Finite Group Databasebeta

← Q8×#41×D53 #28291160

Subgroups — Q8×#41×D53 #28291160

Order 13568.

7522 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11719949C211yesmaximal, characteristic, complemented
2#20288297C213yesmaximal, complemented
3Q8×#11719945C213yesmaximal, complemented
4#41×Dic106C213yesmaximal, complemented
5#20288294C219yesmaximal, complemented
6#20288293C219yesmaximal, complemented
7Q8×#11719947C213yesmaximal, complemented
8Q82×D53C211yesmaximal, characteristic, complemented
9#557×D53C213yesmaximal, complemented
10#554×D53C219yesmaximal, complemented
11D4×Q8×D53C213yesmaximal, complemented
12#533×D53C219yesmaximal, complemented
13C4×#41×D53C213yesmaximal
14C2×C4×Q8×D53C213yesmaximal, complemented
15Q8×#41×C53C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17C22×Q8×D53C2213yes—
18Q8×Dic106C2213yescomplemented
19Q8×Dic106C2213yescomplemented
20#16811353C2219yescomplemented
21#16811352C2213yescomplemented
22#16811351C2219yescomplemented
23#16811350C22118yescomplemented
24#16811349C2216yescomplemented
25#16811348C2219yescomplemented
26#16811334C2219yescomplemented
27#16811333C2219yescomplemented
28#16811332C22118yescomplemented
29#16811331C22118yescomplemented
30#16811330C2219yescomplemented
31#16811329C22118yescomplemented
32#16811328C22118yescomplemented
33#16811327C22136yescomplemented
34Q8×D212C2213yescomplemented
35D4×Dic106C2219yescomplemented
36#16811288C2219yescomplemented
37Q8×C22⋊D53C2216yescomplemented
38#16811286C22118yescomplemented
39#16811180C2219yescomplemented
40#16811179C22118yescomplemented
41#16811178C2219yescomplemented
42#16811178C2219yescomplemented
43#16811177C22118yescomplemented
44#16811177C22118yescomplemented
45#16811176C22118yescomplemented
46#16811175C22118yescomplemented
47#16811175C22118yescomplemented
48C4⋊Q8×D53C2219yes—
49C4⋊Q8×D53C2219yes—
50#125×D53C22118yes—
51C22⋊Q8×D53C22118yes—
52C22⋊Q8×D53C22118yes—
53#41×Dic53C2213yes—
54C4×#11719949C2213yes—
55C4×#11719949C2213yes—
56C4×#11719945C2219yes—
57#16811091C2219yes—
58C4×#11719947C2219yes—
59C4×#11719947C2219yes—
60C2×Q8×Dic53C2213yescomplemented
61C2×C4×Dic106C2219yescomplemented
62C2×#13133182C2219yescomplemented
63C4×Q8×D53C2216yes—
64C4×Q8×D53C2219yes—
65C4×Q8×D53C2213yes—
66C4×Q8×D53C2213yes—
67C4×Q8×D53C2219yes—
68C4×Q8×D53C2213yes—
69C4×Q8×D53C2211yescharacteristic
70C4×Q8×D53C2213yescomplemented
71C4×Q8×D53C2219yescomplemented
72C4×Q8×D53C2219yescomplemented
73C4×Q8×D53C2213yescomplemented
74C4×D4×D53C2219yes—
75C4×D4×D53C2219yes—
76#117×D53C2219yes—
77C2×C4⋊C4×D53C2219yes—
78C2×C42×D53C2219yes—
79Q82×C53C2211yescharacteristic, complemented
80C53×#557C2213yescomplemented
81C53×#554C2219yescomplemented
82D4×Q8×C53C2213yescomplemented
83C53×#533C2219yescomplemented
