Finite Group Databasebeta

← C2×#22601108 #32877233

Subgroups — C2×#22601108 #32877233

Order 18176.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986734C211yesmaximal, characteristic
2#22601108C2116yesmaximal, direct product factor
3C2×#17986365C211yesmaximal, characteristic
4C2×#17986361C211yesmaximal, characteristic, complemented
5C2×#17986356C211yesmaximal, characteristic, complemented
6C2×#17986303C211yesmaximal, characteristic, complemented
7C2×#17986296C211yesmaximal, characteristic, complemented
8C2×#17986286C211yesmaximal, characteristic, complemented
9C2×#17986221C211yesmaximal, characteristic, complemented
10C2×#17986221C211yesmaximal, characteristic, complemented
11C2×#17986199C211yesmaximal, characteristic
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986104C211yesmaximal, characteristic, complemented
14C2×#17986097C211yesmaximal, characteristic, complemented
15C2×C4×#11765852C211yesmaximal, characteristic, complemented
16C2×#557×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20#17986734—24no—
21#17986734C2218yes—
22C2×#14556125C2211yescharacteristic
23C2×#14556117—21no—
24C2×#14556116C2211yescharacteristic
25C2×#14556116C2211yescharacteristic
26C2×#14556113—21no—
27C2×#14556113—21no—
28C2×C4×Dic142C2211yescharacteristic
29C2×C4×D284C2211yescharacteristic
30C2×C4×D284C2211yescharacteristic
31C2×#14556090—21no—
32#17986365C2218yes—
33#17986361C2218yescomplemented
34#17986356C2218yescomplemented
35#17986303C2218yescomplemented
36#17986296C2218yescomplemented
37#17986286C2218yescomplemented
38#17986221C2218yescomplemented
39#17986221C2218yescomplemented
40#17986199C2218yes—
41#17986130C2218yescomplemented
42#17986104C2218yescomplemented
43#17986097C2218yescomplemented
44C4×#11765852C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
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×#14556048C2211yescharacteristic
56C2×#14556048C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
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×D284—21no—
79C22×D284—21no—
80C22×D284C2311yescharacteristic
81C22×D284C2311yescharacteristic
82C22×C4×D71—21no—
83C22×C4×D71—21no—
84C2×#11765855—24no—
85C2×#11765855C2314yes—
86C2×#11765852—24no—
87C2×#11765852—24no—
88C2×#11765852C2314yes—
89C2×#11765852C2314yes—
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94#14556125—22no—
95#14556125C2314yes—
96#14556117—28no—
97#14556116—22no—
98#14556116—22no—
99#14556116C2314yes—
100#14556116C2314yes—
101#14556113—28no—
102#14556113—28no—
103C4×Dic142—22no—
104C4×Dic142C2314yes—
105C4×D284—22no—
106C4×D284—22no—
107C4×D284C2314yes—
108C4×D284C2314yes—
109#14556090—28no—
110C2×C4⋊Dic71C2311yescharacteristic
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×(C2×D71)⋊C4—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556059C2314yes—
121#14556059C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123C4⋊(C71⋊C8)C2314yes—
124C4⋊(C71⋊C8)C2314yes—
125#14556052C2314yes—
126#14556051C2314yes—
127#14556051C2314yes—
128#14556051C2314yes—
129#14556048C2314yes—
130#14556048C2314yes—
131#14556048C2314yes—
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—
180C23×D71—21no—
181C2×Dic142—22no—
182C2×Dic142—22no—
183C2×Dic142—21no—
184C2×Dic142C2412yes—
185C2×D284—22no—
186C2×D284—22no—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—24no—
190C2×D284—21no—
191C2×D284—21no—
192C2×D284—24no—
193C2×D284—44no—
194C2×D284—82no—
195C2×D284C2412yes—
196C2×D284C2412yes—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C2×C4×D71—24no—
200C2×C4×D71—24no—
201C2×C4×D71—82no—
