Finite Group Databasebeta

← C2×#22602428 #32905667

Subgroups — C2×#22602428 #32905667

Order 18176.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602428C2132yesmaximal, direct product factor
2C2×#17986725C212yesmaximal, complemented
3C2×#17986724C211yesmaximal, characteristic, complemented
4C2×#17986724C211yesmaximal, characteristic, complemented
5C2×#17986723C211yesmaximal, characteristic, complemented
6C2×#17986721C212yesmaximal, complemented
7C2×#17986691C212yesmaximal, complemented
8C2×#17986682C214yesmaximal, complemented
9C2×#17986664C211yesmaximal, characteristic, complemented
10C2×#17986662C212yesmaximal, complemented
11C2×#17986608C214yesmaximal, complemented
12C2×#17986607C212yesmaximal, complemented
13C2×#17986551C212yesmaximal, complemented
14C2×#17986535C212yesmaximal
15C2×#17986533C211yesmaximal, characteristic
16C2×#17986475C212yesmaximal, complemented
17C22×C4×Dic142C211yesmaximal, characteristic, complemented
18C2×#533×C71C211yesmaximal, characteristic, complemented
19C23×Dic142C2211yescharacteristic
20C22×Q8×D71C2212yes—
21#17986725C22132yescomplemented
22#17986724C22116yescomplemented
23#17986724C22116yescomplemented
24#17986723C22116yescomplemented
25#17986721C22132yescomplemented
26#17986691C22132yescomplemented
27#17986682C22164yescomplemented
28#17986664C22116yescomplemented
29#17986662C22132yescomplemented
30#17986608C22164yescomplemented
31#17986607C22132yescomplemented
32#17986551C22132yescomplemented
33C2×#14556127C2214yes—
34C2×#14556127C2212yes—
35C2×#14556126C2212yes—
36C2×#14556126C2212yes—
37#17986535C22132yes—
38#17986533C22116yes—
39C2×#14556123C2214yes—
40C2×#14556123C2214yes—
41C2×#14556123C2214yes—
42C2×#14556122C2214yes—
43C2×#14556122C2212yes—
44C2×#14556120C2214yes—
45C2×#14556120C2211yescharacteristic
46C2×#14556119C2212yes—
47C2×#14556119C2214yes—
48C2×#14556119C2212yes—
49C2×#14556118C2214yes—
50C2×#14556118C2214yes—
51C2×#14556118C2214yes—
52C2×#14556117C2212yes—
53C2×#14556116C2211yescharacteristic
54C2×#14556112C2214yes—
55C2×#14556111C2212yes—
56C2×#14556108C2212yes—
57C2×#14556107C2211yescharacteristic
58C2×#14556106C2214yes—
59C2×#14556106C2214yes—
60C2×#14556105C2214yes—
61C2×#14556104C2212yes—
62C2×#14556102C2211yescharacteristic
63#17986475C22132yescomplemented
64C2×Q8×Dic71C2212yes—
65C2×Q8×Dic71C2212yes—
66C2×Q8×Dic71C2212yes—
67C2×C4×Dic142C2211yescharacteristic
68C2×C4×Dic142C2211yescharacteristic
69C2×C4×Dic142C2212yes—
70C2×C4×Dic142C2211yescharacteristic
71C2×C4×Dic142C2211yescharacteristic
