Finite Group Databasebeta

← C2×#22602222 #32905893

Subgroups — C2×#22602222 #32905893

Order 18176.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602222C2132yesmaximal, direct product factor
2C2×#17986726C214yesmaximal, complemented
3C2×#17986716C214yesmaximal, complemented
4C2×#17986685C214yesmaximal, complemented
5C2×#17986681C214yesmaximal, complemented
6C2×#17986612C211yesmaximal, characteristic, complemented
7C2×#17986611C211yesmaximal, characteristic, complemented
8C2×#17986610C211yesmaximal, characteristic, complemented
9C2×#17986572C212yesmaximal
10C2×#17986555C211yesmaximal, characteristic, complemented
11C2×#17986553C212yesmaximal, complemented
12C2×#17986551C212yesmaximal, complemented
13C2×C4⋊Q8×D71C211yesmaximal, characteristic, complemented
14C2×#17986475C212yesmaximal, complemented
15C2×#17986467C211yesmaximal, characteristic
16C2×#541×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×Q8×D71C2212yes—
19#17986726C22164yescomplemented
20#17986716C22164yescomplemented
21#17986685C22164yescomplemented
22#17986681C22164yescomplemented
23#17986612C22116yescomplemented
24#17986611C22116yescomplemented
25#17986610C22116yescomplemented
26#17986572C22132yes—
27#17986555C22116yescomplemented
28#17986553C22132yescomplemented
29#17986551C22132yescomplemented
30C2×#14556128C2211yescharacteristic
31C2×#14556127C2214yes—
32C2×#14556127C2212yes—
33C2×#14556127C2214yes—
34C2×#14556126C2212yes—
35C4⋊Q8×D71C22116yescomplemented
36C2×#14556123C2214yes—
37C2×#14556123C2214yes—
38C2×#14556121C2214yes—
39C2×#14556120C2211yescharacteristic
40C2×#14556119C2214yes—
41C2×#14556118C2214yes—
42C2×#14556118C2214yes—
43C2×#14556118C2214yes—
44C2×#14556118C2214yes—
45C2×#14556114C2214yes—
46C2×#14556113C2214yes—
47C2×#14556110C2214yes—
48C2×#14556108C2212yes—
49C2×#14556107C2212yes—
50C2×#14556106C2214yes—
51C2×#14556106C2214yes—
52C2×#14556105C2214yes—
53C2×#14556104C2212yes—
54#17986475C22132yescomplemented
55#17986467C22116yes—
56C2×Q8×Dic71C2212yes—
57C2×C4×Dic142C2214yes—
58C2×C4×Dic142C2212yes—
59C2×C4×Dic142C2214yes—
60C2×#14556093C2212yes—
61C2×#14556093C2212yes—
62C2×#14556093C2214yes—
63C2×#14556093C2214yes—
64C2×#14556093C2214yes—
65C2×#14556090C2212yes—
66C2×(C22⋊D71)⋊C4C2212yes—
67C2×(C22⋊D71)⋊C4C2212yes—
68C2×#14556086C2214yes—
69C2×#14556086C2212yes—
70C2×#14556085C2211yescharacteristic
71C2×#14556085C2211yescharacteristic
72C2×#14556085C2214yes—
73C2×#14556085C2214yes—
74C2×#14556084C2214yes—
75C2×C4⋊C4×D71C2214yes—
