Finite Group Databasebeta

← C2×#22592357 #32165423

Subgroups — C2×#22592357 #32165423

Order 18176.

2854 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556093C211yesmaximal, characteristic, complemented
2#22592357C2116yesmaximal, direct product factor
3C2×#17985922C211yesmaximal, characteristic
4C2×#17985919C211yesmaximal, characteristic, complemented
5C2×#17985918C211yesmaximal, characteristic, complemented
6C2×#17985911C211yesmaximal, characteristic
7C2×#17985906C211yesmaximal, characteristic, complemented
8C2×#17985894C211yesmaximal, characteristic, complemented
9C2×#17985887C211yesmaximal, characteristic
10C2×#17985887C211yesmaximal, characteristic
11C2×#17985885C211yesmaximal, characteristic, complemented
12C2×#17985880C211yesmaximal, characteristic, complemented
13C2×#17985880C211yesmaximal, characteristic, complemented
14C2×#17985872C211yesmaximal, characteristic
15C2×C4×C22⋊Dic71C211yesmaximal, characteristic
16C22×C22⋊Q8×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C2×#14556093—28no—
19C2×#14556093C2218yescomplemented
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
35#17985922C2218yes—
36#17985919C2218yescomplemented
37#17985918C2218yescomplemented
38#17985911C2218yes—
39#17985906C2218yescomplemented
40#17985894C2218yescomplemented
41#17985887C2218yes—
42#17985887C2218yes—
43#17985885C2218yescomplemented
44#17985880C2218yescomplemented
45#17985880C2218yescomplemented
46#17985872C2218yes—
47C4×C22⋊Dic71C2218yes—
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
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C23×Q8×C71C2211yescharacteristic
61C24×C4×C71C2211yescharacteristic
62C2×C22⋊Q8×C71—28no—
63C2×C22⋊Q8×C71C2218yes—
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69C22×Dic142—24no—
70C22×Dic142—24no—
71C22×Dic142—24no—
72C22×Dic142C2314yes—
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81#14556093—232no—
82C2×C4⋊Dic71—42no—
83C2×C4⋊Dic71C2314yes—
84C2×Dic71⋊C4—24no—
85C2×Dic71⋊C4—24no—
86C2×Dic71⋊C4—24no—
87C2×Dic71⋊C4—24no—
88C2×Dic71⋊C4—24no—
89C2×Dic71⋊C4—42no—
90C2×Dic71⋊C4C2314yes—
91C2×Dic71⋊C4C2314yes—
92C2×Dic71⋊C4C2314yes—
93C2×Dic71⋊C4C2314yes—
94C2×Dic71⋊C4C2314yes—
95C2×Dic71⋊C4C2314yes—
96C2×C22⋊Dic71—24no—
97C2×C22⋊Dic71—24no—
98C2×C22⋊Dic71—42no—
99C2×C22⋊Dic71Q818yescomplemented
100C2×C22⋊Dic71C2314yes—
101C2×C22⋊Dic71C2314yes—
102C2×C22⋊Dic71C2314yes—
103C2×C22⋊Dic71C2314yes—
104C2×C4×Dic71—24no—
105C2×C4×Dic71—24no—
106C2×C4×Dic71—24no—
107C2×C4×Dic71—42no—
108C2×C4×Dic71C2314yes—
109C2×C4×Dic71C2314yes—
110C2×C4×Dic71C2314yes—
111C2×C4×Dic71C2314yes—
112C71⋊#95C2314yes—
113C71⋊#95C2314yes—
114C71⋊#95C2314yes—
115C71⋊#95C2314yes—
116C71⋊#95C2314yes—
117C71⋊#95C2314yes—
118C71⋊#95C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C25×C71C2311yescharacteristic
125C22×Q8×C71—24no—
126C22×Q8×C71—24no—
127C22×Q8×C71—42no—
128C22×Q8×C71C2314yes—
129C23×C4×C71—24no—
130C23×C4×C71—24no—
131C23×C4×C71—42no—
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2314yes—
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C22⋊Q8×C71—232no—
140C2×C4⋊C4×C71—24no—
141C2×C4⋊C4×C71—24no—
142C2×C4⋊C4×C71D418yes—
143C2×C4⋊C4×C71C2314yes—
144C2×C4⋊C4×C71C2314yes—
145C2×C4⋊C4×C71C2314yes—
146C2×C22⋊C4×C71—24no—
147C2×C22⋊C4×C71—24no—
148C2×C22⋊C4×C71C2314yes—
149C2×C22⋊C4×C71C2314yes—
150C2×Dic142—232no—
151C2×Dic142—28no—
152C2×Dic142—28no—
153C2×Dic142—28no—
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×Dic71—22no—