72C2×C4×Dic142C2212yes—
73C2×C4×Dic142C2214yes—
74C2×C4×Dic142C2211yescharacteristic
75C2×C4×Dic142C22116yescomplemented
76C2×#14556093C2212yes—
77C2×#14556093C2214yes—
78C2×#14556093C2212yes—
79C2×C4×D284C2211yescharacteristic
80C2×#14556090C2212yes—
81C2×C4×C22⋊D71C2212yes—
82C2×(C22⋊D71)⋊C4C2214yes—
83C2×#14556086C2212yes—
84C2×#14556086C2214yes—
85C2×#14556085C2214yes—
86C2×#14556085C2212yes—
87C2×#14556084C2214yes—
88C22×C4⋊Dic71C2211yescharacteristic
89C22×Dic71⋊C4C2212yes—
90C22×C4×Dic71C2212yes—
91#533×C71C22116yescomplemented
92C2×C4⋊Q8×C71C2211yescharacteristic
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×#125×C71C2212yes—
95C2×C22⋊Q8×C71C2212yes—
96C2×C22⋊Q8×C71C2212yes—
97C2×C4×Q8×C71C2212yes—
98C2×C4×Q8×C71C2212yes—
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C22×Dic142—28no—
102C22×Dic142C2314yes—
103C22×Dic142C2318yes—
104C22×Dic142C2312yes—
105C22×Dic142C2311yescharacteristic
106C22×Dic142C2311yescharacteristic
107C22×Dic142C2311yescharacteristic
108C2×Q8×D71—216no—
109C2×Q8×D71C23116yes—
110C22×D284C2311yescharacteristic
111C22×C22⋊D71C2312yes—
112C23×Dic71C2312yes—
113C23×Dic71C2312yes—
114C22×C4×D71C2314yes—
115C22×C4×D71C2312yes—
116#14556127C23132yes—
117#14556127C23116yes—
118#14556126C23116yes—
119#14556126C23116yes—
120#14556123C23132yes—
121#14556123C23132yes—
122#14556123C23132yes—
123#14556122C23132yes—
124#14556122C23116yes—
125#14556120C23132yes—
126#14556120C2318yes—
127#14556119C23116yes—
128#14556119C23132yes—
129#14556119C23116yes—
130#14556118C23132yes—
131#14556118C23132yes—
132#14556118C23132yes—
133#14556117C23116yes—
134#14556116C2318yes—
135#14556112C23132yes—
136#14556111C23116yes—
137#14556108C23116yes—
138#14556107C2318yes—
139#14556106C23132yes—
140#14556106C23132yes—
141#14556105C23132yes—
142#14556104C23116yes—
143#14556102C2318yes—
144Q8×Dic71C23116yes—
145Q8×Dic71C23116yes—
146Q8×Dic71C23116yes—
147C4×Dic142C2318yes—
148C4×Dic142C23116yes—
149C4×Dic142C2318yes—
150C4×Dic142C23132yes—
151C4×Dic142C23116yes—
152C4×Dic142C2318yes—
153C4×Dic142C2318yes—
154C4×Dic142C2318yes—
155#14556093C23132yes—
156#14556093C23116yes—
157#14556093C23116yes—
158C4×D284C2318yes—
159#14556090C23116yes—
160C4×C22⋊D71C23116yes—
161(C22⋊D71)⋊C4C23132yes—
162#14556086C23132yes—
163#14556086C23116yes—
164#14556085C23116yes—
165#14556085C23132yes—
166#14556084C23132yes—
167C2×C4⋊Dic71C2318yes—
168C2×C4⋊Dic71C2311yescharacteristic
169C2×C4⋊Dic71C2311yescharacteristic
170C2×C4⋊Dic71C2312yes—
171C2×C4⋊Dic71C2314yes—
172C2×C4⋊Dic71C2311yescharacteristic
