C22⋊C4—718no—
440C2×#95—711no—
441C2×#95—711no—
442C2×#95—711no—
443C2×#95—711no—
444C2×#95—711no—
445C2×#95—711no—
446C2×#95—711no—
447C2×#95—711no—
448C2×#95—711no—
449C2×#95—711no—
450C2×#95—718no—
451C2×#95C2×D7111yescharacteristic
452C2×#95C2×D7111yescharacteristic
453C2×#95C2×D7111yescharacteristic
454C2×#95C2×D7111yescharacteristic
455C2×#95C2×D7111yescharacteristic
456C2×#95C2×D7111yescharacteristic
457C25—711no—
458C25—711no—
459C22×D4—714no—
460C22×D4—1424no—
461C22×D4—1424no—
462C22×D4—1424no—
463C23×C4—2842no—
464C23×C4—2842no—
465C23×C4—2842no—
466C23×C4—2842no—
467C23×C4—714no—
468C23×C4—714no—
469C23×C4—714no—
470C23×C4—711no—
471C23×C4—711no—
472C23×C4—711no—
473C23×C4—711no—
474C23×C4—711no—
475C23×C4—711no—
476C23×C4—1424no—
477C23×C4—1424no—
478C23×C4—1424no—
479C23×C4—1424no—
480C23×C4—1424no—
481C23×C4C22×D7111yescharacteristic
482C23×C4C22×D7111yescharacteristic
483C23×C4C22×D7111yescharacteristic
484C23×C4C22×D7111yescharacteristic
485C23×C4C22×D7111yescharacteristic
486C23×C4C22×D7111yescharacteristic
487C23×C4C22×D7111yescharacteristic
488C2×C4⋊C4—2842no—
489C2×C4⋊C4—2842no—
490C2×C4⋊C4—2842no—
491C2×C4⋊C4—714no—
492C2×C4⋊C4—714no—
493C2×C4⋊C4—714no—
494C2×C4⋊C4—714no—
495C2×C4⋊C4—1424no—
496C2×C22⋊C4—2842no—
497C2×C22⋊C4—2842no—
498C2×C22⋊C4—2842no—
499C2×C22⋊C4—2842no—
500C2×C22⋊C4—714no—
501C2×C22⋊C4—714no—
502C2×C22⋊C4—714no—
503C2×C22⋊C4—714no—
504C2×C22⋊C4—714no—
505C2×C22⋊C4—714no—
506C2×C22⋊C4—714no—
507C2×C22⋊C4—714no—
508C2×C22⋊C4—714no—
509C2×C22⋊C4—1424no—
510C2×C22⋊C4—1424no—
511C2×C22⋊C4—1424no—
512C2×C22⋊C4—1424no—
513C2×C22⋊C4—1424no—
514C2×C42—24no—
515C2×C42—2842no—
516C2×C42—714no—
517C2×C42C22×D7114yes—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95—714no—
523#95—714no—
524#95—714no—
525#95—714no—
526#95—714no—
527#95—714no—
528#95C22×D7114yes—
529#95C22×D7114yes—
530#95C22×D7114yes—
531#95C22×D7114yes—
532#95C22×D7114yes—
533#95C22×D7114yes—
534C24—714no—
535C24—714no—
536C24—714no—
537C24—712no—
538C24—712no—
539C24—1422no—
540C24—1422no—
541C24—1422no—
542C24—1422no—
543C24—1422no—
544C24—1422no—
545C24—1422no—
546C24—1422no—
547C24—1422no—
548C24—1422no—
549C24—1422no—
550C24C23×D7111yescharacteristic
551C2×D4—28416no—
552C2×D4—1428no—
553C2×D4—1428no—
554C2×D4—1428no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—28416no—
576C22×C4—2844no—
577C22×C4—2844no—
578C22×C4—2844no—
579C22×C4—2844no—
580C22×C4—28416no—
581C22×C4—28416no—
582C22×C4—714no—
583C22×C4—712no—
584C22×C4—712no—
585C22×C4—712no—
586C22×C4—712no—
587C22×C4—712no—
588C22×C4—712no—
589C22×C4—1428no—
590C22×C4—1428no—
591C22×C4—1428no—
592C22×C4—1428no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1428no—
609C22×C4—1422no—
610C22×C4—1422no—
611C22×C4#1176586514yes—
612C22×C4C23×D7112yes—
613C22×C4C23×D7112yes—
614C22×C4C23×D7112yes—
615C22×C4C23×D7112yes—
616C22×C4C23×D7112yes—
617C22×C4C23×D7112yes—
618C22×C4C23×D7112yes—
619C4⋊C4—2844no—
620C4⋊C4—2844no—
621C4⋊C4—2844no—
622C4⋊C4—1428no—
623C22⋊C4—2844no—
624C22⋊C4—2844no—
625C22⋊C4—2844no—
626C22⋊C4—2844no—
627C22⋊C4—1428no—
628C22⋊C4—1428no—
629C22⋊C4—1428no—
630C22⋊C4—1428no—
631C22⋊C4—1428no—
632C42—28no—
633C42—2844no—
634C23—2844no—
635C23—2844no—
636C23—2844no—
637C23—2844no—
638C23—2844no—
639C23—2844no—
640C23—2844no—
641C23—714no—
642C23—714no—
643C23—714no—
