Finite Group Databasebeta

← #6343654

Subgroups — #6343654

Order 512.

2942 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60276C211yesmaximal, characteristic, complemented
3#34189C211yesmaximal, characteristic, complemented
4#17617C214yesmaximal, complemented
5#17616C214yesmaximal, complemented
6#17615C218yesmaximal, complemented
7#17575C211yesmaximal, characteristic, complemented
8#17574C211yesmaximal, characteristic, complemented
9#17573C214yesmaximal, complemented
10#17571C214yesmaximal, complemented
11C2×#1518C211yesmaximal, characteristic, complemented
12C2×#1517C211yesmaximal, characteristic, complemented
13#3512—22no—
14#3511C412yescomplemented
15#3511C412yescomplemented
16#3510—22no—
17#3509C412yescomplemented
18#3508C412yescomplemented
19#3507—21no—
20#3507C2212yes—
21#3506—21no—
22#3506C2212yes—
23#3505—22no—
24#3505C2214yes—
25#3480—22no—
26#3480C414yescomplemented
27#3475—22no—
28#3475C414yescomplemented
29#3455—22no—
30#3449—21no—
31#3444C2214yes—
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34#3428—21no—
35C2×C4×#41C2211yescharacteristic
36#2988—22no—
37#2988—22no—
38#2982C2212yescomplemented
39#2972C2214yes—
40#2972C2212yescomplemented
41C8×#41—22no—
42C8×#41—22no—
43C2×#431C2211yescharacteristic
44C2×#431C2211yescharacteristic
45C2×#431C2214yescomplemented
46#2357—21no—
47#2357C2212yescomplemented
48#2356—21no—
49#2356C2212yescomplemented
50#2353—22no—
51#2353C2214yes—
52#2314—22no—
53#2311—21no—
54#2285C2211yescharacteristic
55#2283C2212yescomplemented
56#2283C2212yescomplemented
57C2×#382C2211yescharacteristic
58#2274—21no—
59#1521C22116yescomplemented
60#1520C2214yes—
61#1519C2214yes—
62#1518C2214yescomplemented
63#1518C2214yescomplemented
64#1518C2212yescomplemented
65#1518C2212yescomplemented
66#1517C2214yes—
67#1517C2214yes—
68#1517C2212yes—
69#1517C2212yes—
70#1516C22116yescomplemented
71#1503C2214yescomplemented
72#1502C2214yes—
73#1501C22116yescomplemented
74#1500C22116yescomplemented
75C2×#328C2214yes—
76C2×#327C2214yes—
77C22×#41—21no—
78C22×#41D411yescharacteristic
79#559—22no—
80#559—24no—
81#559—24no—
82#559C2×C414yescomplemented
83#557—22no—
84#557C2×C414yescomplemented
85#556—22no—
86#556—24no—
87#556—24no—
88#556—22no—
89#556C2×C414yescomplemented
90#556C2×C414yescomplemented
91#555—22no—
92#555C2×C414yescomplemented
93#554—22no—
94#554C2×C414yescomplemented
95#553—24no—
96#553—24no—
97#553—28no—
98#553—24no—
99#553—28no—
100#553C2×C418yes—
101#552—24no—
102#552—24no—
103#552—24no—
104#552C2×C418yes—
105#551—28no—
106#551—28no—
107#550—22no—
108#550C2×C414yescomplemented
109#548—24no—
110#548C2×C418yes—
111#547—22no—
112#547C2×C414yescomplemented
113#546—24no—
114#546C2×C418yes—
115#542—24no—
116#542—24no—
117#541—24no—
118#540—24no—
119#539—24no—
120#539—24no—
121#538—24no—
122#538—24no—
123#537—22no—
124#537—22no—
125#536—22no—
126#536—22no—
