Finite Group Databasebeta

← #6343660

Subgroups — #6343660

Order 512.

2888 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C211yesmaximal, characteristic
2#60277C211yesmaximal, characteristic, complemented
3#34195C211yesmaximal, characteristic, complemented
4#17624C214yesmaximal, complemented
5#17623C214yesmaximal, complemented
6#17622C214yesmaximal, complemented
7#17621C212yesmaximal, complemented
8#17620C212yesmaximal, complemented
9#17594C212yesmaximal, complemented
10#17593C212yesmaximal, complemented
11#17580C212yesmaximal, complemented
12#17579C212yesmaximal, complemented
13#17567C212yesmaximal, complemented
14C2×#1521C212yesmaximal, complemented
15#3521—24no—
16#3515C414yescomplemented
17#3514C414yescomplemented
18#3507C2212yes—
19#3505C2212yes—
20#3505C2212yes—
21#3501C2211yescharacteristic
22#3496C2211yescharacteristic
23#3493—21no—
24#3491—21no—
25#3491—21no—
26#3485—21no—
27#3482C414yescomplemented
28#3481C414yescomplemented
29#3475—24no—
30#3461—21no—
31#3459—21no—
32#3459—21no—
33#3444C2212yes—
34C2×#529C2212yes—
35C2×#529C2212yes—
36C4×H(5,𝔽2)—21no—
37C2×C4×#41C2211yescharacteristic
38#2989—24no—
39#2983C2212yescomplemented
40#2975C2212yescomplemented
41#2973C2212yes—
42#2973C2212yescomplemented
43#2965—24no—
44#2920C2212yescomplemented
45#2920C2212yescomplemented
46C2×#431C2212yescomplemented
47#2356C2212yescomplemented
48#2353C2212yes—
49#2353C2212yescomplemented
50#2349C2212yescomplemented
51#2347—21no—
52#2343—21no—
53#2343—21no—
54#2339—21no—
55#2320—21no—
56#2318—21no—
57#2318—21no—
58#2283C2211yescharacteristic, complemented
59#2283C2211yescharacteristic, complemented
60#2283C2211yescharacteristic, complemented
61#2283C2211yescharacteristic, complemented
62C2×#383C2211yescharacteristic, complemented
63C2×#383C2211yescharacteristic, complemented
64#2275—21no—
65#1521C2214yescomplemented
66#1521C2214yescomplemented
67#1521C2218yescomplemented
68#1521C2214yescomplemented
69#1521C2214yescomplemented
70#1520C2214yescomplemented
71#1519C2214yes—
72#1515C2214yescomplemented
73#1514C2214yes—
74#1513C2218yescomplemented
75#1512C2218yescomplemented
76#1511C2214yescomplemented
77#1510C2214yes—
78#1509C2218yescomplemented
79#1508C2214yescomplemented
80#1507C2214yes—
81#1506C2214yescomplemented
82#1505C2214yes—
83#1504C2218yescomplemented
84#1500C2218yescomplemented
85C2×#328C2214yescomplemented
86C2×#327C2214yes—
87C2×H(5,𝔽2)—21no—
88C22×#41D411yescharacteristic
89#559C2×C414yescomplemented
90#557C2×C414yescomplemented
91#556—24no—
92#556—24no—
93#556C2×C414yescomplemented
94#555—24no—
95#554—24no—
96#554C2×C414yescomplemented
97#554C2×C414yescomplemented
98#553—24no—
99#553—24no—
100#553—24no—
101#553C2×C414yes—
102#553C2×C414yescomplemented
103#552—24no—
104#552—24no—
105#552—24no—
106#552—24no—
107#552—24no—
108#552—24no—
109#552C2×C414yes—
110#552C2×C414yescomplemented
111#551—24no—
112#551—24no—
113#551—24no—
114#551—24no—
115#551—24no—
116#551—24no—
117D4×Q8C2×C414yescomplemented
118#548C2×C414yes—
119#548C2×C414yescomplemented
120#547—24no—
121#547—24no—
122#547C2×C414yescomplemented
123#546—24no—
124#546—24no—
