Finite Group Databasebeta

← C2×#22602777 #32905063

Subgroups — C2×#22602777 #32905063

Order 18176.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602777C2132yesmaximal, direct product factor
2C2×#17986751C214yesmaximal, complemented
3C2×#17986727C211yesmaximal, characteristic, complemented
4C2×#17986719C211yesmaximal, characteristic, complemented
5C2×#17986706C212yesmaximal, complemented
6C2×#17986695C212yesmaximal, complemented
7C2×Q8×D284C211yesmaximal, characteristic, complemented
8C2×#17986662C212yesmaximal, complemented
9C2×#17986655C212yesmaximal, complemented
10C2×#17986653C211yesmaximal, characteristic, complemented
11C2×#17986627C212yesmaximal, complemented
12C2×#17986620C212yesmaximal, complemented
13C2×#17986612C212yesmaximal, complemented
14C2×#17986593C214yesmaximal, complemented
15C2×#17986569C212yesmaximal, complemented
16C22×#14556128C211yesmaximal, characteristic, complemented
17C2×#17986533C211yesmaximal, characteristic, complemented
18C2×#529×C71C211yesmaximal, characteristic, complemented
19C22×#11765864C2212yes—
20C23×Dic142C2212yes—
21C22×Q8×D71C2212yes—
22#17986751C22164yescomplemented
23#17986727C22116yescomplemented
24#17986719C22116yescomplemented
25#17986706C22132yescomplemented
26#17986695C22132yescomplemented
27Q8×D284C22116yescomplemented
28#17986662C22132yescomplemented
29#17986655C22132yescomplemented
30#17986653C22116yescomplemented
31#17986627C22132yescomplemented
32#17986620C22132yescomplemented
33#17986612C22132yescomplemented
34#17986593C22164yescomplemented
35#17986569C22132yescomplemented
36C2×#14556128C2212yes—
37C2×#14556128C2212yes—
38C2×#14556128C2211yescharacteristic
39C2×#14556128C2211yescharacteristic
40C2×#14556128C2212yes—
41C2×#14556128C2212yes—
42C2×#14556128C22116yescomplemented
43C2×#14556127C2214yes—
44C2×#14556126C2212yes—
45#17986533C22116yescomplemented
46C2×#14556123C2214yes—
47C2×#14556123C2214yes—
48C2×#14556122C2212yes—
49C2×#14556121C2214yes—
50C2×#14556120C2211yescharacteristic
51C2×#14556120C2212yes—
52C2×#14556119C2214yes—
53C2×#14556119C2214yes—
54C2×#14556118C2214yes—
55C2×#14556116C2211yescharacteristic
56C2×#14556115C2212yes—
57C2×#14556114C2214yes—
58C2×#14556112C2214yes—
59C2×#14556111C2212yes—
60C2×#14556110C2214yes—
61C2×#14556110C2214yes—
62C2×#14556108C2212yes—
63C2×#14556108C2212yes—
64C2×#14556108C2214yes—
65C2×#14556107C2211yescharacteristic
66C2×#14556107C2212yes—
67C2×#14556106C2214yes—
68C2×#14556105C2214yes—
69C2×#14556105C2214yes—
70C2×#14556105C2214yes—
71C2×#14556105C2214yes—
72C2×#14556102C2212yes—
73C2×#14556102C2211yescharacteristic
74C2×#14556100C2214yes—
