Finite Group Databasebeta

← #6393515

Subgroups — #6393515

Order 512.

3586 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62773C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3C2×#2290C211yesmaximal, characteristic, complemented
4#22506C218yesmaximal, complemented
5#22434C218yesmaximal, complemented
6#21899C212yesmaximal, complemented
7#21773C212yesmaximal, complemented
8#21773C212yesmaximal, complemented
9#21417C212yesmaximal, complemented
10#20979C212yesmaximal, complemented
11C2×#1896C212yesmaximal, complemented
12#3520C414yescomplemented
13#3519C414yescomplemented
14#3513—24no—
15#3506C412yescomplemented
16#3505C412yescomplemented
17#3505C412yescomplemented
18#3501C411yescharacteristic, complemented
19#3496C411yescharacteristic, complemented
20#3492—21no—
21#3490—21no—
22#3490—21no—
23#3484—21no—
24#3481—24no—
25#3475C2214yes—
26D4×#41C2214yes—
27#3460—21no—
28#3459—21no—
29#3459—21no—
30#3444C2212yes—
31C2×#525C2212yes—
32C2×#525C2212yes—
33C4×H(5,𝔽2)—21no—
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic, complemented
36C23×C42C2211yescharacteristic, complemented
37#2975—21no—
38#2974—24no—
39#2973—21no—
40#2973—21no—
41#2972—21no—
42D4×M16C2218yescomplemented
43#2920C2212yescomplemented
44C2×#421C2214yescomplemented
45C22×#104C2214yescomplemented
46C2×#407C2212yescomplemented
47C2×#407C2212yescomplemented
48#2290—24no—
49#2290C2218yescomplemented
50C2×#388—21no—
51C2×#387—21no—
52C2×#386—21no—
53C2×#385—21no—
54C2×C4×C4⋊C4C2211yescharacteristic, complemented
55C2×C4×C22⋊C4C2211yescharacteristic, complemented
56C2×C4×C22⋊C4C2211yescharacteristic, complemented
57C2×#376C2211yescharacteristic, complemented
58#1995C2214yescomplemented
59#1986C2214yescomplemented
60#1980C2214yescomplemented
61#1963C2214yescomplemented
62#1897C2218yescomplemented
63#1896C2214yescomplemented
64#1896C2214yescomplemented
65#1896C2214yescomplemented
66#1896C2218yescomplemented
67#1896C2214yescomplemented
68#1871C2218yescomplemented
69#1871C2218yescomplemented
70#1826C2214yescomplemented
71#1826C2214yescomplemented
72#1806C2218yescomplemented
73#1789C2214yescomplemented
74#1789C2214yescomplemented
75#1759C2218yescomplemented
76#1733C2214yescomplemented
77C2×#339C2214yescomplemented
78C2×H(5,𝔽2)—21no—
79C22×#41C2312yes—
80C22×#41C2312yes—
81C23×D4D411yescharacteristic
82C24×C4—21no—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×M16C2314yes—
86C22×M16C2314yes—
87#559—24no—
88#556C2×C414yescomplemented
89#555C2×C414yescomplemented
90#554—24no—
91#554—24no—
92#554C2×C414yescomplemented
93#553—24no—
94#553—24no—
95#553—24no—
96#553—24no—
97#553C2×C414yescomplemented
98#553C2×C414yescomplemented
99#552—24no—
100#552C2×C414yescomplemented
101#552C2×C414yescomplemented
102#551—24no—
103#551—24no—
104#551—24no—
105#551—24no—
106#551—24no—
107#551—24no—
108#550C2×C414yescomplemented
109D4×Q8C2×C414yescomplemented
110#548C2×C414yescomplemented
111#548C2×C414yescomplemented
112#547—24no—