84C4×#41×C53C2213yes—
85C2×C4×Q8×C53C2213yescomplemented
86C2×#11719949C2311yescharacteristic
87C2×#11719945C2313yes—
88C2×#11719947C2313yes—
89#41×D53Q8116yesdirect product factor
90C22×Dic106C2319yes—
91C2×Q8×D53—224no—
92C2×Q8×D53C2319yes—
93C2×Q8×D53C2313yes—
94C2×Q8×D53C2319yes—
95C2×Q8×D53C2316yes—
96C2×Q8×D53C2311yescharacteristic
97C2×Q8×D53C2311yescharacteristic
98C2×D4×D53C2313yes—
99C22×C4×D53C2319yes—
100C22×C4×D53C2319yes—
101C22×C4×D53C2313yes—
102#13133217C2319yes—
103#13133217C2319yes—
104#13133216C23118yes—
105#13133216C23118yes—
106#13133216C23118yes—
107#13133216C23118yes—
108#13133215C23118yes—
109#13133215C23118yes—
110#13133209C23118yes—
111#13133208C23118yes—
112#13133208C23118yes—
113#13133207C23136yes—
114#13133207C23136yes—
115#13133197C23118yes—
116#13133197C23118yes—
117#13133196C23118yes—
118#13133196C23118yes—
119#13133195C23136yes—
120#13133195C23136yes—
121#13133194C23136yes—
122#13133194C23136yes—
123#13133193C23118yes—
124#13133193C23118yes—
125Q8×Dic53C2313yes—
126Q8×Dic53C2319yes—
127Q8×Dic53C2311yescharacteristic
128Q8×Dic53C2319yes—
129Q8×Dic53C2313yes—
130Q8×Dic53C2313yes—
131Q8×Dic53C2316yes—
132C4×Dic106C2319yes—
133C4×Dic106C23118yes—
134C4×Dic106C2319yes—
135C4×Dic106C2313yes—
136C4×Dic106C23118yes—
137C4×Dic106C2319yes—
138C4×Dic106C2319yes—
139C4×Dic106C2319yes—
140C4×Dic106C23118yes—
141#13133182C2319yes—
142#13133182C23118yes—
143#13133182C2319yes—
144#13133182C2313yes—
145#13133182C2319yes—
146#13133182C23118yes—
147#13133182C2319yes—
148#13133182C2319yes—
149#13133182C23118yes—
150C4×D212C2319yes—
151C4×D212C2319yes—
152D4×Dic53C2319yes—
153D4×Dic53C2319yes—
154#13133179C2319yes—
155#13133179C2319yes—
156C4×C22⋊D53C23118yes—
157C4×C22⋊D53C23118yes—
158#13133177C23118yes—
159#13133177C23118yes—
160#13133176C2319yes—
161#13133175C2319yes—
162#13133175C2319yes—
163#13133174C23118yes—
164#13133173C23118yes—
165C2×C4⋊Dic53C2319yes—
166C2×#11719919C23118yes—
167C4⋊C4×D53C23118yes—
168C4⋊C4×D53C2313yes—
169C4⋊C4×D53C2319yes—
170C4⋊C4×D53C2319yes—
171C4⋊C4×D53C23118yes—
172C4⋊C4×D53C2319yes—
173C4⋊C4×D53C2319yes—
174C4⋊C4×D53C2319yes—
175C4⋊C4×D53C23118yes—
176C22⋊C4×D53C23118yes—
177C2×C4×Dic53C2319yes—
178C2×C4×Dic53C2319yes—
179C2×C4×Dic53C2319yes—
180C42×D53C2313yes—
181C42×D53C2319yes—
182C42×D53C2319yes—
183C42×D53C2319yes—
184C42×D53C2319yes—
185C42×D53C2319yes—
186C42×D53C2319yes—
187C42×D53C2319yes—
188C2×#41×C53C2311yescharacteristic
189C22×Q8×C53C2313yes—
190C4⋊Q8×C53C2319yes—
191C4⋊Q8×C53C2319yes—
192#125×C53C23118yes—
193C22⋊Q8×C53C23118yes—
194C22⋊Q8×C53C23118yes—
195C4×Q8×C53C2313yes—
196C4×Q8×C53C2311yescharacteristic
197C4×Q8×C53C2319yes—
198C4×Q8×C53C2319yes—
199C4×Q8×C53C2313yes—
200C4×Q8×C53C2313yes—
201C4×Q8×C53C2316yes—
202C4×D4×C53C2319yes—