75C2×C4×Dic142C2211yescharacteristic
76C2×C4×Dic142C2212yes—
77C2×#14556093C2212yes—
78C2×#14556093C2212yes—
79C2×C4×D284C2211yescharacteristic
80C2×C4×D284C2212yes—
81C2×D4×Dic71C2214yes—
82C2×C4×C22⋊D71C2212yes—
83C2×(C22⋊D71)⋊C4C2214yes—
84C2×#14556087C2212yes—
85C2×#14556085C2212yes—
86C22×C4⋊Dic71C2212yes—
87C22×C4⋊Dic71C2212yes—
88C22×C4⋊Dic71C2212yes—
89#529×C71C22116yescomplemented
90C2×#126×C71C2212yes—
91C2×#125×C71C2211yescharacteristic
92C2×#124×C71C2211yescharacteristic
93C2×#123×C71C2212yes—
94C2×C22⋊Q8×C71C2211yescharacteristic
95C2×#121×C71C2211yescharacteristic
96C2×C4×Q8×C71C2211yescharacteristic
97C2×C4×D4×C71C2211yescharacteristic
98C2×C4×D4×C71C2212yes—
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C2×#11765864—48no—
102C2×#11765864C23116yes—
103C22×Dic142—48no—
104C22×Dic142C2312yes—
105C22×Dic142C2312yes—
106C22×Dic142C2311yescharacteristic
107C22×Dic142C2314yes—
108C22×Dic142C23116yes—
109C22×Dic142C2314yes—
110C2×Q8×D71—48no—
111C2×Q8×D71C23116yes—
112C22×D284C2311yescharacteristic
113C22×C22⋊D71C2312yes—
114C22×C22⋊D71C2314yes—
115C23×Dic71C2314yes—
116C23×Dic71C2314yes—
117C22×C4×D71C2312yes—
118C22×C4×D71C2314yes—
119#14556128C23116yes—
120#14556128C23116yes—
121#14556128C23116yes—
122#14556128C2318yes—
123#14556128C2318yes—
124#14556128C23116yes—
125#14556127C23132yes—
126#14556126C23116yes—
127#14556123C23132yes—
128#14556123C23132yes—
129#14556122C23116yes—
130#14556121C23132yes—
131#14556120C2318yes—
132#14556120C23116yes—
133#14556119C23132yes—
134#14556119C23132yes—
135#14556118C23132yes—
136#14556116C2318yes—
137#14556115C23116yes—
138#14556114C23132yes—
139#14556112C23132yes—
140#14556111C23116yes—
141#14556110C23132yes—
142#14556110C23132yes—
143#14556108C23132yes—
144#14556108C23116yes—
145#14556108C23116yes—
146#14556107C23116yes—
147#14556107C2318yes—
148#14556106C23132yes—
149#14556105C23132yes—
150#14556105C23132yes—
151#14556105C23132yes—
152#14556105C23132yes—
153#14556102C23116yes—
154#14556102C2318yes—
155#14556100C23132yes—
156C4×Dic142C23116yes—
157C4×Dic142C2318yes—
158#14556093C23116yes—
159#14556093C23116yes—
160C4×D284C23116yes—
161C4×D284C2318yes—
162D4×Dic71C23132yes—
163C4×C22⋊D71C23116yes—
164(C22⋊D71)⋊C4C23132yes—
165#14556087C23116yes—
166#14556085C23116yes—
167C2×C4⋊Dic71C23116yes—
168C2×C4⋊Dic71C23116yes—
169C2×C4⋊Dic71C23116yes—
170C2×C4⋊Dic71C2311yescharacteristic
171C2×C4⋊Dic71C2312yes—
172C2×C4⋊Dic71C2312yes—
173C2×C4⋊Dic71C2314yes—
174C2×C4⋊Dic71C2314yes—
175C2×C4⋊Dic71C2314yes—
176C2×C4⋊Dic71C2312yes—
177C2×C4⋊Dic71C2312yes—
178C2×C4⋊Dic71C2311yescharacteristic
179C2×C4⋊Dic71C2314yes—
180C2×Dic71⋊C4C2312yes—