173C2×C4⋊Dic71C2311yescharacteristic
174C2×C4⋊Dic71C2314yes—
175C2×C4⋊Dic71C2314yes—
176C2×Dic71⋊C4C23116yes—
177C2×Dic71⋊C4C2312yes—
178C2×Dic71⋊C4C2312yes—
179C2×Dic71⋊C4C2312yes—
180C2×Dic71⋊C4C2312yes—
181C2×Dic71⋊C4C2314yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2314yes—
187C2×Dic71⋊C4C2312yes—
188C2×Dic71⋊C4C2314yes—
189C2×Dic71⋊C4C2312yes—
190C2×C22⋊Dic71C2312yes—
191C2×(C2×D71)⋊C4C2312yes—
192C2×(C2×D71)⋊C4C2312yes—
193C2×(C2×D71)⋊C4C2314yes—
194C2×(C2×D71)⋊C4C2314yes—
195C2×(C2×D71)⋊C4C2312yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×C4×Dic71C2312yes—
199C2×C4×Dic71C2312yes—
200C2×C4×Dic71C2312yes—
201C2×C4×Dic71C2312yes—
202C2×C4×Dic71C23116yes—
203C2×C4×Dic71C2314yes—
204C2×C4×Dic71C2314yes—
205C2×C4×Dic71C2312yes—
206C2×C4×Dic71C2314yes—
207C22×Q8×C71C2312yes—
208C22×Q8×C71C2312yes—
209C23×C4×C71C2311yescharacteristic
210C23×C4×C71C2311yescharacteristic
211C23×C4×C71C2311yescharacteristic
212C4⋊Q8×C71C2318yes—
213C4⋊Q8×C71C2318yes—
214#125×C71C23116yes—
215C22⋊Q8×C71C23116yes—
216C22⋊Q8×C71C23116yes—
217C4×Q8×C71C23116yes—
218C4×Q8×C71C23116yes—
219#117×C71C23116yes—
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2312yes—
222C2×C4⋊C4×C71C2314yes—
223C2×C4⋊C4×C71C2314yes—
224C2×C4⋊C4×C71C2312yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C22⋊C4×C71C2314yes—
227C2×C42×C71C2311yescharacteristic
228C2×C42×C71C2311yescharacteristic
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2311yescharacteristic
231C2×C42×C71C2318yes—
232C2×C42×C71C2314yes—
233C23×D71C2412yes—
234C2×Dic142—24no—
235C2×Dic142—24no—
236C2×Dic142—216no—
237C2×Dic142—28no—
238C2×Dic142—232no—
239C2×Dic142#4118yes—
240C2×Dic142C24116yes—
241C2×Dic142C2418yes—
242C2×Dic142C2414yes—
243C2×Dic142C2414yes—
244C2×Dic142C2414yes—
245Q8×D71—264no—
246C2×D284—24no—
247C2×D284C2414yes—
248C2×C22⋊D71—28no—
249C2×C22⋊D71C2418yes—
250C22×Dic71—28no—
251C22×Dic71—28no—
252C22×Dic71C2412yes—
253C22×Dic71C2412yes—
254C22×Dic71C2418yes—
255C22×Dic71C2412yes—
256C22×Dic71C2412yes—
257C22×Dic71C2418yes—
258C22×Dic71C2412yes—
259C22×Dic71C2412yes—
260C22×Dic71C2412yes—
261C2×C4×D71—28no—
262C2×C4×D71—216no—
263C2×C4×D71C24116yes—
264C2×C4×D71C2418yes—
265C4⋊Dic71C2414yes—
266C4⋊Dic71C2414yes—
267C4⋊Dic71C2418yes—
268C4⋊Dic71C24116yes—
269C4⋊Dic71C2414yes—
270C4⋊Dic71C2414yes—
271C4⋊Dic71C24116yes—
272C4⋊Dic71C24116yes—
273Dic71⋊C4C2418yes—
274Dic71⋊C4C2418yes—
275Dic71⋊C4C2418yes—
276Dic71⋊C4C2418yes—
277Dic71⋊C4C24116yes—
278Dic71⋊C4C24116yes—
