Finite Group Databasebeta

← C2×#22591110 #32156325

Subgroups — C2×#22591110 #32156325

Order 18176.

2614 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×#14556121C211yesmaximal, characteristic
2#22591110C2116yesmaximal, direct product factor
3C2×#17985894C211yesmaximal, characteristic, complemented
4C2×#17985894C211yesmaximal, characteristic, complemented
5C2×#17985892C211yesmaximal, characteristic
6C2×#17985887C211yesmaximal, characteristic
7C2×#17985887C211yesmaximal, characteristic
8C2×#17985886C211yesmaximal, characteristic, complemented
9C2×#17985882C211yesmaximal, characteristic, complemented
10C2×#17985881C211yesmaximal, characteristic, complemented
11C2×#17985872C211yesmaximal, characteristic
12C2×#17985864C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
14C2×#17985850C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic71C211yesmaximal, characteristic
16C2×#385×C71C211yesmaximal, characteristic
17C2×#14556121C4116yescomplemented
18C2×#14556121C2218yes—
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21C22×Dic71⋊C4C2211yescharacteristic
22C22×Dic71⋊C4C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×C22⋊Dic71C2211yescharacteristic
28C22×C22⋊Dic71C2211yescharacteristic
29C22×C22⋊Dic71C2211yescharacteristic
30C22×C22⋊Dic71C2211yescharacteristic
31C22×C4×Dic71C2211yescharacteristic
32C22×C4×Dic71C2211yescharacteristic
33C22×C4×Dic71C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37#17985894C2218yescomplemented
38#17985894C2218yescomplemented
39#17985892C2218yes—
40#17985887C2218yes—
41#17985887C2218yes—
42#17985886C2218yescomplemented
43#17985882C2218yescomplemented
44#17985881C2218yescomplemented
45#17985872C2218yes—
46#17985864C2218yescomplemented
47C4⋊C4×Dic71C2218yescomplemented
48#17985850C2218yescomplemented
49C4×C22⋊Dic71C2218yes—
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C24×C4×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65#385×C71C2218yes—
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C23×Dic71C2311yescharacteristic
69C23×Dic71C2311yescharacteristic
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76#14556121C2×C4164yescomplemented
77C2×C4⋊Dic71—42no—
78C2×C4⋊Dic71C2×C418yescomplemented
79C2×C4⋊Dic71C2314yes—
80C2×C4⋊Dic71C2314yes—
81C2×Dic71⋊C4—24no—
82C2×Dic71⋊C4—24no—
83C2×Dic71⋊C4—42no—
84C2×Dic71⋊C4—42no—
85C2×Dic71⋊C4C2×C418yescomplemented
86C2×Dic71⋊C4C2×C418yescomplemented
87C2×Dic71⋊C4C2314yes—
88C2×Dic71⋊C4C2314yes—
89C2×Dic71⋊C4C2314yes—
90C2×Dic71⋊C4C2314yes—
91C2×Dic71⋊C4C2314yes—
92C2×Dic71⋊C4C2314yes—
93C2×C22⋊Dic71—24no—
94C2×C22⋊Dic71—42no—
95C2×C22⋊Dic71C2×C418yes—
96C2×C22⋊Dic71C2×C418yes—
97C2×C22⋊Dic71C2314yes—
98C2×C22⋊Dic71C2314yes—
99C2×C22⋊Dic71C2314yes—
100C2×C22⋊Dic71C2314yes—
101C2×C4×Dic71—24no—
102C2×C4×Dic71—42no—
103C2×C4×Dic71—42no—
104C2×C4×Dic71—42no—
105C2×C4×Dic71—42no—
106C2×C4×Dic71C2×C418yescomplemented
107C2×C4×Dic71C2314yes—