203C4×D4×C53C2319yes—
204#117×C53C2319yes—
205C2×C4⋊C4×C53C2319yes—
206C2×C42×C53C2319yes—
207C23×D53C2413yes—
208#41×C53C2×Q818yescomplemented
209C2×Q8×C53—212no—
210C2×Q8×C53C2419yes—
211C2×Q8×C53C2416yes—
212C2×Q8×C53C2411yescharacteristic
213C2×Q8×C53C2411yescharacteristic
214C2×D4×C53C2413yes—
215C22×C4×C53C2419yes—
216C22×C4×C53C2419yes—
217C22×C4×C53C2413yes—
218C2×C22⋊D53C2416yes—
219C22×Dic53C2419yes—
220C22×Dic53C2419yes—
221C22×Dic53C2413yes—
222#11719949C2×Q818yescomplemented
223Q8×D53—212no—
224Q8×D53—236no—
225Q8×D53—236no—
226Q8×D53—412no—
227Q8×D53C2×Q818yescomplemented
228Q8×D53#4118yesdirect product factor
229#11719947C2×Q8124yescomplemented
230D4×D53C2×Q8124yescomplemented
231#11719945C2×Q8124yescomplemented
232C2×D212C2413yes—
233C2×C4×D53—236no—
234C2×C4×D53—418no—
235C2×C4×D53C2×Q8124yescomplemented
236C2×C4×D53C2413yes—
237C2×C4×D53C2419yes—
238C2×C4×D53C2419yes—
239C2×C4×D53C2419yes—
240C2×C4×D53C2419yes—
241C2×C4×D53C2419yes—
242C2×C4×D53C2419yes—
243C2×C4×D53C2411yescharacteristic
244C2×C4×D53C2413yes—
245C2×C4×D53C2413yes—
246C2×C4×D53C2413yes—
247C2×C4×D53C2413yes—
248C2×Dic106—236no—
249C2×Dic106C24118yes—
250C2×Dic106C2419yes—
251C2×Dic106C24118yes—
252C2×Dic106C2413yes—
253C2×Dic106C2413yes—
254C4⋊C4×C53C2413yes—
255C4⋊C4×C53C24118yes—
256C4⋊C4×C53C2419yes—
257C4⋊C4×C53C2419yes—
258C4⋊C4×C53C2419yes—
259C4⋊C4×C53C24118yes—
260C22⋊C4×C53C24118yes—
261C42×C53C2413yes—
262C42×C53C2419yes—
263C42×C53C2419yes—
264C42×C53C2419yes—
265C22⋊Dic53C24118yes—
266#11719921C24118yes—
267#11719921C24118yes—
268C4⋊Dic53C2413yes—
269C4⋊Dic53C2419yes—
270C4⋊Dic53C24118yes—
271C4⋊Dic53C2419yes—
272C4⋊Dic53C2419yes—
273C4⋊Dic53C24118yes—
274#11719919C2416yes—
275#11719919C24118yes—
276#11719919C24118yes—
277#11719919C24118yes—
278#11719919C24118yes—
279#11719919C24118yes—
280#11719919C24136yes—
281C4×Dic53C2413yes—
282C4×Dic53C2413yes—
283C4×Dic53C2413yes—
284C4×Dic53C2419yes—
285C4×Dic53C2419yes—
286C4×Dic53C2419yes—
287C4×Dic53C2419yes—
288C4×Dic53C2419yes—
289C4×Dic53C2419yes—
290C4×Dic53C2419yes—
291C4×Dic53C2419yes—
292C4×Dic53C2419yes—
293C23×C53C2513yes—
294C22×D53—26no—
295C22×D53—26no—
296C22×D53C22×Q8112yes—
297C22×D53C2513yes—
298C22×D53C2511yescharacteristic
299Q8×C53—218no—
300Q8×C53—46no—
301Q8×C53C22×Q814yescomplemented
302Q8×C53C2×#4114yescomplemented
303D4×C53C22×Q8112yescomplemented
304C2×C4×C53—218no—
305C2×C4×C53—49no—
306C2×C4×C53C22×Q8112yescomplemented
307C2×C4×C53C2519yes—
308C2×C4×C53C2519yes—
309C2×C4×C53C2513yes—
310C2×C4×C53C2513yes—
311C2×C4×C53C2513yes—
312C2×C4×C53C2511yescharacteristic
313C22⋊D53C22×Q8124yescomplemented
314C2×Dic53—218no—
315C2×Dic53—49no—
316C2×Dic53C22×Q8112yescomplemented
317C2×Dic53C2519yes—
318C2×Dic53C2519yes—