181C2×Dic71⋊C4C2312yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2312yes—
184C2×Dic71⋊C4C2314yes—
185C2×Dic71⋊C4C2314yes—
186C2×Dic71⋊C4C2314yes—
187C2×Dic71⋊C4C2312yes—
188C2×C22⋊Dic71C2314yes—
189C2×C22⋊Dic71C2312yes—
190C2×C22⋊Dic71C2314yes—
191C2×(C2×D71)⋊C4C2312yes—
192C2×(C2×D71)⋊C4C2312yes—
193C2×(C2×D71)⋊C4C2314yes—
194C2×(C2×D71)⋊C4C2312yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2312yes—
197C2×C4×Dic71C2312yes—
198C2×C4×Dic71C2314yes—
199C2×C4×Dic71C2314yes—
200C22×Q8×C71C2311yescharacteristic
201C22×D4×C71C2311yescharacteristic
202C22×D4×C71C2312yes—
203C23×C4×C71C2311yescharacteristic
204C23×C4×C71C2311yescharacteristic
205C23×C4×C71C2311yescharacteristic
206C23×C4×C71C2312yes—
207#126×C71C23116yes—
208#125×C71C2318yes—
209#124×C71C2318yes—
210#123×C71C23116yes—
211C22⋊Q8×C71C2318yes—
212#121×C71C2318yes—
213C4×Q8×C71C2318yes—
214C4×D4×C71C2318yes—
215C4×D4×C71C23116yes—
216#117×C71C23116yes—
217C2×C4⋊C4×C71C2312yes—
218C2×C4⋊C4×C71C2312yes—
219C2×C4⋊C4×C71C2311yescharacteristic
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2311yescharacteristic
222C2×C4⋊C4×C71C2312yes—
223C2×C22⋊C4×C71C2312yes—
224C2×C22⋊C4×C71C2312yes—
225C2×C22⋊C4×C71C2312yes—
226C2×C22⋊C4×C71C2312yes—
227C2×C22⋊C4×C71C2312yes—
228C2×C42×C71C2311yescharacteristic
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2311yescharacteristic
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2318yes—
233C2×C42×C71C2312yes—
234C23×D71C2412yes—
235#11765864—432no—
236C2×Dic142—28no—
237C2×Dic142—28no—
238C2×Dic142—24no—
239C2×Dic142—432no—
240C2×Dic142—48no—
241C2×Dic142—48no—
242C2×Dic142C2418yes—
243C2×Dic142C2418yes—
244C2×Dic142C2414yes—
245C2×Dic142C24116yes—
246C2×Dic142C24116yes—
247Q8×D71—432no—
248C2×D284—24no—
249C2×D284C2414yes—
250C2×C22⋊D71—28no—
251C2×C22⋊D71—48no—
252C2×C22⋊D71C2418yes—
253C2×C22⋊D71C24116yes—
254C22×Dic71—48no—
255C22×Dic71—48no—
256C22×Dic71C2412yes—
257C22×Dic71C2414yes—
258C22×Dic71C2414yes—
259C22×Dic71C2412yes—
260C22×Dic71C2412yes—
261C22×Dic71C24116yes—
262C22×Dic71C24116yes—
263C2×C4×D71—28no—
264C2×C4×D71—48no—
265C2×C4×D71C2418yes—
266C2×C4×D71C24116yes—
267C4⋊Dic71C2414yes—
268C4⋊Dic71C2418yes—
269C4⋊Dic71C2418yes—
270C4⋊Dic71C24116yes—
271C4⋊Dic71C24116yes—
272C4⋊Dic71C24116yes—
273C4⋊Dic71C2418yes—
274C4⋊Dic71C2418yes—
275C4⋊Dic71C2414yes—
276C4⋊Dic71C24116yes—
277Dic71⋊C4C2418yes—
278Dic71⋊C4C2418yes—
279Dic71⋊C4C24116yes—
280Dic71⋊C4C2418yes—
281Dic71⋊C4C24116yes—
282Dic71⋊C4C24116yes—
283Dic71⋊C4C24116yes—
284Dic71⋊C4C2418yes—
285C22⋊Dic71C24116yes—
286C22⋊Dic71C2418yes—
287C22⋊Dic71C24116yes—
288(C2×D71)⋊C4C2418yes—
