Finite Group Databasebeta

← #30560634

Subgroups — #30560634

Order 15616.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11758222C211yesmaximal, characteristic
2C2×#16840490C211yesmaximal, characteristic, complemented
3#21458788C214yesmaximal, complemented
4#21458766C214yesmaximal, complemented
5#21458753C212yesmaximal, complemented
6#21458742C212yesmaximal, complemented
7#21458711C212yesmaximal, complemented
8#21458696C212yesmaximal, complemented
9#21456371C212yesmaximal, complemented
10#21456365C211yesmaximal, characteristic, complemented
11#21455642C212yesmaximal
12#21455635C211yesmaximal, characteristic
13#21455626C211yesmaximal, characteristic, complemented
14#21455626C212yesmaximal, complemented
15C4×#14519810C211yesmaximal, characteristic
16C4×#14519810C212yesmaximal
17Q8×M16×C61C211yesmaximal, characteristic, complemented
18C2×#14519810C2211yescharacteristic
19Q8×Dic122C2211yescharacteristic
20#16840490—21no—
21#16840490—22no—
22#16840490—21no—
23#16840490C2212yes—
24#16840490C2211yescharacteristic
25#16840490C2212yes—
26#16840490C2214yes—
27#16840490C2212yes—
28#16840472C2211yescharacteristic
29#16840472C2212yes—
30#16840467—21no—
31#16840467—22no—
32Q8×D244C2211yescharacteristic
33Q8×C22⋊D61—21no—
34#16840319C2211yescharacteristic
35#16840319C2212yes—
36#16840316—22no—
37#16840316—21no—
38C2×#14519777C2211yescharacteristic
39C2×#14519775—21no—
40C2×#14519769C2212yes—
41C2×#14519767—22no—
42C4×#11758222C2211yescharacteristic
43C4×#11758222C2212yes—
44C2×C4×Dic122C2212yes—
45C2×C4×Dic122C2211yescharacteristic
46C2×#14519742—21no—
47C4×Q8×D61—21no—
48#16840171C2214yes—
49#16840171C2214yes—
50#16840171C2214yes—
51#16840167C2212yes—
52#16840164C2214yes—
53#16840164C2214yes—
54#16840160C2212yes—
55#16840070C2214yes—
56#16840070C2214yes—
57#16840070C2214yes—
58#16840070C2214yes—
59#16840070C2214yes—
60#16840063C2214yes—
61#16840063C2214yes—
62#16840058C2212yes—
63#16840058C2214yes—
64#16840058C2212yes—
65#16840053C2212yes—
66#16840048C2212yes—
67#16840048C2214yes—
68#16840048C2212yes—
69#16840043C2212yes—
70#16839870C2214yes—
71#16839870C2212yes—
72#16839864C2214yes—
73#16839864C2212yes—
74C4×Dic244C2212yes—
75C4×Dic244C2214yes—
76C4×#11758190C2212yes—
77C4×#11758190C2214yes—
78#16839804C2212yes—
79#16839804C2212yes—
80#16839804C2212yes—
81#16839804C2212yes—
82#16839804C2211yescharacteristic
83#16839772C2211yescharacteristic
84#16839772C2212yes—
85#16839764C2212yes—
86#16839764C2211yescharacteristic
87C2×C4×Q8×C61C2211yescharacteristic
88C61×#446C2212yes—
89C61×#446C2214yes—
90C8×Q8×C61C2212yes—
91C61×#423C2211yescharacteristic
92C61×#423C2212yes—
93C4×M16×C61C2211yescharacteristic
94C4×M16×C61C2212yes—
95C2×#11758222C2311yescharacteristic
96C22×Dic122—21no—
97C22×Dic122C2311yescharacteristic
98C2×Q8×D61—21no—
99#14519810Q818yescomplemented
100C2×Dic244C2312yes—
101C2×#11758190C2312yes—
102#14519777—21no—
103#14519777—21no—
104#14519777C2312yes—
105#14519777C2311yescharacteristic
106#14519777C2312yes—
107#14519777C2312yes—
108#14519777C2311yescharacteristic
