Finite Group Databasebeta

← #6343629

Subgroups — #6343629

Order 512.

2934 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C211yesmaximal, characteristic
2C2×#2924C211yesmaximal, characteristic, complemented
3#34180C211yesmaximal, characteristic, complemented
4#17612C214yesmaximal, complemented
5#17609C218yesmaximal, complemented
6#17605C214yesmaximal, complemented
7#17596C212yesmaximal, complemented
8#17592C211yesmaximal, characteristic
9#17581C212yesmaximal, complemented
10#17578C211yesmaximal, characteristic, complemented
11#17575C212yesmaximal, complemented
12#17572C211yesmaximal, characteristic
13#17567C212yesmaximal, complemented
14C2×#1520C211yesmaximal, characteristic, complemented
15#3495—21no—
16#3495—21no—
17#3495—22no—
18#3495—22no—
19#3495—21no—
20#3495—21no—
21#3495C414yescomplemented
22#3495C412yescomplemented
23#3495C412yescomplemented
24#3495C2214yes—
25#3495C2212yes—
26#3495C2212yes—
27C2×#556—21no—
28C2×#554—21no—
29C2×#552—22no—
30C2×#552—21no—
31C2×#552—21no—
32C2×#551—22no—
33C2×#544C411yescharacteristic, complemented
34C2×#542C412yescomplemented
35C2×#541C412yescomplemented
36C2×#536C411yescharacteristic, complemented
37C2×#533C2212yes—
38C2×#529C2212yes—
39C2×#525C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C2×#520C411yescharacteristic, complemented
42C2×#519C411yescharacteristic, complemented
43C22×#117C2211yescharacteristic
44#2924—21no—
45#2924—22no—
46#2924—21no—
47#2924C2212yescomplemented
48#2924C2214yescomplemented
49#2924C2212yescomplemented
50C2×#433—22no—
51C2×#432C2212yes—
52C2×#431C2212yes—
53C2×#424—21no—
54C2×#407C2211yescharacteristic
55C22×C22⋊C8C2211yescharacteristic
56C2×#405—21no—
57#2347C2212yescomplemented
58#2346C2212yescomplemented
59#2345—21no—
60#2344—21no—
61#2343C2214yescomplemented
62#2342—22no—
63#2317—21no—
64#2314—22no—
65#2285C2212yes—
66#2283C2212yes—
67#2280C2211yescharacteristic
68C2×#380C2211yescharacteristic
69#2274—21no—
70#1521C2218yescomplemented
71#1520C2212yes—
72#1520C2212yes—
73#1520C2212yes—
74#1520C2211yescharacteristic
75#1520C2211yescharacteristic
76#1520C2212yes—
77#1520C2212yes—
78#1520C2214yescomplemented
79#1519C2211yescharacteristic
80#1519C2212yes—
81#1519C2211yescharacteristic
82#1518C2218yescomplemented
83#1516C2214yes—
84#1515C2218yescomplemented
85#1513C2214yes—
86#1512C2218yescomplemented
87#1511C2214yescomplemented
88#1509C2218yescomplemented
89#1508C2214yescomplemented
90#1506C2218yescomplemented
91#1504C2214yes—
92#1503C2218yescomplemented
93#1501C2214yes—
94#1500C2218yescomplemented
95C2×#328C2214yescomplemented
96C22×#41C2×C411yescharacteristic
97C23×Q8C2×C411yescharacteristic
98C24×C4C2311yescharacteristic
99C22×M16—21no—
100C23×C8—21no—
101#556—24no—
102#556—22no—
103#556—22no—
104#556—24no—
105#556—22no—
106#556—22no—
107#554—24no—
108#554—22no—
109#554—22no—
110#554—24no—
111#554—22no—
112#554—22no—
113#552—24no—
114#552—24no—
115#552—24no—
116#552—24no—
117#552—24no—
118#552—22no—
119#552—22no—
120#552—24no—
121#552—24no—
122#552—24no—
123#552—24no—
124#552—24no—
125#552—22no—
126#552—22no—
127#552—24no—
128#552—22no—