289(C2×D71)⋊C4C2418yes—
290(C2×D71)⋊C4C24116yes—
291(C2×D71)⋊C4C2418yes—
292(C2×D71)⋊C4C24116yes—
293(C2×D71)⋊C4C2418yes—
294C4×Dic71C2418yes—
295C4×Dic71C24116yes—
296C4×Dic71C24116yes—
297C24×C71C2412yes—
298C24×C71C2411yescharacteristic
299C2×Q8×C71—24no—
300C2×Q8×C71C2414yes—
301C2×D4×C71—28no—
302C2×D4×C71—24no—
303C2×D4×C71C2414yes—
304C2×D4×C71C2418yes—
305C22×C4×C71—24no—
306C22×C4×C71—24no—
307C22×C4×C71—24no—
308C22×C4×C71—28no—
309C22×C4×C71C2412yes—
310C22×C4×C71C2411yescharacteristic
311C22×C4×C71C2414yes—
312C22×C4×C71C2411yescharacteristic
313C22×C4×C71C2411yescharacteristic
314C22×C4×C71C2411yescharacteristic
315C22×C4×C71C2414yes—
316C22×C4×C71C2414yes—
317C22×C4×C71C2412yes—
318C22×C4×C71C2412yes—
319C22×C4×C71C2418yes—
320C22×C4×C71C2411yescharacteristic
321C22×C4×C71C2411yescharacteristic
322C4⋊C4×C71C2418yes—
323C4⋊C4×C71C2418yes—
324C4⋊C4×C71C2414yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C2414yes—
327C4⋊C4×C71C2418yes—
328C22⋊C4×C71C2418yes—
329C22⋊C4×C71C2418yes—
330C22⋊C4×C71C2418yes—
331C22⋊C4×C71C2418yes—
332C22⋊C4×C71C2418yes—
333C42×C71C2414yes—
334C42×C71C2414yes—
335C42×C71C2414yes—
336C42×C71C2414yes—
337C42×C71C2418yes—
338C23×C71—22no—
339C23×C71—22no—
340C23×C71—24no—
341C23×C71—24no—
342C23×C71—24no—
343C23×C712−1+414yes—
344C23×C71C2514yes—
345C23×C71C2512yes—
346C23×C71C2511yescharacteristic
347C22×D71—24no—
348C22×D71—24no—
349C22×D71—24no—
350C22×D71C2514yes—
351Q8×C71—28no—
352D4×C71—216no—
353D4×C71—28no—
354C2×C4×C71—22no—
355C2×C4×C71—24no—
356C2×C4×C71—28no—
357C2×C4×C71—22no—
358C2×C4×C71—22no—
359C2×C4×C71—22no—
360C2×C4×C71—24no—
361C2×C4×C71—24no—
362C2×C4×C71—28no—
363C2×C4×C71—28no—
364C2×C4×C71—216no—
365C2×C4×C71H(5,𝔽2)14yes—
366C2×C4×C712−1+414yes—
367C2×C4×C71C2512yes—
368C2×C4×C71C2512yes—
369C2×C4×C71C2512yes—
370C2×C4×C71C2512yes—
371C2×C4×C71C2514yes—
372C2×C4×C71C2514yes—
373C2×C4×C71C2514yes—
374C2×C4×C71C2512yes—
375C2×C4×C71C2512yes—
376C22⋊D71—216no—
377C22⋊D71—416no—
378C2×Dic71—24no—
379C2×Dic71—28no—
380C2×Dic71—28no—
381C2×Dic71—24no—
382C2×Dic71—24no—
383C2×Dic71—416no—
384C2×Dic71—416no—
385C2×Dic71C2514yes—
386C2×Dic71C2514yes—
387C2×Dic71C2518yes—
388C2×Dic71C2518yes—
389C2×Dic71C2514yes—
390D284—28no—
391C4×D71—216no—
392C4×D71—416no—
393Dic142—216no—
394Dic142—216no—
395Dic142—28no—
396Dic142—416no—
397Dic142—416no—
398C22×C71—22no—
399C22×C71—22no—
400C22×C71—28no—
401C22×C71—24no—
402C22×C71—24no—
403C22×C71—24no—
404C22×C71—48no—
405C22×C71C2×H(5,𝔽2)12yes—
406C22×C71C2×2−1+414yes—
407C22×C71C2×2−1+412yes—
408C22×C71C2×2−1+412yes—
409C22×C71C2611yescharacteristic
410C2×D71—24no—
