Finite Group Databasebeta

← C2×#22601957 #32904544

Subgroups — C2×#22601957 #32904544

Order 18176.

7706 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
1#22601957C2132yesmaximal, direct product factor
2C2×#17986725C211yesmaximal, characteristic, complemented
3C2×#17986721C213yesmaximal, complemented
4C2×#17986690C213yesmaximal, complemented
5C2×#17986684C213yesmaximal, complemented
6C2×Q8×C22⋊D71C211yesmaximal, characteristic, complemented
7C2×#17986661C211yesmaximal, characteristic, complemented
8C2×#17986660C211yesmaximal, characteristic, complemented
9C2×#17986650C213yesmaximal, complemented
10C2×#17986553C213yesmaximal, complemented
11C2×#17986536C213yesmaximal, complemented
12C2×#17986533C213yesmaximal, complemented
13C2×C4×#11765866C211yesmaximal, characteristic, complemented
14C2×C4×#11765865C213yesmaximal, complemented
15C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×#11765865C2213yes—
19C22×Q8×D71C2211yescharacteristic
20#17986725C22116yescomplemented
21#17986721C22148yescomplemented
22#17986690C22148yescomplemented
23#17986684C22148yescomplemented
24Q8×C22⋊D71C22116yescomplemented
25#17986661C22116yescomplemented
26#17986660C22116yescomplemented
27#17986650C22148yescomplemented
28#17986553C22148yescomplemented
29C2×#14556127C2213yes—
30C2×#14556126C2213yes—
31#17986536C22148yescomplemented
32#17986533C22148yescomplemented
33C2×#14556123C2216yes—
34C2×#14556122C2216yes—
35C2×#14556120C2213yes—
36C2×#14556119C2213yes—
37C2×#14556118C2216yes—
38C2×#14556117C2213yes—
39C2×#14556116C2213yes—
40C2×#14556113C2216yes—
41C2×#14556111C2216yes—
42C2×#14556108C2213yes—
43C2×#14556107C2213yes—
44C2×#14556106C2216yes—
45C2×#14556104C2213yes—
46C2×#14556104C2213yes—
47C2×#14556103C2213yes—
48C2×#14556102C2213yes—
49C4×#11765866C22116yescomplemented
50C4×#11765865C22148yescomplemented
51C2×Q8×Dic71C2211yescharacteristic
52C2×Q8×Dic71C2211yescharacteristic
53C2×C4×Dic142C2213yes—
54C2×C4×Dic142C2213yes—
55C2×C4×Dic142C2213yes—
56C2×#14556093C2213yes—
57C4×Q8×D71C22116yescomplemented
58C2×C4×D284C2213yes—
59C2×C4×D284C2213yes—
60C2×C4×D284C2213yes—
61C2×#14556090C2213yes—
62C2×C4×C22⋊D71C2211yescharacteristic
63C2×C4×C22⋊D71C2213yes—
64C2×C4×C22⋊D71C2213yes—
65C2×C4×C22⋊D71C2213yes—
66C2×#14556087C2213yes—
67C2×#14556086C2213yes—
68C2×#14556085C2213yes—
69C2×#14556085C2213yes—
70C2×#14556085C2216yes—
71C2×C4⋊C4×D71C2213yes—
72C2×C42×D71C2213yes—
73C2×C42×D71C2213yes—
74C23×Q8×C71C2211yescharacteristic
75C2×C4×Q8×C71C2211yescharacteristic
