Finite Group Databasebeta

← C2×#22601182 #32877249

Subgroups — C2×#22601182 #32877249

Order 18176.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986722C211yesmaximal, characteristic
2#22601182C2116yesmaximal, direct product factor
3C2×#17986369C211yesmaximal, characteristic, complemented
4C2×#17986361C211yesmaximal, characteristic
5C2×#17986356C211yesmaximal, characteristic
6C2×#17986303C211yesmaximal, characteristic, complemented
7C2×#17986291C211yesmaximal, characteristic, complemented
8C2×#17986296C211yesmaximal, characteristic
9C2×#17986221C211yesmaximal, characteristic
10C2×#17986221C211yesmaximal, characteristic
11C2×#17986209C211yesmaximal, characteristic, complemented
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986104C211yesmaximal, characteristic, complemented
14C2×#17986097C211yesmaximal, characteristic
15C2×C4×#11765855C211yesmaximal, characteristic, complemented
16C2×#557×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20#17986722—24no—
21#17986722C2218yes—
22C2×#14556128C2211yescharacteristic
23C2×#14556123—21no—
24C2×#14556123—21no—
25C2×#14556116C2211yescharacteristic
26C2×#14556116C2211yescharacteristic
27C2×#14556104—21no—
28C2×C4×Dic142C2211yescharacteristic
29C2×C4×Dic142C2211yescharacteristic
30C2×C4×D284C2211yescharacteristic
31C2×#14556086—21no—
32#17986369C2218yescomplemented
33#17986361C2218yes—
34#17986356C2218yes—
35#17986303C2218yescomplemented
36#17986296C2218yes—
37#17986291C2218yescomplemented
38#17986221C2218yes—
39#17986221C2218yes—
40#17986209C2218yescomplemented
41#17986130C2218yescomplemented
42#17986104C2218yescomplemented
43#17986097C2218yes—
44C4×#11765855C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49C2×C4⋊(C71⋊C8)C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×#14556052C2211yescharacteristic
52C2×#14556051C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#557×C71—24no—
65#557×C71C2218yescomplemented
66C2×C4⋊Q8×C71—21no—
67C2×C4⋊Q8×C71C2211yescharacteristic
68C2×#125×C71—21no—
69C2×#125×C71—21no—
70C2×#125×C71C2211yescharacteristic
71C2×#125×C71C2211yescharacteristic
72C2×C4×Q8×C71—21no—
73C2×C4×Q8×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×Q8×C71C2211yescharacteristic
76C2×C4×Q8×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C4×D71—21no—
81C2×#11765855—24no—
82C2×#11765855—24no—
83C2×#11765855C2314yes—
84C2×#11765855C2314yes—
85C2×#11765852—24no—
86C2×#11765852C2314yes—
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91#14556128—22no—
92#14556128C2314yes—
93#14556123—28no—
94#14556123—28no—
95#14556116—22no—
96#14556116—22no—
97#14556116C2314yes—
98#14556116C2314yes—
99#14556104—28no—
100C4×Dic142—22no—
101C4×Dic142—22no—
102C4×Dic142C2314yes—
103C4×Dic142C2314yes—
104C4×D284—22no—
105C4×D284C2314yes—
106#14556086—28no—
107C2×C4⋊Dic71—21no—
108C2×C4⋊Dic71—21no—
109C2×C4⋊Dic71C2311yescharacteristic
110C2×Dic71⋊C4—21no—
111C2×Dic71⋊C4—21no—
112C2×(C2×D71)⋊C4—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4—21no—
