Finite Group Databasebeta

← #6343029

Subgroups — #6343029

Order 512.

2834 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3461C211yesmaximal, characteristic
2#60278C211yesmaximal, characteristic, complemented
3#60263C211yesmaximal, characteristic, complemented
4#17506C218yesmaximal, complemented
5#17492C212yesmaximal, complemented
6#17491C212yesmaximal, complemented
7#17487C212yesmaximal, complemented
8#17486C212yesmaximal, complemented
9#17484C214yesmaximal, complemented
10#17469C214yesmaximal, complemented
11#17451C211yesmaximal, characteristic, complemented
12#17449C211yesmaximal, characteristic, complemented
13#17443C211yesmaximal, characteristic, complemented
14C2×#1487C211yesmaximal, characteristic, complemented
15#3461—22no—
16#3461—21no—
17#3461—22no—
18#3461—21no—
19#3461—21no—
20#3461—21no—
21#3461C412yes—
22#3461C412yes—
23#3461C414yes—
24#3461C2212yes—
25#3461C2212yes—
26#3461C2214yes—
27C2×#544C411yescharacteristic
28C2×#542—21no—
29C2×#542C412yes—
30C2×#541—21no—
31C2×#541C412yes—
32C2×#539—22no—
33C2×#537C411yescharacteristic
34C2×#536C411yescharacteristic
35C2×#536C411yescharacteristic
36C2×#533—21no—
37C2×#533C2212yes—
38C2×#529—21no—
39C2×#529—22no—
40C2×#529C2212yes—
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2991—21no—
45#2991—21no—
46#2990—22no—
47#2990—21no—
48#2990—22no—
49#2990—21no—
50#2989C2212yescomplemented
51#2989C2214yescomplemented
52#2988C2212yescomplemented
53#2984—21no—
54#2974—22no—
55#2974—21no—
56#2965C2212yescomplemented
57#2965C2214yescomplemented
58C8×#41C2212yescomplemented
59Q8×M16—21no—
60D4×M16—22no—
61D4×M16—21no—
62#2920C2211yescharacteristic
63#2920C2212yes—
64#2920C2211yescharacteristic
65#2920C2212yes—
66C2×#431C2211yescharacteristic
67C2×#431C2212yes—
68C2×#423C2211yescharacteristic
69C2×#423C2212yes—
70#1497C2218yescomplemented
71#1495C2218yescomplemented
72#1494C2218yescomplemented
73#1493C2218yescomplemented
74#1491C2214yescomplemented
75#1489C2214yescomplemented
76#1488C2214yescomplemented
77#1487C2212yes—
78#1487C2212yes—
79#1487C2211yescharacteristic
80#1487C2211yescharacteristic
81#1487C2212yes—
82#1487C2212yes—
83#1487C2212yes—
84#1487C2214yescomplemented
85#1486C2211yescharacteristic
86#1486C2211yescharacteristic
87#1486C2212yes—
88#1485C2218yescomplemented
89#1483C2218yescomplemented
90#1482C2218yescomplemented
91#1481C2218yescomplemented
92#1479C2214yescomplemented
93#1477C2214yescomplemented
94#1476C2214yescomplemented
95C2×Q8⋊C8C2214yescomplemented
96C22×#41C2×C411yescharacteristic
97C22×#41C2×C411yescharacteristic
98C23×Q8C2×C411yescharacteristic
99C22×M16—22no—
100C22×M16—21no—
101#544—22no—
102#544—21no—
103#544—21no—
104#544C2×C412yes—
105#544C2×C412yes—
106#544C2×C414yes—
107#542—22no—
108#542—22no—
109#542—24no—
110#542—22no—
111#542—24no—
112#542—22no—
113#542—22no—
114#542—22no—
115#542—22no—
116#542—22no—
117#542C2×C414yes—
118#542C2×C414yes—
119#542C2×C414yes—
120#542C2×C414yes—
121#541—22no—
122#541—22no—
123#541—24no—
124#541—22no—
125#541—22no—
126#541—24no—
127#541—22no—
128#541—22no—
