Finite Group Databasebeta

← Q8×#41×D61 #30587081

Subgroups — Q8×#41×D61 #30587081

Order 15616.

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×#11758226C211yesmaximal, characteristic, complemented
2#21459401C213yesmaximal, complemented
3Q8×#11758222C213yesmaximal, complemented
4#41×Dic122C213yesmaximal, complemented
5#21459398C219yesmaximal, complemented
6#21459397C219yesmaximal, complemented
7Q8×#11758224C213yesmaximal, complemented
8Q82×D61C211yesmaximal, characteristic, complemented
9#557×D61C213yesmaximal, complemented
10#554×D61C219yesmaximal, complemented
11D4×Q8×D61C213yesmaximal, complemented
12#533×D61C219yesmaximal, complemented
13C4×#41×D61C213yesmaximal
14C2×C4×Q8×D61C213yesmaximal, complemented
15Q8×#41×C61C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×Q8×D61C2213yes—
18Q8×Dic122C2213yescomplemented
19Q8×Dic122C2213yescomplemented
20#16840492C2219yescomplemented
21#16840491C2213yescomplemented
22#16840490C2219yescomplemented
23#16840489C22118yescomplemented
24#16840488C2216yescomplemented
25#16840487C2219yescomplemented
26#16840473C2219yescomplemented
27#16840472C2219yescomplemented
28#16840471C22118yescomplemented
29#16840470C22118yescomplemented
30#16840469C2219yescomplemented
31#16840468C22118yescomplemented
32#16840467C22118yescomplemented
33#16840466C22136yescomplemented
34Q8×D244C2213yescomplemented
35D4×Dic122C2219yescomplemented
36#16840427C2219yescomplemented
37Q8×C22⋊D61C2216yescomplemented
38#16840425C22118yescomplemented
39#16840319C2219yescomplemented
40#16840318C22118yescomplemented
41#16840317C2219yescomplemented
42#16840317C2219yescomplemented
43#16840316C22118yescomplemented
44#16840316C22118yescomplemented
45#16840315C22118yescomplemented
46#16840314C22118yescomplemented
47#16840314C22118yescomplemented
48C4⋊Q8×D61C2219yes—
49C4⋊Q8×D61C2219yes—
50#125×D61C22118yes—
51C22⋊Q8×D61C22118yes—
52C22⋊Q8×D61C22118yes—
53#41×Dic61C2213yes—
54C4×#11758226C2213yes—
55C4×#11758226C2213yes—
56C4×#11758222C2219yes—
57#16840230C2219yes—
58C4×#11758224C2219yes—
59C4×#11758224C2219yes—
60C2×Q8×Dic61C2213yescomplemented
61C2×C4×Dic122C2219yescomplemented
62C2×#14519742C2219yescomplemented
63C4×Q8×D61C2211yescharacteristic
64C4×Q8×D61C2213yes—
65C4×Q8×D61C2219yes—
66C4×Q8×D61C2219yes—
67C4×Q8×D61C2213yes—
68C4×Q8×D61C2213yes—
69C4×Q8×D61C2216yes—
70C4×Q8×D61C2213yescomplemented
71C4×Q8×D61C2219yescomplemented
72C4×Q8×D61C2219yescomplemented
73C4×Q8×D61C2213yescomplemented
74C4×D4×D61C2219yes—
75C4×D4×D61C2219yes—
76#117×D61C2219yes—
77C2×C4⋊C4×D61C2219yes—
78C2×C42×D61C2219yes—
79Q82×C61C2211yescharacteristic, complemented
80C61×#557C2213yescomplemented
81C61×#554C2219yescomplemented
82D4×Q8×C61C2213yescomplemented
83C61×#533C2219yescomplemented
84C4×#41×C61C2213yes—