76C2×C4×Q8×C71C2211yescharacteristic
77C2×C4×Q8×C71C2213yes—
78C2×C4×Q8×C71C2213yes—
79C2×C4×Q8×C71C22116yescomplemented
80C22×C4⋊C4×C71C2213yes—
81C22×C42×C71C2213yes—
82C2×#11765866—28no—
83C2×#11765866C2318yes—
84C2×#11765865—224no—
85C2×#11765865C23124yes—
86C22×Dic142C2313yes—
87C22×Dic142C2313yes—
88C2×Q8×D71—28no—
89C2×Q8×D71C2318yes—
90C22×D284C2313yes—
91C22×D284C2313yes—
92C22×C22⋊D71C2313yes—
93C22×C22⋊D71C2311yescharacteristic
94C22×C4×D71C2313yes—
95C22×C4×D71C2313yes—
96C22×C4×D71C2313yes—
97C22×C4×D71C2313yes—
98C22×C4×D71C2311yescharacteristic
99C22×C4×D71C2313yes—
100#14556127C23124yes—
101#14556126C23124yes—
102#14556123C23148yes—
103#14556122C23148yes—
104#14556120C23124yes—
105#14556119C23124yes—
106#14556118C23148yes—
107#14556117C23124yes—
108#14556116C23124yes—
109#14556113C23148yes—
110#14556111C23148yes—
111#14556108C23124yes—
112#14556107C23124yes—
113#14556106C23148yes—
114#14556104C23124yes—
115#14556104C23124yes—
116#14556103C23124yes—
117#14556102C23124yes—
118Q8×Dic71C2318yes—
119Q8×Dic71C2318yes—
120C4×Dic142C23124yes—
121C4×Dic142C23124yes—
122C4×Dic142C23124yes—
123#14556093C23124yes—
124C4×D284C23124yes—
125C4×D284C23124yes—
126C4×D284C23124yes—
127#14556090C23124yes—
128C4×C22⋊D71C23124yes—
129C4×C22⋊D71C23124yes—
130C4×C22⋊D71C2318yes—
131C4×C22⋊D71C23124yes—
132#14556087C23124yes—
133#14556086C23124yes—
134#14556085C23124yes—
135#14556085C23124yes—
136#14556085C23148yes—
137C2×C4⋊Dic71C2313yes—
138C2×C4⋊Dic71C2313yes—
139C2×C4⋊Dic71C2313yes—
140C2×C4⋊Dic71C2313yes—
141C2×Dic71⋊C4C2316yes—
142C2×Dic71⋊C4C2311yescharacteristic
143C2×Dic71⋊C4C2313yes—
144C2×Dic71⋊C4C2313yes—
145C2×Dic71⋊C4C2313yes—
146C2×Dic71⋊C4C2316yes—
147C2×Dic71⋊C4C2316yes—
148C4⋊C4×D71C23124yes—
149C2×C22⋊Dic71C2311yescharacteristic
150C2×C22⋊Dic71C2313yes—
151C2×(C2×D71)⋊C4C2311yescharacteristic
152C2×(C2×D71)⋊C4C2313yes—
153C2×(C2×D71)⋊C4C2313yes—
154C2×(C2×D71)⋊C4C2313yes—
155C2×(C2×D71)⋊C4C2316yes—
156C2×(C2×D71)⋊C4C2316yes—
157C2×(C2×D71)⋊C4C2316yes—
158C2×C4×Dic71C2311yescharacteristic
159C2×C4×Dic71C2313yes—
160C2×C4×Dic71C2313yes—
161C2×C4×Dic71C2313yes—
162C2×C4×Dic71C2313yes—
163C2×C4×Dic71C2313yes—
164C42×D71C23124yes—
165C42×D71C23124yes—
166C22×Q8×C71—28no—
167C22×Q8×C71C2318yes—
168C22×Q8×C71C2313yes—
169C22×Q8×C71C2311yescharacteristic
170C23×C4×C71C2313yes—
171C23×C4×C71C2311yescharacteristic
172C23×C4×C71C2313yes—
173C4×Q8×C71C2318yes—
174C4×Q8×C71C23124yes—
175C4×Q8×C71C2318yes—
176C4×Q8×C71C23124yes—
177C2×C4⋊C4×C71C23124yes—