129#541—22no—
130#541—22no—
131#541C2×C414yes—
132#541C2×C414yes—
133#541C2×C414yes—
134#541C2×C414yes—
135#539—24no—
136#539—24no—
137#539—24no—
138#539—24no—
139#539—24no—
140#539—24no—
141#539—24no—
142#539—24no—
143#537—22no—
144#537—21no—
145#537—21no—
146#537C2×C412yes—
147#537C2×C412yes—
148#537C2×C414yes—
149#536—22no—
150#536—21no—
151#536—21no—
152#536—21no—
153#536—22no—
154#536—21no—
155#536C2×C412yes—
156#536C2×C412yes—
157#536C2×C414yes—
158#536C2×C412yes—
159#536C2×C412yes—
160#536C2×C414yes—
161#533—22no—
162#533—22no—
163#533—24no—
164#533—22no—
165#533—22no—
166#533—24no—
167#533—22no—
168#533—22no—
169#533—22no—
170#533—22no—
171#533C2×C414yes—
172#533C2×C414yes—
173#533C2314yes—
174#533C2314yes—
175C2×C4⋊Q8—21no—
176C2×C4⋊Q8—21no—
177C2×C4⋊Q8C2×C412yes—
178C2×C4⋊Q8C2×C412yes—
179#529—24no—
180#529—24no—
181#529—24no—
182#529—24no—
183#529—22no—
184#529—22no—
185#529—24no—
186#529—24no—
187#529—24no—
188#529—24no—
189#529—24no—
190#529—22no—
191#529—24no—
192#529—22no—
193#529—22no—
194#529—22no—
195#529—22no—
196#529—22no—
197#529C2×C414yes—
198#529C2×C414yes—
199#529C2314yes—
200#529C2314yes—
201C2×#126—22no—
202C2×#126—22no—
203C2×#126—22no—
204C2×#126—22no—
205C2×#125—22no—
206C2×#125—21no—
207C2×#125—22no—
208C2×#125—22no—
209C2×#125C2×C412yes—
210C2×#124—21no—
211C2×#124—22no—
212C2×#124C2×C412yes—
213C2×#123—22no—
214C2×#123—22no—
215C2×#123—22no—
216C2×#123—22no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—22no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—22no—
222C2×C22⋊Q8—22no—
223C2×C22⋊Q8C2×C412yes—
224C2×C22⋊Q8C2×C412yes—
225C2×C22⋊Q8C2×C412yes—
226C2×#121—22no—
227C2×#121—21no—
228C2×#121C2×C412yes—
229C4×#41—21no—
230C4×#41—21no—
231C4×#41—21no—
232C4×#41—21no—
233C4×#41C2×C412yes—
234C4×#41C2×C412yes—
235C4×#41C2×C411yescharacteristic
236C4×#41C2×C411yescharacteristic
237C4×#41C2×C412yes—
238C4×#41D412yes—
239C4×#41D412yes—
240C4×#41D411yescharacteristic
241C4×#41D411yescharacteristic
242C4×#41D411yescharacteristic
243C4×#41D411yescharacteristic
244C4×#41C2312yes—
245C4×#41C2312yes—
246C4×#41C2311yescharacteristic
247C4×#41C2311yescharacteristic
248C4×#41C2312yes—
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8—21no—
252C2×C4×Q8—21no—
253C2×C4×Q8—21no—
254C2×C4×Q8—21no—
255C2×C4×Q8—22no—
256C2×C4×Q8C2×C412yes—
257C2×C4×Q8C2×C412yes—
258C2×C4×Q8C2×C412yes—
259C2×C4×Q8C2×C411yescharacteristic
260C2×C4×Q8D411yescharacteristic
261C2×C4×Q8D411yescharacteristic
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2311yescharacteristic
266C2×C4×D4—21no—
267C2×C4×D4—21no—
268C2×C4×D4—22no—
269C2×C4×D4C2×C411yescharacteristic
270C2×C4×D4D412yes—
271C2×C4×D4D411yescharacteristic
272C2×C4×D4D412yes—
273C2×C4×D4D411yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×#117—22no—
276C2×#117—21no—
277C2×#117—22no—
278C2×#117C2×C411yescharacteristic
279C2×#117C2×C411yescharacteristic
280C2×#117C2×C412yes—
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2×C411yescharacteristic
283C22×C42—21no—
284C22×C42—21no—
285C22×C42C2311yescharacteristic