202C2×C4×D71—82no—
203#11765855—28no—
204#11765852—28no—
205#11765852—28no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—22no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C2×C71⋊C8C2412yes—
214C4⋊Dic71—21no—
215C4⋊Dic71C2412yes—
216Dic71⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219(C2×D71)⋊C4—24no—
220(C2×D71)⋊C4—24no—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—24no—
223C4×Dic71—24no—
224C2×Q8×C71—21no—
225C2×Q8×C71—24no—
226C2×Q8×C71—22no—
227C2×Q8×C71—42no—
228C2×Q8×C71—44no—
229C2×Q8×C71C2×D414yes—
230C2×Q8×C71#4114yes—
231C2×Q8×C71C2412yes—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×D411yescharacteristic
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2×D411yescharacteristic
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2411yescharacteristic
243C4⋊C4×C71—24no—
244C4⋊C4×C71—24no—
245C4⋊C4×C71—24no—
246C4⋊C4×C71—24no—
247C4⋊C4×C71—24no—
248C4⋊C4×C71—24no—
249C4⋊C4×C71—24no—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71C2×D414yes—
255C4⋊C4×C71C2×D414yes—
256C4⋊C4×C71C2×D414yes—
257C4⋊C4×C71C2412yes—
258C4⋊C4×C71C2412yes—
259C4⋊C4×C71C2412yes—
260C42×C71—24no—
261C42×C71—24no—
262C42×C71—24no—
263C42×C71C2×D412yes—
264C42×C71C2×D412yes—
265C42×C71C2×D412yes—
266C42×C71C2412yes—
267C42×C71C2412yes—
268C42×C71C2412yes—
269C23×C71C22×D411yescharacteristic
270C22×D71—22no—
271C22×D71—22no—
272C22×D71—42no—
273C22×D71—42no—
274C22×D71—42no—
275C22×D71—42no—
276C22×D71—42no—
277C22×D71—42no—
278Q8×C71—24no—
279Q8×C71—22no—
280Q8×C71—44no—
281Q8×C71—48no—
282Q8×C71C2×#4114yes—
283C2×C4×C71—24no—
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—42no—
295C2×C4×C71—42no—
296C2×C4×C71—42no—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D412yes—
299C2×C4×C71C22×D412yes—
300C2×C4×C71C22×D412yes—
301C2×C4×C71C22×D412yes—
302C2×C4×C71C22×D412yes—
303C2×C4×C71C22×D411yescharacteristic
304C2×C4×C71C2×#4112yes—
305C2×C4×C712−1+412yes—
306C2×C4×C71C2511yescharacteristic
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—42no—
310C2×Dic71—42no—
311D284—22no—
312D284—22no—
313D284—22no—
314D284—22no—
315D284—48no—
316D284—42no—
317D284—42no—
318D284—84no—
319C4×D71—84no—
320C4×D71—84no—
321Dic142—22no—
322Dic142—22no—
323Dic142—42no—
324C71⋊C8—22no—
325C71⋊C8—22no—
326C71⋊C8—22no—
327C71⋊C8—22no—
328C22×C71#54812yes—
329C22×C71#57512yes—
330C22×C71#57712yes—
331C22×C71C23×D411yescharacteristic
332C2×D71—42no—
333C2×D71—42no—
334C2×D71—42no—
335C2×D71—42no—
336C2×D71—42no—
337C2×D71—42no—
338C2×D71—84no—
339C2×D71—84no—
340C4×C71—24no—
341C4×C71—22no—
342C4×C71—22no—
343C4×C71—22no—
344C4×C71—22no—
345C4×C71—22no—
346C4×C71—22no—
347C4×C71—42no—
348C4×C71—42no—
349C4×C71—42no—
350C4×C71#54812yes—
351C4×C71C22×#4111yescharacteristic
352C4×C71C2×2−1+411yescharacteristic
353Dic71—42no—
354Dic71—42no—
355C2×#3371—711nomaximal, Sylow
356C2×C71#337114yescomplemented
357C2×C71C2×#54811yescharacteristic
358C2×C71C2×#57511yescharacteristic
359C2×C71C2×#57711yescharacteristic
360D71—82no—
361D71—82no—
362C2×#559—711no—
363C2×#557D7111yescharacteristic, complemented
364#3371—7116no—
365C2×#490—711no—
366C2×#489—711no—
367C2×#488—711no—
368C2×#479—711no—
369C2×#478—711no—
370C2×#476—711no—
371C2×#464—711no—
372C2×#464—711no—
373C2×#460—711no—
374C2×#446—711no—
375C2×#441—711no—
376C2×#440—711no—
377C2×C4×SD16—711no—
378C71C2×#337111yescharacteristic, complemented, Sylow
379C22×Q16—711no—
380C22×SD16—711no—
381C22×SD16—711no—
382#559—718no—
383#559—1424no—
384#557—24no—
385#557C2×D7118yescomplemented
386C2×C4⋊Q8—21no—
387C2×C4⋊Q8C2×D7111yescharacteristic