125#546—24no—
126#546C2×C414yes—
127#546C2×C414yescomplemented
128D42C2×C414yescomplemented
129#544—21no—
130#543—21no—
131#543—21no—
132#542—24no—
133#541—24no—
134#539—24no—
135#539—24no—
136#539—22no—
137#539—22no—
138#539—22no—
139#539—22no—
140#538—24no—
141#538—24no—
142#538—22no—
143#538—22no—
144#537—21no—
145#536—22no—
146#534—22no—
147#534—22no—
148#534—21no—
149#534—21no—
150#533—24no—
151#533C2×C412yescomplemented
152#533C2×C412yescomplemented
153#533C2312yes—
154#532C2×C412yescomplemented
155#532C2×C412yescomplemented
156#532C2312yes—
157#529—24no—
158#529—24no—
159#529—24no—
160#529—22no—
161#529—22no—
162#529—22no—
163#529—22no—
164#529—22no—
165#529—22no—
166#529—22no—
167#529—22no—
168#529—22no—
169#529—22no—
170#529—22no—
171#529—22no—
172#529C2×C414yescomplemented
173#529C2×C414yescomplemented
174#529C2×C414yescomplemented
175#529C2×C414yescomplemented
176#529C2×C414yescomplemented
177#529C2314yes—
178#529C2314yes—
179#529C2314yes—
180C2×#126—22no—
181C2×#126—22no—
182C2×#125C2×C412yescomplemented
183C2×#125C2×C412yescomplemented
184C2×#124C2×C412yescomplemented
185C2×#124C2×C412yescomplemented
186#525—22no—
187#525—22no—
188#525—24no—
189#525—24no—
190#525C2314yes—
191C2×#123—22no—
192C2×#123—22no—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×#121C2312yes—
196C2×#121C2312yes—
197#520—24no—
198#520—22no—
199#518—21no—
200#518—24no—
201#518—22no—
202#518—22no—
203C4×#41—24no—
204C4×#41—22no—
205C4×#41—22no—
206C4×#41C2×C414yes—
207C4×#41C2×C414yes—
208C4×#41C2×C414yescomplemented
209C4×#41D414yes—
210C4×#41D414yes—
211C2×C4×Q8C2×C412yescomplemented
212C2×C4×Q8C2×C412yescomplemented
213C2×C4×Q8D411yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×D4—22no—
216C2×C4×D4—22no—
217C2×C4×D4—24no—
218C2×C4×D4—22no—
219C2×C4×D4C2×C412yescomplemented
220C2×C4×D4C2×C412yescomplemented
221C2×C4×D4D411yescharacteristic
222C2×C4×D4D411yescharacteristic
223C2×C4×D4D411yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—22no—
228C2×#117—22no—
229C2×#117D411yescharacteristic
230C2×#117D411yescharacteristic
231C2×#117D411yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235#446—28no—
236#436—28no—
237#435—28no—
238#435—28no—
239#432—22no—
240#432—22no—
241#432C2314yes—
242#432C2314yes—
243#431—22no—
244#431—22no—
245#431—22no—
246#431—22no—
247#431C2314yes—
248#431C2314yes—
249#423—22no—
250#423—22no—
251C2×C4⋊C8—22no—
252#407C2314yes—
253#407C2314yes—
254C2×C22⋊C8C2314yes—
255C4×M16—22no—
256C4×M16—22no—
257C2×C4×C8—22no—
258#391—22no—
259#389—22no—
260#388—22no—
261#388—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#386—22no—
267#386—22no—
268#385—22no—
269#385—22no—
270#383—21no—
271#383—21no—
272#383—21no—
273#383—21no—
274#383C2312yes—
275#383C2312yes—
276#383C2311yescharacteristic
277#383C2311yescharacteristic
278#383C2311yescharacteristic
279#383C2311yescharacteristic
280#382—21no—
281#382—21no—
282#382—21no—
283#382C2312yes—
284#381—21no—
285#381—21no—
286#381—21no—
287#381C2312yes—
288#380—21no—
289#380—21no—
290#380C2312yes—
291#380C2312yes—
292C4×C4⋊C4—22no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4C2312yes—