286C22×C42C2312yes—
287#446—22no—
288#446—24no—
289#446—22no—
290#446—24no—
291C8×Q8—22no—
292C8×Q8—22no—
293#436—22no—
294#436—24no—
295#436—24no—
296#436—22no—
297#435—24no—
298#435—24no—
299#435—24no—
300#435—24no—
301#435—24no—
302#435—24no—
303C8×D4—22no—
304C8×D4—24no—
305C8×D4—24no—
306C8×D4—22no—
307#432—21no—
308#432—22no—
309#432—21no—
310#432—22no—
311#432—21no—
312#432—22no—
313#432C2312yes—
314#432C2314yes—
315#431—21no—
316#431—22no—
317#431—21no—
318#431—22no—
319#431—21no—
320#431—22no—
321#431C2312yes—
322#431C2314yes—
323#431C2311yescharacteristic
324#431C2311yescharacteristic
325#431C2312yes—
326#431C2314yes—
327#431C2312yes—
328#431C2312yes—
329#431C2314yes—
330#423—22no—
331#423—21no—
332#423—21no—
333#423—22no—
334#423—21no—
335#423—22no—
336#423C2312yes—
337#423C2311yescharacteristic
338#423C2312yes—
339#423C2314yes—
340#423C2311yescharacteristic
341C2×C4⋊C8—21no—
342C2×C4⋊C8—22no—
343C2×C4⋊C8—21no—
344C2×C4⋊C8—22no—
345C2×C4⋊C8C2312yes—
346C2×C4⋊C8C2314yes—
347#407—22no—
348#407—21no—
349#407—21no—
350#407—22no—
351C2×C22⋊C8—21no—
352C2×C22⋊C8—22no—
353C4×M16—22no—
354C4×M16—21no—
355C4×M16C2314yes—
356C4×M16C2312yes—
357C2×C4×C8C2312yes—
358C2×C4×C8C2314yes—
359Q8⋊C8C2318yes—
360Q8⋊C8C2318yes—
361Q8⋊C8C2314yes—
362Q8⋊C8C2314yes—
363Q8⋊C8C2318yes—
364Q8⋊C8C2318yes—
365Q8⋊C8C2318yes—
366D4⋊C8C2314yes—
367D4⋊C8C2314yes—
368D4⋊C8C2318yes—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—44no—
372C2×#41—44no—
373C2×#41C22⋊C412yes—
374C2×#41C22⋊C411yescharacteristic
375C2×#41C22⋊C411yescharacteristic
376C2×#41C22×C412yes—
377C2×#41C22×C412yes—
378C2×#41C22×C411yescharacteristic
379C2×#41C22×C411yescharacteristic
380C2×#41C22×C412yes—
381C22×Q8—21no—
382C22×Q8—21no—
383C22×Q8—21no—
384C22×Q8—22no—
385C22×Q8—44no—
386C22×Q8C22⋊C411yescharacteristic
387C22×Q8C22×C412yes—
388C22×Q8C22×C412yes—
389C22×Q8C22×C411yescharacteristic
390C22×Q8C22×C412yes—
391C22×D4—21no—
392C22×D4—22no—
393C22×D4C22⋊C412yes—
394C22×D4C22⋊C411yescharacteristic
395C22×D4C22×C411yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C23×C4C22×C411yescharacteristic
402C23×C4C22×C412yes—
403C23×C4C2×D412yes—
404C23×C4C2×D411yescharacteristic
405C23×C4C2×D411yescharacteristic
406C23×C4C2×D412yes—
407C2×M16—21no—
408C2×M16—22no—
409C2×M16—21no—
410C2×M16—22no—
411C2×M16—24no—
412C2×M16—22no—
413C2×M16—24no—
414C2×M16—82no—
415C2×M16—84no—
416C22×C8—22no—
417C22×C8—24no—
418C22×C8—22no—
419C22×C8—24no—
420C4⋊Q8—22no—
421C4⋊Q8—22no—
422C4⋊Q8—24no—
423C4⋊Q8—24no—
424C4⋊Q8—22no—
425C4⋊Q8—22no—
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8C22×C414yes—
431C4⋊Q8C22×C414yes—
432C4⋊Q8C22×C414yes—
433C4⋊Q8C22×C414yes—
434#126—24no—
435#126—24no—
436#126—24no—
437#126—24no—
438#126—24no—
439#126—24no—
440#126—24no—
441#126—24no—
442#126—24no—
443#126—24no—
444#126—24no—
445#126—24no—
446#126—24no—
447#126—24no—
448#126—24no—
449#126—24no—
450#125—24no—
451#125—24no—
452#125—24no—
453#125—24no—
454#125—24no—
455#125—22no—
456#125—22no—
457#125—24no—
458#125—24no—
459#125—24no—