115C2×(C2×D71)⋊C4—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556059C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123C4⋊(C71⋊C8)C2314yes—
124C4⋊(C71⋊C8)C2314yes—
125#14556052C2314yes—
126#14556051C2314yes—
127#14556051C2314yes—
128#14556051C2314yes—
129#14556051C2314yes—
130#14556051C2314yes—
131#14556051C2314yes—
132#14556048C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135#14556039C2314yes—
136#14556039C2314yes—
137C4×C71⋊C8C2314yes—
138C22×Q8×C71—21no—
139C22×Q8×C71D411yescharacteristic
140C22×Q8×C71C2311yescharacteristic
141C4⋊Q8×C71—28no—
142C4⋊Q8×C71—22no—
143C4⋊Q8×C71C2314yes—
144#125×C71—28no—
145#125×C71—28no—
146#125×C71—22no—
147#125×C71—22no—
148#125×C71C2314yes—
149#125×C71C2314yes—
150C4×Q8×C71—28no—
151C4×Q8×C71—22no—
152C4×Q8×C71—22no—
153C4×Q8×C71—22no—
154C4×Q8×C71D414yes—
155C4×Q8×C71C2314yes—
156C4×Q8×C71C2314yes—
157C4×Q8×C71C2314yes—
158C4×Q8×C71C2314yes—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C42×C71—21no—
174C2×C42×C71—21no—
175C2×C42×C71—21no—
176C2×C42×C71C2311yescharacteristic
177C2×C42×C71C2311yescharacteristic
178C2×C42×C71C2311yescharacteristic
179C23×D71—21no—
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—22no—
183C2×Dic142—22no—
184C2×Dic142—21no—
185C2×Dic142—21no—
186C2×Dic142C2412yes—
187C2×Dic142C2412yes—
188C2×D284—22no—
189C2×D284—22no—
190C2×D284—21no—
191C2×D284C2412yes—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C2×C4×D71—24no—
196C2×C4×D71—44no—
197#11765855—28no—
198#11765855—28no—
199#11765852—28no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8—22no—
202C2×C71⋊C8—22no—
203C2×C71⋊C8—22no—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C2×C71⋊C8C2412yes—
207C2×C71⋊C8C2412yes—
208C4⋊Dic71—24no—
209C4⋊Dic71—24no—
210C4⋊Dic71—21no—
211C4⋊Dic71C2412yes—
212Dic71⋊C4—24no—
213Dic71⋊C4—24no—
214(C2×D71)⋊C4—24no—
215(C2×D71)⋊C4—24no—
216(C2×D71)⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219C4×Dic71—24no—
220C4×Dic71—24no—
221C2×Q8×C71—21no—
222C2×Q8×C71—24no—
223C2×Q8×C71—22no—
224C2×Q8×C71—42no—
225C2×Q8×C71—44no—
226C2×Q8×C71C2×D414yes—
227C2×Q8×C71#4114yes—
228C2×Q8×C71C2412yes—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71C2×D411yescharacteristic
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×D411yescharacteristic
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2411yescharacteristic
240C4⋊C4×C71—24no—
241C4⋊C4×C71—24no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—24no—
244C4⋊C4×C71—24no—
245C4⋊C4×C71—24no—
246C4⋊C4×C71—24no—
247C4⋊C4×C71—24no—
248C4⋊C4×C71—21no—
249C4⋊C4×C71—21no—
250C4⋊C4×C71—21no—
251C4⋊C4×C71C2×D414yes—
252C4⋊C4×C71C2×D414yes—
253C4⋊C4×C71C2×D414yes—
254C4⋊C4×C71C2412yes—
255C4⋊C4×C71C2412yes—
256C4⋊C4×C71C2412yes—
257C42×C71—24no—
258C42×C71—24no—
259C42×C71—24no—
260C42×C71C2×D412yes—
261C42×C71C2×D412yes—
262C42×C71C2×D412yes—
263C42×C71C2412yes—
264C42×C71C2412yes—
265C42×C71C2412yes—
266C23×C71C22×D411yescharacteristic