113#547C2×C414yescomplemented
114#547C2×C414yescomplemented
115#546—24no—
116#546—24no—
117#546—24no—
118#546—24no—
119#546—24no—
120#546—24no—
121#546—24no—
122#546C2×C414yescomplemented
123#546C2×C414yescomplemented
124D42—24no—
125D42—24no—
126D42C2×C414yescomplemented
127#544—21no—
128#543—21no—
129#543—21no—
130#542—24no—
131#540—24no—
132#539—24no—
133#539—24no—
134#539—22no—
135#539—22no—
136#538—24no—
137#538—24no—
138#538—22no—
139#538—22no—
140#538—22no—
141#538—22no—
142#537—21no—
143#535—22no—
144#534—22no—
145#534—22no—
146#534—21no—
147#534—21no—
148#533C2×C412yescomplemented
149#533C2×C412yescomplemented
150#533C2312yes—
151#532—24no—
152#532C2×C412yescomplemented
153#532C2×C412yescomplemented
154#532C2312yes—
155#529—24no—
156#529—24no—
157#529—24no—
158#529—22no—
159#529—22no—
160#529—22no—
161#529—22no—
162#529C2×C414yescomplemented
163#529C2×C414yescomplemented
164#525—22no—
165#525—22no—
166#525—22no—
167#525—22no—
168#525—22no—
169#525—22no—
170#525—22no—
171#525—22no—
172#525—22no—
173#525—22no—
174#525—24no—
175#525—24no—
176#525C2×C414yes—
177#525C2×C414yes—
178#525C2×C414yescomplemented
179#525C2×C414yescomplemented
180#525C2314yes—
181#525C2314yes—
182#525C2314yes—
183C2×#123—22no—
184C2×#123—22no—
185C2×C22⋊Q8C2×C412yes—
186C2×C22⋊Q8C2×C412yes—
187C2×C22⋊Q8C2×C412yescomplemented
188C2×C22⋊Q8C2×C412yescomplemented
189C2×#121C2×C412yes—
190C2×#121C2×C412yes—
191C2×#121C2×C412yescomplemented
192C2×#121C2×C412yescomplemented
193C2×#120—22no—
194C2×#120—22no—
195#520—24no—
196#520—22no—
197#518—21no—
198#518—24no—
199#518—22no—
200#518—22no—
201C4×#41—24no—
202C4×#41—22no—
203C4×#41—22no—
204C4×#41C2314yes—
205C2×C4×D4—22no—
206C2×C4×D4—22no—
207C2×C4×D4—22no—
208C2×C4×D4—22no—
209C2×C4×D4—24no—
210C2×C4×D4C2×C411yescharacteristic
211C2×C4×D4C2×C411yescharacteristic
212C2×C4×D4C2×C411yescharacteristic
213C2×C4×D4C2×C411yescharacteristic
214C2×C4×D4C2×C414yes—
215C2×C4×D4D411yescharacteristic
216C2×C4×D4D411yescharacteristic
217C2×C4×D4D411yescharacteristic
218C2×C4×D4D411yescharacteristic
219C2×C4×D4D414yes—
220C2×C4×D4D414yes—
221C2×C4×D4C2314yes—
222C2×#117—22no—
223C2×#117—44no—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2314yes—
227C22×C4⋊C4—21no—
228C22×C4⋊C4—21no—
229C22×C4⋊C4D411yescharacteristic
230C22×C22⋊C4—21no—
231C22×C22⋊C4—21no—
232C22×C22⋊C4—21no—
233C22×C22⋊C4D411yescharacteristic
234C22×C22⋊C4D411yescharacteristic
235C22×C42—21no—
236C22×C42—22no—
237C22×C42—44no—
238C22×C42C2311yescharacteristic
239C22×C42C2314yes—
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244#436—28no—
245#435—28no—
246#435—28no—
247C8×D4—28no—
248#432—22no—
249#432—22no—
250#431—22no—
251#431—22no—
252#423C2314yes—
253#421—48no—
254C2×#104—48no—
255C2×#104C2318yes—
256C2×#104C2318yes—
257C2×#104C2318yes—
258C2×#104C2318yes—
259#407—22no—
260#407—22no—
261#407—22no—
262#407—22no—
263#407C2314yes—
264#407C2314yes—
265#407C2314yes—
266C2×C22⋊C8—22no—
267C2×C22⋊C8—22no—