76C22×C4×Dic71C2211yescharacteristic
77C2×C42×D71C2211yescharacteristic
78C2×C42×D71C2211yescharacteristic
79#541×C71C22116yescomplemented
80C2×C4⋊Q8×C71C2211yescharacteristic
81C2×#126×C71C2214yes—
82C2×#125×C71C2214yes—
83C2×#125×C71C2211yescharacteristic
84C2×C22⋊Q8×C71C2212yes—
85C2×C4×Q8×C71C2212yes—
86C2×#117×C71C2211yescharacteristic
87C2×#11765865—28no—
88C2×#11765865C2318yes—
89C22×Dic142C2312yes—
90C22×Dic142C2314yes—
91C22×Dic142C2311yescharacteristic
92C22×Dic142C2314yes—
93C2×Q8×D71—216no—
94C2×Q8×D71C23116yes—
95C22×D284C2311yescharacteristic
96C22×C22⋊D71C2311yescharacteristic
97C22×C22⋊D71C2311yescharacteristic
98C23×Dic71C2312yes—
99C22×C4×D71C2314yes—
100C22×C4×D71C2311yescharacteristic
101C22×C4×D71C2312yes—
102C22×C4×D71C2312yes—
103C22×C4×D71C2311yescharacteristic
104#14556128C2318yes—
105#14556127C23132yes—
106#14556127C23132yes—
107#14556127C23116yes—
108#14556126C23116yes—
109#14556123C23132yes—
110#14556123C23132yes—
111#14556121C23132yes—
112#14556120C2318yes—
113#14556119C23132yes—
114#14556118C23132yes—
115#14556118C23132yes—
116#14556118C23132yes—
117#14556118C23132yes—
118#14556114C23132yes—
119#14556113C23132yes—
120#14556110C23132yes—
121#14556108C23116yes—
122#14556107C23116yes—
123#14556106C23132yes—
124#14556106C23132yes—
125#14556105C23132yes—
126#14556104C23116yes—
127Q8×Dic71C23116yes—
128C4×Dic142C23116yes—
129C4×Dic142C23132yes—
130C4×Dic142C23132yes—
131#14556093C23116yes—
132#14556093C23132yes—
133#14556093C23132yes—
134#14556093C23132yes—
135#14556093C23116yes—
136#14556090C23116yes—
137(C22⋊D71)⋊C4C23116yes—
138(C22⋊D71)⋊C4C23116yes—
139#14556086C23116yes—
140#14556086C23132yes—
141#14556085C2318yes—
142#14556085C23132yes—
143#14556085C23132yes—
144#14556085C2318yes—
145#14556084C23132yes—
146C2×C4⋊Dic71C2314yes—
147C2×C4⋊Dic71C2312yes—
148C2×C4⋊Dic71C2314yes—
149C2×C4⋊Dic71C2314yes—
150C2×Dic71⋊C4C2314yes—
151C2×Dic71⋊C4C2314yes—
152C2×Dic71⋊C4C2314yes—
153C2×Dic71⋊C4C2312yes—
154C2×Dic71⋊C4C2312yes—
155C2×Dic71⋊C4C2314yes—
156C2×Dic71⋊C4C2314yes—
157C2×Dic71⋊C4C2314yes—
158C2×Dic71⋊C4C2314yes—
159C2×Dic71⋊C4C2314yes—
160C4⋊C4×D71C23132yes—
161C2×C22⋊Dic71C2314yes—
162C2×(C2×D71)⋊C4C2312yes—
163C2×(C2×D71)⋊C4C2314yes—
164C2×(C2×D71)⋊C4C2312yes—
165C2×(C2×D71)⋊C4C2314yes—
166C2×(C2×D71)⋊C4C2314yes—
167C2×C4×Dic71C2311yescharacteristic
168C2×C4×Dic71C2312yes—
169C2×C4×Dic71C2312yes—
170C2×C4×Dic71C2311yescharacteristic
171C2×C4×Dic71C2312yes—
172C2×C4×Dic71C2318yes—
173C2×C4×Dic71C2314yes—