279Dic71⋊C4C24116yes—
280Dic71⋊C4C2418yes—
281Dic71⋊C4C2418yes—
282Dic71⋊C4C24116yes—
283Dic71⋊C4C2418yes—
284Dic71⋊C4C24116yes—
285Dic71⋊C4C2418yes—
286C22⋊Dic71C2418yes—
287(C2×D71)⋊C4C2418yes—
288(C2×D71)⋊C4C2418yes—
289(C2×D71)⋊C4C24116yes—
290(C2×D71)⋊C4C24116yes—
291(C2×D71)⋊C4C2418yes—
292(C2×D71)⋊C4C24116yes—
293(C2×D71)⋊C4C2418yes—
294C4×Dic71C2418yes—
295C4×Dic71C2418yes—
296C4×Dic71C2418yes—
297C4×Dic71C2418yes—
298C4×Dic71C24116yes—
299C4×Dic71C24116yes—
300C4×Dic71C2418yes—
301C4×Dic71C24116yes—
302C24×C71C2411yescharacteristic
303C2×Q8×C71—28no—
304C2×Q8×C71—28no—
305C2×Q8×C71C2418yes—
306C2×Q8×C71C2418yes—
307C22×C4×C71—24no—
308C22×C4×C71—24no—
309C22×C4×C71—24no—
310C22×C4×C71C2414yes—
311C22×C4×C71C2411yescharacteristic
312C22×C4×C71C2414yes—
313C22×C4×C71C2411yescharacteristic
314C22×C4×C71C2411yescharacteristic
315C22×C4×C71C2411yescharacteristic
316C22×C4×C71C2414yes—
317C22×C4×C71C2414yes—
318C22×C4×C71C2414yes—
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2411yescharacteristic
321C4⋊C4×C71C2418yes—
322C4⋊C4×C71C2418yes—
323C4⋊C4×C71C24116yes—
324C4⋊C4×C71C24116yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C2418yes—
327C22⋊C4×C71C24116yes—
328C42×C71C2414yes—
329C42×C71C2414yes—
330C42×C71C2414yes—
331C42×C71C2414yes—
332C42×C71C24116yes—
333C23×C71—22no—
334C23×C71—22no—
335C23×C712−1+414yes—
336C23×C71C2512yes—
337C23×C71C2511yescharacteristic
338C22×D71—24no—
339C22×D71—24no—
340C22×D71—24no—
341C22×D71C2514yes—
342Q8×C71—216no—
343Q8×C71—216no—
344C2×C4×C71—22no—
345C2×C4×C71—28no—
346C2×C4×C71—22no—
347C2×C4×C71—28no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—28no—
351C2×C4×C71—28no—
352C2×C4×C71—28no—
353C2×C4×C71C2×#4114yes—
354C2×C4×C712−1+414yes—
355C2×C4×C71C2512yes—
356C2×C4×C71C2512yes—
357C2×C4×C71C2512yes—
358C2×C4×C71C2512yes—
359C2×C4×C71C2518yes—
360C2×C4×C71C2518yes—
361C2×C4×C71C2512yes—
362C2×C4×C71C2512yes—
363C22⋊D71—216no—
364C2×Dic71—24no—
365C2×Dic71—24no—
366C2×Dic71—216no—
367C2×Dic71—24no—
368C2×Dic71—24no—
369C2×Dic71—24no—
370C2×Dic71—24no—
371C2×Dic71—216no—
372C2×Dic71C2×#4118yes—
373C2×Dic71C2514yes—
374C2×Dic71C2514yes—
375C2×Dic71C2514yes—
376C2×Dic71C2514yes—
377C2×Dic71C2514yes—
378C2×Dic71C2514yes—
379C2×Dic71C2514yes—
380D284—28no—
381C4×D71—216no—
382C4×D71—232no—
383Dic142—28no—
384Dic142—28no—
385Dic142—232no—
386Dic142—216no—
387Dic142C2×#41116yes—
388C22×C71—22no—
389C22×C71—22no—
390C22×C71—28no—
391C22×C71C22×#4112yes—
392C22×C71C2×2−1+412yes—
393C22×C71C2×2−1+414yes—