108C2×C4×Dic71C2314yes—
109C2×C4×Dic71C2314yes—
110C2×C4×Dic71C2314yes—
111C2×C4×Dic71C2314yes—
112C2×C4×Dic71C2314yes—
113C71⋊#95C2314yes—
114C71⋊#95C2314yes—
115C71⋊#95C2314yes—
116C71⋊#95C2314yes—
117C71⋊#95C2314yes—
118C71⋊#95C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C25×C71C2311yescharacteristic
124C23×C4×C71—24no—
125C23×C4×C71—42no—
126C23×C4×C71—42no—
127C23×C4×C71C2311yescharacteristic
128C23×C4×C71C2311yescharacteristic
129C23×C4×C71C2311yescharacteristic
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2314yes—
134C2×C4⋊C4×C71—24no—
135C2×C4⋊C4×C71—42no—
136C2×C4⋊C4×C71C2314yes—
137C2×C4⋊C4×C71C2314yes—
138C2×C22⋊C4×C71—42no—
139C2×C22⋊C4×C71C2×C418yes—
140C2×C22⋊C4×C71C2314yes—
141C2×C22⋊C4×C71C2314yes—
142#95×C71C2314yes—
143#95×C71C2314yes—
144C22×Dic71—22no—
145C22×Dic71—22no—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71C22×C414yes—
164C22×Dic71C22×C414yes—
165C22×Dic71C22×C414yes—
166C22×Dic71C22×C414yes—
167C22×Dic71#4114yes—
168C22×Dic71C2412yes—
169C22×Dic71C2412yes—
170C22×Dic71C2412yes—
171C22×Dic71C2412yes—
172C22×Dic71C2412yes—
173C22×Dic71C2412yes—
174C22×Dic71C2412yes—
175C22×Dic71C2412yes—
176C4⋊Dic71—44no—
177C4⋊Dic71C22×C4116yescomplemented
178Dic71⋊C4—28no—
179Dic71⋊C4—28no—
180Dic71⋊C4—44no—
181Dic71⋊C4—44no—
182Dic71⋊C4C22×C4116yescomplemented
183Dic71⋊C4C22×C4116yescomplemented
184C22⋊Dic71—28no—
185C22⋊Dic71—44no—
186C22⋊Dic71C22×C4116yes—
187C22⋊Dic71C22×C4116yes—
188C4×Dic71—28no—
189C4×Dic71—44no—
190C4×Dic71—44no—
191C4×Dic71—44no—
192C4×Dic71—44no—
193C4×Dic71C22×C4116yescomplemented
194C24×C71—22no—
195C24×C71—22no—
196C24×C71—22no—
197C24×C71—22no—
198C24×C71—22no—
199C24×C71—22no—
200C24×C71C22×C414yes—
201C24×C71C2412yes—
202C24×C71C2411yescharacteristic
203C22×C4×C71—22no—
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—28no—
219C22×C4×C71—44no—
220C22×C4×C71—44no—
221C22×C4×C71—416no—
222C22×C4×C71C22×C414yes—
223C22×C4×C71C22×C414yes—
224C22×C4×C71#4114yes—
225C22×C4×C71C2412yes—
226C22×C4×C71C2412yes—
227C22×C4×C71C2412yes—
228C22×C4×C71C2412yes—
229C22×C4×C71C2412yes—
230C22×C4×C71C2412yes—
231C4⋊C4×C71—28no—
232C4⋊C4×C71—44no—
233C22⋊C4×C71—44no—
234C22⋊C4×C71C22×C4116yes—
235C23×C71—28no—
236C23×C71—28no—
237C23×C71—28no—
238C23×C71—22no—
239C23×C71—22no—
240C23×C71—22no—
241C23×C71—22no—
242C23×C71—22no—
243C23×C71—22no—
244C23×C71—44no—
245C23×C71—44no—
246C23×C71—44no—
247C23×C71—44no—
248C23×C71C23×C414yes—
249C23×C71C23×C412yes—
250C23×C71C2×#4112yes—
251C23×C71C2×#4112yes—
252C23×C71H(5,𝔽2)12yes—
253C23×C71H(5,𝔽2)12yes—
254C23×C712−1+412yes—
255C23×C712−1+412yes—
256C23×C71C2511yescharacteristic
257C2×C4×C71—28no—
258C2×C4×C71—28no—
259C2×C4×C71—28no—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—416no—
276C2×C4×C71—44no—
277C2×C4×C71—44no—
278C2×C4×C71—44no—
279C2×C4×C71C23×C414yes—
280C2×C4×C71C23×C414yes—
281C2×C4×C71C2×#4114yes—
282C2×Dic71—28no—