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×Dic71C2×Q814yes—
175C22×Dic71C2×Q814yes—
176C22×Dic71#4114yes—
177C22×Dic71#4114yes—
178C22×Dic71C2412yes—
179C22×Dic71C2412yes—
180C22×Dic71C2412yes—
181C22×Dic71C2412yes—
182C22×Dic71C2412yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C4⋊Dic71—44no—
187Dic71⋊C4—28no—
188Dic71⋊C4—28no—
189Dic71⋊C4—28no—
190Dic71⋊C4—28no—
191Dic71⋊C4—28no—
192Dic71⋊C4—44no—
193C22⋊Dic71—28no—
194C22⋊Dic71—28no—
195C22⋊Dic71—44no—
196C22⋊Dic71C2×Q8116yescomplemented
197C4×Dic71—28no—
198C4×Dic71—28no—
199C4×Dic71—28no—
200C4×Dic71—44no—
201C24×C71—22no—
202C24×C71—22no—
203C24×C71—22no—
204C24×C71—22no—
205C24×C71—22no—
206C24×C71—22no—
207C24×C71C2×Q814yes—
208C24×C71C2412yes—
209C24×C71C2411yescharacteristic
210C2×Q8×C71—28no—
211C2×Q8×C71—28no—
212C2×Q8×C71—44no—
213C2×Q8×C71—416no—
214C22×C4×C71—22no—
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—28no—
229C22×C4×C71—28no—
230C22×C4×C71—44no—
231C22×C4×C71—416no—
232C22×C4×C71C2×D414yes—
233C22×C4×C71C2×D414yes—
234C22×C4×C71C2×D414yes—
235C22×C4×C71#4114yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C22×C4×C71C2412yes—
242C4⋊C4×C71—28no—
243C4⋊C4×C71—28no—
244C4⋊C4×C71C2×D4116yes—
245C22⋊C4×C71—28no—
246C22⋊C4×C71—28no—
247C23×C71—28no—
248C23×C71—28no—
249C23×C71—28no—
250C23×C71—22no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—22no—
254C23×C71—22no—
255C23×C71—22no—
256C23×C71—44no—
257C23×C71—44no—
258C23×C71—44no—
259C23×C71—44no—
260C23×C71C22×D412yes—
261C23×C71C22×Q814yes—
262C23×C71C22×Q812yes—
263C23×C71C2×#4112yes—
264C23×C71C2×#4112yes—
265C23×C71C2×#4112yes—
266C23×C71H(5,𝔽2)12yes—
267C23×C712−1+412yes—
268C23×C71C2511yescharacteristic
269Q8×C71—416no—
270C2×C4×C71—28no—
271C2×C4×C71—28no—
272C2×C4×C71—28no—
273C2×C4×C71—28no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
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—22no—
288C2×C4×C71—416no—
289C2×C4×C71—44no—
290C2×C4×C71—44no—
291C2×C4×C71C22×D414yes—
292C2×C4×C71C22×D414yes—
293C2×C4×C71C22×D414yes—
294C2×C4×C71C2×#4114yes—
295C2×Dic71—28no—
296C2×Dic71—28no—
297C2×Dic71—28no—
298C2×Dic71—28no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
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—44no—
320C2×Dic71—44no—
321C2×Dic71—44no—
322C2×Dic71—44no—
323C2×Dic71C22×Q814yes—
324C2×Dic71C22×Q814yes—
325C2×Dic71C2×#4114yes—
326C2×Dic71C2×#4114yes—
327Dic142—232no—
328C22×C71—24no—
329C22×C71—24no—
330C22×C71—24no—
331C22×C71—42no—
332C22×C71—42no—
333C22×C71—42no—
334C22×C71—42no—
335C22×C71—416no—
336C22×C71#52514yes—
337C22×C71#53314yes—
338C22×C71#54214yes—
339C22×C71#54614yes—
340C22×C71D4×Q814yes—
341C22×C71#55414yes—
342C22×C71#55614yes—
343C22×C71C23×D411yescharacteristic
344C22×C71C23×Q811yescharacteristic
345C22×C71C22×#4111yescharacteristic
346C22×C71C22×#4111yescharacteristic
347C22×C71C22×#4111yescharacteristic
348C22×C71C2×H(5,𝔽2)11yescharacteristic
349C22×C71C2×2−1+411yescharacteristic
350C4×C71—24no—
351C4×C71—24no—
352C4×C71—24no—
353C4×C71—24no—
354C4×C71—42no—
355C4×C71—42no—
356Dic71—24no—
357Dic71—24no—
358Dic71—24no—
359Dic71—24no—
360Dic71—42no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364C2×#2465—711nomaximal, Sylow
365C2×C71—44no—
366C2×C71#246518yescomplemented
367C2×C71C2×#52511yescharacteristic
368C2×C71C2×#53311yescharacteristic
369C2×C71C2×#54211yescharacteristic
370C2×C71C2×#54611yescharacteristic
371C2×C71C2×D4×Q811yescharacteristic
372C2×C71C2×#55411yescharacteristic
373C2×C71C2×#55611yescharacteristic