174C2×C4×Dic71C2314yes—
175C2×C4×Dic71C2314yes—
176C2×C4×Dic71C2314yes—
177C42×D71C2318yes—
178C42×D71C2318yes—
179C22×Q8×C71C2312yes—
180C23×C4×C71C2311yescharacteristic
181C4⋊Q8×C71C2318yes—
182#126×C71C23132yes—
183#125×C71C2318yes—
184#125×C71C23132yes—
185C22⋊Q8×C71C23116yes—
186C4×Q8×C71C23116yes—
187#117×C71C2318yes—
188C2×C4⋊C4×C71C2312yes—
189C2×C4⋊C4×C71C2312yes—
190C2×C4⋊C4×C71C2314yes—
191C2×C4⋊C4×C71C2314yes—
192C2×C4⋊C4×C71C2314yes—
193C2×C4⋊C4×C71C2314yes—
194C2×C22⋊C4×C71C2312yes—
195C2×C22⋊C4×C71C2314yes—
196C2×C42×C71C2311yescharacteristic
197C2×C42×C71C2311yescharacteristic
198C2×C42×C71C2314yes—
199C23×D71C2411yescharacteristic
200C23×D71C2411yescharacteristic
201#11765865—232no—
202C2×Dic142—28no—
203C2×Dic142—216no—
204C2×Dic142—24no—
205C2×Dic142—216no—
206C2×Dic142C2418yes—
207C2×Dic142C24116yes—
208C2×Dic142C2414yes—
209C2×Dic142C24116yes—
210Q8×D71—264no—
211C2×D284—24no—
212C2×D284C2414yes—
213C2×C22⋊D71—24no—
214C2×C22⋊D71—24no—
215C2×C22⋊D71C2414yes—
216C2×C22⋊D71C2414yes—
217C22×Dic71—28no—
218C22×Dic71C2411yescharacteristic
219C22×Dic71C2414yes—
220C22×Dic71C2412yes—
221C22×Dic71C2418yes—
222C22×Dic71C2414yes—
223C22×Dic71C2411yescharacteristic
224C22×Dic71C2412yes—
225C2×C4×D71—216no—
226C2×C4×D71—24no—
227C2×C4×D71—28no—
228C2×C4×D71—28no—
229C2×C4×D71#4118yes—
230C2×C4×D71C24116yes—
231C2×C4×D71C2414yes—
232C2×C4×D71C2418yes—
233C2×C4×D71C2418yes—
234C2×C4×D71C2414yes—
235C4⋊Dic71C24116yes—
236C4⋊Dic71C2418yes—
237C4⋊Dic71C24116yes—
238C4⋊Dic71C24116yes—
239Dic71⋊C4C24116yes—
240Dic71⋊C4C24116yes—
241Dic71⋊C4C24116yes—
242Dic71⋊C4C2418yes—
243Dic71⋊C4C2418yes—
244Dic71⋊C4C24116yes—
245Dic71⋊C4C24116yes—
246Dic71⋊C4C24116yes—
247Dic71⋊C4C24116yes—
248Dic71⋊C4C24116yes—
249C22⋊Dic71C24116yes—
250(C2×D71)⋊C4C2418yes—
251(C2×D71)⋊C4C24116yes—
252(C2×D71)⋊C4C2418yes—
253(C2×D71)⋊C4C24116yes—
254(C2×D71)⋊C4C24116yes—
255C4×Dic71C2414yes—
256C4×Dic71C2418yes—
257C4×Dic71C2418yes—
258C4×Dic71C2414yes—
259C4×Dic71C2418yes—
260C4×Dic71C24116yes—
261C4×Dic71C24116yes—
262C4×Dic71C24116yes—
263C4×Dic71C24116yes—
264C24×C71C2411yescharacteristic
265C2×Q8×C71—28no—
266C2×Q8×C71C2418yes—
267C22×C4×C71—24no—
268C22×C4×C71C2414yes—
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C22×C4×C71C2411yescharacteristic
272C22×C4×C71C2414yes—
273C22×C4×C71C2414yes—
274C22×C4×C71C2411yescharacteristic
275C4⋊C4×C71C2418yes—
276C4⋊C4×C71C2418yes—
277C4⋊C4×C71C24116yes—
278C4⋊C4×C71C24116yes—
279C4⋊C4×C71C24116yes—
