Finite Group Databasebeta

← #6345294

Subgroups — #6345294

Order 512.

1633 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60560C211yesmaximal, characteristic
2#60208C211yesmaximal, characteristic
3C2×Q8×M16C211yesmaximal, characteristic, complemented
4#18049C214yesmaximal, complemented
5#18047C214yesmaximal, complemented
6#18012C214yesmaximal, complemented
7#18010C214yesmaximal, complemented
8#17936C211yesmaximal, characteristic, complemented
9#17934C211yesmaximal, characteristic, complemented
10#17931C211yesmaximal, characteristic, complemented
11#17929C211yesmaximal, characteristic, complemented
12#17908C211yesmaximal, characteristic, complemented
13#17906C211yesmaximal, characteristic, complemented
14#17903C211yesmaximal, characteristic, complemented
15#17901C211yesmaximal, characteristic, complemented
16#17820C211yesmaximal, characteristic, complemented
17#17498C211yesmaximal, characteristic
18#17449C211yesmaximal, characteristic, complemented
19#17334C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22#3117C412yes—
23#3117C412yes—
24#3113C412yes—
25#3112C412yes—
26#3108C2214yes—
27#3104C2211yescharacteristic
28#3104C2211yescharacteristic
29#3103C2211yescharacteristic
30#3103C2211yescharacteristic
31#3092C412yes—
32#3078C412yes—
33#3037C412yes—
34#3004C412yes—
35#2971—21no—
36#2971C2212yes—
37#2970—21no—
38#2970C2212yes—
39#2969—21no—
40#2969—21no—
41#2969C2212yes—
42#2969C2212yes—
43Q8×M16—21no—
44Q8×M16—21no—
45Q8×M16—21no—
46Q8×M16—21no—
47Q8×M16C2212yes—
48Q8×M16C2212yes—
49Q8×M16C2212yes—
50Q8×M16C2212yes—
51#2960C2211yescharacteristic
52#2960C2211yescharacteristic
53C2×#446—21no—
54C2×#446—21no—
55C2×#446C2211yescharacteristic
56C2×#446C2211yescharacteristic
57C2×C8×Q8C2211yescharacteristic
58C2×C8×Q8C2211yescharacteristic
59C4×#137C2214yes—
60#2931C2211yescharacteristic
61#2931C2211yescharacteristic
62#2930—21no—
63#2930—21no—
64#2923—21no—
65#2920C2211yescharacteristic
66#2920C2211yescharacteristic
67#2920C2211yescharacteristic
68C2×#423—21no—
69C2×#423C2211yescharacteristic
70#2875—21no—
71C2×C4×M16—21no—
72C2×C4×M16C2211yescharacteristic
73#1593C2214yescomplemented
74#1592C2214yescomplemented
75#1591C2214yescomplemented
76#1590C2214yescomplemented
77#1588C2214yescomplemented
78#1587C2214yescomplemented
79#1587C2214yescomplemented
80#1585C2214yescomplemented
81#1584C2214yescomplemented
82#1584C2214yescomplemented
83#1583C2214yescomplemented
84#1582C2214yescomplemented
85#1579C2214yescomplemented
86SD16⋊C8C2214yescomplemented
87C8×Q16C2214yescomplemented
88C8×SD16C2214yescomplemented
89#1574C2214yes—
90#1571C2211yescharacteristic
91#1571C2211yescharacteristic
92#1570C2211yescharacteristic
93#1570C2211yescharacteristic
94#1569C2214yes—
95#1495C2214yes—
96#1491C2214yes—
97#1489C2214yes—
98#1487C2211yescharacteristic
99#1487C2211yescharacteristic
100#1487C2211yescharacteristic
101#1487C2211yescharacteristic
102#1481C2211yescharacteristic
103#1481C2211yescharacteristic
104#1480C2211yescharacteristic
105#1480C2211yescharacteristic
106#1479C2214yes—
107#1455C2212yes—
108#1455C2212yes—
109#1453C2212yes—
110#1453C2212yes—
111#1452C2211yescharacteristic
112#1452C2211yescharacteristic
113#1450C2211yescharacteristic
114#1450C2211yescharacteristic
115C23×Q8C2×C411yescharacteristic
116C2×#137C2×C414yes—
117C2×#131—21no—
118C2×#131—21no—