297C4×C22⋊C4—21no—
298C4×C22⋊C4—21no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4C2312yes—
303#376—21no—
304#376—21no—
305#376C2312yes—
306#376C2312yes—
307C2×#95—21no—
308C2×#95—21no—
309C2×#95—21no—
310C2×#95—21no—
311C2×#95C2312yes—
312C2×#95C2312yes—
313#328C2318yes—
314#328C2318yes—
315#328C2318yes—
316#328C2318yes—
317#327C2318yes—
318#327C2318yes—
319#327C2318yes—
320#327C2318yes—
321H(5,𝔽2)—48no—
322C2×#41—24no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—44no—
326C2×#41C22⋊C414yes—
327C2×#41C22⋊C414yes—
328C2×#41C22×C414yes—
329C22×Q8C22×C412yes—
330C22×Q8C22×C412yes—
331C22×Q8C2×D411yescharacteristic
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4C22×C412yes—
336C22×D4C22×C412yes—
337C22×D4C2×D411yescharacteristic
338C22×D4C2×D411yescharacteristic
339C22×D4C2×D411yescharacteristic
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2×D411yescharacteristic
350C23×C4C2411yescharacteristic
351C23×C4C2411yescharacteristic
352C23×C4C2411yescharacteristic
353C2×M16—24no—
354C2×M16—24no—
355C22×C8—24no—
356C4⋊Q8—24no—
357C4⋊Q8—24no—
358C4⋊Q8C22×C412yes—
359C4⋊Q8C22×C412yes—
360C4⋊Q8C22×C412yes—
361#127C22×C412yes—
362#126—24no—
363#126—24no—
364#126—24no—
365#126—24no—
366#126—24no—
367#126—24no—
368#126—24no—
369#126—24no—
370#126—24no—
371#126—24no—
372#126—24no—
373#126—24no—
374#126—24no—
375#126—24no—
376#125—24no—
377#125—24no—
378#125—24no—
379#125—24no—
380#125—24no—
381#125—22no—
382#125—22no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125C22×C414yes—
388#125C22×C414yes—
389#125C22×C414yes—
390#124—24no—
391#124—24no—
392#124—24no—
393#124—22no—
394#124—22no—
395#124—22no—
396#124—22no—
397#124—22no—
398#124—22no—
399#124C22×C414yes—
400#124C22×C414yes—
401#124C22×C414yes—
402#123—24no—
403#123—24no—
404#123—24no—
405#123—24no—
406#123—24no—
407#123—24no—
408#123—24no—
409#123—24no—
410#123—24no—
411#123—24no—
412#123—24no—
413#123—24no—
414#123—24no—
415#123—24no—
416#123—24no—
417#123—24no—
418#123—24no—
419#123—24no—
420#123—24no—
421C22⋊Q8—24no—
422C22⋊Q8—24no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—24no—
432C22⋊Q8—24no—
433C22⋊Q8—24no—
434C22⋊Q8—24no—
435C22⋊Q8—24no—
436C22⋊Q8—24no—
437C22⋊Q8—24no—
438C22⋊Q8—24no—
439C22⋊Q8—24no—
440C22⋊Q8C22×C414yes—
441C22⋊Q8C22×C414yes—
442C22⋊Q8C22×C414yes—
443C22⋊Q8C2414yes—
444#121—24no—
445#121—24no—
446#121—24no—
447#121—24no—
448#121—22no—
449#121—22no—
450#121—22no—
451#121—22no—
452#121—22no—
453#121—22no—
454#121—22no—
455#121—22no—
456#121—24no—
457#121—24no—
458#121—24no—
459#121C22×C414yes—
460#121C22×C414yes—
461#121C22×C414yes—
462#121C2414yes—
463#120—24no—
464#120—24no—
465#120—24no—
466#120—24no—
467#120—24no—
468C4×Q8—24no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8C22⋊C414yes—
478C4×Q8C22⋊C414yes—
479C4×Q8C22×C414yes—
480C4×Q8C22×C414yes—
481C4×Q8C22×C414yes—
482C4×Q8C22×C414yes—
483C4×Q8C22×C414yes—
484C4×Q8C2×D414yes—
485C4×D4—24no—
486C4×D4—24no—
487C4×D4—24no—
488C4×D4—24no—
489C4×D4—24no—
490C4×D4—24no—
491C4×D4—24no—
492C4×D4—24no—
493C4×D4—24no—
494C4×D4—24no—
495C4×D4—24no—
496C4×D4—24no—