127#535—22no—
128#535—22no—
129#534—24no—
130#533—21no—
131#533—21no—
132#533—21no—
133#533—21no—
134#533C2×C412yes—
135#533C2×C412yes—
136#533C2×C414yescomplemented
137#533C2×C414yescomplemented
138#533C2312yes—
139#533C2312yes—
140#532—24no—
141#532—21no—
142#532—21no—
143#532—21no—
144#532—21no—
145#532C2×C412yes—
146#532C2×C412yes—
147#532C2×C414yescomplemented
148#532C2×C414yescomplemented
149#532C2312yes—
150#532C2312yes—
151C2×C4⋊Q8C2×C411yescharacteristic
152C2×C4⋊Q8C2×C411yescharacteristic
153C2×C4⋊Q8C2×C411yescharacteristic
154C2×#127C2×C411yescharacteristic
155#529—28no—
156#529—28no—
157#529—24no—
158#529—24no—
159#529—24no—
160#529—24no—
161#529C2×C418yescomplemented
162#529C2318yes—
163C2×#125—21no—
164C2×#124—21no—
165#525—24no—
166#525—24no—
167#525—24no—
168#525C2318yes—
169C2×C22⋊Q8—21no—
170C2×C22⋊Q8C2312yes—
171C2×#121—21no—
172C2×#121C2312yes—
173#520—22no—
174#520—22no—
175#520—22no—
176#520—22no—
177#519—22no—
178#518—22no—
179#518—24no—
180C4×#41—24no—
181C4×#41—24no—
182C4×#41—24no—
183C4×#41C2×C412yes—
184C4×#41C2×C412yes—
185C4×#41C2×C412yes—
186C4×#41C2×C412yes—
187C4×#41C2×C418yescomplemented
188C4×#41D412yes—
189C4×#41D412yes—
190C4×#41D412yes—
191C4×#41D412yes—
192C2×C4×Q8—21no—
193C2×C4×Q8C2×C412yes—
194C2×C4×Q8D411yescharacteristic
195C2×C4×Q8C2311yescharacteristic
196C2×C4×D4—21no—
197C2×C4×D4C2×C412yes—
198C2×C4×D4D412yes—
199C2×C4×D4D411yescharacteristic
200C2×C4×D4C2312yes—
201C2×C4×D4C2311yescharacteristic
202C2×#117—21no—
203C2×#117—24no—
204C2×#117—21no—
205C2×#117D412yes—
206C2×#117D411yescharacteristic
207C22×C4⋊C4—21no—
208C22×C42C2311yescharacteristic
209C22×C42C2312yes—
210C8×Q8—24no—
211C8×Q8—24no—
212C8×D4—28no—
213C8×D4—28no—
214C8×D4—24no—
215C8×D4—24no—
216#431—21no—
217#431—21no—
218#431—21no—
219#431—21no—
220#431—24no—
221#431—24no—
222#431C2312yes—
223#431C2312yes—
224#431C2312yes—
225#431C2312yes—
226#431C2318yes—
227C2×C4⋊C8—21no—
228C2×C4⋊C8—21no—
229C2×C4⋊C8—24no—
230C2×C22⋊C8C2312yes—
231C2×C22⋊C8C2312yes—
232C2×C22⋊C8C2318yes—
233C2×C4×C8—21no—
234C2×C4×C8—21no—
235C2×C4×C8—24no—
236#391—22no—
237#390—22no—
238#388—24no—
239#388—24no—
240#387—24no—
241#387—24no—
242#386—24no—
243#384—21no—
244#383—22no—
245#383C2314yes—
246#382—21no—
247#382—21no—
248#382C2312yes—
249#382C2312yes—
250#382C2311yescharacteristic
251#382C2311yescharacteristic
252#381—22no—
253#381C2314yes—
254#380—22no—
255#380—22no—
256#380—21no—
257#380C2312yes—
258C4×C4⋊C4—22no—
259C4×C4⋊C4—22no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4C2312yes—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—24no—
266C4×C22⋊C4C2314yes—
267#376—22no—
268#376C2314yes—
269C2×#95—21no—
270C2×#95C2312yes—
271#328C23116yes—
272#328C2318yes—
273#328C2318yes—
274#327C23116yes—
275#327C2318yes—
276#327C2318yes—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—24no—
280C2×#41—24no—