178C2×C4⋊C4×C71C2313yes—
179C2×C4⋊C4×C71C2313yes—
180C2×C4⋊C4×C71C2316yes—
181C2×C42×C71C2313yes—
182C2×C42×C71C2313yes—
183C2×C42×C71C2313yes—
184C2×C42×C71C2313yes—
185C2×C42×C71C23124yes—
186C23×D71C2413yes—
187C23×D71C2411yescharacteristic
188#11765866—232no—
189#11765865—296no—
190C2×Dic142—212no—
191C2×Dic142—212no—
192C2×Dic142C24112yes—
193C2×Dic142C24112yes—
194Q8×D71—232no—
195C2×D284—212no—
196C2×D284—212no—
197C2×D284C24112yes—
198C2×D284C24112yes—
199C2×C22⋊D71—212no—
200C2×C22⋊D71#4118yescomplemented
201C2×C22⋊D71C24112yes—
202C2×C22⋊D71C2414yes—
203C22×Dic71C2411yescharacteristic
204C22×Dic71C2413yes—
205C22×Dic71C2413yes—
206C22×Dic71C2411yescharacteristic
207C22×Dic71C2413yes—
208C22×Dic71C2411yescharacteristic
209C2×C4×D71—212no—
210C2×C4×D71—212no—
211C2×C4×D71—212no—
212C2×C4×D71—24no—
213C2×C4×D71—212no—
214C2×C4×D71—212no—
215C2×C4×D71C24112yes—
216C2×C4×D71C24112yes—
217C2×C4×D71C24112yes—
218C2×C4×D71C24112yes—
219C2×C4×D71C2414yes—
220C2×C4×D71C24112yes—
221C4⋊Dic71C24112yes—
222C4⋊Dic71C24112yes—
223C4⋊Dic71C24112yes—
224C4⋊Dic71C24112yes—
225Dic71⋊C4C24124yes—
226Dic71⋊C4C2414yes—
227Dic71⋊C4C24112yes—
228Dic71⋊C4C24112yes—
229Dic71⋊C4C24112yes—
230Dic71⋊C4C24124yes—
231Dic71⋊C4C24124yes—
232C22⋊Dic71C2414yes—
233C22⋊Dic71C24112yes—
234(C2×D71)⋊C4C2414yes—
235(C2×D71)⋊C4C24112yes—
236(C2×D71)⋊C4C24112yes—
237(C2×D71)⋊C4C24112yes—
238(C2×D71)⋊C4C24124yes—
239(C2×D71)⋊C4C24124yes—
240(C2×D71)⋊C4C24124yes—
241C4×Dic71C2414yes—
242C4×Dic71C24112yes—
243C4×Dic71C24112yes—
244C4×Dic71C24112yes—
245C4×Dic71C24112yes—
246C4×Dic71C24112yes—
247C24×C71C2411yescharacteristic
248C2×Q8×C71—232no—
249C2×Q8×C71—212no—
250C2×Q8×C71#4118yescomplemented
251C2×Q8×C71C24112yes—
252C2×Q8×C71C2414yes—
253C22×C4×C71—212no—
254C22×C4×C71—212no—
255C22×C4×C71—24no—
256C22×C4×C71C2413yes—
257C22×C4×C71C2413yes—
258C22×C4×C71C24112yes—
259C22×C4×C71C2411yescharacteristic
260C22×C4×C71C2414yes—
261C22×C4×C71C2413yes—
262C22×C4×C71C24112yes—
263C22×C4×C71C2413yes—
264C22×C4×C71C2411yescharacteristic
265C4⋊C4×C71C24112yes—
266C4⋊C4×C71C24112yes—
267C4⋊C4×C71C24124yes—
268C42×C71C24112yes—
269C42×C71C24112yes—
270C42×C71C24112yes—
271C42×C71C24112yes—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71C2×#4114yes—
275C23×C71C2512yes—
276C23×C71C2511yescharacteristic
277C22×D71—22no—
278C22×D71—22no—
279C22×D71—26no—
280C22×D71—26no—
281C22×D71—26no—
282C22×D71C2×#4114yes—
283C22×D71C2516yes—
284C22×D71C2512yes—
285Q8×C71—224no—
286Q8×C71C2×#41116yescomplemented