497C4×D4—24no—
498C4×D4—24no—
499C4×D4—24no—
500C4×D4—24no—
501C4×D4—24no—
502C4×D4—24no—
503C4×D4—24no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—48no—
513C4×D4C22⋊C414yes—
514C4×D4C22⋊C414yes—
515C4×D4C22⋊C414yes—
516C4×D4C22⋊C414yes—
517C4×D4C22⋊C414yes—
518C4×D4C22⋊C414yes—
519C4×D4C22×C414yes—
520C4×D4C22×C414yes—
521C4×D4C22×C414yes—
522C4×D4C22×C414yes—
523C4×D4C22×C414yes—
524C4×D4C22×C414yes—
525C4×D4C22×C414yes—
526C4×D4C2×D414yes—
527C4×D4C2×D414yes—
528C4×D4C2×D414yes—
529#117—22no—
530#117—22no—
531#117—24no—
532#117—24no—
533#117—24no—
534#117—24no—
535#117—24no—
536#117—24no—
537#117—24no—
538#117—24no—
539#117—24no—
540#117—24no—
541#117—24no—
542#117—24no—
543#117C22⋊C414yes—
544#117C22⋊C414yes—
545#117C22⋊C414yes—
546#117C22⋊C414yes—
547#117C22⋊C414yes—
548#117C22⋊C414yes—
549#117C22×C414yes—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4C22×C412yes—
564C2×C4⋊C4C22×C412yes—
565C2×C4⋊C4C22×C412yes—
566C2×C4⋊C4C22×C412yes—
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4C2×D411yescharacteristic
590C2×C22⋊C4C2×D411yescharacteristic
591C2×C22⋊C4C2×D411yescharacteristic
592C2×C22⋊C4C2×D411yescharacteristic
593C2×C22⋊C4C2×D411yescharacteristic
594C2×C22⋊C4C2×D411yescharacteristic
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—24no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42C22×C412yes—
603C2×C42C22×C412yes—
604C2×C42C22×C412yes—
605C2×C42C22×C412yes—
606C2×C42C22×C412yes—
607C2×C42C22×C412yes—
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D412yes—
615C2×C42C2×D412yes—
616C2×C42C2×D412yes—
617C2×C42C2×D412yes—
618C2×C42C2×D412yes—
619C2×C42C2×D412yes—
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C4⋊C8—24no—
625C4⋊C8—24no—
626C4⋊C8—24no—
627C4⋊C8—24no—
628C22⋊C8—24no—
629C22⋊C8—24no—
630C22⋊C8—24no—
631C22⋊C8C2418yes—
632#97—24no—
633#97—24no—
634C4×C8—24no—
635C4×C8—24no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641#95—21no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—21no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—21no—
654#95C2412yes—
655#95C2412yes—
656#95C2412yes—
657#95C2412yes—
658C24—22no—
659C24—22no—
660C24C22×D411yescharacteristic
661C24C22×D411yescharacteristic
662C24C22×D411yescharacteristic
663#41—48no—
664#41—48no—
665#41—48no—
666#41—416no—
667#41—84no—
668#41—84no—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—42no—
674C2×Q8—82no—
675C2×Q8—82no—
676C2×Q8C2×C22⋊C414yes—
677C2×Q8C23×C414yes—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—42no—
690C2×D4—416no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—82no—
694C2×D4—82no—
695C2×D4C2×C22⋊C414yes—
696C2×D4C2×C22⋊C414yes—
697C2×D4C2×C22⋊C414yes—
698C2×D4C23×C414yes—
699C22×C4—24no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—81no—
720C22×C4—81no—
721C22×C4—81no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4—81no—
725C22×C4—84no—
726C22×C4—84no—
727C22×C4—82no—
728C22×C4—82no—
729C22×C4—82no—
730C22×C4—82no—
731C22×C4C2×C22⋊C412yes—
732C22×C4C2×C22⋊C412yes—
733C22×C4C2×C22⋊C412yes—
734C22×C4C2×C22⋊C412yes—
735C22×C4C2×C22⋊C412yes—
736C22×C4C2×C22⋊C412yes—