283C2×Dic71—28no—
284C2×Dic71—28no—
285C2×Dic71—28no—
286C2×Dic71—28no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—44no—
307C2×Dic71—44no—
308C2×Dic71—44no—
309C2×Dic71C23×C414yes—
310C2×Dic71C23×C414yes—
311C2×Dic71C23×C414yes—
312C2×Dic71C23×C414yes—
313C2×Dic71C2×#4114yes—
314C22×C71—24no—
315C22×C71—24no—
316C22×C71—24no—
317C22×C71—416no—
318C22×C71—42no—
319C22×C71—42no—
320C22×C71—42no—
321C22×C71—42no—
322C22×C71C4×#4114yes—
323C22×C71#52014yes—
324C22×C71#52014yes—
325C22×C71#53814yes—
326C22×C71#53914yes—
327C22×C71#54114yes—
328C22×C71#54214yes—
329C22×C71C24×C411yescharacteristic
330C22×C71C22×#4111yescharacteristic
331C22×C71C22×#4111yescharacteristic
332C22×C71C2×H(5,𝔽2)11yescharacteristic
333C22×C71C2×H(5,𝔽2)11yescharacteristic
334C22×C71C2×2−1+411yescharacteristic
335C22×C71C2×2−1+411yescharacteristic
336C4×C71—24no—
337C4×C71—24no—
338C4×C71—24no—
339C4×C71—42no—
340C4×C71—42no—
341C4×C71—42no—
342Dic71—24no—
343Dic71—24no—
344Dic71—24no—
345Dic71—24no—
346Dic71—24no—
347Dic71—42no—
348Dic71—42no—
349Dic71—42no—
350C2×#2334—711nomaximal, Sylow
351C2×C71—44no—
352C2×C71#233418yescomplemented
353C2×C71C2×C4×#4111yescharacteristic
354C2×C71C2×#52011yescharacteristic
355C2×C71C2×#52011yescharacteristic
356C2×C71C2×#53811yescharacteristic
357C2×C71C2×#53911yescharacteristic
358C2×C71C2×#54111yescharacteristic
359C2×C71C2×#54211yescharacteristic
360C22×#126—711no—
361#2334—7116no—
362C2×#389—711no—
363C2×#389—711no—
364C2×#388—711no—
365C2×#388—711no—
366C2×#388—711no—
367C2×#387—711no—
368C2×#387—711no—
369C2×#387—711no—
370C2×#385—711no—
371C2×#385D7111yescharacteristic
372C2×#382—711no—
373C2×C4×C4⋊C4—711no—
374C2×C4×C4⋊C4—711no—
375C2×C4×C22⋊C4—711no—
376C71C2×#233411yescharacteristic, complemented, Sylow
377C24×C4C2×D7111yescharacteristic
378C2×#126—7116no—
379C2×#126—718no—
380C22×C4⋊C4—711no—
381C22×C4⋊C4—711no—
382C22×C4⋊C4—711no—
383C22×C4⋊C4—711no—
384C22×C4⋊C4—711no—
385C22×C4⋊C4—711no—
386C22×C4⋊C4—711no—
387C22×C4⋊C4—711no—
388C22×C4⋊C4C2×D7111yescharacteristic
389C22×C4⋊C4C2×D7111yescharacteristic
390C22×C22⋊C4—711no—
391C22×C22⋊C4—711no—
392C22×C22⋊C4—711no—
393C22×C22⋊C4—711no—
394C22×C22⋊C4C2×D7111yescharacteristic
395C22×C22⋊C4C2×D7111yescharacteristic
396C22×C42—711no—
397C22×C42—711no—
398C22×C42—711no—
399C22×C42—711no—
400C22×C42—711no—
401C22×C42—711no—
402#389—718no—
403#389—718no—
404#388—718no—
405#388—718no—
406#388—718no—
407#387—718no—
408#387—718no—
409#387—718no—
410#385—718no—
411#385C2×D7118yes—
412#382—718no—
413C4×C4⋊C4—718no—
414C4×C4⋊C4—718no—
415C4×C22⋊C4—718no—
416C2×#95—711no—
417C2×#95—711no—
418C2×#95—711no—
419C2×#95—711no—
420C2×#95—711no—
421C2×#95—711no—
422C2×#95—711no—
423C2×#95—711no—
424C2×#95—711no—
425C2×#95—711no—
426C2×#95C2×D7111yescharacteristic
427C2×#95C2×D7111yescharacteristic
428C25C22×D7111yescharacteristic
429C23×C4—24no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—711no—