109#14519777C2312yes—
110#14519776—21no—
111#14519776—22no—
112#14519775—22no—
113#14519775—22no—
114#14519775—24no—
115#14519775—21no—
116#14519775—22no—
117#14519769—22no—
118#14519769—22no—
119#14519769C2312yes—
120#14519769C2312yes—
121#14519769C2312yes—
122#14519769C2314yes—
123#14519769C2314yes—
124#14519767—22no—
125#14519767—22no—
126#14519767—22no—
127#14519767—24no—
128#14519767—24no—
129#14519767—24no—
130#14519767—24no—
131#14519757—21no—
132#14519757—22no—
133#14519756—22no—
134#14519756—21no—
135#14519756—21no—
136#14519756—22no—
137#14519755—22no—
138#14519755—22no—
139#14519755—22no—
140#14519753—21no—
141#14519753—22no—
142Q8×Dic61—21no—
143C4×Dic122—22no—
144C4×Dic122—21no—
145C4×Dic122—22no—
146C4×Dic122—22no—
147C4×Dic122—21no—
148C4×Dic122—21no—
149C4×Dic122—22no—
150C4×Dic122—21no—
151C4×Dic122C2312yes—
152C4×Dic122C2314yes—
153C4×Dic122C2314yes—
154C4×Dic122C2312yes—
155C4×Dic122C2311yescharacteristic
156C4×Dic122C2312yes—
157C4×Dic122C2311yescharacteristic
158C4×Dic122C2312yes—
159#14519742—21no—
160#14519742—22no—
161#14519742—22no—
162#14519742—24no—
163#14519742—22no—
164C4×D244C2311yescharacteristic
165C4×D244C2312yes—
166C4×D244C2311yescharacteristic
167C4×D244C2312yes—
168C4×C22⋊D61—22no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—22no—
172#14519736C2311yescharacteristic
173#14519736C2312yes—
174#14519734—22no—
175#14519734—21no—
176C2×C4⋊Dic61—21no—
177C2×C4⋊Dic61C2311yescharacteristic
178C2×C4⋊Dic61C2312yes—
179C2×#11758196—22no—
180C2×#11758196—21no—
181C2×#11758196—22no—
182C2×#11758196—22no—
183C4⋊C4×D61—21no—
184C4⋊C4×D61—22no—
185C2×C4×Dic61—22no—
186C2×C4×Dic61—21no—
187C42×D61—22no—
188C42×D61—21no—
189#14519711C2314yes—
190#14519711C2314yes—
191#14519711C2314yes—
192#14519711C2312yes—
193#14519711C2314yes—
194#14519709C2314yes—
195#14519709C2314yes—
196#14519709C2314yes—
197#14519709C2314yes—
198#14519709C2312yes—
199#14519702C2314yes—
200#14519702C2312yes—
201#14519702C2312yes—
202#14519702C2314yes—
203#14519702C2314yes—
204#14519702C2312yes—
205#14519699C2314yes—
206#14519699C2312yes—
207C22×Q8×C61D411yescharacteristic
208C2×M16×C61C2312yes—
209C2×M16×C61C2311yescharacteristic
210C2×M16×C61C2311yescharacteristic
211C4×Q8×C61D411yescharacteristic
212C4×Q8×C61D412yes—
213C4×Q8×C61D411yescharacteristic
214C4×Q8×C61C2311yescharacteristic
215C4×Q8×C61C2312yes—
216C4×Q8×C61C2311yescharacteristic
217C2×C4⋊C4×C61D411yescharacteristic
218C2×C4⋊C4×C61D412yes—
219C2×C42×C61C2312yes—
220C2×C42×C61C2311yescharacteristic
221C4⋊C8×C61C2312yes—
222C4⋊C8×C61C2314yes—
223C4⋊C8×C61C2312yes—
224C4⋊C8×C61C2314yes—
225#97×C61C2312yes—
226#97×C61C2314yes—
227C4×C8×C61C2312yes—
228C4×C8×C61C2314yes—
229C2×Q8×C61—42no—
230C2×Q8×C61C2×D411yescharacteristic
231C2×Q8×C61C2×D411yescharacteristic
232C2×Q8×C61C2×D412yes—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61—21no—
239C22×Dic61—21no—
240C22×Dic61—22no—
241C22×Dic61—21no—
242Q8×D61—44no—
243#11758222—22no—
244#11758222C2×Q814yes—
245C2×D244C2411yescharacteristic