460#125—24no—
461#125—24no—
462#125—24no—
463#125—22no—
464#125—22no—
465#125—24no—
466#125—24no—
467#125C22×C414yes—
468#125C22×C414yes—
469#124—22no—
470#124—22no—
471#124—24no—
472#124—24no—
473#124—24no—
474#124—24no—
475#124—24no—
476#124—22no—
477#124—22no—
478#124C22×C414yes—
479#124C22×C414yes—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
495#123—24no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8—24no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—24no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8C22×C414yes—
524C22⋊Q8C22×C414yes—
525C22⋊Q8C22×C414yes—
526C22⋊Q8C22×C414yes—
527C22⋊Q8C22×C414yes—
528C22⋊Q8C22×C414yes—
529#121—24no—
530#121—24no—
531#121—24no—
532#121—24no—
533#121—22no—
534#121—22no—
535#121—24no—
536#121—22no—
537#121—22no—
538#121C22×C414yes—
539#121C22×C414yes—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—24no—
547C4×Q8—24no—
548C4×Q8—21no—
549C4×Q8—21no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—24no—
557C4×Q8—24no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8C22⋊C411yescharacteristic
561C4×Q8C22⋊C411yescharacteristic
562C4×Q8C22⋊C412yes—
563C4×Q8C22⋊C411yescharacteristic
564C4×Q8C22⋊C411yescharacteristic
565C4×Q8C22⋊C412yes—
566C4×Q8C22×C414yes—
567C4×Q8C22×C414yes—
568C4×Q8C22×C414yes—
569C4×Q8C22×C412yes—
570C4×Q8C22×C412yes—
571C4×Q8C22×C412yes—
572C4×Q8C2×D411yescharacteristic
573C4×Q8C2×D411yescharacteristic
574C4×Q8C2×D412yes—
575C4×Q8C2×D411yescharacteristic
576C4×Q8C2×D411yescharacteristic
577C4×Q8C2×D412yes—
578C4×Q8C2414yes—
579C4×Q8C2412yes—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4C22⋊C411yescharacteristic
597C4×D4C22⋊C411yescharacteristic
598C4×D4C22⋊C412yes—
599C4×D4C22⋊C412yes—
600C4×D4C22⋊C412yes—
601C4×D4C22⋊C412yes—
602C4×D4C22⋊C412yes—
603C4×D4C22⋊C412yes—
604C4×D4C22⋊C412yes—
605C4×D4C22⋊C412yes—
606C4×D4C22⋊C412yes—
607C4×D4C22⋊C411yescharacteristic
608C4×D4C22⋊C411yescharacteristic
609C4×D4C22⋊C412yes—
610C4×D4C22×C412yes—
611C4×D4C22×C412yes—
612C4×D4C22×C412yes—
613C4×D4C2×D411yescharacteristic
614C4×D4C2×D412yes—
615C4×D4C2×D412yes—
616C4×D4C2×D412yes—
617C4×D4C2×D412yes—
618C4×D4C2×D411yescharacteristic
619C4×D4C2×D412yes—
620C4×D4C2×D412yes—
621C4×D4C2×D412yes—
622C4×D4C2×D412yes—
623C4×D4C2×D412yes—
624C4×D4C2×D411yescharacteristic
625C4×D4C2×D412yes—
626C4×D4C2×D411yescharacteristic
627C4×D4C2412yes—
628#117—24no—
629#117—24no—
630#117—21no—
631#117—21no—
632#117—24no—
633#117—24no—
634#117—22no—
635#117—22no—
636#117—24no—
637#117—24no—
638#117—22no—
639#117—22no—
640#117—24no—
641#117—24no—
642#117C22⋊C411yescharacteristic
643#117C22⋊C412yes—
644#117C22⋊C411yescharacteristic
645#117C22⋊C412yes—
646#117C22⋊C412yes—
647#117C22⋊C412yes—
648#117C22⋊C412yes—
649#117C22×C412yes—
650#117C22×C412yes—
651#117C22×C412yes—
652#117C22×C411yescharacteristic
653#117C22×C411yescharacteristic
654#117C22×C412yes—
655#117C22×C412yes—
656#117C22×C412yes—
657#117C22×C412yes—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C22⋊C411yescharacteristic
678C2×C4⋊C4C22⋊C412yes—