280C4⋊C4×C71C24116yes—
281C22⋊C4×C71C2418yes—
282C22⋊C4×C71C24116yes—
283C42×C71C2414yes—
284C42×C71C2414yes—
285C42×C71C24116yes—
286C23×C71—22no—
287C23×C71—24no—
288C23×C71C2512yes—
289C23×C71C2511yescharacteristic
290C22×D71—24no—
291C22×D71—22no—
292C22×D71—24no—
293C22×D71C2×#4114yes—
294C22×D71C2512yes—
295C22×D71C2512yes—
296Q8×C71—216no—
297C2×C4×C71—22no—
298C2×C4×C71—28no—
299C2×C4×C71—24no—
300C2×C4×C71—24no—
301C2×C4×C71—28no—
302C2×C4×C71—28no—
303C2×C4×C71C2×#4114yes—
304C2×C4×C71C2514yes—
305C2×C4×C71C2518yes—
306C2×C4×C71C2514yes—
307C2×C4×C71C2518yes—
308C2×C4×C71C2512yes—
309C2×C4×C71C2512yes—
310C22⋊D71—28no—
311C22⋊D71—28no—
312C2×Dic71—22no—
313C2×Dic71—28no—
314C2×Dic71—24no—
315C2×Dic71—28no—
316C2×Dic71—216no—
317C2×Dic71C2×#4114yes—
318C2×Dic712−1+418yes—
319C2×Dic71C2514yes—
320C2×Dic71C2518yes—
321C2×Dic71C2518yes—
322C2×Dic71C2512yes—
323C2×Dic71C2512yes—
324C2×Dic71C2514yes—
325D284—28no—
326C4×D71—232no—
327C4×D71—28no—
328C4×D71—216no—
329C4×D71—216no—
330C4×D71C2×#41116yes—
331Dic142—216no—
332Dic142—232no—
333Dic142—28no—
334Dic142—232no—
335C22×C71—22no—
336C22×C71—24no—
337C22×C71—44no—
338C22×C71C22×#4112yes—
339C22×C71C2×2−1+414yes—
340C22×C71C2611yescharacteristic
341C2×D71—24no—
342C2×D71—28no—
343C2×D71—22no—
344C2×D71—24no—
345C2×D71—44no—
346C2×D71C22×#4114yes—
347C4×C71—28no—
348C4×C71—22no—
349C4×C71—28no—
350C4×C71—24no—
351C4×C71—24no—
352C4×C71C22×#4114yes—
353Dic71—28no—
354Dic71—22no—
355Dic71—28no—
356Dic71—24no—
357Dic71C22×#4114yes—
358Dic71C2×2−1+418yes—
359C2×#3509—711nomaximal, Sylow
360C2×C71—42no—
361C2×C71#350914yescomplemented
362C2×C71C23×#4111yescharacteristic
363C2×C71C22×2−1+412yes—
364D71—24no—
365D71—42no—
366#3509—7132no—
367C2×#557—714no—
368C2×#556—714no—
369C2×#552—714no—
370C2×#552—714no—
371C2×#541—711no—
372C2×#541—711no—
373C2×#541—711no—
374C2×#541D7111yescharacteristic, complemented
375C2×#536—712no—
376C2×#533—711no—
377C2×#533—712no—
378C2×#533—712no—
379C22×C4⋊Q8—711no—
380C2×#519—712no—
381C2×C4×#41—711no—
382C71C2×#350911yescharacteristic, complemented, Sylow
383C22×#41—711no—
384C23×Q8—712no—
385#557—7164no—
386#556—7164no—
387#552—7164no—
388#552—7164no—
389#541—7116no—
390#541—7116no—
391#541—7116no—
392#541C2×D71116yescomplemented
393#536—7132no—
394#533—7116no—
395#533—7132no—
396#533—7132no—
397C2×C4⋊Q8—712no—
398C2×C4⋊Q8—7116no—
399C2×C4⋊Q8—714no—
400C2×C4⋊Q8—712no—
401C2×C4⋊Q8—714no—
402C2×C4⋊Q8—711no—
403C2×C4⋊Q8C2×D7111yescharacteristic