388C2×#127—711no—
389C2×#125—21no—
390C2×#125—21no—
391C2×#125C2×D7111yescharacteristic
392C2×#125C2×D7111yescharacteristic
393C2×#124—711no—
394C2×#124—711no—
395C2×#124—1421no—
396C2×#123—1421no—
397C2×#123—1421no—
398C2×C4×Q8—21no—
399C2×C4×Q8—711no—
400C2×C4×Q8C2×D7111yescharacteristic
401C2×C4×Q8C2×D7111yescharacteristic
402C2×C4×Q8C2×D7111yescharacteristic
403C2×C4×Q8C2×D7111yescharacteristic
404C2×C4×D4—711no—
405C2×C4×D4—711no—
406C2×C4×D4—1421no—
407#490—718no—
408#489—718no—
409#488—718no—
410#479—718no—
411#478—718no—
412#476—718no—
413#464—718no—
414#464—718no—
415#460—718no—
416#446—718no—
417#441—718no—
418#440—718no—
419C4×SD16—718no—
420C2×#107—711no—
421C2×#106—711no—
422C2×#106—711no—
423C2×C4⋊C8—711no—
424C2×C4⋊C8—711no—
425C2×C4⋊C8—711no—
426C2×#103—711no—
427C2×#103—711no—
428C2×#103—711no—
429C2×#103—711no—
430C2×#102—711no—
431C2×#102—711no—
432C2×#102—711no—
433C2×#102—711no—
434C2×#102—711no—
435C2×#102—711no—
436C2×#97—711no—
437C2×#97—711no—
438C2×C4×C8—711no—
439C22×Q8—21no—
440C22×Q8—711no—
441C22×Q8C22⋊D7111yescharacteristic
442C22×Q8C22×D7111yescharacteristic
443C22×D4—711no—
444C22×D4—711no—
445C22×D4—1421no—
446C22×D4—1421no—
447C23×C4—1421no—
448C23×C4—1421no—
449C2×Q16—714no—
450C2×Q16—1424no—
451C2×SD16—714no—
452C2×SD16—714no—
453C2×SD16—1424no—
454C2×SD16—1424no—
455C22×C8—711no—
456C22×C8—711no—
457C22×C8—711no—
458C22×C8—711no—
459C4⋊Q8—28no—
460C4⋊Q8—22no—
461C4⋊Q8C22×D7114yes—
462#127—714no—
463#127—1422no—
464#125—28no—
465#125—28no—
466#125—22no—
467#125—22no—
468#125C22×D7114yes—
469#125C22×D7114yes—
470#124—714no—
471#124—714no—
472#124—1428no—
473#124—1422no—
474#124—1422no—
475#123—1428no—
476#123—1428no—
477C4×Q8—28no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—714no—
482C4×Q8—1422no—
483C4×Q8C22⋊D7114yes—
484C4×Q8C22×D7114yes—
485C4×Q8C22×D7114yes—
486C4×Q8C22×D7114yes—
487C4×Q8C22×D7114yes—
488C4×D4—714no—
489C4×D4—714no—
490C4×D4—1428no—
491C4×D4—1422no—
492C4×D4—1422no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4C22⋊D7111yescharacteristic
504C2×C4⋊C4C22⋊D7111yescharacteristic
505C2×C4⋊C4C22⋊D7111yescharacteristic
506C2×C4⋊C4C22×D7111yescharacteristic
507C2×C4⋊C4C22×D7111yescharacteristic
508C2×C4⋊C4C22×D7111yescharacteristic
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1421no—
511C2×C22⋊C4—1421no—
512C2×C22⋊C4—1421no—
513C2×C22⋊C4—1421no—
514C2×C22⋊C4—1421no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—1421no—
519C2×C42C22×D7111yescharacteristic
520C2×C42C22×D7111yescharacteristic
521C2×C42C22×D7111yescharacteristic
522#107—714no—
523#106—714no—
524#106—714no—
525C4⋊C8—714no—
526C4⋊C8—714no—
527C4⋊C8—714no—
528#103—714no—
529#103—714no—
530#103—714no—
531#103—714no—
532#102—714no—
533#102—714no—
534#102—714no—
535#102—714no—
536#102—714no—
537#102—714no—
538#97—714no—
539#97—714no—
540C4×C8—714no—
541C24—1421no—
542C24—1421no—
543C2×Q8—21no—
544C2×Q8—24no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—712no—
549C2×Q8—1422no—
550C2×Q8—1422no—
551C2×Q8—1421no—
552C2×Q8C2×C22⋊D7114yes—
553C2×Q8#1176586614yes—
554C2×Q8C23×D7112yes—
555C2×D4—2844no—
556C2×D4—5682no—
557C2×D4—712no—
558C2×D4—712no—
559C2×D4—1424no—
560C2×D4—1421no—
561C2×D4—1421no—
562C2×D4—1424no—
563C2×D4—1422no—
564C2×D4—1422no—
565C2×D4—1422no—
566C2×D4—1422no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—5682no—
572C22×C4—5682no—
573C22×C4—1421no—
574C22×C4—1421no—
575C22×C4—1424no—
576C22×C4—1424no—
577C22×C4C2×C22⋊D7111yescharacteristic
578C22×C4C2×C22⋊D7111yescharacteristic
579C22×C4C2×C22⋊D7111yescharacteristic