246C2×C4×D61—21no—
247C2×C4×D61—22no—
248C2×C4×D61—21no—
249C2×C4×D61—22no—
250C2×C4×D61—21no—
251C2×Dic122—21no—
252C2×Dic122—22no—
253C2×Dic122—22no—
254C2×Dic122—21no—
255C2×Dic122—22no—
256C2×Dic122—22no—
257C2×Dic122—22no—
258C2×Dic122—21no—
259C2×Dic122—44no—
260C2×Dic122C2×Q814yescomplemented
261C2×Dic122C2412yes—
262C2×Dic122C2411yescharacteristic
263M16×C61—24no—
264M16×C61—22no—
265M16×C61C2×Q814yescomplemented
266C2×C8×C61C2412yes—
267C2×C8×C61C2414yes—
268C2×C8×C61C2412yes—
269C4⋊C4×C61C2×D411yescharacteristic
270C4⋊C4×C61C2×D412yes—
271C4⋊C4×C61C2×D412yes—
272C4⋊C4×C61C2×D411yescharacteristic
273C4⋊C4×C61C2×D412yes—
274C4⋊C4×C61C2×D412yes—
275C4⋊C4×C61C2×D412yes—
276C42×C61C2×D412yes—
277C42×C61C2×D411yescharacteristic
278C42×C61C2×D412yes—
279C42×C61C2×D411yescharacteristic
280C42×C61C2412yes—
281C42×C61C2411yescharacteristic
282C42×C61C2412yes—
283C42×C61C2411yescharacteristic
284C22⋊Dic61—21no—
285C22⋊Dic61—22no—
286#11758198—21no—
287#11758198—22no—
288#11758198—22no—
289#11758198—21no—
290C4⋊Dic61—22no—
291C4⋊Dic61—21no—
292C4⋊Dic61—22no—
293C4⋊Dic61—22no—
294C4⋊Dic61—21no—
295C4⋊Dic61—22no—
296C4⋊Dic61—22no—
297C4⋊Dic61—21no—
298C4⋊Dic61C2412yes—
299C4⋊Dic61C2414yes—
300C4⋊Dic61C2411yescharacteristic
301C4⋊Dic61C2412yes—
302C4⋊Dic61C2412yes—
303C4⋊Dic61C2411yescharacteristic
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307#11758196—24no—
308#11758196—24no—
309#11758196—22no—
310#11758196—22no—
311#11758196—24no—
312#11758196—24no—
313#11758196—24no—
314#11758196—24no—
315#11758196—21no—
316#11758196—22no—
317#11758196—22no—
318#11758196—21no—
319#11758196—22no—
320#11758196—22no—
321#11758196—22no—
322C4×Dic61—22no—
323C4×Dic61—21no—
324C4×Dic61—22no—
325C4×Dic61—21no—
326C4×Dic61—22no—
327C4×Dic61—21no—
328C4×Dic61—24no—
329C4×Dic61—24no—
330C4×Dic61—22no—
331C4×Dic61—22no—
332Dic244C2×Q818yescomplemented
333#11758190C2×Q818yescomplemented
334C23×C61C22×D411yescharacteristic
335C22×D61—21no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—42no—
339C2×C4×C61—22no—
340C2×C4×C61—42no—
341C2×C4×C61—41no—
342C2×C4×C61—42no—
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D412yes—
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D412yes—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×Q812yes—
353C2×C4×C612−1+412yes—
354C2×C4×C61C2511yescharacteristic
355C22⋊D61—24no—
356C2×Dic61—24no—
357C2×Dic61—22no—
358C2×Dic61—21no—
359C2×Dic61—22no—
360C2×Dic61—24no—
361C2×Dic61—22no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—44no—
366C2×Dic61—42no—
367D244—21no—
368D244C22×Q812yes—
369C4×D61—24no—
370C4×D61—44no—
371C4×D61—42no—
372C4×D61—82no—
373C4×D61—81no—
374Dic122—24no—
375Dic122—22no—
376Dic122—21no—
377Dic122—44no—
378Dic122—44no—
379Dic122—44no—
380Dic122—42no—
381Dic122—82no—
382Dic122—81no—
383Dic122C22×Q814yes—
384Dic122C22×Q812yes—
385C8×C61—22no—
386C8×C61—24no—
387C8×C61C22×Q814yes—
388#61369—611nomaximal, Sylow
389C22×C61—21no—
390C22×C61—21no—
391C22×C61D4×Q812yes—
392C22×C61C23×D411yescharacteristic