394C22×C71C2×2−1+412yes—
395C22×C71C2611yescharacteristic
396C2×D71—24no—
397C2×D71—24no—
398C2×D71—24no—
399C2×D71—48no—
400C4×C71—22no—
401C4×C71—28no—
402C4×C71—22no—
403C4×C71—22no—
404C4×C71—22no—
405C4×C71—28no—
406C4×C71C22×#4114yes—
407C4×C71C2×2−1+414yes—
408Dic71—24no—
409Dic71—24no—
410Dic71—24no—
411Dic71—24no—
412Dic71—24no—
413Dic71—24no—
414Dic71C22×#4118yes—
415C2×#3523—711nomaximal, Sylow
416C2×C71—24no—
417C2×C71#352314yescomplemented
418C2×C71C23×#4111yescharacteristic
419C2×C71C22×2−1+411yescharacteristic
420C2×C71C22×2−1+411yescharacteristic
421D71—44no—
422#3523—7132no—
423C2×#557—711no—
424C2×#557—711no—
425C2×#557—712no—
426C2×#556—711no—
427C2×#556—712no—
428C2×#552—712no—
429C2×#552—714no—
430C2×D4×Q8—711no—
431C2×D4×Q8—712no—
432C2×#541—714no—
433C2×#541—712no—
434C2×#533—712no—
435C2×#533D7111yescharacteristic, complemented
436C2×#529—711no—
437C2×#529—712no—
438C2×#519—712no—
439C22×C4×Q8—711no—
440C71C2×#352311yescharacteristic, complemented, Sylow
441C23×Q8—712no—
442C23×Q8—711no—
443#557—7116no—
444#557—7116no—
445#557—7132no—
446#556—7116no—
447#556—7132no—
448#552—7132no—
449#552—7164no—
450D4×Q8—7116no—
451D4×Q8—7132no—
452#541—7164no—
453#541—7132no—
454#533—7132no—
455#533C2×D71116yescomplemented
456C2×C4⋊Q8—712no—
457C2×C4⋊Q8—712no—
458C2×C4⋊Q8—712no—
459C2×C4⋊Q8—714no—
460C2×C4⋊Q8C2×D7111yescharacteristic
461C2×C4⋊Q8C2×D7111yescharacteristic
462#529—7132no—
463#529—7116no—
464C2×#126—714no—
465C2×#126—714no—
466C2×#126—714no—
467C2×#126—712no—
468C2×#126—714no—
469C2×#125—712no—
470C2×#125—714no—
471C2×#125—714no—
472C2×#125—714no—
473C2×#125—714no—
474C2×#125—712no—
475C2×#125—711no—
476C2×#125—714no—
477C2×#125C2×D7112yes—
478C2×#124—712no—
479C2×#124—711no—
480C2×#123—712no—
481C2×#123—714no—
482C2×C22⋊Q8—712no—
483C2×C22⋊Q8—711no—
484C2×C22⋊Q8—714no—
485C2×C22⋊Q8—714no—
486C2×C22⋊Q8—712no—
487C2×C22⋊Q8—714no—
488C2×C22⋊Q8C2×D7112yes—
489C2×C22⋊Q8C2×D7112yes—
490C2×#121—711no—
491#519—7132no—
492C2×C4×Q8—712no—
493C2×C4×Q8—712no—
494C2×C4×Q8—712no—
495C2×C4×Q8—714no—
496C2×C4×Q8—712no—
497C2×C4×Q8—712no—
498C2×C4×Q8—711no—
499C2×C4×Q8—712no—
500C2×C4×Q8—711no—
501C2×C4×Q8—711no—
502C2×C4×Q8—712no—
503C2×C4×Q8—711no—
504C2×C4×Q8—7116no—
505C2×C4×Q8—714no—
506C2×C4×Q8—711no—
507C2×C4×Q8C2×D7112yes—
508C2×C4×Q8C2×D7112yes—
509C2×C4×D4—712no—
510C2×C4×D4—712no—
511C2×C4×D4—714no—
512C2×C4×D4—711no—
513C2×#117—714no—
514C2×#117—712no—
515C2×#117—714no—
516C2×#117—712no—
517C2×#117—714no—
518C2×#117C2×D7112yes—
519C22×C4⋊C4—712no—