267C22×D71—22no—
268C22×D71—42no—
269C22×D71—42no—
270C22×D71—42no—
271Q8×C71—24no—
272Q8×C71—22no—
273Q8×C71—44no—
274Q8×C71—48no—
275Q8×C71C2×#4114yes—
276C2×C4×C71—24no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
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—42no—
288C2×C4×C71—42no—
289C2×C4×C71—42no—
290C2×C4×C71C22×D412yes—
291C2×C4×C71C22×D412yes—
292C2×C4×C71C22×D412yes—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D412yes—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D411yescharacteristic
297C2×C4×C71C2×#4112yes—
298C2×C4×C712−1+412yes—
299C2×C4×C71C2511yescharacteristic
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—42no—
304C2×Dic71—42no—
305C2×Dic71—42no—
306D284—22no—
307D284—22no—
308D284—42no—
309C4×D71—48no—
310Dic142—22no—
311Dic142—22no—
312Dic142—22no—
313Dic142—22no—
314Dic142—42no—
315Dic142—42no—
316C71⋊C8—22no—
317C71⋊C8—22no—
318C71⋊C8—22no—
319C71⋊C8—22no—
320C22×C71#54812yes—
321C22×C71#57512yes—
322C22×C71#57812yes—
323C22×C71C23×D411yescharacteristic
324C2×D71—42no—
325C2×D71—42no—
326C2×D71—42no—
327C2×D71—84no—
328C4×C71—24no—
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—22no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—42no—
338C4×C71#54812yes—
339C4×C71C22×#4111yescharacteristic
340C4×C71C2×2−1+411yescharacteristic
341Dic71—42no—
342Dic71—42no—
343Dic71—42no—
344C2×#3377—711nomaximal, Sylow
345C2×C71#337714yescomplemented
346C2×C71C2×#54811yescharacteristic
347C2×C71C2×#57511yescharacteristic
348C2×C71C2×#57811yescharacteristic
349D71—82no—
350C2×#557D7111yescharacteristic, complemented
351C2×#556—711no—
352#3377—7116no—
353C2×#491—711no—
354C2×#489—711no—
355C2×#488—711no—
356C2×#479—711no—
357C2×#477—711no—
358C2×#478—711no—
359C2×#464—711no—
360C2×#464—711no—
361C2×#462—711no—
362C2×#446—711no—
363C2×#441—711no—
364C2×#440—711no—
365C2×C4×Q16—711no—
366C71C2×#337711yescharacteristic, complemented, Sylow
367C22×Q16—711no—
368C22×Q16—711no—
369C22×SD16—711no—
370#557—24no—
371#557C2×D7118yescomplemented
372#556—718no—
373#556—1424no—
374C2×C4⋊Q8—21no—
375C2×C4⋊Q8—711no—
376C2×C4⋊Q8C2×D7111yescharacteristic
377C2×#126—1421no—
378C2×#126—1421no—
379C2×#125—21no—
380C2×#125—21no—
381C2×#125C2×D7111yescharacteristic
382C2×#125C2×D7111yescharacteristic
383C2×#124—711no—
384C2×#124—711no—
385C2×C22⋊Q8—1421no—
386C2×C4×Q8—21no—
387C2×C4×Q8—711no—
388C2×C4×Q8—711no—
389C2×C4×Q8C2×D7111yescharacteristic
390C2×C4×Q8C2×D7111yescharacteristic
391C2×C4×Q8C2×D7111yescharacteristic
392C2×C4×Q8C2×D7111yescharacteristic
393C2×C4×D4—711no—
394C2×#117—1421no—
395#491—718no—
396#489—718no—
397#488—718no—
398#479—718no—
399#478—718no—
400#477—718no—
401#464—718no—
402#464—718no—
403#462—718no—
404#446—718no—
405#441—718no—
406#440—718no—
407C4×Q16—718no—
408C2×#107—711no—
409C2×#107—711no—
410C2×#106—711no—
411C2×C4⋊C8—711no—
412C2×C4⋊C8—711no—
413C2×C4⋊C8—711no—
414C2×#103—711no—
415C2×#103—711no—
416C2×#103—711no—