433C23×C4—711no—
434C23×C4—711no—
435C23×C4—711no—
436C23×C4—711no—
437C23×C4—711no—
438C23×C4—711no—
439C23×C4—711no—
440C23×C4C22×D7111yescharacteristic
441C23×C4C22×D7111yescharacteristic
442C23×C4C22×D7111yescharacteristic
443C23×C4C22×D7111yescharacteristic
444C23×C4C22×D7111yescharacteristic
445C23×C4C22×D7111yescharacteristic
446C23×C4C22×D7114yes—
447#126—7164no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—2842no—
451C2×C4⋊C4—2842no—
452C2×C4⋊C4—2842no—
453C2×C4⋊C4—714no—
454C2×C4⋊C4—714no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—718no—
457C2×C4⋊C4—718no—
458C2×C4⋊C4—718no—
459C2×C4⋊C4—714no—
460C2×C4⋊C4—714no—
461C2×C4⋊C4—714no—
462C2×C4⋊C4—714no—
463C2×C4⋊C4—714no—
464C2×C4⋊C4—1424no—
465C2×C4⋊C4—1424no—
466C2×C4⋊C4C22×D7114yes—
467C2×C4⋊C4C22×D7114yes—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—2842no—
470C2×C22⋊C4—714no—
471C2×C22⋊C4—718no—
472C2×C22⋊C4—718no—
473C2×C22⋊C4—714no—
474C2×C22⋊C4—714no—
475C2×C22⋊C4—714no—
476C2×C22⋊C4—1424no—
477C2×C22⋊C4C4×D7118yes—
478C2×C22⋊C4C22×D7114yes—
479C2×C22⋊C4C22×D7114yes—
480C2×C42—2842no—
481C2×C42—2842no—
482C2×C42—2842no—
483C2×C42—2842no—
484C2×C42—714no—
485C2×C42—714no—
486C2×C42—714no—
487C2×C42—714no—
488C2×C42—718no—
489C2×C42—714no—
490C2×C42—714no—
491C2×C42—1424no—
492#95—714no—
493#95—714no—
494#95—714no—
495#95—714no—
496#95—714no—
497#95—714no—
498#95—714no—
499#95—714no—
500#95—714no—
501#95—714no—
502#95C22×D7114yes—
503#95C22×D7114yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C2×C4×D7114yes—
511C24C23×D7112yes—
512C24C23×D7111yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—416no—
532C22×C4—714no—
533C22×C4—714no—
534C22×C4—714no—
535C22×C4—714no—
536C22×C4—714no—
537C22×C4—712no—
538C22×C4—712no—
539C22×C4—712no—
540C22×C4—712no—
541C22×C4—712no—
542C22×C4—712no—
543C22×C4—712no—
544C22×C4—712no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1422no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1422no—
551C22×C4—1422no—
552C22×C4—1422no—
553C22×C4—1422no—
554C22×C4—1422no—
555C22×C4—1422no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4—1422no—
562C22×C4—1422no—
563C22×C4—1422no—
564C22×C4C2×C4×D7114yes—
565C22×C4C2×C4×D7114yes—
566C22×C4#1176586414yes—
567C22×C4C23×D7112yes—
568C22×C4C23×D7112yes—
569C22×C4C23×D7112yes—
570C22×C4C23×D7112yes—
571C22×C4C23×D7112yes—
572C22×C4C23×D7112yes—
573C4⋊C4—28no—
574C4⋊C4—44no—
575C4⋊C4—2844no—
576C4⋊C4—2844no—
577C4⋊C4—2844no—
578C4⋊C4—7116no—
579C4⋊C4—7116no—
580C4⋊C4—7116no—
581C4⋊C4—1428no—
582C4⋊C4—1428no—
583C22⋊C4—44no—
584C22⋊C4—2844no—
585C22⋊C4—7116no—
586C22⋊C4—7116no—
587C22⋊C4—1428no—
588C22⋊C4C2×C4×D71116yes—
589C42—2844no—
590C42—2844no—
591C42—2844no—
592C42—2844no—
593C42—7116no—
594C42—1428no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C22×C4×D7114yes—
609C23C22×C4×D7112yes—
610C23#41×D7112yes—
611C23C2×#1176586412yes—
612C23#1455617312yes—
