Finite Group Databasebeta

← #6343505

Subgroups — #6343505

Order 512.

2935 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C211yesmaximal, characteristic
2#60282C211yesmaximal, characteristic, complemented
3#34121C211yesmaximal, characteristic, complemented
4#17625C214yesmaximal, complemented
5#17624C214yesmaximal, complemented
6#17621C212yesmaximal, complemented
7#17620C212yesmaximal, complemented
8#17615C214yesmaximal, complemented
9#17586C212yesmaximal, complemented
10#17581C212yesmaximal, complemented
11#17580C212yesmaximal, complemented
12#17543C212yesmaximal, complemented
13#17537C212yesmaximal, complemented
14C2×#1509C212yesmaximal, 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#2990—24no—
39#2983C2212yescomplemented
40#2973C2212yes—
41#2973C2212yescomplemented
42#2972C2212yescomplemented
43#2970—24no—
44#2920C2212yescomplemented
45C2×#432C2212yescomplemented
46C2×#432C2212yescomplemented
47#2357C2212yescomplemented
48#2356C2212yescomplemented
49#2355—21no—
50#2354—21no—
51#2353C2212yes—
52#2353C2212yescomplemented
53#2352—21no—
54#2352—21no—
55#2298—21no—
56#2298—21no—
57#2297—21no—
58#2285C2211yescharacteristic, complemented
59#2283C2211yescharacteristic, complemented
60#2283C2211yescharacteristic, complemented
61C4×#117—21no—
62C4×#117C2211yescharacteristic, complemented
63C4×#117C2211yescharacteristic, complemented
64C2×C4×C4⋊C4C2211yescharacteristic, complemented
65#1521C2218yescomplemented
66#1520C2214yescomplemented
67#1519C2214yes—
68#1516C2218yescomplemented
69#1515C2214yescomplemented
70#1514C2214yes—
71#1512C2218yescomplemented
72#1511C2214yescomplemented
73#1510C2214yes—
74#1509C2214yescomplemented
75#1509C2214yescomplemented
76#1509C2218yescomplemented
77#1509C2214yescomplemented
78#1509C2214yescomplemented
79#1508C2214yescomplemented
80#1507C2214yes—
81#1506C2214yescomplemented
82#1505C2214yes—
83#1501C2218yescomplemented
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×C414yes—
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×C414yes—
118#548C2×C414yes—
119#548C2×C414yescomplemented
120#547—24no—
121#547—24no—
122#547C2×C414yes—
123#546—24no—
124#546—24no—
125#546—24no—
126#546C2×C414yes—
127#546C2×C414yescomplemented
128D42C2×C414yes—
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×C414yes—
173#529C2×C414yes—
174#529C2×C414yescomplemented
175#529C2×C414yescomplemented
176#529C2×C414yescomplemented
177#529C2314yes—
178#529C2314yes—
179#529C2314yes—
180C2×#126—22no—
181C2×#126—22no—
182C2×#125C2×C412yes—
183C2×#125C2×C412yescomplemented
184C2×#124C2×C412yes—
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×C412yes—
212C2×C4×Q8C2×C412yescomplemented
213C2×C4×Q8D411yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×D4—22no—
216C2×C4×D4—22no—
217C2×C4×D4—24no—
218C2×C4×D4C2×C412yes—
219C2×C4×D4C2×C412yescomplemented
220C2×C4×D4D411yescharacteristic
221C2×C4×D4D411yescharacteristic
222C2×C4×D4D411yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227C2×#117—21no—
228C2×#117—21no—
229C2×#117—22no—
230C2×#117—22no—
231C2×#117D411yescharacteristic
232C2×#117D411yescharacteristic
233C2×#117D411yescharacteristic
234C22×C4⋊C4—21no—
235C22×C42—21no—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239#446—28no—
240#435—28no—
241#435—28no—
242C8×D4—28no—
243#432—22no—
244#432—22no—
245#432—22no—
246#432—22no—
247#432—22no—
248#432C2314yes—
249#432C2314yes—
250#432C2314yes—
251#431—22no—
252#431C2314yes—
253#423—22no—
254C2×C4⋊C8—22no—
255C2×C4⋊C8—22no—
256#407C2314yes—
257C2×C22⋊C8C2314yes—
258C2×C22⋊C8C2314yes—
259C4×M16—22no—
260C2×#97—22no—
261C2×#97—22no—
262#391—22no—
263#390—22no—
264#388—22no—
265#388—22no—
266#388—22no—
267#388—22no—
268#387—22no—