129#552—22no—
130#552—22no—
131#552—24no—
132#552—22no—
133#551—24no—
134#551—24no—
135#551—24no—
136#551—24no—
137#551—24no—
138#551—24no—
139#551—24no—
140#551—24no—
141#544—21no—
142#544—21no—
143#544—22no—
144#544C2×C414yes—
145#544C2×C412yescomplemented
146#544C2×C412yescomplemented
147#542—22no—
148#542—22no—
149#542—22no—
150#542—22no—
151#542C2×C414yes—
152#542C2×C414yes—
153#542C2×C414yescomplemented
154#542C2×C414yescomplemented
155#541—22no—
156#541—22no—
157#541—22no—
158#541—22no—
159#541C2×C414yes—
160#541C2×C414yes—
161#541C2×C414yescomplemented
162#541C2×C414yescomplemented
163#536—22no—
164#536—21no—
165#536—21no—
166#536C2×C414yes—
167#536C2×C412yescomplemented
168#536C2×C412yescomplemented
169#533—22no—
170#533—22no—
171#533—22no—
172#533—22no—
173#533C2×C414yescomplemented
174#533C2×C414yescomplemented
175#533C2314yes—
176#533C2314yes—
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8C2×C412yescomplemented
179C2×C4⋊Q8C2×C412yescomplemented
180#529—22no—
181#529—22no—
182#529—22no—
183#529—22no—
184#529C2×C414yescomplemented
185#529C2×C414yescomplemented
186#529C2314yes—
187#529C2314yes—
188C2×#126—22no—
189C2×#126—22no—
190C2×#126—22no—
191C2×#126—22no—
192C2×#125—22no—
193C2×#125—22no—
194C2×#125—21no—
195C2×#125—22no—
196C2×#125C2×C412yescomplemented
197C2×#124—22no—
198C2×#124C2×C412yescomplemented
199#525—21no—
200#525—21no—
201#525—21no—
202#525—21no—
203#525C2×C412yes—
204#525C2×C412yes—
205#525C2312yes—
206#525C2312yes—
207C2×#123—21no—
208C2×#123—22no—
209C2×#123—22no—
210C2×#123—22no—
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—22no—
221C2×C22⋊Q8—22no—
222C2×C22⋊Q8C2×C412yes—
223C2×C22⋊Q8C2×C412yes—
224C2×C22⋊Q8C2×C412yes—
225C2×C22⋊Q8C2×C411yescharacteristic
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121C2×C411yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233#520—22no—
234#520—21no—
235#520—21no—
236#520C2×C414yes—
237#520C2×C412yescomplemented
238#520C2×C412yescomplemented
239#519—21no—
240#519—21no—
241#519—22no—
242#519C2×C414yes—
243#519C2×C412yescomplemented
244#519C2×C412yescomplemented
245C2×C4×Q8—21no—
246C2×C4×Q8—21no—
247C2×C4×Q8—22no—
248C2×C4×Q8C2×C412yescomplemented
249C2×C4×Q8C2×C412yescomplemented
250C2×C4×Q8C2×C412yescomplemented
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—22no—
254C2×C4×D4—22no—
255C2×C4×D4C2×C412yescomplemented
256C2×#117—22no—
257C2×#117—21no—
258C2×#117—22no—
259C2×#117—21no—
260C2×#117—22no—
261C2×#117—22no—
262C2×#117C2×C411yescharacteristic
263C2×#117C2×C411yescharacteristic
264C2×#117C2×C411yescharacteristic
265C2×#117C2×C412yes—
266C2×#117C2×C412yes—
267C2×#117C2×C411yescharacteristic
268C2×#117C2×C411yescharacteristic
269C2×#117D411yescharacteristic
270C2×#117D411yescharacteristic
271C2×#117D412yes—
272C2×#117D411yescharacteristic
273C2×#117D412yes—
274C2×#117D411yescharacteristic
275C2×#117D412yes—
276C2×#117D411yescharacteristic
277C2×#117D411yescharacteristic
278C2×#117C2312yes—
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C22×C4⋊C4—21no—
282C22×C4⋊C4—21no—
283C22×C4⋊C4—21no—
284C22×C4⋊C4C2×C411yescharacteristic