85C2×C4×Q8×C61C2213yescomplemented
86C2×#11758226C2311yescharacteristic
87C2×#11758222C2313yes—
88C2×#11758224C2313yes—
89#41×D61Q8116yesdirect product factor
90C22×Dic122C2319yes—
91C2×Q8×D61—224no—
92C2×Q8×D61C2319yes—
93C2×Q8×D61C2319yes—
94C2×Q8×D61C2313yes—
95C2×Q8×D61C2316yes—
96C2×Q8×D61C2311yescharacteristic
97C2×Q8×D61C2311yescharacteristic
98C2×D4×D61C2313yes—
99C22×C4×D61C2319yes—
100C22×C4×D61C2319yes—
101C22×C4×D61C2313yes—
102#14519777C2319yes—
103#14519777C2319yes—
104#14519776C23118yes—
105#14519776C23118yes—
106#14519776C23118yes—
107#14519776C23118yes—
108#14519775C23118yes—
109#14519775C23118yes—
110#14519769C23118yes—
111#14519768C23118yes—
112#14519768C23118yes—
113#14519767C23136yes—
114#14519767C23136yes—
115#14519757C23118yes—
116#14519757C23118yes—
117#14519756C23118yes—
118#14519756C23118yes—
119#14519755C23136yes—
120#14519755C23136yes—
121#14519754C23136yes—
122#14519754C23136yes—
123#14519753C23118yes—
124#14519753C23118yes—
125Q8×Dic61C2319yes—
126Q8×Dic61C2311yescharacteristic
127Q8×Dic61C2313yes—
128Q8×Dic61C2319yes—
129Q8×Dic61C2313yes—
130Q8×Dic61C2313yes—
131Q8×Dic61C2316yes—
132C4×Dic122C23118yes—
133C4×Dic122C2319yes—
134C4×Dic122C2313yes—
135C4×Dic122C2319yes—
136C4×Dic122C23118yes—
137C4×Dic122C2319yes—
138C4×Dic122C2319yes—
139C4×Dic122C2319yes—
140C4×Dic122C23118yes—
141#14519742C23118yes—
142#14519742C2319yes—
143#14519742C2313yes—
144#14519742C2319yes—
145#14519742C2319yes—
146#14519742C23118yes—
147#14519742C2319yes—
148#14519742C2319yes—
149#14519742C23118yes—
150C4×D244C2319yes—
151C4×D244C2319yes—
152D4×Dic61C2319yes—
153D4×Dic61C2319yes—
154#14519739C2319yes—
155#14519739C2319yes—
156C4×C22⋊D61C23118yes—
157C4×C22⋊D61C23118yes—
158#14519737C23118yes—
159#14519737C23118yes—
160#14519736C2319yes—
161#14519735C2319yes—
162#14519735C2319yes—
163#14519734C23118yes—
164#14519733C23118yes—
165C2×C4⋊Dic61C2319yes—
166C2×#11758196C23118yes—
167C4⋊C4×D61C23118yes—
168C4⋊C4×D61C2313yes—
169C4⋊C4×D61C2319yes—
170C4⋊C4×D61C2319yes—
171C4⋊C4×D61C23118yes—
172C4⋊C4×D61C2319yes—
173C4⋊C4×D61C2319yes—
174C4⋊C4×D61C2319yes—
175C4⋊C4×D61C23118yes—
176C22⋊C4×D61C23118yes—
177C2×C4×Dic61C2319yes—
178C2×C4×Dic61C2319yes—
179C2×C4×Dic61C2319yes—
180C42×D61C2313yes—
181C42×D61C2319yes—
182C42×D61C2319yes—
183C42×D61C2319yes—
184C42×D61C2319yes—
185C42×D61C2319yes—
186C42×D61C2319yes—
187C42×D61C2319yes—
188C2×#41×C61C2311yescharacteristic
189C22×Q8×C61C2313yes—
190C4⋊Q8×C61C2319yes—
191C4⋊Q8×C61C2319yes—
192#125×C61C23118yes—
193C22⋊Q8×C61C23118yes—
194C22⋊Q8×C61C23118yes—
195C4×Q8×C61C2316yes—
196C4×Q8×C61C2319yes—
197C4×Q8×C61C2313yes—
198C4×Q8×C61C2319yes—
199C4×Q8×C61C2313yes—
200C4×Q8×C61C2313yes—
201C4×Q8×C61C2311yescharacteristic
202C4×D4×C61C2319yes—