520C22×C4⋊C4—711no—
521C22×C42—712no—
522C22×C42C2×D7111yescharacteristic
523C22×Q8—7116no—
524C22×Q8—711no—
525C22×Q8—711no—
526C22×Q8—714no—
527C22×Q8—712no—
528C22×Q8—711no—
529C22×Q8—718no—
530C22×Q8—1428no—
531C22×Q8—14216no—
532C22×Q8C22×D7112yes—
533C22×Q8C22×D7112yes—
534C22×D4—712no—
535C22×D4—711no—
536C23×C4—712no—
537C23×C4—712no—
538C23×C4—714no—
539C23×C4—712no—
540C23×C4C22×D7111yescharacteristic
541C23×C4C22×D7111yescharacteristic
542C23×C4C22×D7111yescharacteristic
543C4⋊Q8—7116no—
544C4⋊Q8—7116no—
545C4⋊Q8—7116no—
546C4⋊Q8—7132no—
547C4⋊Q8C22×D7118yes—
548C4⋊Q8C22×D7118yes—
549#126—7132no—
550#126—7132no—
551#126—7132no—
552#126—7116no—
553#126—7132no—
554#125—7116no—
555#125—7132no—
556#125—7132no—
557#125—7132no—
558#125—7132no—
559#125—7116no—
560#125—718no—
561#125—7132no—
562#125C22×D71116yes—
563#124—7116no—
564#124—718no—
565#123—7116no—
566#123—7132no—
567C22⋊Q8—7116no—
568C22⋊Q8—718no—
569C22⋊Q8—7132no—
570C22⋊Q8—7132no—
571C22⋊Q8—7116no—
572C22⋊Q8—7132no—
573C22⋊Q8C22×D71116yes—
574C22⋊Q8C22×D71116yes—
575#121—718no—
576C4×Q8—7116no—
577C4×Q8—7116no—
578C4×Q8—7116no—
579C4×Q8—7132no—
580C4×Q8—7116no—
581C4×Q8—7116no—
582C4×Q8—718no—
583C4×Q8—7116no—
584C4×Q8—718no—
585C4×Q8—718no—
586C4×Q8—7116no—
587C4×Q8—718no—
588C4×Q8—7132no—
589C4×Q8—718no—
590C4×Q8C22×D71116yes—
591C4×Q8C22×D71116yes—
592C4×D4—7116no—
593C4×D4—7116no—
594C4×D4—7132no—
595C4×D4—718no—
596#117—7132no—
597#117—7116no—
598#117—7132no—
599#117—7116no—
600#117—7132no—
601#117C22×D71116yes—
602C2×C4⋊C4—712no—
603C2×C4⋊C4—711no—
604C2×C4⋊C4—712no—
605C2×C4⋊C4—711no—
606C2×C4⋊C4—712no—
607C2×C4⋊C4—712no—
608C2×C4⋊C4—712no—
609C2×C4⋊C4—7116no—
610C2×C4⋊C4—718no—
611C2×C4⋊C4—714no—
612C2×C4⋊C4—712no—
613C2×C4⋊C4—712no—
614C2×C4⋊C4—714no—
615C2×C4⋊C4—714no—
616C2×C4⋊C4—714no—
617C2×C4⋊C4—711no—
618C2×C4⋊C4—714no—
619C2×C4⋊C4—712no—
620C2×C4⋊C4—711no—
621C2×C4⋊C4—714no—
622C2×C4⋊C4—714no—
623C2×C4⋊C4—712no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4C22×D7112yes—
626C2×C4⋊C4C22×D7114yes—
627C2×C4⋊C4C22×D7112yes—
628C2×C4⋊C4C22×D7112yes—
629C2×C4⋊C4C22×D7112yes—
630C2×C4⋊C4C22×D7114yes—
631C2×C22⋊C4—712no—
632C2×C22⋊C4—712no—
633C2×C22⋊C4—714no—
634C2×C22⋊C4—712no—
635C2×C22⋊C4—714no—
636C2×C22⋊C4—712no—
637C2×C22⋊C4—712no—
638C2×C22⋊C4—714no—
639C2×C22⋊C4C22×D7114yes—
640C2×C42—712no—
641C2×C42—714no—
642C2×C42—714no—
643C2×C42—714no—
644C2×C42—712no—
645C2×C42—712no—
646C2×C42—712no—
647C2×C42—712no—
648C2×C42—7116no—
649C2×C42C22×D7111yescharacteristic
650C2×C42C22×D7114yes—