285C22×C4⋊C4D411yescharacteristic
286C22×C4⋊C4D411yescharacteristic
287C22×C22⋊C4—21no—
288C22×C22⋊C4—21no—
289C22×C22⋊C4D412yes—
290C22×C42C2312yes—
291#433—24no—
292#433—24no—
293#433—24no—
294#433—24no—
295#432—22no—
296#432—22no—
297#432C2314yes—
298#432C2314yes—
299#431—22no—
300#431—22no—
301#431C2314yes—
302#431C2314yes—
303#424—24no—
304#424—22no—
305#424—22no—
306C2×C4⋊C8—22no—
307C2×C4⋊C8—22no—
308#407—21no—
309#407—21no—
310#407C2312yes—
311#407C2312yes—
312C2×C22⋊C8—21no—
313C2×C22⋊C8—21no—
314C2×C22⋊C8—21no—
315C2×C22⋊C8—21no—
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2312yes—
319C2×C22⋊C8C2312yes—
320C2×C22⋊C8C2312yes—
321#405—22no—
322#405—24no—
323#405—22no—
324C2×#97—22no—
325C2×C4×C8—22no—
326#389—22no—
327#389—22no—
328#388—24no—
329#388—24no—
330#387—24no—
331#387—24no—
332#385—24no—
333#384—22no—
334#383C2314yes—
335#382—22no—
336#382C2314yes—
337#381—22no—
338#381C2312yes—
339#380—21no—
340#380—21no—
341#380—22no—
342#380—21no—
343#380C2312yes—
344#380C2312yes—
345#380C2311yescharacteristic
346#380C2311yescharacteristic
347#379—21no—
348C4×C4⋊C4—22no—
349C4×C4⋊C4—22no—
350C4×C4⋊C4—22no—
351C4×C4⋊C4—22no—
352C4×C4⋊C4C2314yes—
353C4×C22⋊C4—22no—
354C4×C22⋊C4—21no—
355C4×C22⋊C4—24no—
356C4×C22⋊C4C2312yes—
357#376C2314yes—
358C2×#95C2312yes—
359#328C2318yes—
360#328C2318yes—
361#328C2318yes—
362#328C2314yes—
363#328C2314yes—
364#328C2318yes—
365#328C2318yes—
366#327C2314yes—
367#327C2318yes—
368#327C2314yes—
369C25C2×D411yescharacteristic
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—44no—
373C2×#41C22×C412yes—
374C2×#41C22×C412yes—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—22no—
379C22×Q8—44no—
380C22×Q8C22×C412yes—
381C22×Q8C22×C411yescharacteristic
382C22×Q8C22×C412yes—
383C22×Q8C22×C412yes—
384C22×D4—21no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4C22×C411yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—44no—
394C23×C4C22×C411yescharacteristic
395C23×C4C22×C411yescharacteristic
396C23×C4C22×C411yescharacteristic
397C23×C4C22×C411yescharacteristic
398C23×C4C2×D412yes—
399C23×C4C2×D411yescharacteristic
400C23×C4C2×D411yescharacteristic
401C23×C4C2×D411yescharacteristic
402C23×C4C2×D411yescharacteristic
403C23×C4C2×D411yescharacteristic
404C23×C4C2×D411yescharacteristic
405C23×C4C2×D411yescharacteristic
406C23×C4C2×D412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—44no—
413C22×C8—21no—
414C22×C8—21no—
415C22×C8—22no—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—44no—
419C4⋊Q8—24no—
420C4⋊Q8—22no—
421C4⋊Q8—22no—
422C4⋊Q8—22no—
423C4⋊Q8—22no—
424C4⋊Q8—22no—
425C4⋊Q8—22no—
426C4⋊Q8C22×C414yes—
427C4⋊Q8C22×C414yes—
428C4⋊Q8C22×C414yes—
429C4⋊Q8C22×C414yes—
430#126—24no—
431#126—24no—
432#126—24no—
433#126—24no—
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#125—24no—
447#125—24no—
448#125—24no—
449#125—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—22no—
460#125—22no—
461#125—24no—
462#125—24no—
463#125C22×C414yes—
464#125C22×C414yes—
465#124—24no—
466#124—24no—
467#124—24no—
468#124—24no—
469#124—22no—
470#124—22no—
471#124C22×C414yes—