119C22×M16—21no—
120C22×M16D411yescharacteristic
121C22×M16D411yescharacteristic
122#533C2×C411yescharacteristic
123#533C2×C411yescharacteristic
124#533C2311yescharacteristic
125#532C2×C411yescharacteristic
126#532C2×C411yescharacteristic
127#532C2311yescharacteristic
128#529—21no—
129#529—21no—
130#529—21no—
131#529—21no—
132#529C2×C412yes—
133#529C2312yes—
134#525—21no—
135#525—21no—
136#525C2×C412yes—
137C4×#41—21no—
138C4×#41—21no—
139C4×#41C2312yes—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8C2×C412yes—
147C2×C4×Q8C2×C412yes—
148C2×C4×Q8C2×C411yescharacteristic
149C2×C4×Q8C2×C411yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2312yes—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2×C411yescharacteristic
156C22×C42—21no—
157C22×C42C2311yescharacteristic
158#484C2×C412yes—
159#484C2×C412yes—
160#483C2×C414yes—
161#481C2×C412yes—
162#481C2×C412yes—
163#480C2×C414yes—
164#479C2×C414yes—
165#479C2×C414yes—
166#477C2×C412yes—
167#477C2×C412yes—
168#475C2×C412yes—
169#475C2×C412yes—
170#464C2×C414yes—
171#464C2×C414yes—
172#462C2×C412yes—
173#462C2×C412yes—
174#460C2×C412yes—
175#460C2×C412yes—
176#451C2×C412yes—
177#451C2×C412yes—
178#451C2×C414yes—
179#448C2×C412yes—
180#448C2×C412yes—
181#448C2×C414yes—
182#446—22no—
183#446—22no—
184#446—22no—
185#446—22no—
186#446—22no—
187#446—22no—
188#446—22no—
189#446—22no—
190#446—21no—
191#446—21no—
192#446—21no—
193#446—21no—
194#446—21no—
195#446—21no—
196#446C2312yes—
197#446C2312yes—
198#446C2312yes—
199#446C2312yes—
200#446C2312yes—
201#446C2312yes—
202C8×Q8—21no—
203C8×Q8—21no—
204C8×Q8—21no—
205C8×Q8—21no—
206C8×Q8—21no—
207C8×Q8—21no—
208C8×Q8C2312yes—
209C8×Q8C2312yes—
210C8×Q8C2312yes—
211C8×Q8C2312yes—
212C8×Q8C2312yes—
213C8×Q8C2312yes—
214#441C2×C414yes—
215#441C2×C414yes—
216#440C2×C414yes—
217#440C2×C414yes—
218C4×Q16C2314yes—
219C4×Q16C2314yes—
220C4×SD16C2314yes—
221C4×SD16C2314yes—
222#436—22no—
223#436—22no—
224#436—22no—
225#436—22no—
226#436—21no—
227#436—21no—
228#436C2312yes—
229#436C2312yes—
230#435—22no—
231#435—22no—
232#435—22no—
233#435—22no—
234C8×D4—21no—
235C8×D4—21no—
236C8×D4C2312yes—
237C8×D4C2312yes—
238#433—22no—
239#433—22no—
240#432—21no—
241#432—21no—
242#432—21no—
243#432—22no—
244#432—22no—
245#432C2×C412yes—
246#432C2×C412yes—
247#432C2312yes—
248#431—21no—
249#431C2312yes—
250#431C2311yescharacteristic
251#431C2311yescharacteristic
252#431C2312yes—
253#431C2311yescharacteristic
254#431C2311yescharacteristic
255#431C2312yes—
256#428C2×C414yes—
257#424—21no—
258#424—21no—
259#423—22no—
260#423—22no—
261#423—22no—
262#423—22no—
263#423—21no—
264#423—21no—
265#423—21no—
266#423C2×C412yes—
267#423C2312yes—
268#423C2311yescharacteristic
269#423C2311yescharacteristic
270#423C2312yes—
271C2×C4⋊C8—21no—
272C2×C4⋊C8—21no—
273C2×C4⋊C8—21no—
274C2×C4⋊C8—21no—
275C2×C4⋊C8—21no—
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#419C2×C414yes—
279#417C2×C414yes—
280#408—21no—
281#408—21no—
282#407—21no—
283#407—21no—
284#407C2×C412yes—
285#405—21no—
286#405—21no—
287#405—22no—
288#405—22no—
289C4×M16—22no—
290C4×M16—22no—
291C4×M16—22no—
292C4×M16—22no—
293C4×M16—21no—
294C4×M16—22no—
295C4×M16D411yescharacteristic
296C4×M16D411yescharacteristic
297C4×M16D411yescharacteristic
298C4×M16D411yescharacteristic
299C4×M16C2312yes—
300C4×M16C2312yes—