319C2×Dic53C2513yes—
320C2×Dic53C2513yes—
321C2×Dic53C2511yescharacteristic
322C2×Dic53C2513yes—
323D212C22×Q8112yescomplemented
324C4×D53—218no—
325C4×D53—26no—
326C4×D53—218no—
327C4×D53—218no—
328C4×D53—218no—
329C4×D53—49no—
330C4×D53—49no—
331C4×D53C22×Q814yes—
332C4×D53C22×Q8112yes—
333C4×D53C22×Q8112yescomplemented
334C4×D53C22×Q8112yescomplemented
335C4×D53C2×#41112yes—
336Dic106—218no—
337Dic106—236no—
338Dic106—418no—
339Dic106C22×Q8112yescomplemented
340Dic106C2×#41112yescomplemented
341C2×Q8×#41—531nomaximal, Sylow
342C22×C53—23no—
343C22×C53—23no—
344C22×C53C23×Q816yes—
345C22×C53C2611yescharacteristic
346C2×D53—23no—
347C2×D53—23no—
348C2×D53—224no—
349C2×D53C23×Q816yes—
350C2×D53C23×Q812yes—
351C2×D53C22×#4112yes—
352C2×D53#58512yes—
353C4×C53—29no—
354C4×C53—29no—
355C4×C53—23no—
356C4×C53C23×Q816yes—
357C4×C53C23×Q812yes—
358C4×C53C22×#4116yes—
359Dic53—29no—
360Dic53—29no—
361Dic53—23no—
362Dic53C23×Q816yes—
363Dic53C23×Q812yes—
364Dic53C22×#4116yes—
365Q8×#41—531no—
366Q8×#41—533no—
367Q8×#41—539no—
368Q8×#41—533no—
369Q8×#41—539no—
370Q8×#41—533no—
371Q8×#41—533no—
372Q8×#41D5311yescharacteristic, direct product factor
373C2×Q82—531no—
374C2×#557—533no—
375C2×#554—539no—
376C2×D4×Q8—533no—
377C2×#533—539no—
378C2×C4×#41—533no—
379C22×C4×Q8—533no—
380C2×C53—26no—
381C2×C53C24×Q811yescharacteristic
382C2×C53C23×#4111yescharacteristic
383C2×C53C2×#58511yescharacteristic
384D53—26no—
385D53Q8×#4114yesdirect product factor
386C22×#41—531no—
387C23×Q8—533no—
388Q82—539no—
389Q82—533no—
390Q82—533no—
391Q82C2×D5311yescharacteristic, complemented
392#557—539no—
393#557—5318no—
394#557—536no—
395#557—539no—
396#557—533no—
397#557C2×D5313yescomplemented
398#554—539no—
399#554—5318no—
400#554—5336no—
401#554—5318no—
402#554—539no—
403#554—539no—
404#554—5318no—
405#554—5318no—
406#554C2×D5319yescomplemented
407D4×Q8—536no—
408D4×Q8—539no—
409D4×Q8—5318no—
410D4×Q8—533no—
411D4×Q8—539no—
412D4×Q8C2×D5313yescomplemented
413#533—539no—
414#533—539no—
415#533—5318no—
416#533—5318no—
417#533—5318no—
418#533—5318no—
419#533—5318no—
420#533—5318no—
421#533—539no—
422#533C2×D5319yescomplemented
423C2×C4⋊Q8—539no—
424C2×C4⋊Q8—539no—
425C2×#125—5318no—
426C2×C22⋊Q8—5318no—
427C2×C22⋊Q8—5318no—
428C4×#41—533no—
429C4×#41—533no—
430C4×#41—533no—
431C4×#41—539no—
432C4×#41—539no—
433C4×#41—539no—
434C4×#41—539no—
435C4×#41C2×D5313yes—
436C2×C4×Q8—533no—
437C2×C4×Q8—531no—
438C2×C4×Q8—539no—
439C2×C4×Q8—533no—
440C2×C4×Q8—539no—
441C2×C4×Q8—533no—
442C2×C4×Q8—533no—
443C2×C4×Q8—536no—
444C2×C4×Q8—533no—
445C2×C4×Q8—539no—
446C2×C4×Q8—533no—
447C2×C4×Q8—539no—
448C2×C4×Q8—539no—
449C2×C4×Q8—539no—
450C2×C4×Q8C2×D5313yescomplemented
451C2×C4×D4—539no—
452C2×C4×D4—539no—
453C2×#117—539no—
454C22×C4⋊C4—539no—