269#387—22no—
270#387—22no—
271#387—22no—
272#386—22no—
273#386—22no—
274#384—21no—
275#383C2312yes—
276#383C2312yes—
277#382—21no—
278#382—21no—
279#382C2312yes—
280#381C2312yes—
281#381C2312yes—
282#380—21no—
283#380—21no—
284#380—21no—
285#380C2312yes—
286C4×C4⋊C4—22no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C22⋊C4—21no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4C2312yes—
305C4×C22⋊C4C2312yes—
306#376—21no—
307#376—21no—
308#376C2312yes—
309#376C2312yes—
310C2×#95C2312yes—
311C43—21no—
312C43—21no—
313#328C2318yes—
314#328C2318yes—
315#328C2318yes—
316#328C2318yes—
317#327C2318yes—
318#327C2318yes—
319#327C2318yes—
320#327C2318yes—
321H(5,𝔽2)—44no—
322H(5,𝔽2)—44no—
323C2×#41—24no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—42no—
327C2×#41—42no—
328C2×#41C22⋊C414yes—
329C2×#41C22⋊C414yes—
330C2×#41C22×C414yes—
331C22×Q8C22×C412yes—
332C22×Q8C22×C412yes—
333C22×Q8C2×D411yescharacteristic
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4C22×C412yes—
338C22×D4C22×C412yes—
339C22×D4C2×D411yescharacteristic
340C22×D4C2×D411yescharacteristic
341C22×D4C2×D411yescharacteristic
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2411yescharacteristic
352C23×C4C2411yescharacteristic
353C23×C4C2411yescharacteristic
354C2×M16—24no—
355C22×C8—24no—
356C22×C8—24no—
357C4⋊Q8—24no—
358C4⋊Q8—24no—
359C4⋊Q8C22×C412yes—
360C4⋊Q8C22×C412yes—
361C4⋊Q8C22×C412yes—
362#127C22×C412yes—
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#126—24no—
377#125—24no—
378#125—24no—
379#125—24no—
380#125—24no—
381#125—24no—
382#125—22no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125C22×C414yes—
389#125C22×C414yes—
390#125C22×C414yes—
391#124—24no—
392#124—24no—
393#124—24no—
394#124—22no—
395#124—22no—
396#124—22no—
397#124—22no—
398#124—22no—
399#124—22no—
400#124C22×C414yes—
401#124C22×C414yes—
402#124C22×C414yes—
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—
421#123—24no—
422C22⋊Q8—24no—
423C22⋊Q8—24no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
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⋊Q8—24no—
441C22⋊Q8C22×C414yes—
442C22⋊Q8C22×C414yes—
443C22⋊Q8C22×C414yes—
444C22⋊Q8C2414yes—
445#121—24no—
446#121—24no—
447#121—24no—
448#121—24no—
449#121—22no—
450#121—22no—
451#121—22no—
452#121—22no—
453#121—22no—
454#121—22no—
455#121—22no—
456#121—22no—
457#121—24no—
458#121—24no—
459#121—24no—
460#121C22×C414yes—
461#121C22×C414yes—
462#121C22×C414yes—
463#121C2414yes—
464#120—24no—
465#120—24no—
466#120—24no—
467#120—24no—
468#120—24no—
469C4×Q8—24no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8C22⋊C414yes—
479C4×Q8C22⋊C414yes—
480C4×Q8C22×C414yes—
481C4×Q8C22×C414yes—
482C4×Q8C22×C414yes—
483C4×Q8C22×C414yes—
484C4×Q8C22×C414yes—
485C4×Q8C2×D414yes—
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—24no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
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#117—44no—
544#117—44no—
545#117—44no—
546#117C22⋊C414yes—
547#117C22⋊C414yes—
548#117C22⋊C414yes—
549#117C22⋊C414yes—
550#117C22⋊C414yes—
551#117C22⋊C414yes—
552#117C22×C414yes—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—44no—
570C2×C4⋊C4C22×C412yes—
571C2×C4⋊C4C22×C412yes—
572C2×C4⋊C4C22×C412yes—
573C2×C4⋊C4C22×C412yes—
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4C2×D411yescharacteristic
598C2×C22⋊C4C2×D411yescharacteristic
599C2×C22⋊C4C2×D411yescharacteristic
600C2×C22⋊C4C2×D411yescharacteristic
601C2×C22⋊C4C2×D411yescharacteristic
602C2×C22⋊C4C2×D411yescharacteristic
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—24no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—44no—
616C2×C42C22×C412yes—
617C2×C42C22×C412yes—