417C2×#103—711no—
418C2×#103—711no—
419C2×#103—711no—
420C2×#103—711no—
421C2×#102—711no—
422C2×#102—711no—
423C2×#102—711no—
424C2×#97—711no—
425C2×#97—711no—
426C2×C4×C8—711no—
427C22×Q8—21no—
428C22×Q8—711no—
429C22×Q8—711no—
430C22×Q8C22⋊D7111yescharacteristic
431C22×Q8C22×D7111yescharacteristic
432C22×D4—711no—
433C23×C4—1421no—
434C2×Q16—714no—
435C2×Q16—714no—
436C2×Q16—1424no—
437C2×Q16—1424no—
438C2×SD16—714no—
439C2×SD16—1424no—
440C22×C8—711no—
441C22×C8—711no—
442C22×C8—711no—
443C22×C8—711no—
444C4⋊Q8—28no—
445C4⋊Q8—22no—
446C4⋊Q8—714no—
447C4⋊Q8—1422no—
448C4⋊Q8C22×D7114yes—
449#126—1428no—
450#126—1428no—
451#125—28no—
452#125—28no—
453#125—22no—
454#125—22no—
455#125C22×D7114yes—
456#125C22×D7114yes—
457#124—714no—
458#124—714no—
459#124—1422no—
460#124—1422no—
461C22⋊Q8—1428no—
462C4×Q8—28no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—714no—
467C4×Q8—714no—
468C4×Q8—1422no—
469C4×Q8—1422no—
470C4×Q8C22⋊D7114yes—
471C4×Q8C22×D7114yes—
472C4×Q8C22×D7114yes—
473C4×Q8C22×D7114yes—
474C4×Q8C22×D7114yes—
475C4×D4—714no—
476C4×D4—1422no—
477#117—1428no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—1421no—
488C2×C4⋊C4—1421no—
489C2×C4⋊C4—1421no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4C22⋊D7111yescharacteristic
492C2×C4⋊C4C22⋊D7111yescharacteristic
493C2×C4⋊C4C22⋊D7111yescharacteristic
494C2×C4⋊C4C22×D7111yescharacteristic
495C2×C4⋊C4C22×D7111yescharacteristic
496C2×C4⋊C4C22×D7111yescharacteristic
497C2×C22⋊C4—1421no—
498C2×C22⋊C4—1421no—
499C2×C22⋊C4—1421no—
500C2×C22⋊C4—1421no—
501C2×C22⋊C4—1421no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—1421no—
506C2×C42—1421no—
507C2×C42C22×D7111yescharacteristic
508C2×C42C22×D7111yescharacteristic
509C2×C42C22×D7111yescharacteristic
510#107—714no—
511#107—714no—
512#106—714no—
513C4⋊C8—714no—
514C4⋊C8—714no—
515C4⋊C8—714no—
516#103—714no—
517#103—714no—
518#103—714no—
519#103—714no—
520#103—714no—
521#103—714no—
522#103—714no—
523#102—714no—
524#102—714no—
525#102—714no—
526#97—714no—
527#97—714no—
528C4×C8—714no—
529C24—1421no—
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—712no—
536C2×Q8—712no—
537C2×Q8—1422no—
538C2×Q8—1422no—
539C2×Q8—1422no—
540C2×Q8—1422no—
541C2×Q8—1421no—
542C2×Q8—1421no—
543C2×Q8C2×C22⋊D7114yes—
544C2×Q8#1176586614yes—
545C2×Q8C23×D7112yes—
546C2×D4—712no—
547C2×D4—1421no—
548C2×D4—1422no—
549C2×D4—1422no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—2844no—
555C22×C4—1421no—
556C22×C4—1421no—
557C22×C4—1421no—
558C22×C4—1424no—
559C22×C4C2×C22⋊D7111yescharacteristic
560C22×C4C2×C22⋊D7111yescharacteristic
561C22×C4C2×C22⋊D7111yescharacteristic
562C22×C4C2×C22⋊D7111yescharacteristic
563C22×C4C2×C22⋊D7111yescharacteristic
564C22×C4C2×C22⋊D7111yescharacteristic
565C22×C4C23×D7111yescharacteristic
566Q16—1428no—
567Q16—1428no—
568SD16—1428no—
569C2×C8—712no—
570C2×C8—712no—
571C2×C8—712no—
572C2×C8—712no—
573C2×C8—1422no—
574C2×C8—1422no—
575C2×C8—1422no—