404C2×#126—714no—
405C2×#126—714no—
406C2×#126—714no—
407C2×#126C2×D7114yes—
408C2×#125—714no—
409C2×#125—714no—
410C2×#125—714no—
411C2×#125—714no—
412C2×#125—714no—
413C2×#125—711no—
414C2×#125C2×D7111yescharacteristic
415C2×#125C2×D7114yes—
416C2×#124—714no—
417C2×#123—714no—
418C2×#123—714no—
419C2×C22⋊Q8—712no—
420C2×C22⋊Q8—712no—
421C2×C22⋊Q8—712no—
422C2×C22⋊Q8—714no—
423C2×C22⋊Q8—714no—
424C2×C22⋊Q8—714no—
425C2×C22⋊Q8C2×D7112yes—
426#519—7132no—
427C4×#41—7116no—
428C2×C4×Q8—712no—
429C2×C4×Q8—712no—
430C2×C4×Q8—712no—
431C2×C4×Q8—714no—
432C2×C4×Q8—714no—
433C2×C4×Q8—714no—
434C2×C4×Q8—712no—
435C2×C4×Q8—714no—
436C2×C4×Q8—714no—
437C2×C4×Q8C2×D7112yes—
438C2×C4×D4—712no—
439C2×C4×D4—712no—
440C2×C4×D4—712no—
441C2×#117—712no—
442C2×#117—714no—
443C2×#117—714no—
444C2×#117—711no—
445C2×#117—711no—
446C2×#117—714no—
447C2×#117—714no—
448C2×#117C2×D7111yescharacteristic
449C22×C4⋊C4—714no—
450C22×C42—711no—
451C22×C42—711no—
452C22×C42—711no—
453C2×#41—718no—
454C2×#41—1428no—
455C22×Q8—7116no—
456C22×Q8—714no—
457C22×Q8—712no—
458C22×Q8—714no—
459C22×Q8—711no—
460C22×Q8—14216no—
461C22×Q8C22×D7112yes—
462C22×D4—711no—
463C22×D4—711no—
464C22×D4—711no—
465C23×C4—711no—
466C23×C4—712no—
467C23×C4—714no—
468C23×C4—712no—
469C23×C4—712no—
470C23×C4—711no—
471C23×C4C22×D7111yescharacteristic
472C4⋊Q8—7116no—
473C4⋊Q8—7132no—
474C4⋊Q8—7116no—
475C4⋊Q8—7132no—
476C4⋊Q8—718no—
477C4⋊Q8C22×D7118yes—
478#126—7132no—
479#126—7132no—
480#126—7132no—
481#126C22×D71132yes—
482#125—7132no—
483#125—7132no—
484#125—7132no—
485#125—7132no—
486#125—7132no—
487#125—718no—
488#125C22×D7118yes—
489#125C22×D71132yes—
490#124—7132no—
491#123—7132no—
492#123—7132no—
493C22⋊Q8—7116no—
494C22⋊Q8—7116no—
495C22⋊Q8—7116no—
496C22⋊Q8—7132no—
497C22⋊Q8—7132no—
498C22⋊Q8—7132no—
499C22⋊Q8C22×D71116yes—
500C4×Q8—7116no—
501C4×Q8—7116no—
502C4×Q8—7116no—
503C4×Q8—7132no—
504C4×Q8—7132no—
505C4×Q8—7132no—
506C4×Q8—7116no—
507C4×Q8—7132no—
508C4×Q8—7132no—
509C4×Q8C22×D71116yes—
510C4×D4—7116no—
511C4×D4—7116no—
512C4×D4—7116no—
513#117—7116no—
514#117—7132no—
515#117—7132no—
516#117—718no—
517#117—718no—
518#117—7132no—
519#117—7132no—
520#117C22×D7118yes—
521C2×C4⋊C4—714no—
522C2×C4⋊C4—714no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—712no—
526C2×C4⋊C4—712no—
527C2×C4⋊C4—712no—
528C2×C4⋊C4—714no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4—714no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—714no—
534C2×C4⋊C4—714no—