472#124C22×C414yes—
473#123—22no—
474#123—22no—
475#123—24no—
476#123—24no—
477#123—22no—
478#123—22no—
479#123—24no—
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—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—24no—
496C22⋊Q8—24no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
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×C412yes—
527C22⋊Q8C22×C412yes—
528C22⋊Q8C22×C412yes—
529C22⋊Q8C2414yes—
530C22⋊Q8C2412yes—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121C22×C412yes—
536#121C22×C412yes—
537#121C22×C412yes—
538#121C2412yes—
539#120—22no—
540#120—22no—
541#120—22no—
542#120—22no—
543C4×Q8—24no—
544C4×Q8—24no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—24no—
550C4×Q8—24no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—24no—
558C4×Q8—24no—
559C4×Q8C22×C414yes—
560C4×Q8C22×C414yes—
561C4×Q8C22×C414yes—
562C4×Q8C22×C414yes—
563C4×Q8C22×C414yes—
564C4×Q8C22×C414yes—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4C22×C414yes—
584C4×D4C22×C414yes—
585#117—24no—
586#117—24no—
587#117—21no—
588#117—21no—
589#117—24no—
590#117—24no—
591#117—24no—
592#117—22no—
593#117—22no—
594#117—24no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—44no—
603#117—84no—
604#117C22⋊C412yes—
605#117C22⋊C411yescharacteristic
606#117C22⋊C411yescharacteristic
607#117C22⋊C412yes—
608#117C22⋊C411yescharacteristic
609#117C22⋊C411yescharacteristic
610#117C22⋊C412yes—
611#117C22⋊C412yes—
612#117C22⋊C412yes—
613#117C22⋊C412yes—
614#117C22⋊C411yescharacteristic
615#117C22⋊C411yescharacteristic
616#117C22⋊C412yes—
617#117C22⋊C412yes—
618#117C22⋊C412yes—
619#117C22⋊C412yes—
620#117C22⋊C412yes—
621#117C22⋊C411yescharacteristic
622#117C22⋊C411yescharacteristic
623#117C22⋊C412yes—
624#117C22×C412yes—
625#117C22×C412yes—
626#117C22×C412yes—
627#117C22×C411yescharacteristic
628#117C22×C411yescharacteristic
629#117C22×C412yes—
630#117C22×C411yescharacteristic
631#117C22×C411yescharacteristic
632#117C22×C412yes—
633#117C22×C412yes—
634#117C22×C412yes—
635#117C22×C412yes—
636#117C2×D411yescharacteristic
637#117C2×D412yes—
638#117C2×D411yescharacteristic
639#117C2×D412yes—
640#117C2×D412yes—
641#117C2×D412yes—
642#117C2×D412yes—
643#117C2×D411yescharacteristic
644#117C2×D411yescharacteristic
645#117C2×D412yes—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—24no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—24no—
673C2×C4⋊C4—24no—
674C2×C4⋊C4—44no—
675C2×C4⋊C4C22⋊C411yescharacteristic
676C2×C4⋊C4C22⋊C411yescharacteristic
677C2×C4⋊C4C22⋊C411yescharacteristic
678C2×C4⋊C4C22⋊C412yes—
679C2×C4⋊C4C22⋊C411yescharacteristic
680C2×C4⋊C4C22⋊C412yes—
681C2×C4⋊C4C22⋊C411yescharacteristic
682C2×C4⋊C4C22⋊C411yescharacteristic
683C2×C4⋊C4C22⋊C412yes—
684C2×C4⋊C4C22⋊C411yescharacteristic
685C2×C4⋊C4C22⋊C411yescharacteristic
686C2×C4⋊C4C22⋊C412yes—
687C2×C4⋊C4C22×C412yes—
688C2×C4⋊C4C22×C412yes—
689C2×C4⋊C4C22×C412yes—
690C2×C4⋊C4C22×C411yescharacteristic
691C2×C4⋊C4C22×C411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D412yes—
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D412yes—
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—82no—