580C22×C4C2×C22⋊D7111yescharacteristic
581C22×C4C2×C22⋊D7111yescharacteristic
582C22×C4C2×C22⋊D7111yescharacteristic
583C22×C4C23×D7111yescharacteristic
584Q16—1428no—
585SD16—1428no—
586SD16—1428no—
587C2×C8—712no—
588C2×C8—712no—
589C2×C8—712no—
590C2×C8—712no—
591C2×C8—1422no—
592C2×C8—1422no—
593C2×C8—1422no—
594C2×C8—1422no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—712no—
607C4⋊C4—1424no—
608C4⋊C4—1421no—
609C4⋊C4C2×C22⋊D7114yes—
610C4⋊C4C2×C22⋊D7114yes—
611C4⋊C4C2×C22⋊D7114yes—
612C4⋊C4C23×D7112yes—
613C4⋊C4C23×D7112yes—
614C4⋊C4C23×D7112yes—
615C22⋊C4—1424no—
616C22⋊C4—1424no—
617C22⋊C4—1424no—
618C22⋊C4—1424no—
619C22⋊C4—1424no—
620C22⋊C4—1424no—
621C42—24no—
622C42—24no—
623C42—24no—
624C42—1424no—
625C42C2×C22⋊D7112yes—
626C42C2×C22⋊D7112yes—
627C42C2×C22⋊D7112yes—
628C42C23×D7112yes—
629C42C23×D7112yes—
630C42C23×D7112yes—
631C23—2842no—
632C23—2842no—
633C23—2842no—
634C23—2842no—
635C23—2842no—
636C23—2842no—
637C23—1422no—
638C23—1422no—
639C23C22×C22⋊D7111yescharacteristic
640Q8—22no—
641Q8—24no—
642Q8—44no—
643Q8—48no—
644Q8—2842no—
645Q8—1422no—
646Q8—1422no—
647Q8C2×#1176586614yes—
648D4—2848no—
649D4—2842no—
650D4—2842no—
651D4—5684no—
652D4—1422no—
653D4—1422no—
654D4—1422no—
655D4—1422no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—2842no—
671C2×C4—2842no—
672C2×C4—5684no—
673C2×C4—5684no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4C22×C22⋊D7112yes—
677C2×C4C22×C22⋊D7112yes—
678C2×C4C22×C22⋊D7112yes—
679C2×C4C22×C22⋊D7112yes—
680C2×C4C22×C22⋊D7112yes—
681C2×C4C22×C22⋊D7112yes—
682C2×C4C22×C22⋊D7111yescharacteristic
683C2×C4C2×#1176586612yes—
684C2×C4#1455617612yes—
685C2×C4C24×D7111yescharacteristic
686C8—1422no—
687C8—1422no—
688C8—1422no—
689C8—1422no—
690C22—2842no—
691C22—2842no—
692C22—2842no—
693C22—2842no—
694C22—2842no—
695C22—2842no—
696C22—5684no—
697C22—5684no—
698C22#1798666012yes—
699C22#1798679712yes—
700C22#1798680712yes—
701C22C23×C22⋊D7111yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—2842no—
713C4—2842no—
714C4#1798666012yes—
715C4C22×#1176586611yescharacteristic
716C4C2×#1455617611yescharacteristic
717C2—5682no—
718C2—5682no—
719C2#2260110814yesdirect product factor
720C2C2×#1798666011yescharacteristic
721C2C2×#1798679711yescharacteristic
722C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#557×C71C2
socleC23×C71C22×D4
prime radicalC2×#14556125C22
hypercenterC2×#557D71
hypocenterC71C2×#3371
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. #22601108C2direct (N × H)
4. C2×#17986361C2semidirect
5. C2×#17986356C2semidirect
6. C2×#17986303C2semidirect
7. C2×#17986296C2semidirect
8. C2×#17986286C2semidirect
9. C2×#17986221C2semidirect
10. C2×#17986221C2semidirect
12. C2×#17986130C2semidirect
13. C2×#17986104C2semidirect
14. C2×#17986097C2semidirect
15. C2×C4×#11765852C2semidirect
16. C2×#557×C71C2semidirect
33. #17986361C22semidirect
34. #17986356C22semidirect
35. #17986303C22semidirect
36. #17986296C22semidirect
37. #17986286C22semidirect
38. #17986221C22semidirect
39. #17986221C22semidirect
41. #17986130C22semidirect
42. #17986104C22semidirect
43. #17986097C22semidirect
44. C4×#11765852C22semidirect
65. #557×C71C22semidirect
356. C2×C71#3371semidirect
363. C2×#557D71semidirect
378. C71C2×#3371semidirect
385. #557C2×D71semidirect
719. C2#22601108direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867342
#226011082
C2×#179863652
C2×#179863612
C2×#179863562
C2×#179863032
C2×#179862962
C2×#179862862
C2×#179862212
C2×#179861992
C2×#179861302
C2×#179861042
C2×#179860972
C2×C4×#117658522
C2×#557×C712
C2×#337171