301C4×M16C2311yescharacteristic
302C4×M16C2311yescharacteristic
303C4×M16C2311yescharacteristic
304C4×M16C2311yescharacteristic
305C2×#97—21no—
306C2×#97—21no—
307C2×#97—22no—
308C2×#97D411yescharacteristic
309C2×#97D411yescharacteristic
310C2×C4×C8—21no—
311C2×C4×C8—21no—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#335C2314yes—
315#335C2314yes—
316#334C2314yes—
317#334C2314yes—
318Q8⋊C8C2314yes—
319Q8⋊C8C2314yes—
320Q8⋊C8C2314yes—
321Q8⋊C8C2314yes—
322Q8⋊C8C2314yes—
323Q8⋊C8C2314yes—
324D4⋊C8C2314yes—
325D4⋊C8C2314yes—
326#322C2312yes—
327#322C2312yes—
328#322C2312yes—
329#322C2312yes—
330#322C2312yes—
331#322C2312yes—
332C82C2312yes—
333C82C2312yes—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41C22×C412yes—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8—44no—
341C22×Q8C22×C411yescharacteristic
342C22×Q8C22×C412yes—
343C22×Q8C22×C412yes—
344C22×Q8C22×C411yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4C22×C411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4#4111yescharacteristic
350#137—48no—
351C2×Q16C22×C414yes—
352C2×Q16C22×C414yes—
353C2×SD16C22×C414yes—
354C2×SD16C22×C414yes—
355#131—44no—
356#131—44no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—22no—
362C2×M16—24no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—42no—
366C2×M16—44no—
367C2×M16C22×C414yes—
368C2×M16C2×D411yescharacteristic
369C2×M16C2×D411yescharacteristic
370C2×M16C2×D411yescharacteristic
371C2×M16C2×D411yescharacteristic
372C2×M16C2×D411yescharacteristic
373C2×M16C2×D411yescharacteristic
374C2×M16C2×D411yescharacteristic
375C2×M16C2×D411yescharacteristic
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8C2×D411yescharacteristic
381C22×C8C2×D411yescharacteristic
382C22×C8C2×D411yescharacteristic
383C22×C8C2×D411yescharacteristic
384C4⋊Q8C22×C411yescharacteristic
385C4⋊Q8C22×C411yescharacteristic
386C4⋊Q8C22×C411yescharacteristic
387#127C22×C411yescharacteristic
388#126—22no—
389#126—22no—
390#125—21no—
391#125—21no—
392#125C22×C412yes—
393#124—21no—
394#124—21no—
395#124C22×C412yes—
396#123—22no—
397#123—22no—
398#123—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8C22×C412yes—
404C22⋊Q8C22×C412yes—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121C22×C412yes—
410#121C22×C412yes—
411#120—22no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—22no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—22no—
432C4×Q8C22×C412yes—
433C4×Q8C22×C412yes—
434C4×Q8C22×C412yes—
435C4×Q8C22×C412yes—
436C4×Q8C22×C412yes—
437C4×Q8C22×C412yes—
438C4×Q8C22×C412yes—
439C4×Q8C2412yes—
440C4×Q8C2412yes—
441C4×Q8C2412yes—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4C22×C412yes—
453C4×D4C2412yes—
454#117—21no—
455#117—21no—
456#117—22no—
457#117—22no—
458#117—22no—
459#117C22×C412yes—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4C22×C412yes—
472C2×C4⋊C4C22×C412yes—
473C2×C4⋊C4C22×C411yescharacteristic
474C2×C4⋊C4C22×C411yescharacteristic
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42C22×C411yescharacteristic
485C2×C42C22×C411yescharacteristic
486C2×C42C22×C411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42#4111yescharacteristic
491C2×C42#4111yescharacteristic
492C2×C42#4111yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496#107C22×C414yes—
497#107C22×C414yes—
498#106C22×C414yes—
