Finite Group Databasebeta

← #7677481

Subgroups — #7677481

Order 512.

7066 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#59086C214yesmaximal, complemented
4#59083C214yesmaximal, complemented
5#59079C214yesmaximal, complemented
6#59042C214yesmaximal, complemented
7#45195C214yesmaximal, complemented
8#45195C214yesmaximal, complemented
9#45111C214yesmaximal, complemented
10#44883C214yesmaximal, complemented
11#39422C214yesmaximal, complemented
12#37754C214yesmaximal, complemented
13#37702C214yesmaximal, complemented
14#36108C214yesmaximal, complemented
15#35628C212yesmaximal, complemented
16#35617C212yesmaximal, complemented
17#35168C211yesmaximal, characteristic
18#35158C211yesmaximal, characteristic, complemented
19#35154C211yesmaximal, characteristic, complemented
20#34745C212yesmaximal, complemented
21#34271C211yesmaximal, characteristic, complemented
22#34269C212yesmaximal, complemented
23C2×#2367C211yesmaximal, characteristic, complemented
24#3501—216no—
25C2×#554C2214yes—
26C2×#554C2214yes—
27C2×#554C2214yes—
28C2×D4×Q8C2214yes—
29#3461—216no—
30C2×#544C2211yescharacteristic
31C2×#544C2211yescharacteristic
32C2×#543C2214yes—
33C2×#542C2214yescomplemented
34C2×#541C2214yescomplemented
35C2×#539C2214yes—
36C2×#537C2211yescharacteristic
37C2×#536C2212yes—
38C2×#535C2212yes—
39C2×#533C2212yes—
40C2×#533C2214yescomplemented
41C2×#529C2214yes—
42C2×#529C2214yescomplemented
43C22×#124C2211yescharacteristic
44C22×C22⋊Q8C2214yes—
45C2×#518C2212yes—
46C2×C4×#41C2212yes—
47C22×C4×Q8C2211yescharacteristic
48C22×C4×D4C2211yescharacteristic
49#2855C2214yes—
50#2850C2214yes—
51#2847C2214yes—
52#2730C2218yescomplemented
53#2728C2218yescomplemented
54#2728C2218yescomplemented
55#2723C2218yescomplemented
56#2723C2218yescomplemented
57#2702C2218yescomplemented
58#2702C2218yescomplemented
59#2696C2218yescomplemented
60#2690C2218yescomplemented
61#2690C2218yescomplemented
62#2690C2218yescomplemented
63#2681C2218yescomplemented
64#2639C2214yes—
65#2627C2214yes—
66#2617C2214yes—
67#2592C2214yescomplemented
68#2592C2214yescomplemented
69#2568C2214yescomplemented
70#2568C2214yescomplemented
71#2560C2218yescomplemented
72#2560C2218yescomplemented
73#2547C2214yes—
74#2547C2214yes—
75#2544C2214yes—
76#2544C2214yes—
77#2536C2218yescomplemented
78#2492C2214yescomplemented
79#2492C2214yescomplemented
80#2492C2214yescomplemented
81#2491C2214yescomplemented
82#2490C2214yescomplemented
83#2489C2214yescomplemented
84#2489C2214yescomplemented
85#2489C2214yescomplemented
86#2489C2214yescomplemented
87#2489C2218yescomplemented
88#2488C2218yes—
89#2488C2218yes—
90#2481C2218yescomplemented
91#2481C2218yescomplemented
92#2477C2218yescomplemented
93#2477C2218yescomplemented
94#2463C2218yescomplemented
95#2461C2218yescomplemented
96#2454C2212yescomplemented
97#2454C2212yescomplemented
98#2453C2214yescomplemented
99#2453C2214yescomplemented
100#2453C2212yescomplemented
101#2453C2212yescomplemented
102#2452C2212yescomplemented
103#2452C2212yescomplemented
104#2451C2214yescomplemented
105#2451C2214yescomplemented
106#2451C2212yescomplemented
107#2451C2212yescomplemented
108#2450C2214yes—
109#2450C2214yes—
110#2449C2214yes—
111#2449C2214yes—
112#2443C2218yescomplemented
113#2442C2214yescomplemented
114#2442C2218yescomplemented
115#2436C2214yescomplemented
116#2428C2214yes—
117#2428C2214yes—
118#2427C2214yes—
119#2427C2214yes—
120#2427C2214yes—
121#2427C2214yes—
122#2427C2214yes—
123#2427C2214yes—
124#2427C2214yescomplemented