576C2×C8—1422no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—712no—
589C4⋊C4—1424no—
590C4⋊C4—1424no—
591C4⋊C4—1421no—
592C4⋊C4—1424no—
593C4⋊C4—1424no—
594C4⋊C4C2×C22⋊D7114yes—
595C4⋊C4C2×C22⋊D7114yes—
596C4⋊C4C2×C22⋊D7114yes—
597C4⋊C4C23×D7112yes—
598C4⋊C4C23×D7112yes—
599C4⋊C4C23×D7112yes—
600C22⋊C4—1424no—
601C22⋊C4—1424no—
602C22⋊C4—1424no—
603C22⋊C4—1424no—
604C22⋊C4—1424no—
605C42—24no—
606C42—24no—
607C42—24no—
608C42—1424no—
609C42—1424no—
610C42C2×C22⋊D7112yes—
611C42C2×C22⋊D7112yes—
612C42C2×C22⋊D7112yes—
613C42C23×D7112yes—
614C42C23×D7112yes—
615C42C23×D7112yes—
616C23—2842no—
617C23—2842no—
618C23—2842no—
619C23—1422no—
620C23C22×C22⋊D7111yescharacteristic
621Q8—22no—
622Q8—24no—
623Q8—44no—
624Q8—48no—
625Q8—2842no—
626Q8—2842no—
627Q8—1422no—
628Q8—1422no—
629Q8—1422no—
630Q8—1422no—
631Q8C2×#1176586614yes—
632D4—2842no—
633D4—1422no—
634D4—1422no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—2848no—
650C2×C4—2842no—
651C2×C4—2842no—
652C2×C4—2842no—
653C2×C4—1422no—
654C2×C4—1422no—
655C2×C4—1422no—
656C2×C4C22×C22⋊D7112yes—
657C2×C4C22×C22⋊D7112yes—
658C2×C4C22×C22⋊D7112yes—
659C2×C4C22×C22⋊D7112yes—
660C2×C4C22×C22⋊D7112yes—
661C2×C4C22×C22⋊D7112yes—
662C2×C4C22×C22⋊D7111yescharacteristic
663C2×C4C2×#1176586612yes—
664C2×C4#1455617612yes—
665C2×C4C24×D7111yescharacteristic
666C8—1422no—
667C8—1422no—
668C8—1422no—
669C8—1422no—
670C22—2842no—
671C22—2842no—
672C22—2842no—
673C22—5684no—
674C22#1798666012yes—
675C22#1798679712yes—
676C22#1798681412yes—
677C22C23×C22⋊D7111yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—24no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2842no—
689C4—2842no—
690C4—2842no—
691C4#1798666012yes—
692C4C22×#1176586611yescharacteristic
693C4C2×#1455617611yescharacteristic
694C2—5682no—
695C2#2260118214yesdirect product factor
696C2C2×#1798666011yescharacteristic
697C2C2×#1798679711yescharacteristic
698C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#557×C71C2
socleC23×C71C22×D4
prime radicalC22×D284C23
hypercenterC2×#557D71
hypocenterC71C2×#3377
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #22601182C2direct (N × H)
3. C2×#17986369C2semidirect
6. C2×#17986303C2semidirect
7. C2×#17986291C2semidirect
11. C2×#17986209C2semidirect
12. C2×#17986130C2semidirect
13. C2×#17986104C2semidirect
15. C2×C4×#11765855C2semidirect
16. C2×#557×C71C2semidirect
32. #17986369C22semidirect
35. #17986303C22semidirect
37. #17986291C22semidirect
40. #17986209C22semidirect
41. #17986130C22semidirect
42. #17986104C22semidirect
44. C4×#11765855C22semidirect
65. #557×C71C22semidirect
345. C2×C71#3377semidirect
350. C2×#557D71semidirect
366. C71C2×#3377semidirect
371. #557C2×D71semidirect
695. C2#22601182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867222
#226011822
C2×#179863692
C2×#179863612
C2×#179863562
C2×#179863032
C2×#179862912
C2×#179862962
C2×#179862212
C2×#179862092
C2×#179861302
C2×#179861042
C2×#179860972
C2×C4×#117658552
C2×#557×C712
C2×#337771