411C2×D71—24no—
412C2×D71—24no—
413C2×D71—48no—
414C4×C71—22no—
415C4×C71—24no—
416C4×C71—22no—
417C4×C71—22no—
418C4×C71—22no—
419C4×C71—24no—
420C4×C71—24no—
421C4×C71C2×H(5,𝔽2)14yes—
422C4×C71C2×2−1+414yes—
423Dic71—28no—
424Dic71—28no—
425Dic71—24no—
426Dic71—24no—
427Dic71—24no—
428C2×#3552—711nomaximal, Sylow
429C2×C71—24no—
430C2×C71—44no—
431C2×C71#355214yescomplemented
432C2×C71C22×H(5,𝔽2)11yescharacteristic
433C2×C71C22×2−1+411yescharacteristic
434C2×C71C22×2−1+411yescharacteristic
435D71—44no—
436#3552—7132no—
437C2×#563—714no—
438C2×#557—711no—
439C2×#556—711no—
440C2×#554—712no—
441C2×#553—712no—
442C2×D4×Q8—712no—
443C2×D4×Q8—711no—
444C2×#548—712no—
445C2×#547—711no—
446C2×#544—712no—
447C2×#542—712no—
448C2×#541—712no—
449C2×#539—714no—
450C2×#536—712no—
451C22×C4⋊Q8—711no—
452C2×#529—711no—
453C2×#529D7111yescharacteristic, complemented
454C71C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—712no—
456C23×Q8—712no—
457C23×Q8—712no—
458#563—7164no—
459#557—7116no—
460#556—7116no—
461#554—7132no—
462#553—7132no—
463D4×Q8—7132no—
464D4×Q8—7116no—
465#548—7132no—
466#547—7116no—
467#544—7132no—
468#542—7132no—
469#541—7132no—
470#539—7164no—
471#536—7132no—
472C2×C4⋊Q8—712no—
473C2×C4⋊Q8—714no—
474C2×C4⋊Q8—712no—
475C2×C4⋊Q8—712no—
476C2×C4⋊Q8—711no—
477C2×C4⋊Q8—711no—
478C2×C4⋊Q8—712no—
479C2×C4⋊Q8—7116no—
480C2×C4⋊Q8—712no—
481#529—7116no—
482#529C2×D71116yescomplemented
483C2×#126—714no—
484C2×#126—714no—
485C2×#126—714no—
486C2×#126—712no—
487C2×#126C2×D7112yes—
488C2×#125—714no—
489C2×#125—714no—
490C2×#125—714no—
491C2×#125—711no—
492C2×#125—712no—
493C2×#125C2×D7111yescharacteristic
494C2×#124—712no—
495C2×#124—714no—
496C2×#124—711no—
497C2×#124C2×D7111yescharacteristic
498C2×#123—712no—
499C2×#123—714no—
500C2×#123—714no—
501C2×#123—714no—
502C2×#123C2×D7112yes—
503C2×C22⋊Q8—711no—
504C2×C22⋊Q8—712no—
505C2×C22⋊Q8—714no—
506C2×C22⋊Q8—712no—
507C2×C22⋊Q8—712no—
508C2×C22⋊Q8—714no—
509C2×C22⋊Q8—714no—
510C2×C22⋊Q8—714no—
511C2×C22⋊Q8—714no—
512C2×C22⋊Q8—714no—
513C2×C22⋊Q8C2×D7111yescharacteristic
514C2×#121—714no—
515C2×#121—711no—
516C2×#121—712no—
517C2×#121C2×D7111yescharacteristic
518C2×C4×Q8—712no—
519C2×C4×Q8—712no—
520C2×C4×Q8—711no—
521C2×C4×Q8—712no—
522C2×C4×Q8C2×D7111yescharacteristic
523C2×C4×D4—714no—
524C2×C4×D4—712no—
525C2×C4×D4—714no—
526C2×C4×D4—711no—
527C2×C4×D4—712no—
528C2×C4×D4C2×D7111yescharacteristic
529C2×C4×D4C2×D7112yes—
530C2×#117—712no—
531C2×#117—712no—
532C2×#117C2×D7112yes—
533C22×C4⋊C4—712no—
534C22×C4⋊C4—712no—
535C22×C4⋊C4—712no—
536C22×C42C2×D7111yescharacteristic
537C2×#41—2848no—
538C2×#41—7116no—