679C2×C4⋊C4C22⋊C411yescharacteristic
680C2×C4⋊C4C22⋊C412yes—
681C2×C4⋊C4C22×C412yes—
682C2×C4⋊C4C22×C412yes—
683C2×C4⋊C4C22×C412yes—
684C2×C4⋊C4C22×C411yescharacteristic
685C2×C4⋊C4C22×C411yescharacteristic
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4C22⋊C412yes—
696C2×C22⋊C4C22⋊C412yes—
697C2×C22⋊C4C22⋊C412yes—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—22no—
701C2×C42—22no—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—21no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42C22×C411yescharacteristic
712C2×C42C22×C412yes—
713C2×C42C22×C411yescharacteristic
714C2×C42C22×C411yescharacteristic
715C2×C42C22×C412yes—
716C2×C42C22×C412yes—
717C2×C42C2×D412yes—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D412yes—
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D412yes—
726C2×C42C2×D412yes—
727C2×C42C2×D412yes—
728C2×C42C2×D412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2412yes—
733C2×C42C2412yes—
734C4⋊C8—21no—
735C4⋊C8—22no—
736C4⋊C8—21no—
737C4⋊C8—21no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740C4⋊C8—24no—
741C4⋊C8—22no—
742C4⋊C8—24no—
743C4⋊C8—22no—
744C4⋊C8—24no—
745C4⋊C8—22no—
746C4⋊C8—24no—
747C4⋊C8—21no—
748C4⋊C8C2412yes—
749C4⋊C8C2414yes—
750C4⋊C8C2412yes—
751C22⋊C8—21no—
752C22⋊C8—21no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—24no—
756C22⋊C8—22no—
757C22⋊C8—24no—
758C22⋊C8—22no—
759C22⋊C8—24no—
760C22⋊C8—22no—
761C22⋊C8—24no—
762#97—22no—
763#97—24no—
764#97—22no—
765#97—24no—
766C4×C8—22no—
767C4×C8—24no—
768C4×C8—22no—
769C4×C8—24no—
770C4×C8C2412yes—
771C4×C8C2412yes—
772C4×C8C2414yes—
773C24—21no—
774C24C2×C22⋊C411yescharacteristic
775C24C2×C22⋊C412yes—
776#41—24no—
777#41—24no—
778#41—28no—
779#41—44no—
780#41—44no—
781#41—42no—
782#41—42no—
783#41—44no—
784#41—44no—
785#41—44no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—21no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—28no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—84no—
801C2×Q8C2×C22⋊C411yescharacteristic
802C2×Q8C2×C22⋊C411yescharacteristic
803C2×Q8C2×C22⋊C412yes—
804C2×Q8C23×C414yes—
805C2×Q8C23×C412yes—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—21no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—84no—
816C2×D4C2×C22⋊C412yes—
817C2×D4C2×C22⋊C412yes—
818C2×D4C2×C22⋊C411yescharacteristic
819C2×D4C2×C22⋊C411yescharacteristic
820C2×D4C2×C22⋊C412yes—
821C2×D4C2×C22⋊C412yes—
822C2×D4C2×C22⋊C412yes—
823C2×D4C23×C412yes—
824C22×C4—24no—
825C22×C4—22no—
826C22×C4—24no—
827C22×C4—22no—
828C22×C4—24no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—81no—
850C22×C4—82no—
851C22×C4—82no—
852C22×C4—82no—
853C22×C4C2×C22⋊C411yescharacteristic
854C22×C4C2×C22⋊C411yescharacteristic
855C22×C4C2×C22⋊C411yescharacteristic
856C22×C4C2×C22⋊C411yescharacteristic
857C22×C4C2×C22⋊C412yes—
858C22×C4C2×C22⋊C412yes—
859C22×C4C2×C22⋊C412yes—
860C22×C4C2×C22⋊C411yescharacteristic
861C22×C4C2×C22⋊C411yescharacteristic
862C22×C4C2×C22⋊C411yescharacteristic
863C22×C4C2×C22⋊C412yes—
864C22×C4C2×C22⋊C411yescharacteristic