281C2×#41—24no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—44no—
285C2×#41—44no—
286C2×#41C22⋊C412yes—
287C2×#41C22⋊C412yes—
288C2×#41C22⋊C412yes—
289C2×#41C22⋊C412yes—
290C2×#41C22×C418yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8C22×C412yes—
294C22×Q8C2×D411yescharacteristic
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C22×C412yes—
299C22×D4C2×D412yes—
300C22×D4C2×D411yescharacteristic
301C23×C4—22no—
302C23×C4—22no—
303C23×C4C2×D412yes—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—28no—
312C4⋊Q8—24no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8C22×C412yes—
320C4⋊Q8C22×C412yes—
321C4⋊Q8C22×C412yes—
322C4⋊Q8C22×C412yes—
323C4⋊Q8C22×C412yes—
324C4⋊Q8C22×C412yes—
325#127—24no—
326#127—21no—
327#127—21no—
328#127C22×C412yes—
329#127C22×C412yes—
330#126—28no—
331#126—28no—
332#126—28no—
333#126—28no—
334#126—28no—
335#126—28no—
336#125—28no—
337#125—28no—
338#125—22no—
339#125—22no—
340#125—24no—
341#125—22no—
342#125—22no—
343#125C22×C418yes—
344#124—24no—
345#124—24no—
346#124—28no—
347#124—28no—
348#124—22no—
349#124—22no—
350#124—24no—
351#124—22no—
352#124—22no—
353#124C22×C418yes—
354#123—28no—
355#123—28no—
356#123—28no—
357#123—28no—
358#123—28no—
359#123—28no—
360#123—28no—
361#123—28no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—24no—
367C22⋊Q8—24no—
368C22⋊Q8—24no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—28no—
374C22⋊Q8—28no—
375C22⋊Q8C22×C414yes—
376C22⋊Q8C22×C418yes—
377C22⋊Q8C2414yes—
378#121—24no—
379#121—24no—
380#121—28no—
381#121—28no—
382#121—22no—
383#121—22no—
384#121—24no—
385#121—24no—
386#121—24no—
387#121—22no—
388#121—22no—
389#121—22no—
390#121—22no—
391#121—28no—
392#121—28no—
393#121C22×C414yes—
394#121C22×C418yes—
395#121C2414yes—
396#120—28no—
397#120—28no—
398C4×Q8—24no—
399C4×Q8—24no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—24no—
407C4×Q8—22no—
408C4×Q8—22no—
409C4×Q8C22⋊C412yes—
410C4×Q8C22⋊C412yes—
411C4×Q8C22⋊C412yes—
412C4×Q8C22⋊C412yes—
413C4×Q8C22×C414yes—
414C4×Q8C22×C414yes—
415C4×Q8C22×C418yes—
416C4×Q8C22×C412yes—
417C4×Q8C22×C412yes—
418C4×Q8C2×D412yes—
419C4×Q8C2×D412yes—
420C4×D4—28no—
421C4×D4—28no—
422C4×D4—28no—
423C4×D4—28no—
424C4×D4—28no—
425C4×D4—28no—
426C4×D4—24no—
427C4×D4—24no—
428C4×D4—28no—
429C4×D4—28no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—24no—
435C4×D4—24no—
436C4×D4—24no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4C22⋊C414yes—
440C4×D4C22⋊C412yes—
441C4×D4C22⋊C414yes—
442C4×D4C22⋊C412yes—
443C4×D4C22⋊C414yes—
444C4×D4C22⋊C414yes—
445C4×D4C22⋊C412yes—
446C4×D4C22⋊C412yes—
447C4×D4C22×C414yes—
448C4×D4C22×C414yes—
449C4×D4C22×C418yes—
450C4×D4C22×C414yes—
451C4×D4C22×C412yes—
452C4×D4C22×C414yes—
453C4×D4C22×C412yes—
454C4×D4C2×D414yes—
455C4×D4C2×D414yes—
456C4×D4C2×D412yes—
457C4×D4C2×D412yes—
458#117—22no—
459#117—22no—
460#117—24no—