719C2×C22⋊C4C22⋊C412yes—
720C2×C22⋊C4C22⋊C412yes—
721C2×C22⋊C4C22⋊C412yes—
722C2×C22⋊C4C22⋊C412yes—
723C2×C22⋊C4C22⋊C412yes—
724C2×C22⋊C4C22⋊C412yes—
725C2×C22⋊C4C22⋊C412yes—
726C2×C22⋊C4C22⋊C412yes—
727C2×C22⋊C4C2×D412yes—
728C2×C22⋊C4C2×D412yes—
729C2×C22⋊C4C2×D412yes—
730C2×C22⋊C4C2×D412yes—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—21no—
735C2×C42—22no—
736C2×C42—24no—
737C2×C42—24no—
738C2×C42C22×C412yes—
739C2×C42C22×C412yes—
740C2×C42C22×C412yes—
741C2×C42C22×C412yes—
742C2×C42C2×D412yes—
743C2×C42C2×D412yes—
744C2×C42C2×D412yes—
745C2×C42C2×D412yes—
746C2×C42C2×D412yes—
747C2×C42C2×D412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C4⋊C8—24no—
751C4⋊C8—24no—
752C4⋊C8—24no—
753C4⋊C8—24no—
754C22⋊C8—21no—
755C22⋊C8—21no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8C2412yes—
762C22⋊C8C2412yes—
763C22⋊C8C2414yes—
764#97—24no—
765#97—24no—
766C4×C8—24no—
767C4×C8—24no—
768#95—22no—
769#95—24no—
770#95—24no—
771#95—24no—
772#95—22no—
773#95—24no—
774#95C2414yes—
775#95C2412yes—
776#95C2412yes—
777C24—22no—
778C24—22no—
779C24—21no—
780C24—42no—
781C24—81no—
782C24C2×C22⋊C411yescharacteristic
783C24C2×C22⋊C411yescharacteristic
784C24C2×C22⋊C411yescharacteristic
785C24C2×C22⋊C411yescharacteristic
786C24C22×D411yescharacteristic
787C24C22×D411yescharacteristic
788C24C22×D411yescharacteristic
789#41—44no—
790#41—44no—
791#41—44no—
792#41—44no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—21no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—42no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—44no—
806C2×Q8—84no—
807C2×Q8C23×C414yes—
808C2×Q8C23×C412yes—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—21no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—82no—
821C2×D4C23×C412yes—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—22no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—82no—
858C22×C4—84no—
859C22×C4—82no—
860C22×C4—82no—
861C22×C4—82no—
862C22×C4C2×C22⋊C412yes—
863C22×C4C2×C22⋊C411yescharacteristic
864C22×C4C2×C22⋊C412yes—
865C22×C4C2×C22⋊C412yes—
866C22×C4C2×C22⋊C412yes—
867C22×C4C2×C22⋊C411yescharacteristic
868C22×C4C2×C22⋊C411yescharacteristic
869C22×C4C2×C22⋊C411yescharacteristic
870C22×C4C2×C22⋊C411yescharacteristic
871C22×C4C2×C22⋊C411yescharacteristic
872C22×C4C2×C22⋊C411yescharacteristic
873C22×C4C2×C22⋊C412yes—
874C22×C4C2×C22⋊C412yes—
875C22×C4C2×C22⋊C412yes—
876C22×C4C2×C22⋊C412yes—
877C22×C4C2×C22⋊C411yescharacteristic
878C22×C4C2×C22⋊C411yescharacteristic
879C22×C4C2×C22⋊C411yescharacteristic
880C22×C4C2×C22⋊C411yescharacteristic
881C22×C4C2×C22⋊C411yescharacteristic
882C22×C4C23×C411yescharacteristic
883C22×C4C23×C411yescharacteristic
884C22×C4C23×C411yescharacteristic
885C22×C4C23×C411yescharacteristic
886C22×C4C23×C411yescharacteristic
887C22×C4C23×C411yescharacteristic
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C2511yescharacteristic
902M16—44no—
903M16—44no—
904C2×C8—22no—
905C2×C8—24no—
906C2×C8—22no—
907C2×C8—44no—
908C2×C8—42no—
909C2×C8—42no—
910C2×C8—44no—
911C2×C8—44no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—22no—