268C2×C22⋊C8—22no—
269C2×C22⋊C8—22no—
270C4×M16C2314yes—
271#388—28no—
272#387—28no—
273#386—28no—
274#385—28no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4C2314yes—
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4C2314yes—
280C4×C22⋊C4C2314yes—
281#376—22no—
282#376C2314yes—
283C2×#95—21no—
284C2×#95—21no—
285C2×#95—21no—
286C2×#95—21no—
287C2×#95—21no—
288#339C2318yes—
289#339C2318yes—
290#339C2318yes—
291#339C2318yes—
292C25C2×D411yescharacteristic
293C25C2×D411yescharacteristic
294H(5,𝔽2)—48no—
295C2×#41—24no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—44no—
303C2×#41—44no—
304C2×#41—44no—
305C2×#41—44no—
306C2×#41C22×C414yes—
307C2×#41C22×C414yescomplemented
308C2×#41C2414yes—
309C22×Q8C22×C412yes—
310C22×Q8C22×C412yescomplemented
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—44no—
319C22×D4C22⋊C411yescharacteristic
320C22×D4C22⋊C411yescharacteristic
321C22×D4C22⋊C411yescharacteristic
322C22×D4C22⋊C411yescharacteristic
323C22×D4C22⋊C414yes—
324C22×D4C22×C412yes—
325C22×D4C22×C412yescomplemented
326C22×D4C2×D414yes—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—24no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4—42no—
337C23×C4—42no—
338C23×C4—44no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4C22×C411yescharacteristic
342C23×C4C22×C412yes—
343C23×C4C22×C411yescharacteristic
344C23×C4C22×C412yes—
345C23×C4C22×C411yescharacteristic
346C23×C4C22×C411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D412yes—
352C23×C4C2×D412yes—
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D412yes—
356C23×C4C2×D412yes—
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362C2×M16—24no—
363C2×M16—24no—
364C2×M16—44no—
365C2×M16—44no—
366C2×M16—44no—
367C2×M16—44no—
368C2×M16C2418yes—
369C22×C8—24no—
370C22×C8—24no—
371C4⋊Q8—24no—
372C4⋊Q8C22×C412yescomplemented
373C4⋊Q8C22×C412yescomplemented
374C4⋊Q8C22×C412yescomplemented
375#127—24no—
376#127C22×C412yescomplemented
377#126—24no—
378#126—24no—
379#126—24no—
380#126—24no—
381#126—24no—
382#126—24no—
383#126—24no—
384#126—24no—
385#125—24no—
386#125—24no—
387#125—24no—
388#125—22no—
389#125—22no—
390#125C22×C414yescomplemented
391#124—24no—
392#124—24no—
393#124—24no—
394#124—24no—
395#124—24no—
396#124—22no—
397#124—22no—
398#124C22×C414yescomplemented
399#123—24no—
400#123—24no—
401#123—24no—
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—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—24no—
431C22⋊Q8—24no—
432C22⋊Q8—24no—
433C22⋊Q8—24no—
434C22⋊Q8—24no—
435C22⋊Q8—24no—
436C22⋊Q8—24no—
437C22⋊Q8C22×C414yes—
438C22⋊Q8C22×C414yes—
439C22⋊Q8C22×C414yes—
440C22⋊Q8C22×C414yes—
441C22⋊Q8C22×C414yescomplemented
442C22⋊Q8C22×C414yescomplemented
443#121—24no—
444#121—24no—
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—22no—
458#121—22no—
459#121—22no—
460#121—22no—
461#121—24no—
462#121—24no—
463#121—24no—
464#121—24no—
465#121—24no—
466#121C22×C414yes—
467#121C22×C414yes—