287C2×C4×C71—26no—
288C2×C4×C71—26no—
289C2×C4×C71—26no—
290C2×C4×C71—224no—
291C2×C4×C71—22no—
292C2×C4×C71—224no—
293C2×C4×C71—28no—
294C2×C4×C71C2×#41112yes—
295C2×C4×C712−1+414yes—
296C2×C4×C71C2512yes—
297C2×C4×C71C2516yes—
298C2×C4×C71C2516yes—
299C2×C4×C71C2516yes—
300C2×C4×C71C2516yes—
301C2×C4×C71C2512yes—
302C22⋊D71—224no—
303C22⋊D71C2×#41116yescomplemented
304C2×Dic71—22no—
305C2×Dic71—26no—
306C2×Dic71—26no—
307C2×Dic71—22no—
308C2×Dic71—26no—
309C2×Dic71C2×#4114yes—
310C2×Dic71C2512yes—
311C2×Dic71C2512yes—
312C2×Dic71C2516yes—
313C2×Dic71C2516yes—
314C2×Dic71C2516yes—
315C2×Dic71C2512yes—
316D284—224no—
317D284—224no—
318C4×D71—224no—
319C4×D71—224no—
320C4×D71—224no—
321C4×D71—28no—
322C4×D71—224no—
323C4×D71—224no—
324Dic142—224no—
325Dic142—224no—
326C22×C71—22no—
327C22×C71—22no—
328C22×C71—28no—
329C22×C71C22×#4114yes—
330C22×C71C22×#4112yes—
331C22×C71C22×#4112yes—
332C22×C71C2×2−1+412yes—
333C22×C71C2611yescharacteristic
334C2×D71—22no—
335C2×D71—22no—
336C2×D71—28no—
337C2×D71—26no—
338C2×D71—26no—
339C2×D71—26no—
340C2×D71—412no—
341C2×D71C22×#4114yes—
342C4×C71—26no—
343C4×C71—26no—
344C4×C71—26no—
345C4×C71—22no—
346C4×C71C22×#41112yes—
347C4×C71C2×2−1+414yes—
348Dic71—26no—
349Dic71—26no—
350Dic71—22no—
351Dic71—22no—
352Dic71—26no—
353Dic71C22×#4114yes—
354C2×#3482—711nomaximal, Sylow
355C2×C71—24no—
356C2×C71#348214yescomplemented
357C2×C71C23×#4111yescharacteristic
358C2×C71C23×#4111yescharacteristic
359C2×C71C22×2−1+411yescharacteristic
360D71—24no—
361D71—46no—
362#3482—7132no—
363C2×#557—711no—
364C2×#556—713no—
365C2×#552—713no—
366C2×#552—713no—
367C2×D4×Q8—711no—
368C2×#548—711no—
369C2×#548—711no—
370C2×#547—713no—
371C2×#533—713no—
372C2×#529—713no—
373C2×#529—713no—
374C2×C4×#41—713no—
375C2×C4×#41—711no—
376C22×C4×Q8—711no—
377C22×C4×Q8D7111yescharacteristic, complemented
378C71C2×#348211yescharacteristic, complemented, Sylow
379C22×#41—711no—
380C22×#41—713no—
381C23×Q8—711no—
382C23×Q8C2×D7111yescharacteristic
383#557—7116no—
384#556—7148no—
385#552—7148no—
386#552—7148no—
387D4×Q8—7116no—
388#548—7116no—
389#548—7116no—
390#547—7148no—
391#533—7148no—
392C2×C4⋊Q8—713no—
393C2×C4⋊Q8—713no—
394#529—7148no—
395#529—7148no—
396C2×#126—716no—
397C2×#126—716no—
398C2×#125—713no—
399C2×#125—716no—
400C2×#125—713no—
401C2×#124—713no—
402C2×#124—713no—
403C2×#123—716no—
404C2×#123—716no—
405C2×C22⋊Q8—713no—
406C2×C22⋊Q8—713no—
407C2×C22⋊Q8—713no—
408C2×C22⋊Q8—716no—
409C2×C22⋊Q8—713no—
410C2×#121—713no—
411C2×#121—713no—