618C2×C42C22×C412yes—
619C2×C42C22×C412yes—
620C2×C42C22×C412yes—
621C2×C42C22×C412yes—
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D412yes—
629C2×C42C2×D412yes—
630C2×C42C2×D412yes—
631C2×C42C2×D412yes—
632C2×C42C2×D412yes—
633C2×C42C2×D412yes—
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C4⋊C8—24no—
639C4⋊C8—24no—
640C4⋊C8—24no—
641C4⋊C8—24no—
642C22⋊C8—24no—
643C22⋊C8—24no—
644C22⋊C8—24no—
645C22⋊C8C2418yes—
646#97—24no—
647#97—24no—
648#97—24no—
649C4×C8—24no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95C2412yes—
661#95C2412yes—
662#95C2412yes—
663#95C2412yes—
664C24—22no—
665C24—22no—
666C24C22×D411yescharacteristic
667C24C22×D411yescharacteristic
668C24C22×D411yescharacteristic
669#41—48no—
670#41—48no—
671#41—44no—
672#41—44no—
673#41—416no—
674#41—84no—
675#41—84no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—41no—
681C2×Q8—41no—
682C2×Q8—82no—
683C2×Q8—82no—
684C2×Q8C2×C22⋊C414yes—
685C2×Q8C23×C414yes—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—416no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—82no—
707C2×D4—82no—
708C2×D4C2×C22⋊C414yes—
709C2×D4C2×C22⋊C414yes—
710C2×D4C2×C22⋊C414yes—
711C2×D4C23×C414yes—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—41no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—84no—
739C22×C4—84no—
740C22×C4—81no—
741C22×C4—81no—
742C22×C4—81no—
743C22×C4—82no—
744C22×C4C2×C22⋊C412yes—
745C22×C4C2×C22⋊C412yes—
746C22×C4C2×C22⋊C412yes—
747C22×C4C2×C22⋊C412yes—
748C22×C4C2×C22⋊C412yes—
749C22×C4C2×C22⋊C412yes—
750C22×C4C2×C22⋊C412yes—
751C22×C4C2×C22⋊C412yes—
752C22×C4C2×C22⋊C412yes—
753C22×C4C2×C22⋊C412yes—
754C22×C4C2×C22⋊C412yes—
755C22×C4C2×C22⋊C412yes—
756C22×C4C23×C412yes—
757C22×C4C23×C412yes—
758C22×C4C23×C412yes—
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D412yes—
771C22×C4C22×D412yes—
772C22×C4C22×D412yes—
773C22×C4C2511yescharacteristic
774M16—84no—
775C2×C8—28no—
776C2×C8—84no—
777C2×C8—84no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—22no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—24no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—42no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—42no—
805C4⋊C4—42no—
806C4⋊C4—82no—
807C4⋊C4C2×C22⋊C414yes—
808C4⋊C4C2×C22⋊C414yes—
809C4⋊C4C2×C22⋊C414yes—
810C4⋊C4C2×C22⋊C414yes—
811C4⋊C4C2×C22⋊C414yes—
812C4⋊C4C2×C22⋊C414yes—
813C4⋊C4C23×C414yes—
814C4⋊C4C23×C414yes—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—24no—
829C22⋊C4—24no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—82no—
838C22⋊C4—82no—
839C22⋊C4C2×C22⋊C414yes—
840C22⋊C4C2×C22⋊C414yes—
841C22⋊C4C2×C22⋊C414yes—
842C22⋊C4C2×C22⋊C414yes—
843C22⋊C4C2×C22⋊C414yes—
844C22⋊C4C2×C22⋊C414yes—
845C42—24no—
846C42—24no—
847C42—24no—
848C42—24no—
849C42—24no—
850C42—42no—
851C42—42no—
852C42—44no—
853C42—42no—
854C42—42no—
855C42—44no—
856C42—44no—
857C42—82no—
858C42—82no—
859C42C2×C22⋊C412yes—
860C42C2×C22⋊C412yes—
861C42C2×C22⋊C412yes—
862C42C2×C22⋊C412yes—
863C42C2×C22⋊C412yes—
864C42C2×C22⋊C412yes—
865C42C2×C22⋊C412yes—
866C42C2×C22⋊C412yes—
867C42C2×C22⋊C412yes—
868C42C2×C22⋊C412yes—
869C42C2×C22⋊C412yes—
870C42C2×C22⋊C412yes—
871C42C23×C411yescharacteristic
872C42C23×C411yescharacteristic
873C42C23×C412yes—
874C42C23×C412yes—
875C42C23×C412yes—
876C42C22×D412yes—
877C42C22×D411yescharacteristic
878C42C22×D412yes—
879C42C22×D412yes—
880C42C22×D411yescharacteristic
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—24no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—44no—
893C23—44no—
894C23—82no—
895C23—82no—
896C23—82no—
897C23—82no—
898C23C22×C22⋊C412yes—
899C23C22×C22⋊C412yes—
900C23C22×C22⋊C412yes—
901C23#57512yes—
902C23#57512yes—
903C23C23×D411yescharacteristic
