Finite Group Databasebeta

← #7678273

Subgroups — #7678273

Order 512.

7030 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3492C211yesmaximal, characteristic
2C2×#3461C211yesmaximal, characteristic, complemented
3#59121C214yesmaximal, complemented
4#59116C214yesmaximal, complemented
5#59113C214yesmaximal, complemented
6#59031C214yesmaximal, complemented
7#45185C214yesmaximal, complemented
8#45177C214yesmaximal, complemented
9#45107C214yesmaximal, complemented
10#44875C214yesmaximal, complemented
11#39376C214yesmaximal, complemented
12#37763C214yesmaximal, complemented
13#37760C214yesmaximal, complemented
14#36143C214yesmaximal, complemented
15#35633C212yesmaximal, complemented
16#35619C212yesmaximal, complemented
17#35224C211yesmaximal, characteristic, complemented
18#35167C211yesmaximal, characteristic, complemented
19#35154C211yesmaximal, characteristic, complemented
20#34742C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22#34250C212yesmaximal, complemented
23C2×#2360C211yesmaximal, characteristic, complemented
24#3492—216no—
25C2×#554C2214yes—
26C2×#553C2214yes—
27C2×#552C2214yes—
28C2×#547C2214yes—
29#3461—216no—
30C2×#544C2211yescharacteristic
31C2×#544C2211yescharacteristic
32C2×#542C2214yescomplemented
33C2×#541C2214yescomplemented
34C2×#539C2214yes—
35C2×#539C2214yes—
36C2×#537C2211yescharacteristic
37C2×#536C2212yes—
38C2×#533C2214yescomplemented
39C2×#529C2214yes—
40C2×#529C2214yescomplemented
41C2×#525C2214yes—
42C2×#525C2212yes—
43C22×C22⋊Q8C2211yescharacteristic
44C2×#520C2212yes—
45C2×#520C2212yes—
46C2×C4×#41C2212yes—
47C22×C4×Q8C2211yescharacteristic
48C23×C4⋊C4C2211yescharacteristic
49#2857C2214yes—
50#2855C2214yes—
51#2848C2214yes—
52#2726C2218yescomplemented
53#2724C2218yescomplemented
54#2722C2218yescomplemented
55#2720C2218yes—
56#2719C2218yescomplemented
57#2717C2218yescomplemented
58#2708C2218yes—
59#2698C2218yescomplemented
60#2695C2218yes—
61#2689C2218yescomplemented
62#2689C2218yescomplemented
63#2680C2218yes—
64#2659C2214yes—
65#2627C2214yes—
66#2627C2214yes—
67#2553C2218yes—
68#2552C2214yescomplemented
69#2551C2214yescomplemented
70#2550C2214yescomplemented
71#2550C2214yescomplemented
72#2534C2218yes—
73#2506C2218yescomplemented
74#2503C2214yescomplemented
75#2502C2214yescomplemented
76#2499C2214yescomplemented
77#2499C2214yescomplemented
78#2496C2218yescomplemented
79#2489C2214yes—
80#2486C2218yes—
81#2486C2218yescomplemented
82#2478C2218yescomplemented
83#2475C2218yes—
84#2470C2218yes—
85#2468C2218yes—
86#2466C2218yes—
87#2462C2218yescomplemented
88#2453C2214yescomplemented
89#2453C2214yescomplemented
90#2451C2214yescomplemented
91#2451C2214yescomplemented
92#2449C2218yes—
93#2447C2214yescomplemented
94#2447C2214yescomplemented
95#2446C2214yescomplemented
96#2446C2214yescomplemented
97#2442C2214yes—
98#2442C2214yes—
99#2441C2214yes—
100#2440C2214yes—
101#2440C2214yes—
102#2440C2218yescomplemented
103#2438C2218yescomplemented
104#2432C2214yes—
105#2429C2214yes—
106#2429C2214yes—
107#2429C2214yes—
108#2427C2214yes—
109#2427C2214yes—
110#2427C2214yes—