125#2426C2214yescomplemented
126#2421C2214yescomplemented
127#2421C2218yescomplemented
128#2415C2218yescomplemented
129#2412C2218yes—
130#2412C2218yes—
131#2409C2218yescomplemented
132#2396C2214yescomplemented
133#2396C2214yescomplemented
134#2370C2214yescomplemented
135#2370C2214yescomplemented
136#2369C2214yescomplemented
137#2367C2214yes—
138#2367C2214yes—
139#2367C2214yes—
140#2367C2214yes—
141#2367C2214yes—
142#2367C2214yes—
143#2366C2214yes—
144#2366C2214yes—
145#2365C2214yescomplemented
146#2361C2214yescomplemented
147#2358C2218yes—
148#2358C2218yes—
149#2352C2218yescomplemented
150Q8×C22⋊C4C2214yescomplemented
151#2329C2214yes—
152#2324C2214yes—
153#2324C2214yes—
154#2316C2211yescharacteristic
155#2311C2212yes—
156#2310C2212yes—
157C4×C22⋊Q8C2214yes—
158C4×C22⋊Q8C2214yescomplemented
159C4×C22⋊Q8C2214yescomplemented
160C4×#121C2214yes—
161C4×#121C2214yes—
162#2297C2212yes—
163#2297C2212yes—
164#2296C2212yes—
165#2296C2212yes—
166C2×#391C2211yescharacteristic
167C2×#390C2211yescharacteristic
168C2×#388C2212yes—
169C2×#388C2212yes—
170C2×#385C2212yes—
171#2274C2212yes—
172C2×C4×C4⋊C4C2211yescharacteristic
173C2×C4×C4⋊C4C2211yescharacteristic
174C2×C4×C22⋊C4C2212yes—
175C22×#41C2312yes—
176C23×Q8C2311yescharacteristic
177C23×Q8C2314yes—
178C23×D4C2311yescharacteristic
179C24×C4C2312yes—
180#554—232no—
181#554—232no—
182#554—232no—
183D4×Q8—232no—
184#544—28no—
185#544D4116yescomplemented
186#543—232no—
187#542—232no—
188#541—232no—
189#539—232no—
190#537—28no—
191#536—216no—
192#535—216no—
193#533—232no—
194#533—216no—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2314yes—
200C2×#127C2314yes—
201#529—232no—
202#529—232no—
203C2×#126C2318yes—
204C2×#126C2318yes—
205C2×#125C2314yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2318yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#124—28no—
212C2×#124C2314yes—
213C2×#124C2314yes—
214C2×#124C2314yes—
215C2×#124C2314yes—
216C2×#124C2314yes—
217C2×#124C2314yes—
218C2×#123C2318yes—
219C2×#123C2318yes—
220C2×C22⋊Q8—232no—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#120C2318yes—
245#518—216no—
246C4×#41—216no—
247C2×C4×Q8—28no—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×D4—28no—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2318yes—
269C2×C4×D4C2318yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2314yes—
273C2×#117C2318yes—
274C2×#117C2312yes—
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2318yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C22⋊C4C2318yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C42C2312yes—
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2314yes—
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294#400C2318yes—
295#400C2318yes—
296#400C2318yes—
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C2314yes—
301#400C2314yes—
302#399C2314yes—
303#399C2314yes—
304#398C2314yes—
305#398C2318yes—
306#398C2318yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#396C2314yes—
319#396C2314yes—
320#396C2314yes—
321#396C2314yes—
322#395C2318yes—
323#395C2314yes—
324#395C2314yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#393C2314yes—
333#393C2314yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#392C2318yes—
338#391C2318yes—
339#391C2318yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2314yes—
348#391C2314yes—
349#391C2318yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2312yes—
357#391C2312yes—
358#390C2318yes—
359#390C2318yes—
360#390C2314yes—