535C2×C4⋊C4—7132no—
536C2×C4⋊C4C22×D7114yes—
537C2×C4⋊C4C22×D7112yes—
538C2×C4⋊C4C22×D7114yes—
539C2×C4⋊C4C22×D7112yes—
540C2×C4⋊C4C22×D7114yes—
541C2×C4⋊C4C22×D7114yes—
542C2×C22⋊C4—714no—
543C2×C22⋊C4—712no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—712no—
546C2×C22⋊C4—714no—
547C2×C22⋊C4—714no—
548C2×C22⋊C4C22×D7114yes—
549C2×C22⋊C4C22×D7112yes—
550C2×C42—711no—
551C2×C42—714no—
552C2×C42—714no—
553C2×C42—714no—
554C2×C42—714no—
555C2×C42—712no—
556C2×C42—712no—
557C2×C42—712no—
558C2×C42—718no—
559C2×C42—711no—
560C2×C42—718no—
561C2×C42—718no—
562C2×C42C22×D7114yes—
563C2×C42C22×D7111yescharacteristic
564C2×C42C22×D7111yescharacteristic
565C24—711no—
566C24—711no—
567C24C23×D7111yescharacteristic
568#41—14232no—
569C2×Q8—28no—
570C2×Q8—7116no—
571C2×Q8—718no—
572C2×Q8—7116no—
573C2×Q8—714no—
574C2×Q8—14216no—
575C2×Q8—14216no—
576C2×Q8—1424no—
577C2×Q8—14264no—
578C2×Q8—1428no—
579C2×Q8C23×D7118yes—
580C2×D4—714no—
581C2×D4—714no—
582C2×D4—714no—
583C2×D4—1424no—
584C2×D4—1424no—
585C2×D4—1424no—
586C22×C4—24no—
587C22×C4—711no—
588C22×C4—712no—
589C22×C4—718no—
590C22×C4—714no—
591C22×C4—718no—
592C22×C4—712no—
593C22×C4—714no—
594C22×C4—714no—
595C22×C4—711no—
596C22×C4—718no—
597C22×C4—718no—
598C22×C4—714no—
599C22×C4—7116no—
600C22×C4—1428no—
601C22×C4—1428no—
602C22×C4—14216no—
603C22×C4—1428no—
604C22×C4—1424no—
605C22×C4C23×D7114yes—
606C22×C4C23×D7112yes—
607C22×C4C23×D7114yes—
608C22×C4C23×D7111yescharacteristic
609C22×C4C23×D7112yes—
610C22×C4C23×D7114yes—
611C22×C4C23×D7111yescharacteristic
612C4⋊C4—7116no—
613C4⋊C4—7116no—
614C4⋊C4—7116no—
615C4⋊C4—718no—
616C4⋊C4—718no—
617C4⋊C4—7116no—
618C4⋊C4—7116no—
619C4⋊C4—7116no—
620C4⋊C4—7116no—
621C4⋊C4—7116no—
622C4⋊C4—7116no—
623C4⋊C4—718no—
624C4⋊C4—7116no—
625C4⋊C4—7116no—
626C4⋊C4C23×D71116yes—
627C4⋊C4C23×D7118yes—
628C4⋊C4C23×D71116yes—
629C4⋊C4C23×D7118yes—
630C4⋊C4C23×D71116yes—
631C4⋊C4C23×D71116yes—
632C22⋊C4—7116no—
633C22⋊C4—718no—
634C22⋊C4—7116no—
635C22⋊C4—718no—
636C22⋊C4—7116no—
637C22⋊C4—7116no—
638C22⋊C4C23×D71116yes—
639C22⋊C4C23×D7118yes—
640C42—714no—
641C42—714no—
642C42—718no—
643C42—718no—
644C42—718no—
645C42—7116no—
646C42—7116no—
647C42—7116no—
648C42—7116no—
649C42C23×D7114yes—
650C42C23×D7114yes—
651C42C23×D71116yes—
652C23—22no—
653C23—24no—
654C23—714no—
655C23—712no—
656C23—712no—
657C23—1422no—
658C23—1424no—
659C23—1424no—
660C23C24×D7112yes—
661C23C24×D7111yescharacteristic
662Q8—216no—
663Q8—14232no—
664Q8—1428no—