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—24no—
929C4⋊C4—24no—
930C4⋊C4—22no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—24no—
940C4⋊C4—22no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—84no—
946C4⋊C4—84no—
947C4⋊C4C2×C22⋊C412yes—
948C4⋊C4C2×C22⋊C411yescharacteristic
949C4⋊C4C2×C22⋊C411yescharacteristic
950C4⋊C4C2×C22⋊C412yes—
951C4⋊C4C2×C22⋊C411yescharacteristic
952C4⋊C4C2×C22⋊C411yescharacteristic
953C4⋊C4C2×C22⋊C412yes—
954C4⋊C4C2×C22⋊C412yes—
955C4⋊C4C2×C22⋊C412yes—
956C4⋊C4C2×C22⋊C412yes—
957C4⋊C4C2×C22⋊C412yes—
958C4⋊C4C2×C22⋊C411yescharacteristic
959C4⋊C4C2×C22⋊C411yescharacteristic
960C4⋊C4C2×C22⋊C412yes—
961C4⋊C4C2×C22⋊C411yescharacteristic
962C4⋊C4C2×C22⋊C411yescharacteristic
963C4⋊C4C2×C22⋊C412yes—
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C2×C22⋊C412yes—
967C4⋊C4C23×C414yes—
968C4⋊C4C23×C412yes—
969C4⋊C4C23×C412yes—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—24no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—22no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—82no—
995C22⋊C4—82no—
996C22⋊C4C2×C22⋊C412yes—
997C22⋊C4C2×C22⋊C412yes—
998C22⋊C4C2×C22⋊C412yes—
999C22⋊C4C2×C22⋊C412yes—
1000C22⋊C4C2×C22⋊C412yes—
1001C22⋊C4C2×C22⋊C412yes—
1002C22⋊C4C2×C22⋊C412yes—
1003C22⋊C4C2×C22⋊C412yes—
1004C22⋊C4C2×C22⋊C412yes—
1005C22⋊C4C2×C22⋊C412yes—
1006C22⋊C4C2×C22⋊C412yes—
1007C22⋊C4C2×C22⋊C412yes—
1008C22⋊C4C2×C22⋊C412yes—
1009C22⋊C4C2×C22⋊C412yes—
1010C22⋊C4C2×C22⋊C412yes—
1011C22⋊C4C2×C22⋊C412yes—
1012C42—24no—
1013C42—24no—
1014C42—24no—
1015C42—24no—
1016C42—24no—
1017C42—24no—
1018C42—22no—
1019C42—22no—
1020C42—44no—
1021C42—84no—
1022C42—84no—
1023C42C2×C22⋊C412yes—
1024C42C2×C22⋊C412yes—
1025C42C2×C22⋊C412yes—
1026C42C2×C22⋊C412yes—
1027C42C2×C22⋊C412yes—
1028C42C2×C22⋊C412yes—
1029C42C2×C22⋊C412yes—
1030C42C2×C22⋊C412yes—
1031C42C23×C412yes—
1032C42C23×C412yes—
1033C42C23×C412yes—
1034C42C23×C412yes—
1035C42C22×D412yes—
1036C42C22×D412yes—
1037C42C22×D412yes—
1038C42C22×D412yes—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—21no—
1045C23—21no—
1046C23—22no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—84no—
1066C23—84no—
1067C23C22×C22⋊C411yescharacteristic
1068C23C22×C22⋊C411yescharacteristic
1069C23C22×C22⋊C411yescharacteristic
1070C23C22×C22⋊C411yescharacteristic
1071C23C22×C22⋊C411yescharacteristic
1072C23C22×C22⋊C411yescharacteristic
1073C23#57712yes—
1074C23#57812yes—
1075C23C23×D411yescharacteristic
1076Q8—44no—
1077Q8—42no—
1078Q8—44no—
1079Q8—44no—
1080Q8—44no—
1081Q8—42no—
1082Q8—84no—
1083Q8—84no—
1084D4—42no—
1085D4—44no—
1086D4—44no—
1087D4—44no—
1088D4—42no—
1089D4—42no—
1090D4—42no—
1091D4—82no—
1092D4—82no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—44no—
1140C2×C4—42no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—42no—
1145C2×C4—44no—
1146C2×C4—42no—
1147C2×C4—44no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—44no—
1152C2×C4—42no—
1153C2×C4—44no—
1154C2×C4—42no—
1155C2×C4—44no—
1156C2×C4—42no—
1157C2×C4—84no—
1158C2×C4—84no—
1159C2×C4—82no—
1160C2×C4—82no—
1161C2×C4—164no—
1162C2×C4#41014yes—