613C23#1455617312yes—
614C23#1455617512yes—
615C23#1455617612yes—
616C23C24×D7111yescharacteristic
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—416no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—2844no—
640C2×C4—2844no—
641C2×C4—2844no—
642C2×C4—714no—
643C2×C4—714no—
644C2×C4—714no—
645C2×C4—714no—
646C2×C4—714no—
647C2×C4—1422no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4—1422no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4—1422no—
655C2×C4—1422no—
656C2×C4—1422no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1428no—
667C2×C4—1428no—
668C2×C4—1428no—
669C2×C4—1428no—
670C2×C4—1428no—
671C2×C4C22×C4×D7114yes—
672C2×C4C22×C4×D7114yes—
673C2×C4C2×#1176586414yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22C4×#1176586414yes—
683C22#1798647814yes—
684C22#1798648014yes—
685C22#1798658414yes—
686C22#1798659214yes—
687C22#1798660914yes—
688C22#1798661914yes—
689C22C23×C4×D7111yescharacteristic
690C22C2×#41×D7111yescharacteristic
691C22C22×#1176586411yescharacteristic
692C22C2×#1455617311yescharacteristic
693C22C2×#1455617311yescharacteristic
694C22C2×#1455617511yescharacteristic
695C22C2×#1455617611yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—2842no—
703C4—2842no—
704C4—2842no—
705C4—1424no—
706C4—1424no—
707C4—1424no—
708C4—1424no—
709C4—1424no—
710C2—44no—
711C2#2259111018yesdirect product factor
712C2C2×C4×#1176586411yescharacteristic
713C2C2×#1798647811yescharacteristic
714C2C2×#1798648011yescharacteristic
715C2C2×#1798658411yescharacteristic
716C2C2×#1798659211yescharacteristic
717C2C2×#1798660911yescharacteristic
718C2C2×#1798661911yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC25×C71C23
cosocleC23×C71C25
hypercenterC2×#385D71
hypocenterC71C2×#2334
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #22591110C2direct (N × H)
3. C2×#17985894C2semidirect
4. C2×#17985894C2semidirect
8. C2×#17985886C2semidirect
9. C2×#17985882C2semidirect
10. C2×#17985881C2semidirect
12. C2×#17985864C2semidirect
13. C2×C4⋊C4×Dic71C2semidirect
14. C2×#17985850C2semidirect
17. C2×#14556121C4semidirect
37. #17985894C22semidirect
38. #17985894C22semidirect
42. #17985886C22semidirect
43. #17985882C22semidirect
44. #17985881C22semidirect
46. #17985864C22semidirect
47. C4⋊C4×Dic71C22semidirect
48. #17985850C22semidirect
76. #14556121C2×C4semidirect
78. C2×C4⋊Dic71C2×C4semidirect
85. C2×Dic71⋊C4C2×C4semidirect
86. C2×Dic71⋊C4C2×C4semidirect
106. C2×C4×Dic71C2×C4semidirect
177. C4⋊Dic71C22×C4semidirect
182. Dic71⋊C4C22×C4semidirect
183. Dic71⋊C4C22×C4semidirect
193. C4×Dic71C22×C4semidirect
352. C2×C71#2334semidirect
376. C71C2×#2334semidirect
711. C2#22591110direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561212
#225911102
C2×#179858942
C2×#179858922
C2×#179858872
C2×#179858862
C2×#179858822
C2×#179858812
C2×#179858722
C2×#179858642
C2×C4⋊C4×Dic712
C2×#179858502
C2×C4×C22⋊Dic712
C2×#385×C712
C2×#233471