111#2423C2212yes—
112#2423C2212yes—
113#2422C2214yes—
114#2422C2212yes—
115#2422C2212yes—
116#2421C2212yes—
117#2421C2212yes—
118#2420C2212yes—
119#2420C2212yes—
120#2419C2218yes—
121#2419C2218yes—
122#2419C2214yes—
123#2419C2214yes—
124#2419C2218yescomplemented
125#2418C2214yes—
126#2418C2214yes—
127#2417C2214yes—
128#2417C2214yes—
129#2415C2214yes—
130#2415C2214yes—
131#2406C2218yes—
132#2395C2214yes—
133#2395C2214yes—
134#2363C2214yescomplemented
135#2362C2214yes—
136#2362C2214yescomplemented
137#2361C2214yescomplemented
138#2360C2214yes—
139#2360C2214yes—
140#2360C2214yes—
141#2360C2214yes—
142#2360C2214yescomplemented
143#2359C2218yes—
144#2351C2214yescomplemented
145Q8×C4⋊C4C2214yescomplemented
146#2349C2218yes—
147#2349C2214yescomplemented
148D4×C4⋊C4C2218yes—
149D4×C4⋊C4C2214yescomplemented
150#2339C2214yes—
151#2325C2214yes—
152#2317C2212yes—
153#2317C2214yescomplemented
154#2316C2212yes—
155#2316C2211yescharacteristic
156#2316C2214yescomplemented
157#2310C2212yes—
158C4×#123C2214yes—
159C4×#123C2214yes—
160C4×#121C2214yes—
161#2297C2212yes—
162#2296C2212yes—
163#2296C2214yescomplemented
164C2×#391C2211yescharacteristic
165C2×#389C2211yescharacteristic
166C2×#389C2212yes—
167C2×#389C2214yescomplemented
168C2×#387C2212yes—
169C2×#385C2212yes—
170#2285C2212yes—
171#2280C2212yes—
172C2×C4×C4⋊C4C2211yescharacteristic
173C2×C4×C22⋊C4C2212yes—
174C2×C4×C22⋊C4C2211yescharacteristic
175C22×#41C2312yes—
176C22×#41C2314yes—
177C23×Q8C2311yescharacteristic
178C24×C4C2311yescharacteristic
179C24×C4C2312yes—
180#554—232no—
181#553—232no—
182#552—232no—
183#547—232no—
184#544—28no—
185#544—28no—
186#542—232no—
187#541—232no—
188#539—232no—
189#539—232no—
190#537D4116yes—
191#536—216no—
192#533—232no—
193C2×C4⋊Q8C2314yes—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197#529—232no—
198#529—232no—
199C2×#126C2318yes—
200C2×#126C2318yes—
201C2×#126C2318yes—
202C2×#125C2314yes—
203C2×#125C2314yes—
204C2×#125C2318yes—
205C2×#125C2318yes—
206C2×#125C2314yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209#525—216no—
210#525—232no—
211C2×#123C2314yes—
212C2×#123C2318yes—
213C2×#123C2314yes—
214C2×#123C2318yes—
215C2×#123C2318yes—
216C2×#123C2318yes—
217C2×#123C2314yes—
218C2×C22⋊Q8—28no—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#120C2314yes—
239#520—216no—
240#520—216no—
241C4×#41—216no—
242C2×C4×Q8—28no—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2318yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2318yes—
270C2×#117C2314yes—
271C22×C4⋊C4—28no—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2318yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C42C2312yes—
288C22×C42C2311yescharacteristic
289C22×C42C2314yes—
290C22×C42C2311yescharacteristic
291C22×C42C2312yes—
292#400C2318yes—
293#400C2318yes—
294#400C2314yes—
295#400C2314yes—
296#400C2318yes—
297#400C2318yes—
298#399C2314yes—
299#399C2314yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2314yes—
305#398C2314yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#396C2318yes—