539C22×Q8—2848no—
540C22×Q8—2848no—
541C22×Q8—7116no—
542C22×Q8—714no—
543C22×Q8—714no—
544C22×Q8—7116no—
545C22×Q8—711no—
546C22×Q8—712no—
547C22×Q8—712no—
548C22×Q8C22×D7111yescharacteristic
549C22×D4—714no—
550C22×D4—712no—
551C22×D4—711no—
552C22×D4C22×D7112yes—
553C22×D4C22×D7111yescharacteristic
554C23×C4—714no—
555C23×C4—714no—
556C23×C4—714no—
557C23×C4—712no—
558C23×C4C22×D7111yescharacteristic
559C23×C4C22×D7111yescharacteristic
560C23×C4C22×D7112yes—
561C23×C4C22×D7111yescharacteristic
562C4⋊Q8—7116no—
563C4⋊Q8—7132no—
564C4⋊Q8—7116no—
565C4⋊Q8—7116no—
566C4⋊Q8—718no—
567C4⋊Q8—718no—
568C4⋊Q8—7116no—
569C4⋊Q8—7116no—
570#126—7132no—
571#126—7132no—
572#126—7132no—
573#126—7116no—
574#126C22×D71116yes—
575#125—7132no—
576#125—7132no—
577#125—7132no—
578#125—718no—
579#125—7116no—
580#125C22×D7118yes—
581#124—7116no—
582#124—7132no—
583#124—718no—
584#124C22×D7118yes—
585#123—7116no—
586#123—7132no—
587#123—7132no—
588#123—7132no—
589#123C22×D71116yes—
590C22⋊Q8—718no—
591C22⋊Q8—7116no—
592C22⋊Q8—7132no—
593C22⋊Q8—7116no—
594C22⋊Q8—7116no—
595C22⋊Q8—7132no—
596C22⋊Q8—7132no—
597C22⋊Q8—7132no—
598C22⋊Q8—7132no—
599C22⋊Q8—7132no—
600C22⋊Q8C22×D7118yes—
601#121—7132no—
602#121—718no—
603#121—7116no—
604#121C22×D7118yes—
605C4×Q8—7116no—
606C4×Q8—7116no—
607C4×Q8—718no—
608C4×Q8—7116no—
609C4×Q8C22×D7118yes—
610C4×D4—7132no—
611C4×D4—7116no—
612C4×D4—7132no—
613C4×D4—718no—
614C4×D4—7116no—
615C4×D4C22×D7118yes—
616C4×D4C22×D71116yes—
617#117—7116no—
618#117—7116no—
619#117C22×D71116yes—
620C2×C4⋊C4—711no—
621C2×C4⋊C4—712no—
622C2×C4⋊C4—712no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—712no—
625C2×C4⋊C4—714no—
626C2×C4⋊C4—714no—
627C2×C4⋊C4—712no—
628C2×C4⋊C4—7116no—
629C2×C4⋊C4—7116no—
630C2×C4⋊C4—7116no—
631C2×C4⋊C4—711no—
632C2×C4⋊C4—712no—
633C2×C4⋊C4—712no—
634C2×C4⋊C4—714no—
635C2×C4⋊C4—712no—
636C2×C4⋊C4—714no—
637C2×C4⋊C4—714no—
638C2×C4⋊C4—714no—
639C2×C4⋊C4—714no—
640C2×C4⋊C4—712no—
641C2×C4⋊C4C22×D7112yes—
642C2×C4⋊C4C22×D7112yes—
643C2×C4⋊C4C22×D7111yescharacteristic
644C2×C4⋊C4C22×D7112yes—
645C2×C4⋊C4C22×D7111yescharacteristic
646C2×C4⋊C4C22×D7112yes—
647C2×C22⋊C4—714no—
648C2×C22⋊C4—712no—
649C2×C22⋊C4—714no—
650C2×C22⋊C4—712no—
651C2×C22⋊C4—712no—
652C2×C22⋊C4—714no—
653C2×C22⋊C4—714no—
654C2×C22⋊C4—712no—
655C2×C22⋊C4—712no—
656C2×C22⋊C4C22×D7112yes—
657C2×C22⋊C4C22×D7112yes—
658C2×C22⋊C4C22×D7112yes—
659C2×C22⋊C4C22×D7112yes—
660C2×C22⋊C4C22×D7112yes—
661C2×C42—712no—
662C2×C42—714no—
663C2×C42—714no—
664C2×C42C22×D7111yescharacteristic
665C2×C42C22×D7111yescharacteristic
666C2×C42C22×D7112yes—
667C2×C42C22×D7111yescharacteristic