461#117—22no—
462#117—22no—
463#117—24no—
464#117—24no—
465#117—28no—
466#117—28no—
467#117—28no—
468#117—28no—
469#117—44no—
470#117C22⋊C412yes—
471#117C22⋊C412yes—
472#117C22⋊C412yes—
473#117C22⋊C412yes—
474#117C22⋊C414yes—
475#117C22⋊C414yes—
476#117C22⋊C414yes—
477#117C22⋊C414yes—
478#117C22×C418yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—44no—
494C2×C4⋊C4C22×C412yes—
495C2×C4⋊C4C22×C412yes—
496C2×C4⋊C4C2×D411yescharacteristic
497C2×C4⋊C4C2×D412yes—
498C2×C4⋊C4C2×D411yescharacteristic
499C2×C4⋊C4C2×D412yes—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—28no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4C2×D412yes—
508C2×C22⋊C4C2×D412yes—
509C2×C22⋊C4C2×D412yes—
510C2×C42—22no—
511C2×C42—28no—
512C2×C42—22no—
513C2×C42—24no—
514C2×C42—24no—
515C2×C42C22×C411yescharacteristic
516C2×C42C22×C411yescharacteristic
517C2×C42C22×C414yes—
518C2×C42C22×C411yescharacteristic
519C2×C42C22×C411yescharacteristic
520C2×C42C22×C414yes—
521C2×C42C2×D412yes—
522C2×C42C2×D411yescharacteristic
523C2×C42C2×D412yes—
524C2×C42C2×D411yescharacteristic
525C2×C42C2×D411yescharacteristic
526C2×C42C2×D411yescharacteristic
527C2×C42C2×D414yes—
528C2×C42C2×D411yescharacteristic
529C2×C42C2×D411yescharacteristic
530C2×C42C2×D414yes—
531C2×C42C2412yes—
532C2×C42C2411yescharacteristic
533C2×C42C2411yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—28no—
537C4⋊C8—22no—
538C4⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—28no—
542C22⋊C8C2414yes—
543C22⋊C8C2414yes—
544C4×C8—22no—
545C4×C8—22no—
546C4×C8—28no—
547C4×C8—22no—
548C4×C8—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—21no—
553#95—24no—
554#95—24no—
555#95—21no—
556#95—24no—
557#95—24no—
558#95C2414yes—
559#95C2412yes—
560#95C2412yes—
561C24—22no—
562C24C22×D412yes—
563C24C22×D411yescharacteristic
564#41—28no—
565#41—28no—
566#41—28no—
567#41—28no—
568#41—44no—
569#41—44no—
570#41—44no—
571#41—44no—
572#41—48no—
573#41—48no—
574#41—88no—
575#41—88no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—44no—
584C2×Q8—82no—
585C2×Q8—82no—
586C2×Q8C2×C22⋊C412yes—
587C2×Q8C2×C22⋊C412yes—
588C2×Q8C23×C414yes—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4C2×C22⋊C414yes—
608C2×D4C2×C22⋊C414yes—
609C2×D4C2×C22⋊C412yes—
610C2×D4C2×C22⋊C412yes—
611C2×D4C23×C414yes—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—48no—
625C22×C4—44no—
626C22×C4—82no—
627C22×C4—81no—
628C22×C4—82no—
629C22×C4—81no—
630C22×C4—82no—
631C22×C4—82no—
632C22×C4C2×C22⋊C414yes—
633C22×C4C2×C22⋊C414yes—
634C22×C4C2×C22⋊C411yescharacteristic
635C22×C4C2×C22⋊C411yescharacteristic
636C22×C4C2×C22⋊C411yescharacteristic
637C22×C4C2×C22⋊C411yescharacteristic
638C22×C4C2×C22⋊C414yes—
639C22×C4C2×C22⋊C414yes—
640C22×C4C2×C22⋊C411yescharacteristic
641C22×C4C2×C22⋊C411yescharacteristic
642C22×C4C2×C22⋊C411yescharacteristic
643C22×C4C2×C22⋊C411yescharacteristic