203C4×D4×C61C2319yes—
204#117×C61C2319yes—
205C2×C4⋊C4×C61C2319yes—
206C2×C42×C61C2319yes—
207C23×D61C2413yes—
208#41×C61C2×Q818yescomplemented
209C2×Q8×C61—212no—
210C2×Q8×C61C2419yes—
211C2×Q8×C61C2416yes—
212C2×Q8×C61C2411yescharacteristic
213C2×Q8×C61C2411yescharacteristic
214C2×D4×C61C2413yes—
215C22×C4×C61C2419yes—
216C22×C4×C61C2419yes—
217C22×C4×C61C2413yes—
218C2×C22⋊D61C2416yes—
219C22×Dic61C2419yes—
220C22×Dic61C2419yes—
221C22×Dic61C2413yes—
222#11758226C2×Q818yescomplemented
223Q8×D61—212no—
224Q8×D61—236no—
225Q8×D61—236no—
226Q8×D61—412no—
227Q8×D61C2×Q818yescomplemented
228Q8×D61#4118yesdirect product factor
229#11758224C2×Q8124yescomplemented
230D4×D61C2×Q8124yescomplemented
231#11758222C2×Q8124yescomplemented
232C2×D244C2413yes—
233C2×C4×D61—236no—
234C2×C4×D61—418no—
235C2×C4×D61C2×Q8124yescomplemented
236C2×C4×D61C2413yes—
237C2×C4×D61C2419yes—
238C2×C4×D61C2419yes—
239C2×C4×D61C2419yes—
240C2×C4×D61C2419yes—
241C2×C4×D61C2419yes—
242C2×C4×D61C2419yes—
243C2×C4×D61C2411yescharacteristic
244C2×C4×D61C2413yes—
245C2×C4×D61C2413yes—
246C2×C4×D61C2413yes—
247C2×C4×D61C2413yes—
248C2×Dic122—236no—
249C2×Dic122C24118yes—
250C2×Dic122C2419yes—
251C2×Dic122C24118yes—
252C2×Dic122C2413yes—
253C2×Dic122C2413yes—
254C4⋊C4×C61C2413yes—
255C4⋊C4×C61C24118yes—
256C4⋊C4×C61C2419yes—
257C4⋊C4×C61C2419yes—
258C4⋊C4×C61C2419yes—
259C4⋊C4×C61C24118yes—
260C22⋊C4×C61C24118yes—
261C42×C61C2413yes—
262C42×C61C2419yes—
263C42×C61C2419yes—
264C42×C61C2419yes—
265C22⋊Dic61C24118yes—
266#11758198C24118yes—
267#11758198C24118yes—
268C4⋊Dic61C2413yes—
269C4⋊Dic61C2419yes—
270C4⋊Dic61C24118yes—
271C4⋊Dic61C2419yes—
272C4⋊Dic61C2419yes—
273C4⋊Dic61C24118yes—
274#11758196C2416yes—
275#11758196C24118yes—
276#11758196C24118yes—
277#11758196C24118yes—
278#11758196C24118yes—
279#11758196C24118yes—
280#11758196C24136yes—
281C4×Dic61C2413yes—
282C4×Dic61C2413yes—
283C4×Dic61C2413yes—
284C4×Dic61C2419yes—
285C4×Dic61C2419yes—
286C4×Dic61C2419yes—
287C4×Dic61C2419yes—
288C4×Dic61C2419yes—
289C4×Dic61C2419yes—
290C4×Dic61C2419yes—
291C4×Dic61C2419yes—
292C4×Dic61C2419yes—
293C23×C61C2513yes—
294C22×D61—26no—
295C22×D61—26no—
296C22×D61C22×Q8112yes—
297C22×D61C2513yes—
298C22×D61C2511yescharacteristic
299Q8×C61—218no—
300Q8×C61—46no—
301Q8×C61C22×Q814yescomplemented
302Q8×C61C2×#4114yescomplemented
303D4×C61C22×Q8112yescomplemented
304C2×C4×C61—218no—
305C2×C4×C61—49no—
306C2×C4×C61C22×Q8112yescomplemented
307C2×C4×C61C2513yes—
308C2×C4×C61C2519yes—
309C2×C4×C61C2519yes—
310C2×C4×C61C2513yes—
311C2×C4×C61C2511yescharacteristic
312C2×C4×C61C2513yes—
313C22⋊D61C22×Q8124yescomplemented
314C2×Dic61—218no—
315C2×Dic61—49no—
316C2×Dic61C22×Q8112yescomplemented
317C2×Dic61C2513yes—
318C2×Dic61C2519yes—
319C2×Dic61C2519yes—