499#106C22×C414yes—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511C4⋊C8—22no—
512C4⋊C8—22no—
513C4⋊C8—22no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—22no—
521C4⋊C8C22×C412yes—
522C4⋊C8C22×C412yes—
523C4⋊C8C22×C414yes—
524C4⋊C8C2412yes—
525C4⋊C8C2412yes—
526C4⋊C8C2412yes—
527C4⋊C8C2412yes—
528#103C22×C414yes—
529#103C22×C414yes—
530#103C22×C414yes—
531#103C22×C414yes—
532#103C22×C414yes—
533#103C22×C414yes—
534#102C22×C414yes—
535#102C22×C414yes—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8C22×C414yes—
546C22⋊C8C22×C412yes—
547C22⋊C8C22×C412yes—
548#97—22no—
549#97—22no—
550#97—22no—
551#97—22no—
552#97—22no—
553#97—22no—
554#97—22no—
555#97—22no—
556#97C22×C414yes—
557#97C2×D411yescharacteristic
558#97C2×D411yescharacteristic
559#97C2×D411yescharacteristic
560#97C2×D411yescharacteristic
561#97C2×D411yescharacteristic
562#97C2×D411yescharacteristic
563#97C2×D411yescharacteristic
564#97C2×D411yescharacteristic
565C4×C8—22no—
566C4×C8—22no—
567C4×C8—22no—
568C4×C8—22no—
569C4×C8—22no—
570C4×C8—22no—
571C4×C8—22no—
572C4×C8C2×D411yescharacteristic
573C4×C8C2×D411yescharacteristic
574C4×C8C2×D411yescharacteristic
575C4×C8C2×D411yescharacteristic
576C4×C8C2412yes—
577C4×C8C2412yes—
578C4×C8C2412yes—
579C4×C8C2412yes—
580C4×C8C2411yescharacteristic
581C4×C8C2411yescharacteristic
582C4×C8C2411yescharacteristic
583C4×C8C2411yescharacteristic
584C24C4×D411yescharacteristic
585#41—44no—
586#41—42no—
587#41—42no—
588#41—82no—
589C2×Q8—24no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—24no—
597C2×Q8—24no—
598C2×Q8—42no—
599C2×Q8—42no—
600C2×Q8—42no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—44no—
604C2×Q8C23×C412yes—
605C2×Q8C23×C412yes—
606C2×Q8C23×C412yes—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4C23×C412yes—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—42no—
627C22×C4—44no—
628C22×C4—81no—
629C22×C4—82no—
630C22×C4C4×D411yescharacteristic
631C22×C4C4×D411yescharacteristic
632C22×C4C4×D411yescharacteristic
633C22×C4C4×D411yescharacteristic
634C22×C4C4×D411yescharacteristic
635C22×C4C4×D411yescharacteristic
636C22×C4C4×D411yescharacteristic
637C22×C4C4×D411yescharacteristic
638C22×C4C4×D411yescharacteristic
639C22×C4C23×C411yescharacteristic
640C22×C4C23×C411yescharacteristic
641C22×C4C23×C411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C2×#4111yescharacteristic
646C22×C4C2×#4111yescharacteristic
647C22×C4C2×#4111yescharacteristic
648Q16—28no—
649Q16—44no—
650SD16—28no—
651SD16—44no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—41no—
657M16—41no—
658M16—41no—
659M16—41no—
660M16—44no—
661M16—44no—
662M16—44no—
663M16—44no—
664M16—42no—
665M16—42no—
666M16—44no—
667M16—82no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—44no—
678C2×C8—42no—
679C2×C8—42no—
680C2×C8—44no—
681C2×C8#13714yescomplemented
682C2×C8C23×C414yes—
683C2×C8C23×C414yes—
684C2×C8C22×D411yescharacteristic
685C2×C8C22×D411yescharacteristic
686C2×C8C22×D411yescharacteristic
687C2×C8C22×D411yescharacteristic
688C2×C8C22×D411yescharacteristic
689C2×C8C22×D411yescharacteristic
690C2×C8C22×D411yescharacteristic
691C2×C8C22×D411yescharacteristic
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4C23×C412yes—
715C4⋊C4C23×C412yes—
716C4⋊C4C23×C412yes—
717C4⋊C4C23×C412yes—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—22no—