468#121C22×C414yes—
469#121C22×C414yes—
470#121C22×C414yescomplemented
471#121C22×C414yescomplemented
472#120—24no—
473#120—24no—
474#120—24no—
475#120—24no—
476#120—24no—
477#120—24no—
478#120—24no—
479#120—24no—
480#120—24no—
481#120—24no—
482#120—24no—
483C4×Q8—24no—
484C4×Q8—22no—
485C4×Q8—22no—
486C4×Q8—22no—
487C4×Q8—22no—
488C4×Q8C22×C414yescomplemented
489C4×Q8C22×C414yescomplemented
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—24no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—24no—
512C4×D4—24no—
513C4×D4—24no—
514C4×D4—24no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4C22⋊C414yes—
520C4×D4C22⋊C414yes—
521C4×D4C22⋊C414yes—
522C4×D4C22⋊C414yes—
523C4×D4C22⋊C414yes—
524C4×D4C22⋊C414yes—
525C4×D4C22⋊C414yes—
526C4×D4C22⋊C414yes—
527C4×D4C22×C414yes—
528C4×D4C22×C414yes—
529C4×D4C22×C414yes—
530C4×D4C22×C414yes—
531C4×D4C22×C414yescomplemented
532C4×D4C22×C414yescomplemented
533C4×D4C2×D414yes—
534C4×D4C2×D414yes—
535C4×D4C2×D414yes—
536C4×D4C2×D414yes—
537#117—22no—
538#117—22no—
539#117—22no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—24no—
544#117—24no—
545#117—24no—
546#117—24no—
547#117—24no—
548#117—24no—
549#117—28no—
550#117—44no—
551#117—48no—
552#117C22×C414yes—
553#117C22×C414yescomplemented
554#117C2414yes—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—44no—
563C2×C4⋊C4—44no—
564C2×C4⋊C4C22⋊C411yescharacteristic
565C2×C4⋊C4C22⋊C411yescharacteristic
566C2×C4⋊C4C22⋊C411yescharacteristic
567C2×C4⋊C4C22⋊C411yescharacteristic
568C2×C4⋊C4C22⋊C414yes—
569C2×C4⋊C4C22×C412yes—
570C2×C4⋊C4C22×C412yes—
571C2×C4⋊C4C22×C412yescomplemented
572C2×C4⋊C4C22×C412yescomplemented
573C2×C4⋊C4C2×D414yes—
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—22no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—44no—
590C2×C22⋊C4—44no—
591C2×C22⋊C4—44no—
592C2×C22⋊C4C22⋊C411yescharacteristic
593C2×C22⋊C4C22⋊C411yescharacteristic
594C2×C22⋊C4C22⋊C411yescharacteristic
595C2×C22⋊C4C22⋊C411yescharacteristic
596C2×C22⋊C4C22⋊C411yescharacteristic
597C2×C22⋊C4C22⋊C411yescharacteristic
598C2×C22⋊C4C22⋊C411yescharacteristic
599C2×C22⋊C4C22⋊C411yescharacteristic
600C2×C22⋊C4C22⋊C414yes—
601C2×C22⋊C4C22⋊C414yes—
602C2×C22⋊C4C2×D414yes—
603C2×C22⋊C4C2×D414yes—
604C2×C42—21no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—24no—
608C2×C42—24no—
609C2×C42—28no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—24no—
614C2×C42—42no—
615C2×C42—44no—
616C2×C42—42no—
617C2×C42—42no—
618C2×C42—48no—
619C2×C42—44no—
620C2×C42C22×C411yescharacteristic
621C2×C42C22×C412yes—
622C2×C42C22×C411yescharacteristic
623C2×C42C2×D412yes—
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D412yes—
626C2×C42C2×D411yescharacteristic
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C4⋊C8—24no—
633C4⋊C8—24no—
634#104—216no—
635#104—48no—
636#104—48no—
637#104—48no—
638C22⋊C8—24no—
639C22⋊C8—24no—
640C22⋊C8—24no—
641C22⋊C8—24no—
642C22⋊C8—24no—
643C22⋊C8—24no—
644#97—24no—