651C2×C42C22×D7111yescharacteristic
652C2×C42C22×D7111yescharacteristic
653C2×C42C22×D7111yescharacteristic
654C2×C42C22×D7118yes—
655C24—712no—
656C24C23×D7111yescharacteristic
657C2×Q8—28no—
658C2×Q8—28no—
659C2×Q8—718no—
660C2×Q8—714no—
661C2×Q8—714no—
662C2×Q8—7116no—
663C2×Q8—718no—
664C2×Q8—714no—
665C2×Q8—1428no—
666C2×Q8—14216no—
667C2×Q8—14232no—
668C2×Q8—14264no—
669C2×Q8—1424no—
670C2×Q8—1424no—
671C2×Q8C23×D7118yes—
672C2×Q8C23×D7118yes—
673C2×D4—718no—
674C2×D4—714no—
675C2×D4—1428no—
676C2×D4—1424no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—712no—
681C22×C4—718no—
682C22×C4—718no—
683C22×C4—712no—
684C22×C4—712no—
685C22×C4—712no—
686C22×C4—712no—
687C22×C4—712no—
688C22×C4—712no—
689C22×C4—7116no—
690C22×C4—718no—
691C22×C4—14216no—
692C22×C4—1428no—
693C22×C4—1428no—
694C22×C4—1428no—
695C22×C4C23×D7114yes—
696C22×C4C23×D7114yes—
697C22×C4C23×D7114yes—
698C22×C4C23×D7111yescharacteristic
699C22×C4C23×D7114yes—
700C22×C4C23×D7114yes—
701C22×C4C23×D7111yescharacteristic
702C22×C4C23×D7111yescharacteristic
703C22×C4C23×D7111yescharacteristic
704C22×C4C23×D7111yescharacteristic
705C22×C4C23×D7111yescharacteristic
706C4⋊C4—718no—
707C4⋊C4—718no—
708C4⋊C4—718no—
709C4⋊C4—718no—
710C4⋊C4—7116no—
711C4⋊C4—718no—
712C4⋊C4—718no—
713C4⋊C4—7116no—
714C4⋊C4—7116no—
715C4⋊C4—7116no—
716C4⋊C4—718no—
717C4⋊C4—7116no—
718C4⋊C4—718no—
719C4⋊C4—714no—
720C4⋊C4—714no—
721C4⋊C4—718no—
722C4⋊C4—7116no—
723C4⋊C4—714no—
724C4⋊C4—714no—
725C4⋊C4—7116no—
726C4⋊C4—7116no—
727C4⋊C4C23×D7118yes—
728C4⋊C4C23×D71116yes—
729C4⋊C4C23×D7118yes—
730C4⋊C4C23×D7118yes—
731C4⋊C4C23×D7118yes—
732C4⋊C4C23×D71116yes—
733C22⋊C4—718no—
734C22⋊C4—718no—
735C22⋊C4—7116no—
736C22⋊C4—718no—
737C22⋊C4—7116no—
738C22⋊C4—718no—
739C22⋊C4—718no—
740C22⋊C4—7116no—
741C22⋊C4C23×D71116yes—
742C42—718no—
743C42—718no—
744C42—718no—
745C42—718no—
746C42—7116no—
747C42—7116no—
748C42—7116no—
749C42—718no—
750C42C23×D7114yes—
751C42C23×D7114yes—
752C42C23×D7114yes—
753C42C23×D7114yes—
754C42C23×D71116yes—
755C23—22no—
756C23—22no—
757C23—714no—
758C23—1424no—
759C23—1424no—
760C23—1424no—
761C23#1455617614yes—
762C23C24×D7112yes—
763C23C24×D7111yescharacteristic
764Q8—216no—
765Q8—216no—
766Q8—7116no—
767Q8—14216no—
768Q8—14232no—
769Q8—1428no—
770Q8—1428no—
771D4—14216no—
772D4—1428no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—718no—
783C2×C4—714no—
784C2×C4—714no—
785C2×C4—714no—
786C2×C4—714no—
787C2×C4—714no—
788C2×C4—714no—
789C2×C4—714no—
790C2×C4—14232no—
791C2×C4—14216no—