668C2×C42C22×D7111yescharacteristic
669C2×C42C22×D7118yes—
670C24—712no—
671C24C23×D7112yes—
672C24C23×D7111yescharacteristic
673#41—28432no—
674C2×Q8—24no—
675C2×Q8—28432no—
676C2×Q8—2848no—
677C2×Q8—2848no—
678C2×Q8—28432no—
679C2×Q8—7116no—
680C2×Q8—7116no—
681C2×Q8—714no—
682C2×Q8—718no—
683C2×Q8—718no—
684C2×Q8—1428no—
685C2×Q8—1428no—
686C2×Q8—1424no—
687C2×Q8C23×D7114yes—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—2848no—
691C2×D4—7116no—
692C2×D4—718no—
693C2×D4—714no—
694C2×D4—1428no—
695C2×D4—1424no—
696C2×D4C23×D7118yes—
697C2×D4C23×D7114yes—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—2848no—
703C22×C4—2848no—
704C22×C4—2848no—
705C22×C4—7116no—
706C22×C4—7116no—
707C22×C4—7116no—
708C22×C4—712no—
709C22×C4—712no—
710C22×C4—714no—
711C22×C4—714no—
712C22×C4—712no—
713C22×C4—718no—
714C22×C4—1428no—
715C22×C4C23×D7114yes—
716C22×C4C23×D7114yes—
717C22×C4C23×D7114yes—
718C22×C4C23×D7118yes—
719C22×C4C23×D7112yes—
720C22×C4C23×D7112yes—
721C22×C4C23×D7111yescharacteristic
722C22×C4C23×D7111yescharacteristic
723C22×C4C23×D7111yescharacteristic
724C22×C4C23×D7111yescharacteristic
725C22×C4C23×D7112yes—
726C22×C4C23×D7111yescharacteristic
727C22×C4C23×D7111yescharacteristic
728C4⋊C4—718no—
729C4⋊C4—718no—
730C4⋊C4—718no—
731C4⋊C4—7116no—
732C4⋊C4—7116no—
733C4⋊C4—7116no—
734C4⋊C4—7116no—
735C4⋊C4—718no—
736C4⋊C4—714no—
737C4⋊C4—718no—
738C4⋊C4—718no—
739C4⋊C4—7116no—
740C4⋊C4—718no—
741C4⋊C4—7116no—
742C4⋊C4—7116no—
743C4⋊C4—718no—
744C4⋊C4—714no—
745C4⋊C4—7116no—
746C4⋊C4C23×D7118yes—
747C4⋊C4C23×D7118yes—
748C4⋊C4C23×D7114yes—
749C4⋊C4C23×D7118yes—
750C4⋊C4C23×D7114yes—
751C4⋊C4C23×D7118yes—
752C22⋊C4—7116no—
753C22⋊C4—718no—
754C22⋊C4—7116no—
755C22⋊C4—718no—
756C22⋊C4—718no—
757C22⋊C4—7116no—
758C22⋊C4—7116no—
759C22⋊C4—718no—
760C22⋊C4—718no—
761C22⋊C4C23×D7118yes—
762C22⋊C4C23×D7118yes—
763C22⋊C4C23×D7118yes—
764C22⋊C4C23×D7118yes—
765C22⋊C4C23×D7118yes—
766C42—718no—
767C42—7116no—
768C42—7116no—
769C42C23×D7114yes—
770C42C23×D7114yes—
771C42C23×D7114yes—
772C42C23×D7114yes—
773C42C23×D7118yes—
774C23—22no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—714no—
780C23—1424no—
781C23—1424no—
782C23—1424no—
783C23#1455617514yes—
784C23C24×D7114yes—
785C23C24×D7112yes—
786C23C24×D7111yescharacteristic
787Q8—28no—
788Q8—28416no—
789Q8—28416no—
790Q8—14216no—
791Q8—14216no—
792Q8—1428no—
793D4—216no—
794D4—28no—
795D4—28416no—
796D4—14216no—
797D4—1428no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—216no—
809C2×C4—28416no—
810C2×C4—28416no—
811C2×C4—28416no—
812C2×C4—714no—
813C2×C4—714no—
814C2×C4—718no—
815C2×C4—718no—