645C4×C8—24no—
646#95—24no—
647#95—24no—
648#95—24no—
649#95—24no—
650#95—24no—
651C24—24no—
652C24—22no—
653C24—22no—
654C24—41no—
655C24—42no—
656C24—41no—
657C24—41no—
658C24—42no—
659C24—41no—
660C24—42no—
661C24C2×C22⋊C412yes—
662C24C2×C22⋊C411yescharacteristic
663C24C2×C22⋊C412yes—
664C24C2×C22⋊C411yescharacteristic
665C24C2×C22⋊C411yescharacteristic
666C24C2×C22⋊C411yescharacteristic
667C24C22×D411yescharacteristic
668C24C22×D412yes—
669C24C22×D412yes—
670#41—28no—
671#41—28no—
672#41—48no—
673#41—48no—
674#41—48no—
675#41—416no—
676#41—84no—
677#41—84no—
678#41—84no—
679#41—82no—
680#41—82no—
681#41—82no—
682#41—82no—
683C2×Q8—22no—
684C2×Q8—22no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8C23×C414yes—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—416no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—84no—
715C2×D4—84no—
716C2×D4—82no—
717C2×D4—82no—
718C2×D4—82no—
719C2×D4—82no—
720C2×D4C2×C22⋊C414yes—
721C2×D4C2×C22⋊C414yes—
722C2×D4C2×C22⋊C414yes—
723C2×D4C2×C22⋊C414yes—
724C2×D4C23×C414yes—
725C22×C4—22no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—22no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—44no—
756C22×C4—42no—
757C22×C4—44no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—42no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—48no—
777C22×C4—432no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—84no—
785C22×C4—84no—
786C22×C4C2×C22⋊C412yes—
787C22×C4C2×C22⋊C411yescharacteristic
788C22×C4C2×C22⋊C411yescharacteristic
789C22×C4C2×C22⋊C411yescharacteristic
790C22×C4C2×C22⋊C411yescharacteristic
791C22×C4C2×C22⋊C412yes—
792C22×C4C2×C22⋊C412yes—
793C22×C4C2×C22⋊C412yes—
794C22×C4C2×C22⋊C412yes—
795C22×C4C2×C22⋊C412yes—
796C22×C4C2×C22⋊C411yescharacteristic
797C22×C4C2×C22⋊C411yescharacteristic
798C22×C4C2×C22⋊C412yes—
799C22×C4C2×C22⋊C412yes—
800C22×C4C2×C22⋊C411yescharacteristic
801C22×C4C2×C22⋊C411yescharacteristic
802C22×C4C2×C22⋊C412yes—
803C22×C4C2×C22⋊C412yes—
804C22×C4C2×C22⋊C412yes—
805C22×C4C2×C22⋊C412yes—
806C22×C4C23×C411yescharacteristic
807C22×C4C23×C411yescharacteristic
808C22×C4C23×C412yes—
809C22×C4C23×C412yes—
810C22×C4C23×C412yes—
811C22×C4C23×C412yes—
812C22×C4C22×D412yes—
813C22×C4C22×D412yes—
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D412yes—
818C22×C4C22×D412yes—
819C22×C4C22×D412yes—
820C22×C4C22×D412yes—
821C22×C4C22×D412yes—
822C22×C4C22×D412yes—
823C22×C4C2511yescharacteristic
824M16—28no—
825M16—28no—
826M16—84no—
827M16—84no—
828C2×C8—28no—
829C2×C8—84no—
830C2×C8—84no—
831C4⋊C4—22no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4C2×C22⋊C414yes—
852C4⋊C4C2×C22⋊C414yes—
853C4⋊C4C2×C22⋊C414yes—
854C4⋊C4C2×C22⋊C414yes—
855C4⋊C4C23×C414yes—
856C4⋊C4C23×C414yes—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4C2×C22⋊C414yes—
880C22⋊C4C2×C22⋊C414yes—
881C22⋊C4C2×C22⋊C414yes—
882C22⋊C4C2×C22⋊C414yes—
883C22⋊C4C2×C22⋊C414yes—
884C22⋊C4C2×C22⋊C414yes—
885C22⋊C4C2×C22⋊C414yes—