361#390C2314yes—
362#390C2312yes—
363#390C2312yes—
364#390C2314yes—
365#390C2314yes—
366#390C2312yes—
367#390C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2314yes—
413#386C2318yes—
414#386C2314yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2314yes—
419#386C2314yes—
420#386C2318yes—
421#386C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#382C2318yes—
435#382C2318yes—
436#382C2314yes—
437#381C2318yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2318yes—
444#380C2314yes—
445#380C2318yes—
446#380C2318yes—
447#380C2318yes—
448#380C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C2×#95C2312yes—
477C2×#95C2311yescharacteristic
478C2×#95C2311yescharacteristic
479C2×#95C2312yes—
480C2×#95C2312yes—
481C25C2412yes—
482C2×#41—28no—
483C2×#41—28no—
484C2×#41—28no—
485C22×Q8—216no—
486C22×Q8—24no—
487C22×Q8—24no—
488C22×Q8—24no—
489C22×Q8—48no—
490C22×Q8—84no—
491C22×Q8C2414yes—
492C22×Q8C2412yes—
493C22×Q8C2414yes—
494C22×Q8C2414yes—
495C22×Q8C2414yes—
496C22×Q8C2414yes—
497C22×D4—24no—
498C22×D4—24no—
499C22×D4#4118yes—
500C22×D4C2414yes—
501C22×D4C2412yes—
502C22×D4C2414yes—
503C22×D4C2418yes—
504C22×D4C2418yes—
505C22×D4C2414yes—
506C23×C4—28no—
507C23×C4—44no—
508C23×C4—82no—
509C23×C4C2412yes—
510C23×C4C2414yes—
511C23×C4C2411yescharacteristic
512C23×C4C2414yes—
513C23×C4C2411yescharacteristic
514C23×C4C2414yes—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2412yes—
519C23×C4C2411yescharacteristic
520C23×C4C2418yes—
521C23×C4C2418yes—
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2412yes—
525C23×C4C2411yescharacteristic
526C4⋊Q8—28no—
527C4⋊Q8—28no—
528C4⋊Q8—216no—
529C4⋊Q8—216no—
530C4⋊Q8C2×D4132yes—
531#127—216no—
532#126—232no—
533#126—232no—
534#125—216no—
535#125—232no—
536#125—28no—
537#125—28no—
538#125—216no—
539#125C2×D4132yes—
540#124—216no—
541#124—216no—
542#124—216no—
543#124—216no—
544#124—216no—
545#124—84no—
546#123—232no—
547#123—232no—
548C22⋊Q8—216no—
549C22⋊Q8—232no—
550C22⋊Q8—232no—
551C22⋊Q8—216no—
552C22⋊Q8—232no—
553C22⋊Q8—216no—
554C22⋊Q8—216no—
555C22⋊Q8—216no—
556C22⋊Q8—216no—
557C22⋊Q8—232no—
558C22⋊Q8—232no—
559C22⋊Q8—232no—
560C22⋊Q8—216no—
561C22⋊Q8—216no—
562C22⋊Q8—48no—
563C22⋊Q8—48no—
564C22⋊Q8C2×D4132yes—
565#121—216no—
566#121—216no—
567#121—216no—
568#121—216no—
569#121—48no—
570#121—84no—
571#120—232no—
572C4×Q8—216no—
573C4×Q8—216no—
574C4×Q8—216no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—216no—
578C4×Q8—216no—
579C4×Q8—84no—
580C4×D4—216no—
581C4×D4—216no—
582C4×D4—28no—
583C4×D4—28no—
584C4×D4—216no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—216no—
589C4×D4—216no—
590C4×D4—216no—
591C4×D4—416no—
592C4×D4—88no—
593#117—28no—
594#117—28no—
595#117—232no—
596#117—216no—
597#117C2×D4116yes—
598C2×C4⋊C4—28no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—232no—
601C2×C4⋊C4—216no—
602C2×C4⋊C4—42no—
603C2×C4⋊C4—42no—
604C2×C4⋊C4C2×D418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C22⋊C4—28no—
644C2×C22⋊C4—28no—
645C2×C22⋊C4—28no—
646C2×C22⋊C4—232no—
647C2×C22⋊C4—44no—
648C2×C22⋊C4—82no—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C42—24no—
679C2×C42—24no—
680C2×C42—28no—
681C2×C42—24no—
682C2×C42—216no—
683C2×C42—82no—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2418yes—
697C2×C42C2418yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701#95C2411yescharacteristic
702#95C2411yescharacteristic
703#95C2411yescharacteristic
704#95C2411yescharacteristic
705#95C2414yes—
706#95C2414yes—