320C2×Dic61C2511yescharacteristic
321C2×Dic61C2513yes—
322C2×Dic61C2513yes—
323D244C22×Q8112yescomplemented
324C4×D61—218no—
325C4×D61—26no—
326C4×D61—218no—
327C4×D61—218no—
328C4×D61—218no—
329C4×D61—49no—
330C4×D61—49no—
331C4×D61C22×Q814yes—
332C4×D61C22×Q8112yes—
333C4×D61C22×Q8112yescomplemented
334C4×D61C22×Q8112yescomplemented
335C4×D61C2×#41112yes—
336Dic122—218no—
337Dic122—236no—
338Dic122—418no—
339Dic122C22×Q8112yescomplemented
340Dic122C2×#41112yescomplemented
341C2×Q8×#41—611nomaximal, Sylow
342C22×C61—23no—
343C22×C61—23no—
344C22×C61C23×Q816yes—
345C22×C61C2611yescharacteristic
346C2×D61—23no—
347C2×D61—23no—
348C2×D61—224no—
349C2×D61C23×Q816yes—
350C2×D61C23×Q812yes—
351C2×D61C22×#4112yes—
352C2×D61#58512yes—
353C4×C61—29no—
354C4×C61—29no—
355C4×C61—23no—
356C4×C61C23×Q816yes—
357C4×C61C23×Q812yes—
358C4×C61C22×#4116yes—
359Dic61—29no—
360Dic61—29no—
361Dic61—23no—
362Dic61C23×Q816yes—
363Dic61C23×Q812yes—
364Dic61C22×#4116yes—
365Q8×#41—611no—
366Q8×#41—613no—
367Q8×#41—619no—
368Q8×#41—613no—
369Q8×#41—619no—
370Q8×#41—613no—
371Q8×#41—613no—
372Q8×#41D6111yescharacteristic, direct product factor
373C2×Q82—611no—
374C2×#557—613no—
375C2×#554—619no—
376C2×D4×Q8—613no—
377C2×#533—619no—
378C2×C4×#41—613no—
379C22×C4×Q8—613no—
380C2×C61—26no—
381C2×C61C24×Q811yescharacteristic
382C2×C61C23×#4111yescharacteristic
383C2×C61C2×#58511yescharacteristic
384D61—26no—
385D61Q8×#4114yesdirect product factor
386C22×#41—611no—
387C23×Q8—613no—
388Q82—619no—
389Q82—613no—
390Q82—613no—
391Q82C2×D6111yescharacteristic, complemented
392#557—619no—
393#557—6118no—
394#557—616no—
395#557—619no—
396#557—613no—
397#557C2×D6113yescomplemented
398#554—619no—
399#554—6118no—
400#554—6136no—
401#554—6118no—
402#554—619no—
403#554—619no—
404#554—6118no—
405#554—6118no—
406#554C2×D6119yescomplemented
407D4×Q8—616no—
408D4×Q8—619no—
409D4×Q8—6118no—
410D4×Q8—613no—
411D4×Q8—619no—
412D4×Q8C2×D6113yescomplemented
413#533—619no—
414#533—619no—
415#533—6118no—
416#533—6118no—
417#533—6118no—
418#533—6118no—
419#533—6118no—
420#533—6118no—
421#533—619no—
422#533C2×D6119yescomplemented
423C2×C4⋊Q8—619no—
424C2×C4⋊Q8—619no—
425C2×#125—6118no—
426C2×C22⋊Q8—6118no—
427C2×C22⋊Q8—6118no—
428C4×#41—613no—
429C4×#41—613no—
430C4×#41—613no—
431C4×#41—619no—
432C4×#41—619no—
433C4×#41—619no—
434C4×#41—619no—
435C4×#41C2×D6113yes—
436C2×C4×Q8—613no—
437C2×C4×Q8—611no—
438C2×C4×Q8—619no—
439C2×C4×Q8—613no—
440C2×C4×Q8—619no—
441C2×C4×Q8—613no—
442C2×C4×Q8—613no—
443C2×C4×Q8—616no—
444C2×C4×Q8—613no—
445C2×C4×Q8—619no—
446C2×C4×Q8—613no—
447C2×C4×Q8—619no—
448C2×C4×Q8—619no—
449C2×C4×Q8—619no—
450C2×C4×Q8C2×D6113yescomplemented
451C2×C4×D4—619no—
452C2×C4×D4—619no—
453C2×#117—619no—
454C22×C4⋊C4—619no—