816C2×C4—714no—
817C2×C4—1424no—
818C2×C4—1428no—
819C2×C4—1428no—
820C2×C4—1424no—
821C2×C4—1424no—
822C2×C4—14216no—
823C2×C4#1455617414yes—
824C2×C4#1455617514yes—
825C2×C4C24×D7114yes—
826C2×C4C24×D7114yes—
827C2×C4C24×D7112yes—
828C2×C4C24×D7112yes—
829C2×C4C24×D7112yes—
830C2×C4C24×D7112yes—
831C2×C4C24×D7114yes—
832C2×C4C24×D7112yes—
833C2×C4C24×D7112yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—2848no—
842C22—1424no—
843C22—1424no—
844C22—1424no—
845C22C2×#1455617412yes—
846C22C2×#1455617514yes—
847C22C2×#1455617512yes—
848C22C2×#1455617512yes—
849C22C25×D7111yescharacteristic
850C4—22no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—24no—
855C4—22no—
856C4—24no—
857C4—1424no—
858C4—1428no—
859C4—1428no—
860C4—1424no—
861C4—1424no—
862C4C2×#1455617414yes—
863C4C2×#1455617514yes—
864C2—24no—
865C2—44no—
866C2—2844no—
867C2#2260277714yesdirect product factor
868C2C22×#1455617411yescharacteristic
869C2C22×#1455617511yescharacteristic
870C2C22×#1455617511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#529×C71C2
socleC23×C71C25
hypercenterC2×#529D71
hypocenterC71C2×#3552
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22602777C2direct (N × H)
2. C2×#17986751C2semidirect
3. C2×#17986727C2semidirect
4. C2×#17986719C2semidirect
5. C2×#17986706C2semidirect
6. C2×#17986695C2semidirect
7. C2×Q8×D284C2semidirect
8. C2×#17986662C2semidirect
9. C2×#17986655C2semidirect
10. C2×#17986653C2semidirect
11. C2×#17986627C2semidirect
12. C2×#17986620C2semidirect
13. C2×#17986612C2semidirect
14. C2×#17986593C2semidirect
15. C2×#17986569C2semidirect
16. C22×#14556128C2semidirect
17. C2×#17986533C2semidirect
18. C2×#529×C71C2semidirect
22. #17986751C22semidirect
23. #17986727C22semidirect
24. #17986719C22semidirect
25. #17986706C22semidirect
26. #17986695C22semidirect
27. Q8×D284C22semidirect
28. #17986662C22semidirect
29. #17986655C22semidirect
30. #17986653C22semidirect
31. #17986627C22semidirect
32. #17986620C22semidirect
33. #17986612C22semidirect
34. #17986593C22semidirect
35. #17986569C22semidirect
42. C2×#14556128C22semidirect
45. #17986533C22semidirect
89. #529×C71C22semidirect
431. C2×C71#3552semidirect
453. C2×#529D71semidirect
454. C71C2×#3552semidirect
482. #529C2×D71semidirect
867. C2#22602777direct (N × H)

Maximal subgroups

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

subgroupindex
#226027772
C2×#179867512
C2×#179867272
C2×#179867192
C2×#179867062
C2×#179866952
C2×Q8×D2842
C2×#179866622
C2×#179866552
C2×#179866532
C2×#179866272
C2×#179866202
C2×#179866122
C2×#179865932
C2×#179865692
C22×#145561282
C2×#179865332
C2×#529×C712
C2×#355271