865C22×C4C2×C22⋊C411yescharacteristic
866C22×C4C2×C22⋊C412yes—
867C22×C4C2×C22⋊C412yes—
868C22×C4C2×C22⋊C412yes—
869C22×C4C2×C22⋊C412yes—
870C22×C4C2×C22⋊C412yes—
871C22×C4C23×C411yescharacteristic
872C22×C4C23×C411yescharacteristic
873C22×C4C23×C412yes—
874C22×C4C23×C412yes—
875C22×C4C23×C411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D411yescharacteristic
886M16—42no—
887M16—44no—
888M16—42no—
889M16—82no—
890M16—84no—
891M16—82no—
892M16—84no—
893C2×C8—22no—
894C2×C8—22no—
895C2×C8—24no—
896C2×C8—22no—
897C2×C8—22no—
898C2×C8—24no—
899C2×C8—82no—
900C2×C8—84no—
901C2×C8—82no—
902C2×C8—84no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4C2×C22⋊C412yes—
933C4⋊C4C2×C22⋊C412yes—
934C4⋊C4C2×C22⋊C412yes—
935C4⋊C4C2×C22⋊C412yes—
936C4⋊C4C2×C22⋊C412yes—
937C4⋊C4C2×C22⋊C411yescharacteristic
938C4⋊C4C2×C22⋊C411yescharacteristic
939C4⋊C4C2×C22⋊C412yes—
940C4⋊C4C2×C22⋊C411yescharacteristic
941C4⋊C4C2×C22⋊C411yescharacteristic
942C4⋊C4C2×C22⋊C412yes—
943C4⋊C4C2×C22⋊C412yes—
944C4⋊C4C2×C22⋊C412yes—
945C4⋊C4C2×C22⋊C412yes—
946C4⋊C4C23×C414yes—
947C4⋊C4C23×C412yes—
948C4⋊C4C23×C412yes—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—22no—
967C22⋊C4C2×C22⋊C412yes—
968C22⋊C4C2×C22⋊C412yes—
969C22⋊C4C2×C22⋊C412yes—
970C22⋊C4C2×C22⋊C412yes—
971C22⋊C4C2×C22⋊C412yes—
972C22⋊C4C2×C22⋊C412yes—
973C22⋊C4C2×C22⋊C412yes—
974C22⋊C4C2×C22⋊C412yes—
975C22⋊C4C2×C22⋊C412yes—
976C22⋊C4C2×C22⋊C412yes—
977C22⋊C4C2×C22⋊C412yes—
978C22⋊C4C2×C22⋊C412yes—
979C42—24no—
980C42—22no—
981C42—22no—
982C42—22no—
983C42—22no—
984C42—22no—
985C42—24no—
986C42—24no—
987C42—24no—
988C42—22no—
989C42C2×C22⋊C411yescharacteristic
990C42C2×C22⋊C411yescharacteristic
991C42C2×C22⋊C411yescharacteristic
992C42C2×C22⋊C411yescharacteristic
993C42C2×C22⋊C412yes—
994C42C2×C22⋊C412yes—
995C42C2×C22⋊C411yescharacteristic
996C42C2×C22⋊C411yescharacteristic
997C42C2×C22⋊C412yes—
998C42C2×C22⋊C412yes—
999C42C2×C22⋊C412yes—
1000C42C2×C22⋊C412yes—
1001C42C23×C411yescharacteristic
1002C42C23×C411yescharacteristic
1003C42C23×C411yescharacteristic
1004C42C23×C412yes—
1005C42C23×C412yes—
1006C42C22×D411yescharacteristic
1007C42C22×D412yes—
1008C42C22×D411yescharacteristic
1009C42C22×D412yes—
1010C42C22×D411yescharacteristic
1011C42C22×D411yescharacteristic
1012C42C22×D412yes—
1013C42C22×D411yescharacteristic
1014C42C22×D412yes—
1015C42C22×D411yescharacteristic
1016C42C2511yescharacteristic
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—22no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23C22×C22⋊C412yes—
1028C23C22×C22⋊C412yes—
1029C23C22×C22⋊C411yescharacteristic
1030C23C22×C22⋊C411yescharacteristic
1031C23C22×C22⋊C411yescharacteristic
1032Q8—22no—
1033Q8—22no—
1034Q8—28no—
1035Q8—24no—
1036Q8—42no—
1037Q8—44no—
1038Q8—44no—
1039Q8—42no—
1040Q8—44no—
1041Q8—84no—
1042Q8—84no—
1043D4—24no—
1044D4—24no—
1045D4—22no—
1046D4—22no—
1047D4—24no—
1048D4—42no—
1049D4—42no—
1050D4—42no—
1051D4—42no—
1052D4—44no—
1053D4—44no—
1054D4—84no—
1055D4—84no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—41no—
1083C2×C4—42no—