455C22×C42—539no—
456C53C2×Q8×#4111yescharacteristic, complemented, Sylow
457C2×#41—5316no—
458C2×#41—531no—
459C2×#41—533no—
460C2×#41—533no—
461C2×#41C22×D5311yescharacteristic
462C22×Q8—531no—
463C22×Q8—531no—
464C22×Q8—539no—
465C22×Q8—539no—
466C22×Q8—533no—
467C22×Q8—536no—
468C22×Q8—539no—
469C22×Q8—10624no—
470C22×Q8C22×D5313yes—
471C22×D4—533no—
472C23×C4—533no—
473C23×C4—539no—
474C23×C4—539no—
475C4⋊Q8—5318no—
476C4⋊Q8—5318no—
477C4⋊Q8—5318no—
478C4⋊Q8—5318no—
479C4⋊Q8—5318no—
480C4⋊Q8—5318no—
481C4⋊Q8—539no—
482C4⋊Q8—539no—
483C4⋊Q8C22×D5319yes—
484C4⋊Q8C22×D5319yes—
485#125—5336no—
486#125—5336no—
487#125—5318no—
488#125—5318no—
489#125—5318no—
490#125C22×D53118yes—
491C22⋊Q8—5318no—
492C22⋊Q8—5318no—
493C22⋊Q8—5318no—
494C22⋊Q8—5318no—
495C22⋊Q8—5336no—
496C22⋊Q8—5318no—
497C22⋊Q8—5336no—
498C22⋊Q8—5318no—
499C22⋊Q8—5336no—
500C22⋊Q8—5336no—
501C22⋊Q8C22×D53118yes—
502C22⋊Q8C22×D53118yes—
503C4×Q8—531no—
504C4×Q8—539no—
505C4×Q8—533no—
506C4×Q8—539no—
507C4×Q8—533no—
508C4×Q8—533no—
509C4×Q8—536no—
510C4×Q8—533no—
511C4×Q8—539no—
512C4×Q8—5318no—
513C4×Q8—539no—
514C4×Q8—5318no—
515C4×Q8—539no—
516C4×Q8—539no—
517C4×Q8—539no—
518C4×Q8—5318no—
519C4×Q8—533no—
520C4×Q8—5318no—
521C4×Q8—539no—
522C4×Q8—539no—
523C4×Q8—539no—
524C4×Q8—5318no—
525C4×Q8—539no—
526C4×Q8—539no—
527C4×Q8—5318no—
528C4×Q8C22×D5311yescharacteristic
529C4×Q8C22×D5319yes—
530C4×Q8C22×D5313yes—
531C4×Q8C22×D5319yes—
532C4×Q8C22×D5313yes—
533C4×Q8C22×D5313yes—
534C4×Q8C22×D5316yes—
535C4×D4—539no—
536C4×D4—539no—
537C4×D4—5318no—
538C4×D4—5318no—
539C4×D4—539no—
540C4×D4—539no—
541C4×D4—5318no—
542C4×D4—5318no—
543C4×D4—539no—
544C4×D4—539no—
545C4×D4C22×D5319yes—
546C4×D4C22×D5319yes—
547#117—539no—
548#117—539no—
549#117—539no—
550#117—5318no—
551#117—5318no—
552#117C22×D5319yes—
553C2×C4⋊C4—5318no—
554C2×C4⋊C4—539no—
555C2×C4⋊C4—533no—
556C2×C4⋊C4—5318no—
557C2×C4⋊C4—539no—
558C2×C4⋊C4—5318no—
559C2×C4⋊C4—539no—
560C2×C4⋊C4—539no—
561C2×C4⋊C4—539no—
562C2×C4⋊C4—539no—
563C2×C4⋊C4—5318no—
564C2×C4⋊C4C22×D5319yes—
565C2×C22⋊C4—5318no—
566C2×C42—539no—
567C2×C42—539no—
568C2×C42—539no—
569C2×C42—539no—
570C2×C42—539no—
571C2×C42—539no—
572C2×C42—533no—
573C2×C42—539no—
574C2×C42—539no—
575C2×C42—539no—
576C2×C42—539no—
577C2×C42C22×D5319yes—
578C24—533no—
579#41—538no—
580#41—5324no—
581#41—5324no—
582#41Q8×D5318yesdirect product factor
583C2×Q8—212no—
584C2×Q8—538no—
585C2×Q8—538no—
586C2×Q8—533no—
587C2×Q8—533no—
588C2×Q8—5318no—
589C2×Q8—539no—
590C2×Q8—5318no—
591C2×Q8—10636no—
592C2×Q8—10636no—
593C2×Q8—10636no—
594C2×Q8—10612no—
595C2×Q8—21212no—
596C2×Q8C23×D5319yes—
597C2×Q8C23×D5316yes—
598C2×Q8C23×D5311yescharacteristic
599C2×Q8C23×D5311yescharacteristic
600C2×D4—536no—
601C2×D4—5324no—
602C2×D4—533no—