455C22×C42—619no—
456C61C2×Q8×#4111yescharacteristic, complemented, Sylow
457C2×#41—6116no—
458C2×#41—611no—
459C2×#41—613no—
460C2×#41—613no—
461C2×#41C22×D6111yescharacteristic
462C22×Q8—611no—
463C22×Q8—611no—
464C22×Q8—619no—
465C22×Q8—619no—
466C22×Q8—613no—
467C22×Q8—616no—
468C22×Q8—619no—
469C22×Q8—12224no—
470C22×Q8C22×D6113yes—
471C22×D4—613no—
472C23×C4—613no—
473C23×C4—619no—
474C23×C4—619no—
475C4⋊Q8—6118no—
476C4⋊Q8—6118no—
477C4⋊Q8—6118no—
478C4⋊Q8—6118no—
479C4⋊Q8—6118no—
480C4⋊Q8—6118no—
481C4⋊Q8—619no—
482C4⋊Q8—619no—
483C4⋊Q8C22×D6119yes—
484C4⋊Q8C22×D6119yes—
485#125—6136no—
486#125—6136no—
487#125—6118no—
488#125—6118no—
489#125—6118no—
490#125C22×D61118yes—
491C22⋊Q8—6118no—
492C22⋊Q8—6118no—
493C22⋊Q8—6118no—
494C22⋊Q8—6118no—
495C22⋊Q8—6136no—
496C22⋊Q8—6118no—
497C22⋊Q8—6136no—
498C22⋊Q8—6118no—
499C22⋊Q8—6136no—
500C22⋊Q8—6136no—
501C22⋊Q8C22×D61118yes—
502C22⋊Q8C22×D61118yes—
503C4×Q8—611no—
504C4×Q8—619no—
505C4×Q8—613no—
506C4×Q8—619no—
507C4×Q8—613no—
508C4×Q8—613no—
509C4×Q8—616no—
510C4×Q8—613no—
511C4×Q8—619no—
512C4×Q8—6118no—
513C4×Q8—619no—
514C4×Q8—6118no—
515C4×Q8—619no—
516C4×Q8—619no—
517C4×Q8—619no—
518C4×Q8—6118no—
519C4×Q8—613no—
520C4×Q8—6118no—
521C4×Q8—619no—
522C4×Q8—619no—
523C4×Q8—619no—
524C4×Q8—6118no—
525C4×Q8—619no—
526C4×Q8—619no—
527C4×Q8—6118no—
528C4×Q8C22×D6111yescharacteristic
529C4×Q8C22×D6119yes—
530C4×Q8C22×D6113yes—
531C4×Q8C22×D6119yes—
532C4×Q8C22×D6113yes—
533C4×Q8C22×D6113yes—
534C4×Q8C22×D6116yes—
535C4×D4—619no—
536C4×D4—619no—
537C4×D4—6118no—
538C4×D4—6118no—
539C4×D4—619no—
540C4×D4—619no—
541C4×D4—6118no—
542C4×D4—6118no—
543C4×D4—619no—
544C4×D4—619no—
545C4×D4C22×D6119yes—
546C4×D4C22×D6119yes—
547#117—619no—
548#117—619no—
549#117—619no—
550#117—6118no—
551#117—6118no—
552#117C22×D6119yes—
553C2×C4⋊C4—6118no—
554C2×C4⋊C4—619no—
555C2×C4⋊C4—613no—
556C2×C4⋊C4—6118no—
557C2×C4⋊C4—619no—
558C2×C4⋊C4—6118no—
559C2×C4⋊C4—619no—
560C2×C4⋊C4—619no—
561C2×C4⋊C4—619no—
562C2×C4⋊C4—619no—
563C2×C4⋊C4—6118no—
564C2×C4⋊C4C22×D6119yes—
565C2×C22⋊C4—6118no—
566C2×C42—619no—
567C2×C42—619no—
568C2×C42—619no—
569C2×C42—619no—
570C2×C42—619no—
571C2×C42—619no—
572C2×C42—613no—
573C2×C42—619no—
574C2×C42—619no—
575C2×C42—619no—
576C2×C42—619no—
577C2×C42C22×D6119yes—
578C24—613no—
579#41—618no—
580#41—6124no—
581#41—6124no—
582#41Q8×D6118yesdirect product factor
583C2×Q8—212no—
584C2×Q8—618no—
585C2×Q8—618no—
586C2×Q8—613no—
587C2×Q8—613no—
588C2×Q8—6118no—
589C2×Q8—619no—
590C2×Q8—6118no—
591C2×Q8—12236no—
592C2×Q8—12236no—
593C2×Q8—12236no—
594C2×Q8—12212no—
595C2×Q8—24412no—
596C2×Q8C23×D6119yes—
597C2×Q8C23×D6116yes—
598C2×Q8C23×D6111yescharacteristic
599C2×Q8C23×D6111yescharacteristic
600C2×D4—616no—
601C2×D4—6124no—
602C2×D4—613no—