886C22⋊C4C2×C22⋊C414yes—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—22no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—48no—
898C42—42no—
899C42—42no—
900C42—42no—
901C42C2×C22⋊C412yes—
902C42C2×C22⋊C412yes—
903C42C2×C22⋊C412yes—
904C42C2×C22⋊C412yes—
905C42C23×C412yes—
906C42C23×C412yes—
907C42C22×D412yes—
908C42C22×D412yes—
909C42H(5,𝔽2)14yescomplemented
910C23—22no—
911C23—22no—
912C23—21no—
913C23—21no—
914C23—24no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—24no—
923C23—22no—
924C23—22no—
925C23—24no—
926C23—41no—
927C23—42no—
928C23—41no—
929C23—42no—
930C23—41no—
931C23—41no—
932C23—42no—
933C23—41no—
934C23—42no—
935C23—41no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—48no—
941C23—48no—
942C23—44no—
943C23—44no—
944C23—82no—
945C23—82no—
946C23—82no—
947C23—82no—
948C23—84no—
949C23—84no—
950C23#42114yescomplemented
951C23C22×C22⋊C412yes—
952C23C22×C22⋊C412yes—
953C23C22×C22⋊C412yes—
954C23C22×C22⋊C411yescharacteristic
955C23C22×C22⋊C412yes—
956C23C22×C22⋊C411yescharacteristic
957C23C23×D411yescharacteristic
958Q8—28no—
959Q8—44no—
960Q8—82no—
961Q8—82no—
962Q8—82no—
963D4—28no—
964D4—28no—
965D4—28no—
966D4—44no—
967D4—44no—
968D4—44no—
969D4—48no—
970D4—48no—
971D4—48no—
972D4—48no—
973D4—44no—
974D4—44no—
975D4—82no—
976D4—82no—
977D4—82no—
978D4—84no—
979D4—84no—
980D4—84no—
981D4—84no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—48no—
1028C2×C4—48no—
1029C2×C4—48no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—44no—
1034C2×C4—432no—
1035C2×C4—44no—
1036C2×C4—42no—
1037C2×C4—48no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—84no—
1045C2×C4—84no—
1046C2×C4—84no—
1047C2×C4—82no—
1048C2×C4—82no—
1049C2×C4—82no—
1050C2×C4—82no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4C22×C22⋊C412yes—
1054C2×C4C22×C22⋊C412yes—
1055C2×C4C22×C22⋊C412yes—
1056C2×C4C22×C22⋊C412yes—
1057C2×C4C22×C22⋊C411yescharacteristic
1058C2×C4C22×C22⋊C411yescharacteristic
1059C2×C4C22×C22⋊C412yes—
1060C2×C4C22×C22⋊C412yes—
1061C2×C4C22×C22⋊C412yes—
1062C2×C4C22×C22⋊C412yes—
1063C2×C4C24×C411yescharacteristic
1064C2×C4C23×D411yescharacteristic
1065C2×C4C2×H(5,𝔽2)12yes—
1066C2×C4#58512yes—
1067C8—48no—
1068C22—24no—
1069C22—24no—
1070C22—21no—
1071C22—21no—
1072C22—21no—
1073C22—21no—
1074C22—22no—
1075C22—21no—
1076C22—21no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—48no—
1091C22—44no—
1092C22—44no—
1093C22—44no—
1094C22—44no—
1095C22—82no—
1096C22—82no—
1097C22—82no—
1098C22—82no—
1099C22—84no—
1100C22—164no—
1101C22—164no—
1102C22C2×#42112yes—
1103C22C2×#42114yes—
1104C22#290112yes—
1105C22C23×C22⋊C411yescharacteristic
1106C22#348411yescharacteristic
1107C22#348511yescharacteristic
1108C4—22no—
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—21no—
1113C4—21no—
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—44no—
1119C4—44no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—82no—
1124C4—82no—
1125C4C4×H(5,𝔽2)12yes—
1126C4#349612yes—