603C2×D4C23×D5313yes—
604C22×C4—533no—
605C22×C4—5324no—
606C22×C4—533no—
607C22×C4—533no—
608C22×C4—533no—
609C22×C4—531no—
610C22×C4—533no—
611C22×C4—539no—
612C22×C4—539no—
613C22×C4—533no—
614C22×C4—539no—
615C22×C4—539no—
616C22×C4—539no—
617C22×C4—539no—
618C22×C4—539no—
619C22×C4—539no—
620C22×C4—10636no—
621C22×C4—21218no—
622C22×C4C23×D5319yes—
623C22×C4C23×D5319yes—
624C22×C4C23×D5313yes—
625C4⋊C4—536no—
626C4⋊C4—533no—
627C4⋊C4—5318no—
628C4⋊C4—5318no—
629C4⋊C4—5318no—
630C4⋊C4—5318no—
631C4⋊C4—539no—
632C4⋊C4—5318no—
633C4⋊C4—5318no—
634C4⋊C4—539no—
635C4⋊C4—539no—
636C4⋊C4—5336no—
637C4⋊C4—5318no—
638C4⋊C4C23×D5313yes—
639C4⋊C4C23×D53118yes—
640C4⋊C4C23×D5319yes—
641C4⋊C4C23×D5319yes—
642C4⋊C4C23×D5319yes—
643C4⋊C4C23×D53118yes—
644C22⋊C4—5318no—
645C22⋊C4—5318no—
646C22⋊C4—5318no—
647C22⋊C4C23×D53118yes—
648C42—533no—
649C42—533no—
650C42—539no—
651C42—539no—
652C42—539no—
653C42—539no—
654C42—539no—
655C42—539no—
656C42—539no—
657C42—539no—
658C42—533no—
659C42—539no—
660C42C23×D5319yes—
661C42C23×D5319yes—
662C42C23×D5313yes—
663C42C23×D5319yes—
664C23—531no—
665C23—5312no—
666C23—533no—
667C23—1066no—
668C23—1066no—
669C23C24×D5313yes—
670Q8—218no—
671Q8—46no—
672Q8—5312no—
673Q8—5312no—
674Q8—10636no—
675Q8—10618no—
676Q8—21218no—
677Q8C2×Q8×D5314yescomplemented
678Q8#41×D5314yesdirect product factor
679D4—5324no—
680D4—5312no—
681D4C2×Q8×D53112yescomplemented
682C2×C4—218no—
683C2×C4—49no—
684C2×C4—5312no—
685C2×C4—531no—
686C2×C4—533no—
687C2×C4—533no—
688C2×C4—534no—
689C2×C4—5312no—
690C2×C4—5312no—
691C2×C4—5312no—
692C2×C4—5312no—
693C2×C4—533no—
694C2×C4—539no—
695C2×C4—539no—
696C2×C4—10618no—
697C2×C4—10618no—
698C2×C4—1066no—
699C2×C4—10618no—
700C2×C4—10618no—
701C2×C4—10618no—
702C2×C4—2129no—
703C2×C4—2129no—
704C2×C4—2129no—
705C2×C4C2×Q8×D53112yescomplemented
706C2×C4C24×D5313yes—
707C2×C4C24×D5319yes—
708C2×C4C24×D5319yes—
709C2×C4C24×D5313yes—
710C2×C4C24×D5313yes—
711C2×C4C24×D5311yescharacteristic
712C22—23no—
713C22—23no—
714C22—532no—
715C22—532no—
716C22—532no—
717C22—536no—
718C22—10624no—
719C22—1063no—
720C22—1063no—
721C22C22×Q8×D5316yes—
722C22C25×D5311yescharacteristic
723C4—29no—
724C4—23no—
725C4—29no—
726C4—532no—
727C4—536no—
728C4—536no—
729C4—1069no—
730C4—1063no—
731C4—1069no—
732C4C22×Q8×D5312yes—
733C4C22×Q8×D5316yes—
734C4C2×#41×D5316yes—
735C2—26no—
736C2—534no—
737C2—1066no—
738C2C23×Q8×D5311yescharacteristic
739C2C22×#41×D5311yescharacteristic
740C2#585×D5311yescharacteristic
subgroupG/H
centerC2×C4C24×D53
commutator, socle, cosocleC22×C53C26
FrattiniC22C25×D53
FittingQ8×#41×C53C2
prime radicalC2×#41×D53C22
hypercenterQ8×#41D53
hypocenterC53C2×Q8×#41
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. Q8×#11719949C2semidirect