644C23—7116no—
645C23—1422no—
646C23—1422no—
647C23—1422no—
648C23—1422no—
649C23—1422no—
650C23—1422no—
651C23—1422no—
652C23—1422no—
653C23—1422no—
654C23—1422no—
655C23—1422no—
656C23—1428no—
657C23—1428no—
658C23—1428no—
659C23—1428no—
660C23—1428no—
661C23—1428no—
662C23#41×D7112yes—
663C23#41×D7112yes—
664C23#41×D7112yes—
665C23#41×D7112yes—
666C23C2×#1176586512yes—
667C23#1455617412yes—
668C23#1455617412yes—
669C23C24×D7111yescharacteristic
670D4—28416no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—28416no—
699C2×C4—28416no—
700C2×C4—28416no—
701C2×C4—2844no—
702C2×C4—2844no—
703C2×C4—2844no—
704C2×C4—2844no—
705C2×C4—2844no—
706C2×C4—714no—
707C2×C4—1422no—
708C2×C4—1422no—
709C2×C4—1422no—
710C2×C4—1422no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4—1422no—
719C2×C4—1422no—
720C2×C4—1422no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4—1428no—
725C2×C4C2×#1176586514yes—
726C22—2842no—
727C22—2842no—
728C22—2842no—
729C22—2842no—
730C22—2842no—
731C22—2842no—
732C22—2842no—
733C22—5688no—
734C22—718no—
735C22—1424no—
736C22—1424no—
737C22—1424no—
738C22—1424no—
739C22—1424no—
740C22—14232no—
741C22—1424no—
742C22#126×D7114yes—
743C22#1798652714yes—
744C22#1798658814yes—
745C22#1798667314yes—
746C22#1798667414yes—
747C22#1798669314yes—
748C22#1798670014yes—
749C22C2×#41×D7111yescharacteristic
750C22C2×#41×D7111yescharacteristic
751C22C2×#41×D7111yescharacteristic
752C22C2×#41×D7111yescharacteristic
753C22C22×#1176586511yescharacteristic
754C22C2×#1455617411yescharacteristic
755C22C2×#1455617411yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—2842no—
764C4—2842no—
765C4—2842no—
766C4—2842no—
767C4—2842no—
768C4—1424no—
769C2—5682no—
770C2—1428no—
771C2#2259290718yesdirect product factor
772C2C2×#126×D7111yescharacteristic
773C2C2×#1798652711yescharacteristic
774C2C2×#1798658811yescharacteristic
775C2C2×#1798667311yescharacteristic
776C2C2×#1798667411yescharacteristic
777C2C2×#1798669311yescharacteristic
778C2C2×#1798670011yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#383×C71C2
socleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#383D71
hypocenterC71C2×#2510
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. #22592907C2direct (N × H)
2. C2×C71⋊#401C2semidirect
3. C2×#17985940C2semidirect
4. C2×#17985928C2semidirect
5. C2×#17985926C2semidirect
6. C2×#17985890C2semidirect
7. C2×#17985888C2semidirect
8. C2×#17985886C2semidirect
12. C2×#17985873C2semidirect
13. C2×#17985858C2semidirect
14. C2×C4×(C2×D71)⋊C4C2semidirect
15. C2×#95×D71C2semidirect
16. C2×#383×C71C2semidirect
35. C71⋊#401C22semidirect
36. #17985940C22semidirect
37. #17985928C22semidirect
38. #17985926C22semidirect
39. #17985890C22semidirect
40. #17985888C22semidirect
41. #17985886C22semidirect
45. #17985873C22semidirect
46. #17985858C22semidirect
47. C4×(C2×D71)⋊C4C22semidirect
58. #95×D71C22semidirect
60. #383×C71C22semidirect
380. C2×C71#2510semidirect
402. C2×#383D71semidirect
406. C71C2×#2510semidirect
437. #383C2×D71semidirect
771. C2#22592907direct (N × H)

Maximal subgroups

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

subgroupindex
#225929072
C2×C71⋊#4012
C2×#179859402
C2×#179859282
C2×#179859262
C2×#179858902
C2×#179858882
C2×#179858862
C2×#179858772
C2×#179858732
C2×#179858582
C2×C4×(C2×D71)⋊C42
C2×#95×D712
C2×#383×C712
C2×#251071