393C2×D61—22no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—21no—
398C4×C61—22no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—22no—
402C4×C61—22no—
403C4×C61D4×Q812yes—
404C4×C61#57512yes—
405C4×C61C23×Q811yescharacteristic
406C4×C61C2×2−1+411yescharacteristic
407Dic61—24no—
408Dic61—22no—
409Dic61—41no—
410Dic61—42no—
411Dic61—42no—
412Dic61—41no—
413Dic61—42no—
414Dic61—44no—
415Q8×#41—611no—
416C2×#557—611no—
417#3390—614no—
418#3388—614no—
419#3387—612no—
420#3386—612no—
421#3383—612no—
422#3381—612no—
423#3166—612no—
424#3165—611no—
425#3080—612no—
426#3079—611no—
427#3078—611no—
428#3078—612no—
429Q8×M16D6111yescharacteristic, complemented
430C4×#137—611no—
431C4×#137—612no—
432C2×C61—22no—
433C2×C61C2×D4×Q811yescharacteristic
434C2×C61C2×#57511yescharacteristic
435C2×C61#358611yescharacteristic
436D61—42no—
437C2×#137—611no—
438Q82—611no—
439#557—612no—
440#557—611no—
441#557—612no—
442#557—614no—
443#557—612no—
444#557—1221no—
445#557—1222no—
446#557—1221no—
447#554—611no—
448#554—612no—
449#554—1221no—
450#554—1222no—
451D4×Q8—611no—
452D4×Q8—1221no—
453#533—611no—
454#533—612no—
455#533—1222no—
456#533—1221no—
457C2×C4⋊Q8—611no—
458C2×C4⋊Q8—1221no—
459C2×#125—612no—
460C2×#125—1222no—
461C4×#41—611no—
462C4×#41—612no—
463C2×C4×Q8—612no—
464C2×C4×Q8—611no—
465C2×C4×Q8—1221no—
466C2×C4×Q8—1221no—
467C2×C4×Q8C2×D6111yescharacteristic
468#501—614no—
469#501—614no—
470#501—614no—
471#500—612no—
472#499—614no—
473#499—614no—
474#498—612no—
475#479—614no—
476#479—614no—
477#479—614no—
478#479—614no—
479#479—614no—
480#478—614no—
481#478—614no—
482#477—612no—
483#477—614no—
484#477—612no—
485#476—612no—
486#475—612no—
487#475—614no—
488#475—612no—
489#474—612no—
490#446C2×D6112yes—
491#446C2×D6114yes—
492C8×Q8C2×D6112yes—
493#441—614no—
494#441—612no—
495#440—614no—
496#440—612no—
497C4×Q16—612no—
498C4×Q16—614no—
499C4×SD16—612no—
500C4×SD16—614no—
501#428—612no—
502#428—612no—
503#428—612no—
504#428—612no—
505#428—611no—
506#423C2×D6111yescharacteristic
507#423C2×D6112yes—
508#419—612no—
509#419—611no—
510#417—612no—
511#417—611no—
512C4×M16C2×D6111yescharacteristic
513C4×M16C2×D6112yes—
514C61#6136911yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C22×Q8—611no—
517C22×Q8—1221no—
518C22×Q8—1221no—
519C22×Q8D24411yescharacteristic
520#137—618no—
521C2×Q16—612no—
522C2×SD16—612no—
523C2×M16C22×D6111yescharacteristic
524C2×M16C22×D6112yes—
525C2×M16C22×D6111yescharacteristic
526C4⋊Q8—612no—
527C4⋊Q8—612no—
528C4⋊Q8—611no—
529C4⋊Q8—612no—
530C4⋊Q8—612no—
531C4⋊Q8—611no—
532C4⋊Q8—1222no—
533C4⋊Q8—1222no—
534C4⋊Q8—1224no—
535C4⋊Q8—1221no—
536C4⋊Q8—1222no—
537C4⋊Q8—1221no—
538C4⋊Q8—1222no—
539C4⋊Q8—1221no—
540C4⋊Q8—1221no—
541#125—614no—
542#125—614no—
543#125—612no—
544#125—612no—
545#125—612no—
546#125—1224no—
547#125—1224no—
548#125—1224no—
549#125—1224no—
550#125—1222no—
551#125—1222no—
552#125—1222no—
553#125—1222no—
554#125—1222no—
555C22⋊Q8—1221no—
556C22⋊Q8—1222no—
557C22⋊Q8—1221no—
558C22⋊Q8—1222no—
559C22⋊Q8—1222no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C4×Q8—612no—