412C4×#41—7116no—
413C4×#41—7148no—
414C2×C4×Q8—711no—
415C2×C4×Q8—711no—
416C2×C4×Q8—7116no—
417C2×C4×Q8—713no—
418C2×C4×Q8—713no—
419C2×C4×Q8—713no—
420C2×C4×Q8—713no—
421C2×C4×Q8C2×D7111yescharacteristic
422C2×C4×Q8C2×D7113yes—
423C2×C4×Q8C2×D7111yescharacteristic
424C2×C4×Q8C2×D7113yes—
425C2×C4×Q8C2×D71116yescomplemented
426C2×C4×D4—711no—
427C2×C4×D4—713no—
428C2×C4×D4—713no—
429C2×C4×D4—713no—
430C2×C4×D4—713no—
431C2×C4×D4—713no—
432C2×C4×D4—713no—
433C2×C4×D4—713no—
434C2×#117—713no—
435C2×#117—713no—
436C2×#117—713no—
437C2×#117—713no—
438C2×#117—716no—
439C22×C4⋊C4—713no—
440C22×C4⋊C4C2×D7113yes—
441C22×C42—713no—
442C22×C42—713no—
443C22×C42C2×D7113yes—
444C2×#41—718no—
445C2×#41—7124no—
446C2×#41—14224no—
447C2×#41—1428no—
448C22×Q8—28no—
449C22×Q8—718no—
450C22×Q8—713no—
451C22×Q8—713no—
452C22×Q8—1428no—
453C22×Q8C22×D7113yes—
454C22×Q8C22×D7118yes—
455C22×Q8C22×D7111yescharacteristic
456C22×D4—711no—
457C22×D4—713no—
458C22×D4—713no—
459C22×D4—713no—
460C23×C4—713no—
461C23×C4—713no—
462C23×C4—713no—
463C23×C4—713no—
464C23×C4—713no—
465C23×C4—711no—
466C23×C4C22×D7113yes—
467C23×C4C22×D7113yes—
468C23×C4C22×D7111yescharacteristic
469C4⋊Q8—7124no—
470C4⋊Q8—7124no—
471#126—7148no—
472#126—7148no—
473#125—7124no—
474#125—7148no—
475#125—7124no—
476#124—7124no—
477#124—7124no—
478#123—7148no—
479#123—7148no—
480C22⋊Q8—7124no—
481C22⋊Q8—7124no—
482C22⋊Q8—7124no—
483C22⋊Q8—7148no—
484C22⋊Q8—7124no—
485#121—7124no—
486#121—7124no—
487C4×Q8—718no—
488C4×Q8—718no—
489C4×Q8—7124no—
490C4×Q8—7124no—
491C4×Q8—7124no—
492C4×Q8—7124no—
493C4×Q8C22×D7118yes—
494C4×Q8C22×D71124yes—
495C4×Q8C22×D7118yes—
496C4×Q8C22×D71124yes—
497C4×D4—718no—
498C4×D4—7124no—
499C4×D4—7124no—
500C4×D4—7124no—
501C4×D4—7124no—
502C4×D4—7124no—
503C4×D4—7124no—
504C4×D4—7124no—
505#117—7124no—
506#117—7124no—
507#117—7124no—
508#117—7124no—
509#117—7148no—
510C2×C4⋊C4—713no—
511C2×C4⋊C4—716no—
512C2×C4⋊C4—711no—
513C2×C4⋊C4—713no—
514C2×C4⋊C4—713no—
515C2×C4⋊C4—713no—
516C2×C4⋊C4—713no—
517C2×C4⋊C4—713no—
518C2×C4⋊C4—713no—
519C2×C4⋊C4—716no—
520C2×C4⋊C4—716no—
521C2×C4⋊C4—7124no—
522C2×C4⋊C4C22×D7113yes—
523C2×C4⋊C4C22×D7113yes—
524C2×C4⋊C4C22×D7116yes—
525C2×C4⋊C4C22×D71124yes—
526C2×C22⋊C4—711no—
527C2×C22⋊C4—713no—
528C2×C22⋊C4—711no—
529C2×C22⋊C4—713no—
530C2×C22⋊C4—716no—
531C2×C22⋊C4—713no—
532C2×C22⋊C4—713no—
533C2×C22⋊C4—716no—
534C2×C22⋊C4—716no—
535C2×C42—713no—
536C2×C42—713no—
537C2×C42—713no—
538C2×C42—713no—
539C2×C42—713no—
540C2×C42—711no—
541C2×C42—7124no—