644C22×C4#13514yes—
645C22×C4#13514yes—
646C22×C4C23×C411yescharacteristic
647C22×C4C23×C411yescharacteristic
648C22×C4C23×C414yes—
649C22×C4C22×D412yes—
650C22×C4C22×D411yescharacteristic
651C22×C4C22×D412yes—
652C22×C4C22×D412yes—
653C22×C4C22×D411yescharacteristic
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D414yes—
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D411yescharacteristic
660C22×C4C2511yescharacteristic
661C2×C8—24no—
662C2×C8—24no—
663C2×C8—88no—
664C2×C8—82no—
665C2×C8—82no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—24no—
675C4⋊C4—22no—
676C4⋊C4—24no—
677C4⋊C4—22no—
678C4⋊C4—24no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—24no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4C2×C22⋊C412yes—
691C4⋊C4C2×C22⋊C412yes—
692C4⋊C4C2×C22⋊C412yes—
693C4⋊C4C2×C22⋊C412yes—
694C4⋊C4C2×C22⋊C414yes—
695C4⋊C4C2×C22⋊C414yes—
696C4⋊C4C2×C22⋊C414yes—
697C4⋊C4C2×C22⋊C414yes—
698C4⋊C4C23×C414yes—
699C4⋊C4C23×C414yes—
700C22⋊C4—24no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—24no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—24no—
712C22⋊C4—44no—
713C22⋊C4—84no—
714C22⋊C4—84no—
715C22⋊C4C2×C22⋊C414yes—
716C22⋊C4C2×C22⋊C414yes—
717C22⋊C4C2×C22⋊C414yes—
718C22⋊C4C2×C22⋊C414yes—
719C22⋊C4C2×C22⋊C414yes—
720C22⋊C4C2×C22⋊C414yes—
721C42—24no—
722C42—28no—
723C42—28no—
724C42—24no—
725C42—44no—
726C42—84no—
727C42—84no—
728C42C2×C22⋊C414yes—
729C42C2×C22⋊C414yes—
730C42C2×C22⋊C414yes—
731C42C2×C22⋊C411yescharacteristic
732C42C2×C22⋊C411yescharacteristic
733C42C2×C22⋊C411yescharacteristic
734C42C2×C22⋊C411yescharacteristic
735C42C2×C22⋊C411yescharacteristic
736C42C2×C22⋊C411yescharacteristic
737C42C2×C22⋊C414yes—
738C42C2×C22⋊C411yescharacteristic
739C42C2×C22⋊C411yescharacteristic
740C42C23×C411yescharacteristic
741C42C23×C411yescharacteristic
742C42C23×C411yescharacteristic
743C42C23×C414yes—
744C42C23×C411yescharacteristic
745C42C22×D411yescharacteristic
746C42C22×D414yes—
747C42C22×D411yescharacteristic
748C42C22×D411yescharacteristic
749C42C22×D411yescharacteristic
750C23—22no—
751C23—22no—
752C23—24no—
753C23—41no—
754C23—41no—
755C23—42no—
756C23—42no—
757C23—44no—
758C23—82no—
759C23—82no—
760C23C22×C22⋊C414yes—
761C23C22×C22⋊C411yescharacteristic
762C23C22×C22⋊C411yescharacteristic
763C23C2×#13512yes—
764C23C2×#13512yes—
765C23C23×D411yescharacteristic
766Q8—24no—
767Q8—24no—
768Q8—44no—
769Q8—44no—
770Q8—44no—
771Q8—44no—
772Q8—82no—
773Q8—82no—
774D4—28no—
775D4—28no—
776D4—24no—
777D4—24no—
778D4—44no—
779D4—44no—
780D4—48no—
781D4—44no—
782D4—44no—
783D4—44no—
784D4—44no—
785D4—82no—
786D4—82no—
787D4—88no—
788D4—88no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—44no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—44no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—48no—
816C2×C4—48no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—88no—