1084C2×C4—41no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—42no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—44no—
1097C2×C4—42no—
1098C2×C4—44no—
1099C2×C4—44no—
1100C2×C4—44no—
1101C2×C4—42no—
1102C2×C4—44no—
1103C2×C4—42no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—82no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—82no—
1112C2×C4C22×C22⋊C411yescharacteristic
1113C2×C4C22×C22⋊C411yescharacteristic
1114C2×C4C22×C22⋊C411yescharacteristic
1115C2×C4C22×C22⋊C411yescharacteristic
1116C2×C4C22×C22⋊C411yescharacteristic
1117C2×C4C22×C22⋊C411yescharacteristic
1118C2×C4C22×C22⋊C411yescharacteristic
1119C2×C4C22×C22⋊C412yes—
1120C2×C4C22×C22⋊C412yes—
1121C2×C4C22×C22⋊C412yes—
1122C2×C4C22×C22⋊C412yes—
1123C2×C4C22×C22⋊C412yes—
1124C2×C4C22×C22⋊C412yes—
1125C2×C4C22×C22⋊C411yescharacteristic
1126C2×C4C22×C22⋊C411yescharacteristic
1127C2×C4#56814yes—
1128C2×C4#57712yes—
1129C2×C4#57812yes—
1130C2×C4C24×C411yescharacteristic
1131C2×C4C23×D411yescharacteristic
1132C2×C4C23×D411yescharacteristic
1133C8—42no—
1134C8—42no—
1135C8—44no—
1136C8—42no—
1137C8—44no—
1138C8—42no—
1139C22—21no—
1140C22—21no—
1141C22—21no—
1142C22—21no—
1143C22—21no—
1144C22—22no—
1145C22—22no—
1146C22—21no—
1147C22—22no—
1148C22—22no—
1149C22—21no—
1150C22—22no—
1151C22—22no—
1152C22—44no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—84no—
1157C22—84no—
1158C22#287912yes—
1159C22#289812yes—
1160C22C23×C22⋊C411yescharacteristic
1161C4—21no—
1162C4—21no—
1163C4—22no—
1164C4—22no—
1165C4—21no—
1166C4—22no—
1167C4—21no—
1168C4—22no—
1169C4—21no—
1170C4—21no—
1171C4—21no—
1172C4—21no—
1173C4—22no—
1174C4—22no—
1175C4—42no—
1176C4—44no—
1177C4—42no—
1178C4—44no—
1179C4—42no—
1180C4#287912yes—
1181C4#289812yes—
1182C4C2×#56812yes—
1183C4C2×#57711yescharacteristic
1184C4C2×#57811yescharacteristic
1185C2—22no—
1186C2—22no—
1187C2—41no—
1188C2—42no—
1189C2—42no—
1190C2—82no—
1191C2C2×#287911yescharacteristic
1192C2C2×#289811yescharacteristic
1193C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radicalC2×#537C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60278C2semidirect
3. #60263C2semidirect
4. #17506C2semidirect
5. #17492C2semidirect
6. #17491C2semidirect
7. #17487C2semidirect
8. #17486C2semidirect
9. #17484C2semidirect
10. #17469C2semidirect
11. #17451C2semidirect
12. #17449C2semidirect
13. #17443C2semidirect
14. C2×#1487C2semidirect
50. #2989C22semidirect
51. #2989C22semidirect
52. #2988C22semidirect
56. #2965C22semidirect
57. #2965C22semidirect
58. C8×#41C22semidirect
70. #1497C22semidirect
71. #1495C22semidirect
72. #1494C22semidirect
73. #1493C22semidirect
74. #1491C22semidirect
75. #1489C22semidirect
76. #1488C22semidirect
84. #1487C22semidirect
88. #1485C22semidirect
89. #1483C22semidirect
90. #1482C22semidirect
91. #1481C22semidirect
92. #1479C22semidirect
93. #1477C22semidirect
94. #1476C22semidirect
95. C2×Q8⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34612
#602782
#602632
#175062
#174922
#174912
#174872
#174862
#174842
#174692
#174512
#174492
#174432
C2×#14872