567C4×Q8—614no—
568C4×Q8—614no—
569C4×Q8—612no—
570C4×Q8—612no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—612no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1222no—
577C4×Q8—1222no—
578C4×Q8—1224no—
579C4×Q8—1222no—
580C4×Q8—1222no—
581C4×Q8—1222no—
582C4×Q8—1221no—
583C4×Q8—1221no—
584C4×Q8—1222no—
585C4×Q8—1221no—
586C4×Q8—1222no—
587C4×Q8—1221no—
588C4×Q8D24411yescharacteristic
589C4×Q8D24412yes—
590C4×Q8D24411yescharacteristic
591C4×Q8C22×D6111yescharacteristic
592C4×Q8C22×D6111yescharacteristic
593C4×Q8C22×D6112yes—
594C4×D4—611no—
595C4×D4—612no—
596C4×D4—612no—
597C4×D4—611no—
598C4×D4—1221no—
599C4×D4—1222no—
600C4×D4—1222no—
601C4×D4—1221no—
602#117—611no—
603#117—612no—
604#117—1222no—
605#117—1221no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—612no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4D24411yescharacteristic
616C2×C4⋊C4D24412yes—
617C2×C42—1222no—
618C2×C42—1221no—
619C2×C42—1222no—
620C2×C42—1221no—
621C2×C42C22×D6112yes—
622C2×C42C22×D6111yescharacteristic
623#107—612no—
624#107—614no—
625#107—614no—
626#107—614no—
627#107—614no—
628#106—614no—
629#106—612no—
630#106—614no—
631#106—614no—
632#106—614no—
633C4⋊C8C22×D6112yes—
634C4⋊C8C22×D6114yes—
635C4⋊C8C22×D6114yes—
636C4⋊C8C22×D6112yes—
637#103—614no—
638#103—612no—
639#103—614no—
640#103—612no—
641#103—612no—
642#103—614no—
643#102—614no—
644#102—612no—
645#97C22×D6112yes—
646#97C22×D6114yes—
647C4×C8C22×D6112yes—
648C4×C8C22×D6114yes—
649#41—614no—
650#41—1222no—
651C2×Q8—42no—
652C2×Q8—614no—
653C2×Q8—612no—
654C2×Q8—611no—
655C2×Q8—1221no—
656C2×Q8—1222no—
657C2×Q8—1221no—
658C2×Q8—1222no—
659C2×Q8—1221no—
660C2×Q8—1222no—
661C2×Q8—1222no—
662C2×Q8—1222no—
663C2×Q8—2444no—
664C2×Q8—2444no—
665C2×Q8C2×D24411yescharacteristic
666C2×Q8C2×D24411yescharacteristic
667C2×Q8C2×D24412yes—
668C2×D4—611no—
669C2×D4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1221no—
676C22×C4—1222no—
677C22×C4—1221no—
678C22×C4C2×D24411yescharacteristic
679C22×C4C2×D24412yes—
680C22×C4C2×D24411yescharacteristic
681C22×C4C2×D24412yes—
682C22×C4C23×D6111yescharacteristic
683Q16—618no—
684SD16—618no—
685M16—22no—
686M16—24no—
687M16Q8×D6114yescomplemented
688C2×C8C23×D6112yes—
689C2×C8C23×D6114yes—
690C2×C8C23×D6112yes—
691C4⋊C4—612no—
692C4⋊C4—614no—
693C4⋊C4—612no—
694C4⋊C4—611no—
695C4⋊C4—611no—
696C4⋊C4—612no—
697C4⋊C4—1221no—
698C4⋊C4—1222no—
699C4⋊C4—1222no—
700C4⋊C4—1222no—
701C4⋊C4—1224no—
702C4⋊C4—1224no—
703C4⋊C4—1222no—
704C4⋊C4—1222no—
705C4⋊C4—1222no—
706C4⋊C4—1224no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1224no—
710C4⋊C4—1222no—
711C4⋊C4—1221no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C4⋊C4—1222no—
715C4⋊C4—1221no—
716C4⋊C4—1222no—
717C4⋊C4—1221no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1221no—
723C4⋊C4C2×D24411yescharacteristic
724C4⋊C4C2×D24412yes—
725C4⋊C4C2×D24412yes—
726C4⋊C4C2×D24411yescharacteristic
727C4⋊C4C2×D24412yes—
728C4⋊C4C2×D24412yes—
729C4⋊C4C2×D24412yes—