542C2×C42—7124no—
543C2×C42C22×D7113yes—
544C2×C42C22×D7113yes—
545C2×C42C22×D71124yes—
546C2×C42C22×D7113yes—
547C2×C42C22×D7113yes—
548C24—711no—
549C24—713no—
550C24C23×D7111yescharacteristic
551#41—14296no—
552#41—14232no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—7112no—
556C2×Q8—7112no—
557C2×Q8—14212no—
558C2×Q8—14232no—
559C2×Q8—14212no—
560C2×Q8#1176586518yescomplemented
561C2×Q8C23×D71112yes—
562C2×Q8C23×D7114yes—
563C2×D4—718no—
564C2×D4—714no—
565C2×D4—7112no—
566C2×D4—7112no—
567C2×D4—7112no—
568C2×D4—14212no—
569C2×D4—14212no—
570C2×D4—14212no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—711no—
575C22×C4—711no—
576C22×C4—711no—
577C22×C4—713no—
578C22×C4—713no—
579C22×C4—713no—
580C22×C4—714no—
581C22×C4—7112no—
582C22×C4—7112no—
583C22×C4—7112no—
584C22×C4—7112no—
585C22×C4—7112no—
586C22×C4—14212no—
587C22×C4—14212no—
588C22×C4—14212no—
589C22×C4—14212no—
590C22×C4—14212no—
591C22×C4—1424no—
592C22×C4C23×D7113yes—
593C22×C4C23×D7111yescharacteristic
594C22×C4C23×D7114yes—
595C22×C4C23×D7113yes—
596C22×C4C23×D7113yes—
597C22×C4C23×D71112yes—
598C22×C4C23×D71112yes—
599C22×C4C23×D7113yes—
600C22×C4C23×D7111yescharacteristic
601C4⋊C4—7124no—
602C4⋊C4—714no—
603C4⋊C4—7112no—
604C4⋊C4—7112no—
605C4⋊C4—7112no—
606C4⋊C4—7124no—
607C4⋊C4—7124no—
608C4⋊C4—7112no—
609C4⋊C4—7112no—
610C4⋊C4—7112no—
611C4⋊C4—7112no—
612C4⋊C4C23×D71112yes—
613C4⋊C4C23×D71112yes—
614C4⋊C4C23×D71124yes—
615C22⋊C4—714no—
616C22⋊C4—7112no—
617C22⋊C4—714no—
618C22⋊C4—7112no—
619C22⋊C4—7124no—
620C22⋊C4—7112no—
621C22⋊C4—7112no—
622C22⋊C4—7124no—
623C22⋊C4—7124no—
624C42—714no—
625C42—7112no—
626C42—7112no—
627C42—7112no—
628C42—7112no—
629C42—7112no—
630C42C23×D71112yes—
631C42C23×D71112yes—
632C42C23×D71112yes—
633C42C23×D71112yes—
634C23—22no—
635C23—22no—
636C23—714no—
637C23—712no—
638C23—716no—
639C23—1426no—
640C23—1426no—
641C23—1426no—
642C23—1422no—
643C23—1422no—
644C23#41×D7114yes—
645C23C24×D7112yes—
646C23C24×D7111yescharacteristic
647Q8—224no—
648Q8—14224no—
649Q8—14224no—
650Q8C2×#11765865116yescomplemented
651D4—7116no—
652D4—14224no—
653D4—14224no—
654D4—14224no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—714no—
663C2×C4—712no—
664C2×C4—712no—
665C2×C4—712no—
666C2×C4—716no—
667C2×C4—716no—
668C2×C4—716no—
669C2×C4—14224no—
670C2×C4—14224no—
671C2×C4—1426no—
672C2×C4—1422no—
673C2×C4—1426no—
674C2×C4—1422no—
675C2×C4—1426no—
676C2×C4—14224no—
677C2×C4—14224no—
678C2×C4—14224no—
679C2×C4—1428no—
680C2×C4C2×#11765865112yes—