374C22×C22⋊Q8D7111yescharacteristic
375C22×C4×Q8—711no—
376#2465—7116no—
377C2×#396—711no—
378C2×#395—711no—
379C2×#395—711no—
380C2×#393—711no—
381C2×#391—711no—
382C2×#389—711no—
383C2×#388—711no—
384C2×#388—711no—
385C2×#387—711no—
386C2×#387—711no—
387C2×#387—711no—
388C2×#385—711no—
389C2×C4×C22⋊C4—711no—
390C71C2×#246511yescharacteristic, complemented, Sylow
391C23×Q8—711no—
392C23×Q8C2×D7111yescharacteristic
393C24×C4C2×D7111yescharacteristic
394C2×C22⋊Q8—28no—
395C2×C22⋊Q8C2×D7118yes—
396C2×C4×Q8—718no—
397C2×C4×Q8—1428no—
398C22×C4⋊C4—711no—
399C22×C4⋊C4—711no—
400C22×C4⋊C4—711no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405C22×C4⋊C4C2×D7111yescharacteristic
406C22×C4⋊C4C2×D7111yescharacteristic
407C22×C4⋊C4C2×D7111yescharacteristic
408C22×C22⋊C4—711no—
409C22×C22⋊C4—711no—
410C22×C22⋊C4—711no—
411C22×C22⋊C4—711no—
412C22×C22⋊C4C2×D7111yescharacteristic
413C22×C22⋊C4C2×D7111yescharacteristic
414C22×C42—711no—
415C22×C42—711no—
416C22×C42—711no—
417C22×C42—711no—
418#396—718no—
419#395—718no—
420#395—718no—
421#393—718no—
422#391—718no—
423#389—718no—
424#388—718no—
425#388—718no—
426#387—718no—
427#387—718no—
428#387—718no—
429#385—718no—
430C4×C22⋊C4—718no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—711no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95—711no—
437C2×#95—711no—
438C2×#95—711no—
439C2×#95—711no—
440C2×#95—711no—
441C2×#95—711no—
442C2×#95—711no—
443C25C22×D7111yescharacteristic
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8—42no—
447C22×Q8—714no—
448C22×Q8—1424no—
449C22×Q8—1424no—
450C22×Q8—1424no—
451C22×Q8C22×D7114yes—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—42no—
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—711no—
458C23×C4—711no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—711no—
463C23×C4C22×D7111yescharacteristic
464C23×C4C22×D7111yescharacteristic
465C23×C4C22×D7114yes—
466C23×C4C22×D7111yescharacteristic
467C23×C4C22×D7111yescharacteristic
468C23×C4C22×D7111yescharacteristic
469C23×C4C22×D7111yescharacteristic
470C22⋊Q8—232no—
471C4×Q8—14232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—2842no—
475C2×C4⋊C4—2842no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—714no—
479C2×C4⋊C4—714no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—1424no—
484C2×C4⋊C4—1424no—
485C2×C4⋊C4—1424no—
486C2×C4⋊C4—1424no—
487C2×C4⋊C4—1424no—
488C2×C4⋊C4C22⋊D7118yes—
489C2×C4⋊C4C22×D7114yes—
490C2×C4⋊C4C22×D7114yes—
491C2×C4⋊C4C22×D7114yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—2842no—
495C2×C22⋊C4—714no—
496C2×C22⋊C4—718no—
497C2×C22⋊C4—714no—
498C2×C22⋊C4—714no—
499C2×C22⋊C4—714no—
500C2×C22⋊C4—1424no—
501C2×C22⋊C4—1424no—
502C2×C22⋊C4C22×D7114yes—
503C2×C22⋊C4C22×D7114yes—
504C2×C42—2842no—
505C2×C42—714no—
506C2×C42—714no—
507C2×C42—714no—
508C2×C42—714no—
509C2×C42—1424no—
510C2×C42—1424no—
511C2×C42—1424no—
512#95—714no—
513#95—714no—
514#95—714no—
515#95—714no—
516#95—714no—
517#95—714no—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95—714no—
523#95—714no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24Q8×D7114yes—
531C24C23×D7112yes—
532C24C23×D7111yescharacteristic
533C2×Q8—28no—
534C2×Q8—28no—
535C2×Q8—44no—
536C2×Q8—416no—
537C2×Q8—1428no—
538C2×Q8—1428no—
539C2×Q8—14232no—
540C2×Q8—1428no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—44no—
558C22×C4—416no—
559C22×C4—714no—
560C22×C4—714no—
561C22×C4—714no—
562C22×C4—714no—
563C22×C4—712no—
564C22×C4—712no—
565C22×C4—712no—
566C22×C4—712no—