904Q8—44no—
905Q8—44no—
906Q8—44no—
907Q8—82no—
908Q8—82no—
909Q8—82no—
910D4—28no—
911D4—28no—
912D4—44no—
913D4—44no—
914D4—44no—
915D4—48no—
916D4—48no—
917D4—44no—
918D4—44no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—84no—
923D4—84no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—48no—
963C2×C4—42no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—42no—
967C2×C4—48no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—84no—
978C2×C4—84no—
979C2×C4—84no—
980C2×C4—82no—
981C2×C4—82no—
982C2×C4—82no—
983C2×C4—82no—
984C2×C4—88no—
985C2×C4C22×C22⋊C412yes—
986C2×C4C22×C22⋊C412yes—
987C2×C4C22×C22⋊C412yes—
988C2×C4C22×C22⋊C412yes—
989C2×C4C22×C22⋊C411yescharacteristic
990C2×C4C22×C22⋊C411yescharacteristic
991C2×C4C22×C22⋊C411yescharacteristic
992C2×C4C22×C22⋊C412yes—
993C2×C4C22×C22⋊C412yes—
994C2×C4C22×C22⋊C412yes—
995C2×C4C22×C22⋊C412yes—
996C2×C4C22×C22⋊C412yes—
997C2×C4C22×C22⋊C411yescharacteristic
998C2×C4C24×C411yescharacteristic
999C2×C4C23×D411yescharacteristic
1000C8—48no—
1001C22—21no—
1002C22—22no—
1003C22—21no—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—42no—
1012C22—42no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—81no—
1017C22—81no—
1018C22—81no—
1019C22—81no—
1020C22—164no—
1021C22—164no—
1022C22#289614yes—
1023C22C23×C22⋊C411yescharacteristic
1024C22C2×#57511yescharacteristic
1025C22C2×#57511yescharacteristic
1026C4—21no—
1027C4—21no—
1028C4—22no—
1029C4—22no—
1030C4—22no—
1031C4—21no—
1032C4—21no—
1033C4—22no—
1034C4—22no—
1035C4—22no—
1036C4—21no—
1037C4—22no—
1038C4—22no—
1039C4—22no—
1040C4—44no—
1041C4—44no—
1042C4—44no—
1043C4—44no—
1044C4—82no—
1045C4—82no—
1046C4—82no—
1047C4#290112yes—
1048C2—21no—
1049C2—21no—
1050C2—24no—
1051C2—42no—
1052C2—42no—
1053C2—84no—
1054C2#6007011yescharacteristic
1055C2C2×#289611yescharacteristic
1056C2C2×#290111yescharacteristic
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. #60282C2semidirect
3. #34121C2semidirect
4. #17625C2semidirect
5. #17624C2semidirect
6. #17621C2semidirect
7. #17620C2semidirect
8. #17615C2semidirect
9. #17586C2semidirect
10. #17581C2semidirect
11. #17580C2semidirect
12. #17543C2semidirect
13. #17537C2semidirect
14. C2×#1509C2semidirect
16. #3515C4semidirect
17. #3514C4semidirect
27. #3482C4semidirect
28. #3481C4semidirect
39. #2983C22semidirect
41. #2973C22semidirect
42. #2972C22semidirect
44. #2920C22semidirect
45. C2×#432C22semidirect
46. C2×#432C22semidirect
47. #2357C22semidirect
48. #2356C22semidirect
52. #2353C22semidirect
58. #2285C22semidirect
59. #2283C22semidirect
60. #2283C22semidirect
62. C4×#117C22semidirect
63. C4×#117C22semidirect
64. C2×C4×C4⋊C4C22semidirect
65. #1521C22semidirect
66. #1520C22semidirect
68. #1516C22semidirect
69. #1515C22semidirect
71. #1512C22semidirect
72. #1511C22semidirect
74. #1509C22semidirect
75. #1509C22semidirect
76. #1509C22semidirect
77. #1509C22semidirect
78. #1509C22semidirect
79. #1508C22semidirect
81. #1506C22semidirect
83. #1501C22semidirect
84. #1500C22semidirect
85. C2×#328C22semidirect
89. #559C2×C4semidirect
90. #557C2×C4semidirect
93. #556C2×C4semidirect
97. #554C2×C4semidirect
102. #553C2×C4semidirect
110. #552C2×C4semidirect
119. #548C2×C4semidirect
127. #546C2×C4semidirect
151. #533C2×C4semidirect
152. #533C2×C4semidirect
154. #532C2×C4semidirect
155. #532C2×C4semidirect
174. #529C2×C4semidirect
175. #529C2×C4semidirect
176. #529C2×C4semidirect
183. C2×#125C2×C4semidirect
185. C2×#124C2×C4semidirect
208. C4×#41C2×C4semidirect
212. C2×C4×Q8C2×C4semidirect
219. 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
#602822
#341212
#176252
#176242
#176212
#176202
#176152
#175862
#175812
#175802
#175432
#175372
C2×#15092