737C22×C4C2×C22⋊C412yes—
738C22×C4C2×C22⋊C412yes—
739C22×C4C2×C22⋊C412yes—
740C22×C4C2×C22⋊C412yes—
741C22×C4C2×C22⋊C412yes—
742C22×C4C2×C22⋊C412yes—
743C22×C4C23×C412yes—
744C22×C4C23×C412yes—
745C22×C4C23×C412yes—
746C22×C4C22×D411yescharacteristic
747C22×C4C22×D411yescharacteristic
748C22×C4C22×D411yescharacteristic
749C22×C4C22×D411yescharacteristic
750C22×C4C22×D411yescharacteristic
751C22×C4C22×D411yescharacteristic
752C22×C4C22×D411yescharacteristic
753C22×C4C22×D411yescharacteristic
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C22×D412yes—
758C22×C4C22×D412yes—
759C22×C4C22×D412yes—
760C22×C4C2511yescharacteristic
761M16—84no—
762M16—84no—
763C2×C8—28no—
764C2×C8—84no—
765C4⋊C4—24no—
766C4⋊C4—22no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—24no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—22no—
778C4⋊C4—22no—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—24no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—44no—
788C4⋊C4—82no—
789C4⋊C4—82no—
790C4⋊C4—82no—
791C4⋊C4C2×C22⋊C414yes—
792C4⋊C4C2×C22⋊C414yes—
793C4⋊C4C2×C22⋊C414yes—
794C4⋊C4C2×C22⋊C414yes—
795C4⋊C4C2×C22⋊C414yes—
796C4⋊C4C2×C22⋊C414yes—
797C4⋊C4C23×C414yes—
798C4⋊C4C23×C414yes—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—24no—
804C22⋊C4—24no—
805C22⋊C4—24no—
806C22⋊C4—24no—
807C22⋊C4—24no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—24no—
811C22⋊C4—24no—
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—82no—
821C22⋊C4—82no—
822C22⋊C4C2×C22⋊C414yes—
823C22⋊C4C2×C22⋊C414yes—
824C22⋊C4C2×C22⋊C414yes—
825C22⋊C4C2×C22⋊C414yes—
826C22⋊C4C2×C22⋊C414yes—
827C22⋊C4C2×C22⋊C414yes—
828C42—24no—
829C42—24no—
830C42—24no—
831C42—24no—
832C42—24no—
833C42—44no—
834C42—82no—
835C42—82no—
836C42—82no—
837C42C2×C22⋊C412yes—
838C42C2×C22⋊C412yes—
839C42C2×C22⋊C412yes—
840C42C2×C22⋊C412yes—
841C42C2×C22⋊C412yes—
842C42C2×C22⋊C412yes—
843C42C2×C22⋊C412yes—
844C42C2×C22⋊C412yes—
845C42C2×C22⋊C412yes—
846C42C2×C22⋊C412yes—
847C42C2×C22⋊C412yes—
848C42C2×C22⋊C412yes—
849C42C23×C411yescharacteristic
850C42C23×C411yescharacteristic
851C42C23×C412yes—
852C42C23×C412yes—
853C42C23×C412yes—
854C42C22×D411yescharacteristic
855C42C22×D412yes—
856C42C22×D412yes—
857C42C22×D412yes—
858C42C22×D411yescharacteristic
859C23—22no—
860C23—22no—
861C23—24no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—44no—
869C23—44no—
870C23—82no—
871C23—82no—
872C23—82no—
873C23—82no—
874C23C22×C22⋊C412yes—
875C23C22×C22⋊C412yes—
876C23C22×C22⋊C412yes—
877C23#57514yes—
878C23C23×D411yescharacteristic
879Q8—44no—
880Q8—44no—
881Q8—44no—
882Q8—82no—
883Q8—82no—
884Q8—82no—
885D4—28no—
886D4—28no—
887D4—44no—
888D4—44no—
889D4—44no—
890D4—48no—
891D4—48no—
892D4—48no—
893D4—82no—
894D4—82no—
895D4—82no—
896D4—84no—
897D4—84no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—48no—
932C2×C4—48no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—84no—
948C2×C4—84no—
949C2×C4—84no—
950C2×C4—82no—
951C2×C4—82no—
952C2×C4—82no—
953C2×C4—82no—
954C2×C4—164no—
955C2×C4—164no—
956C2×C4C22×C22⋊C411yescharacteristic
957C2×C4C22×C22⋊C412yes—
958C2×C4C22×C22⋊C412yes—