827C2×C4—88no—
828C2×C4—82no—
829C2×C4—82no—
830C2×C4—164no—
831C2×C4#41614yes—
832C2×C4#41614yes—
833C2×C4#41614yes—
834C2×C4#41614yes—
835C2×C4C22×C22⋊C414yes—
836C2×C4C22×C22⋊C414yes—
837C2×C4C22×C22⋊C411yescharacteristic
838C2×C4C22×C22⋊C411yescharacteristic
839C2×C4C22×C22⋊C411yescharacteristic
840C2×C4C22×C22⋊C411yescharacteristic
841C2×C4C22×C22⋊C411yescharacteristic
842C2×C4C22×C22⋊C414yes—
843C2×C4C22×C22⋊C411yescharacteristic
844C2×C4C22×C22⋊C411yescharacteristic
845C2×C4C22×C22⋊C411yescharacteristic
846C2×C4C22×C22⋊C411yescharacteristic
847C2×C4C22×C22⋊C411yescharacteristic
848C2×C4C2×#13512yes—
849C2×C4C2×#13512yes—
850C2×C4C2×#13512yes—
851C2×C4C2×#13512yes—
852C2×C4C24×C411yescharacteristic
853C2×C4C23×D411yescharacteristic
854C8—44no—
855C8—44no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—42no—
866C22—42no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—82no—
871C22—82no—
872C22—164no—
873C22C2×#41612yes—
874C22C2×#41612yes—
875C22C23×C22⋊C411yescharacteristic
876C22C22×#13511yescharacteristic
877C22C22×#13511yescharacteristic
878C4—21no—
879C4—21no—
880C4—24no—
881C4—21no—
882C4—21no—
883C4—24no—
884C4—21no—
885C4—21no—
886C4—24no—
887C4—21no—
888C4—21no—
889C4—44no—
890C4—44no—
891C4—44no—
892C4—82no—
893C4—82no—
894C4—84no—
895C4C2×#41612yes—
896C4C2×#41612yes—
897C4C2×#41612yes—
898C4C2×#41612yes—
899C2—21no—
900C2—21no—
901C2—22no—
902C2—22no—
903C2—44no—
904C2—84no—
905C2#6007011yescharacteristic
906C2C22×#41611yescharacteristic
907C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62815C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60276C2semidirect
3. #34189C2semidirect
4. #17617C2semidirect
5. #17616C2semidirect
6. #17615C2semidirect
7. #17575C2semidirect
8. #17574C2semidirect
9. #17573C2semidirect
10. #17571C2semidirect
11. C2×#1518C2semidirect
12. C2×#1517C2semidirect
14. #3511C4semidirect
15. #3511C4semidirect
17. #3509C4semidirect
18. #3508C4semidirect
26. #3480C4semidirect
28. #3475C4semidirect
38. #2982C22semidirect
40. #2972C22semidirect
45. C2×#431C22semidirect
47. #2357C22semidirect
49. #2356C22semidirect
55. #2283C22semidirect
56. #2283C22semidirect
59. #1521C22semidirect
62. #1518C22semidirect
63. #1518C22semidirect
64. #1518C22semidirect
65. #1518C22semidirect
70. #1516C22semidirect
71. #1503C22semidirect
73. #1501C22semidirect
74. #1500C22semidirect
82. #559C2×C4semidirect
84. #557C2×C4semidirect
89. #556C2×C4semidirect
90. #556C2×C4semidirect
92. #555C2×C4semidirect
94. #554C2×C4semidirect
108. #550C2×C4semidirect
112. #547C2×C4semidirect
136. #533C2×C4semidirect
137. #533C2×C4semidirect
147. #532C2×C4semidirect
148. #532C2×C4semidirect
161. #529C2×C4semidirect
187. C4×#41C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628152
#602762
#341892
#176172
#176162
#176152
#175752
#175742
#175732
#175712
C2×#15182
C2×#15172