603C2×D4C23×D6113yes—
604C22×C4—613no—
605C22×C4—6124no—
606C22×C4—613no—
607C22×C4—613no—
608C22×C4—613no—
609C22×C4—611no—
610C22×C4—613no—
611C22×C4—619no—
612C22×C4—619no—
613C22×C4—613no—
614C22×C4—619no—
615C22×C4—619no—
616C22×C4—619no—
617C22×C4—619no—
618C22×C4—619no—
619C22×C4—619no—
620C22×C4—12236no—
621C22×C4—24418no—
622C22×C4C23×D6119yes—
623C22×C4C23×D6119yes—
624C22×C4C23×D6113yes—
625C4⋊C4—616no—
626C4⋊C4—613no—
627C4⋊C4—6118no—
628C4⋊C4—6118no—
629C4⋊C4—6118no—
630C4⋊C4—6118no—
631C4⋊C4—619no—
632C4⋊C4—6118no—
633C4⋊C4—6118no—
634C4⋊C4—6136no—
635C4⋊C4—619no—
636C4⋊C4—619no—
637C4⋊C4—6118no—
638C4⋊C4C23×D6113yes—
639C4⋊C4C23×D61118yes—
640C4⋊C4C23×D6119yes—
641C4⋊C4C23×D6119yes—
642C4⋊C4C23×D6119yes—
643C4⋊C4C23×D61118yes—
644C22⋊C4—6118no—
645C22⋊C4—6118no—
646C22⋊C4—6118no—
647C22⋊C4C23×D61118yes—
648C42—613no—
649C42—613no—
650C42—619no—
651C42—619no—
652C42—619no—
653C42—619no—
654C42—619no—
655C42—619no—
656C42—619no—
657C42—619no—
658C42—613no—
659C42—619no—
660C42C23×D6119yes—
661C42C23×D6119yes—
662C42C23×D6113yes—
663C42C23×D6119yes—
664C23—611no—
665C23—6112no—
666C23—613no—
667C23—1226no—
668C23—1226no—
669C23C24×D6113yes—
670Q8—218no—
671Q8—46no—
672Q8—6112no—
673Q8—6112no—
674Q8—12236no—
675Q8—12218no—
676Q8—24418no—
677Q8C2×Q8×D6114yescomplemented
678Q8#41×D6114yesdirect product factor
679D4—6124no—
680D4—6112no—
681D4C2×Q8×D61112yescomplemented
682C2×C4—218no—
683C2×C4—49no—
684C2×C4—6112no—
685C2×C4—611no—
686C2×C4—613no—
687C2×C4—613no—
688C2×C4—614no—
689C2×C4—6112no—
690C2×C4—6112no—
691C2×C4—6112no—
692C2×C4—6112no—
693C2×C4—613no—
694C2×C4—619no—
695C2×C4—619no—
696C2×C4—12218no—
697C2×C4—12218no—
698C2×C4—1226no—
699C2×C4—12218no—
700C2×C4—12218no—
701C2×C4—12218no—
702C2×C4—2449no—
703C2×C4—2449no—
704C2×C4—2449no—
705C2×C4C2×Q8×D61112yescomplemented
706C2×C4C24×D6113yes—
707C2×C4C24×D6119yes—
708C2×C4C24×D6119yes—
709C2×C4C24×D6113yes—
710C2×C4C24×D6113yes—
711C2×C4C24×D6111yescharacteristic
712C22—23no—
713C22—23no—
714C22—612no—
715C22—612no—
716C22—612no—
717C22—616no—
718C22—12224no—
719C22—1223no—
720C22—1223no—
721C22C22×Q8×D6116yes—
722C22C25×D6111yescharacteristic
723C4—29no—
724C4—23no—
725C4—29no—
726C4—612no—
727C4—616no—
728C4—616no—
729C4—1229no—
730C4—1223no—
731C4—1229no—
732C4C22×Q8×D6112yes—
733C4C22×Q8×D6116yes—
734C4C2×#41×D6116yes—
735C2—26no—
736C2—614no—
737C2—1226no—
738C2C23×Q8×D6111yescharacteristic
739C2C22×#41×D6111yescharacteristic
740C2#585×D6111yescharacteristic
subgroupG/H
centerC2×C4C24×D61
commutator, socle, cosocleC22×C61C26
FrattiniC22C25×D61
FittingQ8×#41×C61C2
prime radicalC2×#41×D61C22
hypercenterQ8×#41D61
hypocenterC61C2×Q8×#41
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. Q8×#11758226C2semidirect