959C2×C4C22×C22⋊C412yes—
960C2×C4C22×C22⋊C412yes—
961C2×C4C22×C22⋊C411yescharacteristic
962C2×C4C22×C22⋊C411yescharacteristic
963C2×C4C22×C22⋊C411yescharacteristic
964C2×C4C22×C22⋊C412yes—
965C2×C4C22×C22⋊C412yes—
966C2×C4C22×C22⋊C412yes—
967C2×C4C22×C22⋊C412yes—
968C2×C4C22×C22⋊C412yes—
969C2×C4C24×C411yescharacteristic
970C2×C4C23×D411yescharacteristic
971C8—48no—
972C22—21no—
973C22—22no—
974C22—21no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—82no—
988C22—164no—
989C22—164no—
990C22#289614yes—
991C22C23×C22⋊C411yescharacteristic
992C22C2×#57512yes—
993C4—21no—
994C4—21no—
995C4—22no—
996C4—22no—
997C4—22no—
998C4—21no—
999C4—21no—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—21no—
1004C4—21no—
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4—82no—
1012C4—82no—
1013C4—82no—
1014C4—82no—
1015C2—22no—
1016C2—24no—
1017C2—42no—
1018C2—42no—
1019C2—84no—
1020C2#6007011yescharacteristic
1021C2C2×#289611yescharacteristic
1022C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62781C2
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. #60277C2semidirect
3. #34195C2semidirect
4. #17624C2semidirect
5. #17623C2semidirect
6. #17622C2semidirect
7. #17621C2semidirect
8. #17620C2semidirect
9. #17594C2semidirect
10. #17593C2semidirect
11. #17580C2semidirect
12. #17579C2semidirect
13. #17567C2semidirect
14. C2×#1521C2semidirect
16. #3515C4semidirect
17. #3514C4semidirect
27. #3482C4semidirect
28. #3481C4semidirect
39. #2983C22semidirect
40. #2975C22semidirect
42. #2973C22semidirect
44. #2920C22semidirect
45. #2920C22semidirect
46. C2×#431C22semidirect
47. #2356C22semidirect
49. #2353C22semidirect
50. #2349C22semidirect
58. #2283C22semidirect
59. #2283C22semidirect
60. #2283C22semidirect
61. #2283C22semidirect
62. C2×#383C22semidirect
63. C2×#383C22semidirect
65. #1521C22semidirect
66. #1521C22semidirect
67. #1521C22semidirect
68. #1521C22semidirect
69. #1521C22semidirect
70. #1520C22semidirect
72. #1515C22semidirect
74. #1513C22semidirect
75. #1512C22semidirect
76. #1511C22semidirect
78. #1509C22semidirect
79. #1508C22semidirect
81. #1506C22semidirect
83. #1504C22semidirect
84. #1500C22semidirect
85. C2×#328C22semidirect
89. #559C2×C4semidirect
90. #557C2×C4semidirect
93. #556C2×C4semidirect
96. #554C2×C4semidirect
97. #554C2×C4semidirect
102. #553C2×C4semidirect
110. #552C2×C4semidirect
117. D4×Q8C2×C4semidirect
119. #548C2×C4semidirect
122. #547C2×C4semidirect
127. #546C2×C4semidirect
128. D42C2×C4semidirect
151. #533C2×C4semidirect
152. #533C2×C4semidirect
154. #532C2×C4semidirect
155. #532C2×C4semidirect
172. #529C2×C4semidirect
173. #529C2×C4semidirect
174. #529C2×C4semidirect
175. #529C2×C4semidirect
176. #529C2×C4semidirect
182. C2×#125C2×C4semidirect
183. C2×#125C2×C4semidirect
184. C2×#124C2×C4semidirect
185. C2×#124C2×C4semidirect
208. C4×#41C2×C4semidirect
211. C2×C4×Q8C2×C4semidirect
212. C2×C4×Q8C2×C4semidirect
219. C2×C4×D4C2×C4semidirect
220. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#627812
#602772
#341952
#176242
#176232
#176222
#176212
#176202
#175942
#175932
#175802
#175792
#175672
C2×#15212