567C22×C4—712no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—712no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4—1422no—
591C22×C4C2×C22⋊D7114yes—
592C22×C4C2×C22⋊D7114yes—
593C22×C4C2×C22⋊D7114yes—
594C22×C4#1176586414yes—
595C22×C4C23×D7112yes—
596C22×C4C23×D7112yes—
597C22×C4C23×D7112yes—
598C22×C4C23×D7112yes—
599C22×C4C23×D7112yes—
600C22×C4C23×D7112yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—2844no—
604C4⋊C4—2844no—
605C4⋊C4—1428no—
606C4⋊C4—1428no—
607C4⋊C4—1428no—
608C4⋊C4—1428no—
609C4⋊C4—1428no—
610C4⋊C4C2×C22⋊D71116yes—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—2844no—
614C22⋊C4—7116no—
615C22⋊C4—1428no—
616C22⋊C4—1428no—
617C42—2844no—
618C42—1428no—
619C42—1428no—
620C42—1428no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23C22×C22⋊D7112yes—
635C23C2×Q8×D7114yes—
636C23C2×Q8×D7112yes—
637C23#41×D7112yes—
638C23#41×D7112yes—
639C23C2×#1176586412yes—
640C23#1455617312yes—
641C23#1455617612yes—
642C23C24×D7111yescharacteristic
643Q8—416no—
644Q8—14232no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—416no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—2844no—
667C2×C4—2844no—
668C2×C4—2844no—
669C2×C4—2844no—
670C2×C4—714no—
671C2×C4—714no—
672C2×C4—714no—
673C2×C4—714no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4—1422no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1428no—
695C2×C4—1428no—
696C2×C4—1428no—
697C2×C4—1428no—
698C2×C4C22×C22⋊D7114yes—
699C2×C4C22×C22⋊D7114yes—
700C2×C4C22×C22⋊D7114yes—
701C2×C4C2×#1176586414yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—416no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22#1798650614yes—
711C22#1798655114yes—
712C22#1798661914yes—
713C22#1798664314yes—
714C22Q8×C22⋊D7114yes—
715C22#1798670314yes—
716C22#1798672014yes—
717C22C23×C22⋊D7111yescharacteristic
718C22C22×Q8×D7111yescharacteristic
719C22C2×#41×D7111yescharacteristic
720C22C2×#41×D7111yescharacteristic
721C22C22×#1176586411yescharacteristic
722C22C2×#1455617311yescharacteristic
723C22C2×#1455617611yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4—2842no—
734C4—1424no—
735C4—1424no—
736C4—1424no—
737C4—1424no—
738C2—44no—
739C2#2259235718yesdirect product factor
740C2C2×#1798650611yescharacteristic
741C2C2×#1798655111yescharacteristic
742C2C2×#1798661911yescharacteristic
743C2C2×#1798664311yescharacteristic
744C2C2×Q8×C22⋊D7111yescharacteristic
745C2C2×#1798670311yescharacteristic
746C2C2×#1798672011yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC25×C71C23
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2465
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556093C2semidirect
2. #22592357C2direct (N × H)
4. C2×#17985919C2semidirect
5. C2×#17985918C2semidirect
7. C2×#17985906C2semidirect
8. C2×#17985894C2semidirect
11. C2×#17985885C2semidirect
12. C2×#17985880C2semidirect
13. C2×#17985880C2semidirect
19. C2×#14556093C22semidirect
36. #17985919C22semidirect
37. #17985918C22semidirect
39. #17985906C22semidirect
40. #17985894C22semidirect
43. #17985885C22semidirect
44. #17985880C22semidirect
45. #17985880C22semidirect
99. C2×C22⋊Dic71Q8semidirect
196. C22⋊Dic71C2×Q8semidirect
366. C2×C71#2465semidirect
390. C71C2×#2465semidirect
739. C2#22592357direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560932
#225923572
C2×#179859222
C2×#179859192
C2×#179859182
C2×#179859112
C2×#179859062
C2×#179858942
C2×#179858872
C2×#179858852
C2×#179858802
C2×#179858722
C2×C4×C22⋊Dic712
C22×C22⋊Q8×C712
C2×#246571