1127C2—21no—
1128C2—21no—
1129C2—22no—
1130C2—22no—
1131C2—24no—
1132C2—42no—
1133C2—42no—
1134C2—42no—
1135C2—84no—
1136C2#3425611yescharacteristic
1137C2C22×#42111yescharacteristic
1138C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radical#62773C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. C2×#2290C2semidirect
4. #22506C2semidirect
5. #22434C2semidirect
6. #21899C2semidirect
7. #21773C2semidirect
8. #21773C2semidirect
9. #21417C2semidirect
10. #20979C2semidirect
11. C2×#1896C2semidirect
12. #3520C4semidirect
13. #3519C4semidirect
15. #3506C4semidirect
16. #3505C4semidirect
17. #3505C4semidirect
18. #3501C4semidirect
19. #3496C4semidirect
35. C22×#117C22semidirect
36. C23×C42C22semidirect
42. D4×M16C22semidirect
43. #2920C22semidirect
44. C2×#421C22semidirect
45. C22×#104C22semidirect
46. C2×#407C22semidirect
47. C2×#407C22semidirect
49. #2290C22semidirect
54. C2×C4×C4⋊C4C22semidirect
55. C2×C4×C22⋊C4C22semidirect
56. C2×C4×C22⋊C4C22semidirect
57. C2×#376C22semidirect
58. #1995C22semidirect
59. #1986C22semidirect
60. #1980C22semidirect
61. #1963C22semidirect
62. #1897C22semidirect
63. #1896C22semidirect
64. #1896C22semidirect
65. #1896C22semidirect
66. #1896C22semidirect
67. #1896C22semidirect
68. #1871C22semidirect
69. #1871C22semidirect
70. #1826C22semidirect
71. #1826C22semidirect
72. #1806C22semidirect
73. #1789C22semidirect
74. #1789C22semidirect
75. #1759C22semidirect
76. #1733C22semidirect
77. C2×#339C22semidirect
88. #556C2×C4semidirect
89. #555C2×C4semidirect
92. #554C2×C4semidirect
97. #553C2×C4semidirect
98. #553C2×C4semidirect
100. #552C2×C4semidirect
101. #552C2×C4semidirect
108. #550C2×C4semidirect
109. D4×Q8C2×C4semidirect
110. #548C2×C4semidirect
111. #548C2×C4semidirect
113. #547C2×C4semidirect
114. #547C2×C4semidirect
122. #546C2×C4semidirect
123. #546C2×C4semidirect
126. D42C2×C4semidirect
148. #533C2×C4semidirect
149. #533C2×C4semidirect
152. #532C2×C4semidirect
153. #532C2×C4semidirect
162. #529C2×C4semidirect
163. #529C2×C4semidirect
178. #525C2×C4semidirect
179. #525C2×C4semidirect
187. C2×C22⋊Q8C2×C4semidirect
188. C2×C22⋊Q8C2×C4semidirect
191. C2×#121C2×C4semidirect
192. C2×#121C2×C4semidirect
307. C2×#41C22×C4semidirect
310. C22×Q8C22×C4semidirect
325. C22×D4C22×C4semidirect
372. C4⋊Q8C22×C4semidirect
373. C4⋊Q8C22×C4semidirect
374. C4⋊Q8C22×C4semidirect
376. #127C22×C4semidirect
390. #125C22×C4semidirect
398. #124C22×C4semidirect
441. C22⋊Q8C22×C4semidirect
442. C22⋊Q8C22×C4semidirect
470. #121C22×C4semidirect
471. #121C22×C4semidirect
488. C4×Q8C22×C4semidirect
489. C4×Q8C22×C4semidirect
531. C4×D4C22×C4semidirect
532. C4×D4C22×C4semidirect
553. #117C22×C4semidirect
571. C2×C4⋊C4C22×C4semidirect
572. C2×C4⋊C4C22×C4semidirect
909. C42H(5,𝔽2)semidirect
950. C23#421semidirect

Maximal subgroups

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

subgroupindex
#627732
#602302
C2×#22902
#225062
#224342
#218992
#217732
#214172
#209792
C2×#18962