731C42—22no—
732C42—22no—
733C42—22no—
734C42—22no—
735C42—22no—
736C42—22no—
737C42—22no—
738C42C4×D411yescharacteristic
739C42C4×D411yescharacteristic
740C42C4×D411yescharacteristic
741C42C4×D411yescharacteristic
742C42C4×D411yescharacteristic
743C42C4×D411yescharacteristic
744C42C23×C411yescharacteristic
745C42C23×C411yescharacteristic
746C42C23×C411yescharacteristic
747C42C22×D411yescharacteristic
748C42C22×D411yescharacteristic
749C42C22×D411yescharacteristic
750C42C2×#4111yescharacteristic
751C42C2×#4111yescharacteristic
752C42C2×#4111yescharacteristic
753C42C2511yescharacteristic
754C23—22no—
755C23—22no—
756C23—41no—
757C23—41no—
758C23C2×C4×D411yescharacteristic
759C23C2×C4×D411yescharacteristic
760C23C2×C4×D411yescharacteristic
761Q8—24no—
762Q8—22no—
763Q8—22no—
764Q8—24no—
765Q8—22no—
766Q8—44no—
767Q8—44no—
768Q8—42no—
769Q8—42no—
770Q8—42no—
771Q8#56814yes—
772D4—24no—
773D4—42no—
774D4—44no—
775D4—42no—
776D4—82no—
777D4—82no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4C2×C4×D411yescharacteristic
817C2×C4C2×C4×D411yescharacteristic
818C2×C4C2×C4×D411yescharacteristic
819C2×C4C2×C4×D411yescharacteristic
820C2×C4C2×C4×D411yescharacteristic
821C2×C4C2×C4×D411yescharacteristic
822C2×C4C2×C4×D411yescharacteristic
823C2×C4C2×C4×D411yescharacteristic
824C2×C4C2×C4×D411yescharacteristic
825C2×C4C2×#13712yes—
826C2×C4#57512yes—
827C2×C4C24×C411yescharacteristic
828C2×C4C23×D411yescharacteristic
829C2×C4C22×#4111yescharacteristic
830C8—24no—
831C8—24no—
832C8—21no—
833C8—21no—
834C8—21no—
835C8—21no—
836C8—21no—
837C8—21no—
838C8—42no—
839C8—42no—
840C8—42no—
841C8—42no—
842C8—42no—
843C8—42no—
844C8C2×#13712yes—
845C8C2×#13712yes—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—44no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22C4×#13712yes—
859C22C22×C4×D411yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—24no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4C4×#13712yes—
877C4C2×#56812yes—
878C4C22×#13711yescharacteristic
879C4C2×#57511yescharacteristic
880C2—22no—
881C2—41no—
882C2—41no—
883C2—82no—
884C2#6014111yescharacteristic
885C2C2×C4×#13711yescharacteristic
886C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#3444C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×M16 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×Q8×M16C2semidirect
4. #18049C2semidirect
5. #18047C2semidirect
6. #18012C2semidirect
7. #18010C2semidirect
8. #17936C2semidirect
9. #17934C2semidirect
10. #17931C2semidirect
11. #17929C2semidirect
12. #17908C2semidirect
13. #17906C2semidirect
14. #17903C2semidirect
15. #17901C2semidirect
16. #17820C2semidirect
18. #17449C2semidirect
19. #17334C2semidirect
73. #1593C22semidirect
74. #1592C22semidirect
75. #1591C22semidirect
76. #1590C22semidirect
77. #1588C22semidirect
78. #1587C22semidirect
79. #1587C22semidirect
80. #1585C22semidirect
81. #1584C22semidirect
82. #1584C22semidirect
83. #1583C22semidirect
84. #1582C22semidirect
85. #1579C22semidirect
86. SD16⋊C8C22semidirect
87. C8×Q16C22semidirect
88. C8×SD16C22semidirect
681. C2×C8#137semidirect

Maximal subgroups

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

subgroupindex
#605602
#602082
C2×Q8×M162
#180492
#180472
#180122
#180102
#179362
#179342
#179312
#179292
#179082
#179062
#179032
#179012
#178202
#174982
#174492
#173342