1163C2×C4C22×C22⋊C412yes—
1164C2×C4C22×C22⋊C412yes—
1165C2×C4C22×C22⋊C412yes—
1166C2×C4C22×C22⋊C412yes—
1167C2×C4C22×C22⋊C411yescharacteristic
1168C2×C4C22×C22⋊C411yescharacteristic
1169C2×C4C22×C22⋊C412yes—
1170C2×C4C22×C22⋊C412yes—
1171C2×C4C22×C22⋊C412yes—
1172C2×C4C22×C22⋊C412yes—
1173C2×C4C22×C22⋊C411yescharacteristic
1174C2×C4C22×C22⋊C411yescharacteristic
1175C2×C4C22×C22⋊C411yescharacteristic
1176C2×C4C22×C22⋊C411yescharacteristic
1177C2×C4C24×C411yescharacteristic
1178C2×C4C23×D411yescharacteristic
1179C8—42no—
1180C8—42no—
1181C8—44no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—44no—
1204C22—44no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—81no—
1209C22—81no—
1210C22—82no—
1211C22—82no—
1212C22—84no—
1213C22C2×#41012yes—
1214C22#289812yes—
1215C22#289812yes—
1216C22C23×C22⋊C411yescharacteristic
1217C22C2×#57711yescharacteristic
1218C22C2×#57811yescharacteristic
1219C4—21no—
1220C4—21no—
1221C4—21no—
1222C4—21no—
1223C4—21no—
1224C4—21no—
1225C4—22no—
1226C4—22no—
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—42no—
1234C4—44no—
1235C4—42no—
1236C4—44no—
1237C4—42no—
1238C4—82no—
1239C4—82no—
1240C4—84no—
1241C4C2×#41012yes—
1242C4C2×#41012yes—
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—22no—
1247C2—22no—
1248C2—41no—
1249C2—41no—
1250C2—41no—
1251C2—82no—
1252C2C22×#41011yescharacteristic
1253C2C2×#289811yescharacteristic
1254C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2924C2semidirect
3. #34180C2semidirect
4. #17612C2semidirect
5. #17609C2semidirect
6. #17605C2semidirect
7. #17596C2semidirect
9. #17581C2semidirect
10. #17578C2semidirect
11. #17575C2semidirect
13. #17567C2semidirect
14. C2×#1520C2semidirect
21. #3495C4semidirect
22. #3495C4semidirect
23. #3495C4semidirect
33. C2×#544C4semidirect
34. C2×#542C4semidirect
35. C2×#541C4semidirect
36. C2×#536C4semidirect
41. C2×#520C4semidirect
42. C2×#519C4semidirect
47. #2924C22semidirect
48. #2924C22semidirect
49. #2924C22semidirect
57. #2347C22semidirect
58. #2346C22semidirect
61. #2343C22semidirect
70. #1521C22semidirect
78. #1520C22semidirect
82. #1518C22semidirect
84. #1515C22semidirect
86. #1512C22semidirect
87. #1511C22semidirect
88. #1509C22semidirect
89. #1508C22semidirect
90. #1506C22semidirect
92. #1503C22semidirect
94. #1500C22semidirect
95. C2×#328C22semidirect
145. #544C2×C4semidirect
146. #544C2×C4semidirect
153. #542C2×C4semidirect
154. #542C2×C4semidirect
161. #541C2×C4semidirect
162. #541C2×C4semidirect
167. #536C2×C4semidirect
168. #536C2×C4semidirect
173. #533C2×C4semidirect
174. #533C2×C4semidirect
178. C2×C4⋊Q8C2×C4semidirect
179. C2×C4⋊Q8C2×C4semidirect
184. #529C2×C4semidirect
185. #529C2×C4semidirect
196. C2×#125C2×C4semidirect
198. C2×#124C2×C4semidirect
237. #520C2×C4semidirect
238. #520C2×C4semidirect
243. #519C2×C4semidirect
244. #519C2×C4semidirect
248. C2×C4×Q8C2×C4semidirect
249. C2×C4×Q8C2×C4semidirect
250. C2×C4×Q8C2×C4semidirect
255. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
C2×#29242
#341802
#176122
#176092
#176052
#175962
#175922
#175812
#175782
#175752
#175722
#175672
C2×#15202