665Q8—14232no—
666Q8—14216no—
667D4—1428no—
668D4—1428no—
669D4—1428no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—714no—
677C2×C4—718no—
678C2×C4—712no—
679C2×C4—714no—
680C2×C4—7116no—
681C2×C4—714no—
682C2×C4—718no—
683C2×C4—718no—
684C2×C4—712no—
685C2×C4—14216no—
686C2×C4—14216no—
687C2×C4—14232no—
688C2×C4—14216no—
689C2×C4—1422no—
690C2×C4—1428no—
691C2×C4—1424no—
692C2×C4—1428no—
693C2×C4—1428no—
694C2×C4#41×D7114yes—
695C2×C4C24×D7114yes—
696C2×C4C24×D7118yes—
697C2×C4C24×D7112yes—
698C2×C4C24×D7114yes—
699C2×C4C24×D7118yes—
700C2×C4C24×D7112yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—2844no—
705C22—714no—
706C22—1422no—
707C22—1424no—
708C22—1424no—
709C22—1428no—
710C22C2×#41×D7112yes—
711C222−1+4×D7114yes—
712C22C25×D7111yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—714no—
719C4—718no—
720C4—1422no—
721C4—1428no—
722C4—1424no—
723C4—1428no—
724C4C2×#41×D7114yes—
725C2—42no—
726C2—2842no—
727C2—1424no—
728C2#2260222214yesdirect product factor
729C2C22×#41×D7111yescharacteristic
730C2C2×2−1+4×D7112yes—
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#541×C71C2
socleC23×C71C25
prime radicalC22×#11765865C22
hypercenterC2×#541D71
hypocenterC71C2×#3509
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #22602222C2direct (N × H)
2. C2×#17986726C2semidirect
3. C2×#17986716C2semidirect
4. C2×#17986685C2semidirect
5. C2×#17986681C2semidirect
6. C2×#17986612C2semidirect
7. C2×#17986611C2semidirect
8. C2×#17986610C2semidirect
10. C2×#17986555C2semidirect
11. C2×#17986553C2semidirect
12. C2×#17986551C2semidirect
13. C2×C4⋊Q8×D71C2semidirect
14. C2×#17986475C2semidirect
16. C2×#541×C71C2semidirect
19. #17986726C22semidirect
20. #17986716C22semidirect
21. #17986685C22semidirect
22. #17986681C22semidirect
23. #17986612C22semidirect
24. #17986611C22semidirect
25. #17986610C22semidirect
27. #17986555C22semidirect
28. #17986553C22semidirect
29. #17986551C22semidirect
35. C4⋊Q8×D71C22semidirect
54. #17986475C22semidirect
79. #541×C71C22semidirect
361. C2×C71#3509semidirect
374. C2×#541D71semidirect
382. C71C2×#3509semidirect
392. #541C2×D71semidirect
728. C2#22602222direct (N × H)

Maximal subgroups

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

subgroupindex
#226022222
C2×#179867262
C2×#179867162
C2×#179866852
C2×#179866812
C2×#179866122
C2×#179866112
C2×#179866102
C2×#179865722
C2×#179865552
C2×#179865532
C2×#179865512
C2×C4⋊Q8×D712
C2×#179864752
C2×#179864672
C2×#541×C712
C2×#350971