707#95C2412yes—
708#95C2418yes—
709#95C2412yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736C24—24no—
737C24—24no—
738C24—42no—
739C24—42no—
740C24—42no—
741C24—42no—
742C24C2×#4118yes—
743C24C2514yes—
744C24C2514yes—
745C24C2511yescharacteristic
746#41—432no—
747C2×Q8—28no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—28no—
751C2×Q8—28no—
752C2×Q8—28no—
753C2×Q8—24no—
754C2×Q8—28no—
755C2×Q8—24no—
756C2×Q8—28no—
757C2×Q8—44no—
758C2×Q8—44no—
759C2×Q8—44no—
760C2×Q8—44no—
761C2×Q8—44no—
762C2×Q8—44no—
763C2×Q8—44no—
764C2×Q8—416no—
765C2×Q8—832no—
766C2×Q8C22×D4116yes—
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—216no—
771C2×D4—216no—
772C2×D4—232no—
773C2×D4—28no—
774C2×D4—24no—
775C2×D4—28no—
776C2×D4—24no—
777C2×D4—28no—
778C2×D4—24no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—44no—
782C2×D4—48no—
783C2×D4—44no—
784C2×D4—48no—
785C2×D4C2×#41116yes—
786C22×C4—22no—
787C22×C4—24no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—216no—
807C22×C4—216no—
808C22×C4—28no—
809C22×C4—41no—
810C22×C4—42no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—48no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—41no—
832C22×C4—48no—
833C22×C4—816no—
834C22×C4C22×D418yes—
835C22×C4C22×D414yes—
836C22×C4C2×#4114yes—
837C22×C42−1+414yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2511yescharacteristic
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2512yes—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—216no—
862C4⋊C4—28no—
863C4⋊C4—216no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—216no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—216no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4C22×D4132yes—
892C4⋊C4C22×D4116yes—
893C4⋊C4C22×D4116yes—
894C4⋊C4C22×D418yes—
895C4⋊C4C22×D418yes—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—216no—
900C22⋊C4—28no—
901C22⋊C4—216no—
902C22⋊C4—216no—
903C22⋊C4—216no—
904C22⋊C4—216no—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—216no—
909C22⋊C4—216no—
910C22⋊C4—216no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4C22×D4116yes—
925C42—24no—
926C42—28no—
927C42—28no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—28no—
932C42—28no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—28no—
937C42—44no—
938C42—44no—
939C42—48no—
940C42—48no—
941C42C22×D4116yes—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—216no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—48no—
961C23—48no—
962C23—84no—
963C23—84no—
964C23—84no—
965C23—84no—
966C23C23×D412yes—
967C23C22×#4118yes—
968C23C22×#4112yes—
969C23C2×2−1+412yes—
970C23C2611yescharacteristic
971Q8—416no—
972Q8—416no—
973Q8—416no—
974Q8—48no—
975Q8—88no—
976Q8—88no—
977D4—232no—
978D4—416no—
979D4—48no—
980D4—88no—
981D4—816no—
982D4—816no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—21no—
991C2×C4—24no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—21no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—21no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—48no—
1036C2×C4—416no—
1037C2×C4—416no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—48no—
1043C2×C4—416no—
1044C2×C4—88no—
1045C2×C4—816no—
1046C2×C4—88no—
1047C2×C4—816no—
1048C2×C4—82no—
1049C2×C4—82no—
1050C2×C4—84no—
1051C2×C4#548116yes—
1052C2×C4C23×D418yes—
1053C2×C4C23×D418yes—
1054C2×C4C23×D418yes—
1055C2×C4C23×D414yes—
1056C2×C4C22×#4114yes—
1057C2×C4C2×2−1+414yes—
1058C2×C4#58512yes—
1059C2×C4#58512yes—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—22no—