681C2×C4#1455617614yes—
682C2×C4C24×D7116yes—
683C2×C4C24×D7112yes—
684C2×C4C24×D7116yes—
685C2×C4C24×D7116yes—
686C2×C4C24×D7116yes—
687C2×C4C24×D7112yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—28412no—
692C22—714no—
693C22—1426no—
694C22—1426no—
695C22—1426no—
696C22—1422no—
697C22—1422no—
698C22—1428no—
699C22C2×#41×D7114yes—
700C22C2×#41×D7112yes—
701C22C22×#1176586512yes—
702C22C2×#1455617612yes—
703C22C25×D7111yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—714no—
709C4—1426no—
710C4—1422no—
711C4—1426no—
712C4—1422no—
713C4—1426no—
714C4C22×#11765865112yes—
715C4C2×#1455617614yes—
716C2—24no—
717C2—2846no—
718C2—1424no—
719C2#2260195714yesdirect product factor
720C2C22×#41×D7111yescharacteristic
721C2C23×#1176586511yescharacteristic
722C2C22×#1455617611yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC22×C4×Q8×C71C2
socleC23×C71C25
hypercenterC22×C4×Q8D71
hypocenterC71C2×#3482
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #22601957C2direct (N × H)
2. C2×#17986725C2semidirect
3. C2×#17986721C2semidirect
4. C2×#17986690C2semidirect
5. C2×#17986684C2semidirect
6. C2×Q8×C22⋊D71C2semidirect
7. C2×#17986661C2semidirect
8. C2×#17986660C2semidirect
9. C2×#17986650C2semidirect
10. C2×#17986553C2semidirect
11. C2×#17986536C2semidirect
12. C2×#17986533C2semidirect
13. C2×C4×#11765866C2semidirect
14. C2×C4×#11765865C2semidirect
15. C2×C4×Q8×D71C2semidirect
16. C22×C4×Q8×C71C2semidirect
20. #17986725C22semidirect
21. #17986721C22semidirect
22. #17986690C22semidirect
23. #17986684C22semidirect
24. Q8×C22⋊D71C22semidirect
25. #17986661C22semidirect
26. #17986660C22semidirect
27. #17986650C22semidirect
28. #17986553C22semidirect
31. #17986536C22semidirect
32. #17986533C22semidirect
49. C4×#11765866C22semidirect
50. C4×#11765865C22semidirect
57. C4×Q8×D71C22semidirect
79. C2×C4×Q8×C71C22semidirect
200. C2×C22⋊D71#41semidirect
250. C2×Q8×C71#41semidirect
286. Q8×C71C2×#41semidirect
303. C22⋊D71C2×#41semidirect
356. C2×C71#3482semidirect
377. C22×C4×Q8D71semidirect
378. C71C2×#3482semidirect
425. C2×C4×Q8C2×D71semidirect
560. C2×Q8#11765865semidirect
650. Q8C2×#11765865semidirect
719. C2#22601957direct (N × H)

Maximal subgroups

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

subgroupindex
#226019572
C2×#179867252
C2×#179867212
C2×#179866902
C2×#179866842
C2×Q8×C22⋊D712
C2×#179866612
C2×#179866602
C2×#179866502
C2×#179865532
C2×#179865362
C2×#179865332
C2×C4×#117658662
C2×C4×#117658652
C2×C4×Q8×D712
C22×C4×Q8×C712
C2×#348271