792C2×C4—1424no—
793C2×C4—1424no—
794C2×C4—1424no—
795C2×C4—14216no—
796C2×C4—1424no—
797C2×C4—1424no—
798C2×C4—1424no—
799C2×C4—14216no—
800C2×C4#41×D7114yes—
801C2×C4#1455617514yes—
802C2×C4C24×D7112yes—
803C2×C4C24×D7118yes—
804C2×C4C24×D7118yes—
805C2×C4C24×D7112yes—
806C2×C4C24×D7112yes—
807C2×C4C24×D7112yes—
808C2×C4C24×D7112yes—
809C2×C4C24×D7112yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—2848no—
814C22—1424no—
815C22—1424no—
816C22—1424no—
817C22C2×#41×D7112yes—
818C22C2×#1455617512yes—
819C22C2×#1455617614yes—
820C22C2×#1455617612yes—
821C22C25×D7111yescharacteristic
822C4—22no—
823C4—28no—
824C4—22no—
825C4—28no—
826C4—22no—
827C4—22no—
828C4—718no—
829C4—1424no—
830C4—1424no—
831C4—1424no—
832C4—1424no—
833C4—1424no—
834C4—1424no—
835C4C2×#41×D7114yes—
836C4C2×#1455617514yes—
837C2—24no—
838C2—2844no—
839C2#2260242814yesdirect product factor
840C2C22×#41×D7111yescharacteristic
841C2C22×#1455617511yescharacteristic
842C2C22×#1455617611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#533×C71C2
socleC23×C71C25
prime radicalC2×#14556102C22
hypercenterC2×#533D71
hypocenterC71C2×#3523
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22602428C2direct (N × H)
2. C2×#17986725C2semidirect
3. C2×#17986724C2semidirect
4. C2×#17986724C2semidirect
5. C2×#17986723C2semidirect
6. C2×#17986721C2semidirect
7. C2×#17986691C2semidirect
8. C2×#17986682C2semidirect
9. C2×#17986664C2semidirect
10. C2×#17986662C2semidirect
11. C2×#17986608C2semidirect
12. C2×#17986607C2semidirect
13. C2×#17986551C2semidirect
16. C2×#17986475C2semidirect
17. C22×C4×Dic142C2semidirect
18. C2×#533×C71C2semidirect
21. #17986725C22semidirect
22. #17986724C22semidirect
23. #17986724C22semidirect
24. #17986723C22semidirect
25. #17986721C22semidirect
26. #17986691C22semidirect
27. #17986682C22semidirect
28. #17986664C22semidirect
29. #17986662C22semidirect
30. #17986608C22semidirect
31. #17986607C22semidirect
32. #17986551C22semidirect
63. #17986475C22semidirect
75. C2×C4×Dic142C22semidirect
91. #533×C71C22semidirect
417. C2×C71#3523semidirect
435. C2×#533D71semidirect
440. C71C2×#3523semidirect
455. #533C2×D71semidirect
839. C2#22602428direct (N × H)

Maximal subgroups

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

subgroupindex
#226024282
C2×#179867252
C2×#179867242
C2×#179867232
C2×#179867212
C2×#179866912
C2×#179866822
C2×#179866642
C2×#179866622
C2×#179866082
C2×#179866072
C2×#179865512
C2×#179865352
C2×#179865332
C2×#179864752
C22×C4×Dic1422
C2×#533×C712
C2×#352371