1066C22—28no—
1067C22—28no—
1068C22—28no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—816no—
1081C22C2×#54814yes—
1082C22C24×D411yescharacteristic
1083C22C23×#4111yescharacteristic
1084C22C22×2−1+411yescharacteristic
1085C22C2×#58511yescharacteristic
1086C22C2×#58511yescharacteristic
1087C22H(7,𝔽2)11yescharacteristic
1088C222−1+611yescharacteristic
1089C4—22no—
1090C4—28no—
1091C4—28no—
1092C4—22no—
1093C4—28no—
1094C4—41no—
1095C4—42no—
1096C4—44no—
1097C4—41no—
1098C4—44no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—41no—
1103C4—41no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4C2×#54818yes—
1109C2—24no—
1110C2—48no—
1111C2—84no—
1112C2C22×#54811yescharacteristic
1113C2#6278111yescharacteristic
1114C2#6284711yescharacteristic
1115C2#6293211yescharacteristic
1116C2#6296211yescharacteristic
1117C2#6298711yescharacteristic
1118C2#6300211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35168C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3501C2semidirect
2. C2×#3461C2semidirect
3. #59086C2semidirect
4. #59083C2semidirect
5. #59079C2semidirect
6. #59042C2semidirect
7. #45195C2semidirect
8. #45195C2semidirect
9. #45111C2semidirect
10. #44883C2semidirect
11. #39422C2semidirect
12. #37754C2semidirect
13. #37702C2semidirect
14. #36108C2semidirect
15. #35628C2semidirect
16. #35617C2semidirect
18. #35158C2semidirect
19. #35154C2semidirect
20. #34745C2semidirect
21. #34271C2semidirect
22. #34269C2semidirect
23. C2×#2367C2semidirect
33. C2×#542C22semidirect
34. C2×#541C22semidirect
40. C2×#533C22semidirect
42. C2×#529C22semidirect
52. #2730C22semidirect
53. #2728C22semidirect
54. #2728C22semidirect
55. #2723C22semidirect
56. #2723C22semidirect
57. #2702C22semidirect
58. #2702C22semidirect
59. #2696C22semidirect
60. #2690C22semidirect
61. #2690C22semidirect
62. #2690C22semidirect
63. #2681C22semidirect
67. #2592C22semidirect
68. #2592C22semidirect
69. #2568C22semidirect
70. #2568C22semidirect
71. #2560C22semidirect
72. #2560C22semidirect
77. #2536C22semidirect
78. #2492C22semidirect
79. #2492C22semidirect
80. #2492C22semidirect
81. #2491C22semidirect
82. #2490C22semidirect
83. #2489C22semidirect
84. #2489C22semidirect
85. #2489C22semidirect
86. #2489C22semidirect
87. #2489C22semidirect
90. #2481C22semidirect
91. #2481C22semidirect
92. #2477C22semidirect
93. #2477C22semidirect
94. #2463C22semidirect
95. #2461C22semidirect
96. #2454C22semidirect
97. #2454C22semidirect
98. #2453C22semidirect
99. #2453C22semidirect
100. #2453C22semidirect
101. #2453C22semidirect
102. #2452C22semidirect
103. #2452C22semidirect
104. #2451C22semidirect
105. #2451C22semidirect
106. #2451C22semidirect
107. #2451C22semidirect
112. #2443C22semidirect
113. #2442C22semidirect
114. #2442C22semidirect
115. #2436C22semidirect
124. #2427C22semidirect
125. #2426C22semidirect
126. #2421C22semidirect
127. #2421C22semidirect
128. #2415C22semidirect
131. #2409C22semidirect
132. #2396C22semidirect
133. #2396C22semidirect
134. #2370C22semidirect
135. #2370C22semidirect
136. #2369C22semidirect
145. #2365C22semidirect
146. #2361C22semidirect
149. #2352C22semidirect
150. Q8×C22⋊C4C22semidirect
158. C4×C22⋊Q8C22semidirect
159. C4×C22⋊Q8C22semidirect
185. #544D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35012
C2×#34612
#590862
#590832
#590792
#590422
#451952
#451112
#448832
#394222
#377542
#377022
#361082
#356282
#356172
#351682
#351582
#351542
#347452
#342712
#342692
C2×#23672