2. #21459401C2semidirect
3. Q8×#11758222C2semidirect
4. #41×Dic122C2semidirect
5. #21459398C2semidirect
6. #21459397C2semidirect
7. Q8×#11758224C2semidirect
8. Q82×D61C2semidirect
9. #557×D61C2semidirect
10. #554×D61C2semidirect
11. D4×Q8×D61C2semidirect
12. #533×D61C2semidirect
14. C2×C4×Q8×D61C2semidirect
15. Q8×#41×C61C2semidirect
18. Q8×Dic122C22semidirect
19. Q8×Dic122C22semidirect
20. #16840492C22semidirect
21. #16840491C22semidirect
22. #16840490C22semidirect
23. #16840489C22semidirect
24. #16840488C22semidirect
25. #16840487C22semidirect
26. #16840473C22semidirect
27. #16840472C22semidirect
28. #16840471C22semidirect
29. #16840470C22semidirect
30. #16840469C22semidirect
31. #16840468C22semidirect
32. #16840467C22semidirect
33. #16840466C22semidirect
34. Q8×D244C22semidirect
35. D4×Dic122C22semidirect
36. #16840427C22semidirect
37. Q8×C22⋊D61C22semidirect
38. #16840425C22semidirect
39. #16840319C22semidirect
40. #16840318C22semidirect
41. #16840317C22semidirect
42. #16840317C22semidirect
43. #16840316C22semidirect
44. #16840316C22semidirect
45. #16840315C22semidirect
46. #16840314C22semidirect
47. #16840314C22semidirect
60. C2×Q8×Dic61C22semidirect
61. C2×C4×Dic122C22semidirect
62. C2×#14519742C22semidirect
70. C4×Q8×D61C22semidirect
71. C4×Q8×D61C22semidirect
72. C4×Q8×D61C22semidirect
73. C4×Q8×D61C22semidirect
79. Q82×C61C22semidirect
80. C61×#557C22semidirect
81. C61×#554C22semidirect
82. D4×Q8×C61C22semidirect
83. C61×#533C22semidirect
85. C2×C4×Q8×C61C22semidirect
89. #41×D61Q8direct (N × H)
208. #41×C61C2×Q8semidirect
222. #11758226C2×Q8semidirect
227. Q8×D61C2×Q8semidirect
228. Q8×D61#41direct (N × H)
229. #11758224C2×Q8semidirect
230. D4×D61C2×Q8semidirect
231. #11758222C2×Q8semidirect
235. C2×C4×D61C2×Q8semidirect
301. Q8×C61C22×Q8semidirect
302. Q8×C61C2×#41semidirect
303. D4×C61C22×Q8semidirect
306. C2×C4×C61C22×Q8semidirect
313. C22⋊D61C22×Q8semidirect
316. C2×Dic61C22×Q8semidirect
323. D244C22×Q8semidirect
333. C4×D61C22×Q8semidirect
334. C4×D61C22×Q8semidirect
339. Dic122C22×Q8semidirect
340. Dic122C2×#41semidirect
372. Q8×#41D61direct (N × H)
385. D61Q8×#41direct (N × H)
391. Q82C2×D61semidirect
397. #557C2×D61semidirect
406. #554C2×D61semidirect
412. D4×Q8C2×D61semidirect
422. #533C2×D61semidirect
450. C2×C4×Q8C2×D61semidirect
456. C61C2×Q8×#41semidirect
582. #41Q8×D61direct (N × H)
677. Q8C2×Q8×D61semidirect
678. Q8#41×D61direct (N × H)
681. D4C2×Q8×D61semidirect
705. C2×C4C2×Q8×D61semidirect

Maximal subgroups

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

subgroupindex
Q8×#117582262
#214594012
Q8×#117582222
#41×Dic1222
#214593982
#214593972
Q8×#117582242
Q82×D612
#557×D612
#554×D612
D4×Q8×D612
#533×D612
C4×#41×D612
C2×C4×Q8×D612
Q8×#41×C612
C2×Q8×#4161