2. #20288297C2semidirect
3. Q8×#11719945C2semidirect
4. #41×Dic106C2semidirect
5. #20288294C2semidirect
6. #20288293C2semidirect
7. Q8×#11719947C2semidirect
8. Q82×D53C2semidirect
9. #557×D53C2semidirect
10. #554×D53C2semidirect
11. D4×Q8×D53C2semidirect
12. #533×D53C2semidirect
14. C2×C4×Q8×D53C2semidirect
15. Q8×#41×C53C2semidirect
18. Q8×Dic106C22semidirect
19. Q8×Dic106C22semidirect
20. #16811353C22semidirect
21. #16811352C22semidirect
22. #16811351C22semidirect
23. #16811350C22semidirect
24. #16811349C22semidirect
25. #16811348C22semidirect
26. #16811334C22semidirect
27. #16811333C22semidirect
28. #16811332C22semidirect
29. #16811331C22semidirect
30. #16811330C22semidirect
31. #16811329C22semidirect
32. #16811328C22semidirect
33. #16811327C22semidirect
34. Q8×D212C22semidirect
35. D4×Dic106C22semidirect
36. #16811288C22semidirect
37. Q8×C22⋊D53C22semidirect
38. #16811286C22semidirect
39. #16811180C22semidirect
40. #16811179C22semidirect
41. #16811178C22semidirect
42. #16811178C22semidirect
43. #16811177C22semidirect
44. #16811177C22semidirect
45. #16811176C22semidirect
46. #16811175C22semidirect
47. #16811175C22semidirect
60. C2×Q8×Dic53C22semidirect
61. C2×C4×Dic106C22semidirect
62. C2×#13133182C22semidirect
70. C4×Q8×D53C22semidirect
71. C4×Q8×D53C22semidirect
72. C4×Q8×D53C22semidirect
73. C4×Q8×D53C22semidirect
79. Q82×C53C22semidirect
80. C53×#557C22semidirect
81. C53×#554C22semidirect
82. D4×Q8×C53C22semidirect
83. C53×#533C22semidirect
85. C2×C4×Q8×C53C22semidirect
89. #41×D53Q8direct (N × H)
208. #41×C53C2×Q8semidirect
222. #11719949C2×Q8semidirect
227. Q8×D53C2×Q8semidirect
228. Q8×D53#41direct (N × H)
229. #11719947C2×Q8semidirect
230. D4×D53C2×Q8semidirect
231. #11719945C2×Q8semidirect
235. C2×C4×D53C2×Q8semidirect
301. Q8×C53C22×Q8semidirect
302. Q8×C53C2×#41semidirect
303. D4×C53C22×Q8semidirect
306. C2×C4×C53C22×Q8semidirect
313. C22⋊D53C22×Q8semidirect
316. C2×Dic53C22×Q8semidirect
323. D212C22×Q8semidirect
333. C4×D53C22×Q8semidirect
334. C4×D53C22×Q8semidirect
339. Dic106C22×Q8semidirect
340. Dic106C2×#41semidirect
372. Q8×#41D53direct (N × H)
385. D53Q8×#41direct (N × H)
391. Q82C2×D53semidirect
397. #557C2×D53semidirect
406. #554C2×D53semidirect
412. D4×Q8C2×D53semidirect
422. #533C2×D53semidirect
450. C2×C4×Q8C2×D53semidirect
456. C53C2×Q8×#41semidirect
582. #41Q8×D53direct (N × H)
677. Q8C2×Q8×D53semidirect
678. Q8#41×D53direct (N × H)
681. D4C2×Q8×D53semidirect
705. C2×C4C2×Q8×D53semidirect

Maximal subgroups

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

subgroupindex
Q8×#117199492
#202882972
Q8×#117199452
#41×Dic1062
#202882942
#202882932
Q8×#117199472
Q82×D532
#557×D532
#554×D532
D4×Q8×D532
#533×D532
C4×#41×D532
C2×C4×Q8×D532
Q8×#41×C532
C2×Q8×#4153