730C22⋊C4—1221no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1221no—
734C22⋊C4—1222no—
735C22⋊C4—1221no—
736C42—1222no—
737C42—1221no—
738C42—1222no—
739C42—1221no—
740C42—1222no—
741C42—1221no—
742C42—1224no—
743C42—1224no—
744C42—1222no—
745C42—1222no—
746C42C2×D24412yes—
747C42C2×D24411yescharacteristic
748C42C2×D24412yes—
749C42C2×D24411yescharacteristic
750C42C23×D6112yes—
751C42C23×D6111yescharacteristic
752C42C23×D6112yes—
753C42C23×D6111yescharacteristic
754C23—1221no—
755C23C22×D24411yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—42no—
759Q8—614no—
760Q8—612no—
761Q8—1222no—
762Q8—1221no—
763Q8—1224no—
764Q8—4882no—
765Q8—4881no—
766Q8—2444no—
767Q8—2444no—
768Q8—2444no—
769Q8—2442no—
770D4—612no—
771D4—1224no—
772D4—1221no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—1221no—
778C2×C4—1222no—
779C2×C4—1224no—
780C2×C4—1224no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1222no—
784C2×C4—1221no—
785C2×C4—1222no—
786C2×C4—1224no—
787C2×C4—4882no—
788C2×C4—4881no—
789C2×C4—2444no—
790C2×C4—2442no—
791C2×C4—2444no—
792C2×C4—2442no—
793C2×C4C22×D24412yes—
794C2×C4C22×D24412yes—
795C2×C4C22×D24411yescharacteristic
796C2×C4C22×D24411yescharacteristic
797C2×C4C22×D24412yes—
798C2×C4C22×D24412yes—
799C2×C4C22×D24411yescharacteristic
800C2×C4C22×D24411yescharacteristic
801C2×C4C22×D24411yescharacteristic
802C2×C4C2×Q8×D6112yes—
803C2×C4#1451982412yes—
804C2×C4C24×D6111yescharacteristic
805C8—22no—
806C8—24no—
807C8C2×Q8×D6114yes—
808C22—21no—
809C22—21no—
810C22—1222no—
811C22—2441no—
812C22—2441no—
813C22Q8×D24412yes—
814C22C23×D24411yescharacteristic
815C4—21no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—21no—
820C4—22no—
821C4—21no—
822C4—1222no—
823C4—1224no—
824C4—2442no—
825C4—2441no—
826C4—2444no—
827C4—2442no—
828C4—2441no—
829C4—2442no—
830C4Q8×D24412yes—
831C4#1684056212yes—
832C4C22×Q8×D6111yescharacteristic
833C4C2×#1451982411yescharacteristic
834C2—22no—
835C2—2442no—
836C2C2×Q8×D24411yescharacteristic
837C2C2×#1684056211yescharacteristic
838C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingQ8×M16×C61C2
socleC22×C61C23×D4
prime radicalC2×#11758222C23
hypercenterQ8×M16D61
hypocenterC61#61369
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. C2×#16840490C2semidirect
3. #21458788C2semidirect
4. #21458766C2semidirect
5. #21458753C2semidirect
6. #21458742C2semidirect
7. #21458711C2semidirect
8. #21458696C2semidirect
9. #21456371C2semidirect
10. #21456365C2semidirect
13. #21455626C2semidirect
14. #21455626C2semidirect
17. Q8×M16×C61C2semidirect
99. #14519810Q8semidirect
260. C2×Dic122C2×Q8semidirect
265. M16×C61C2×Q8semidirect
332. Dic244C2×Q8semidirect
333. #11758190C2×Q8semidirect
429. Q8×M16D61semidirect
514. C61#61369semidirect
687. M16Q8×D61semidirect

Maximal subgroups

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

subgroupindex
Q8×#117582222
C2×#168404902
#214587882
#214587662
#214587532
#214587422
#214587112
#214586962
#214563712
#214563652
#214556422
#214556352
#214556262
C4×#145198102
Q8×M16×C612
#6136961