325#396C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#395C2318yes—
330#394C2314yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2318yes—
335#394C2318yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2312yes—
347#391C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2318yes—
372#389C2318yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2312yes—
377#389C2312yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2318yes—
384#388C2314yes—
385#388C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#386C2314yes—
400#386C2318yes—
401#386C2314yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2314yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#384C2314yes—
423#384C2318yes—
424#384C2314yes—
425#384C2312yes—
426#384C2312yes—
427#382C2314yes—
428#382C2318yes—
429#382C2312yes—
430#382C2312yes—
431#381C2318yes—
432#381C2318yes—
433#381C2314yes—
434#381C2318yes—
435#381C2314yes—
436#381C2314yes—
437#380C2314yes—
438#380C2318yes—
439#380C2318yes—
440#380C2318yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2312yes—
446#380C2312yes—
447#380C2312yes—
448#380C2312yes—
449#380C2318yes—
450#380C2318yes—
451#379C2314yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C2×#95C2312yes—
475C2×#95C2318yes—
476C2×#95C2312yes—
477C2×#95C2311yescharacteristic
478C2×#95C2311yescharacteristic
479C2×#95C2312yes—
480C2×#95C2312yes—
481C25C2411yescharacteristic
482C2×#41—216no—
483C2×#41—28no—
484C2×#41—28no—
485C2×#41—48no—
486C2×#41—84no—
487C2×#41C2×D4116yes—
488C22×Q8—24no—
489C22×Q8—24no—
490C22×Q8—24no—
491C22×Q8C2414yes—
492C22×Q8C2412yes—
493C22×Q8C2414yes—
494C22×Q8C2414yes—
495C22×D4C2414yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2412yes—
499C22×D4C2414yes—
500C23×C4—24no—
501C23×C4—24no—
502C23×C4—24no—
503C23×C4—28no—
504C23×C4—44no—
505C23×C4—82no—
506C23×C4C2412yes—
507C23×C4C2411yescharacteristic
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2414yes—
513C23×C4C2414yes—
514C23×C4C2414yes—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2412yes—
518C23×C4C2418yes—
519C23×C4C2418yes—
520C23×C4C2414yes—
521C23×C4C2414yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2411yescharacteristic
525C4⋊Q8—216no—
526C4⋊Q8—216no—
527C4⋊Q8—216no—
528C4⋊Q8—84no—
529#126—232no—
530#126—232no—
531#126—232no—
532#125—216no—
533#125—216no—
534#125—232no—
535#125—232no—
536#125—216no—
537#124—216no—
538#124—216no—
539#123—216no—
540#123—232no—
541#123—232no—
542#123—232no—
543#123—232no—
544#123—216no—
545#123—48no—
546C22⋊Q8—28no—
547C22⋊Q8—28no—
548C22⋊Q8—216no—
549C22⋊Q8—216no—
550C22⋊Q8—216no—
551C22⋊Q8—216no—
552C22⋊Q8—216no—
553C22⋊Q8—216no—
554C22⋊Q8—216no—
555C22⋊Q8—232no—
556C22⋊Q8—232no—
557C22⋊Q8—48no—
558C22⋊Q8—84no—
559C22⋊Q8C2×D4132yes—
560#121—28no—
561#121—216no—
562#121—28no—
563#121C2×D4132yes—
564#121C2×D4132yes—
565#120—216no—
566C4×Q8—28no—
567C4×Q8—28no—
568C4×Q8—216no—
569C4×Q8—216no—
570C4×Q8—216no—
571C4×Q8—216no—
572C4×Q8—216no—
573C4×D4—28no—
574C4×D4—216no—
575C4×D4—216no—
576C4×D4—28no—
577C4×D4—232no—
578C4×D4—216no—
579C4×D4—216no—
580C4×D4—216no—
581C4×D4—216no—
582C4×D4—232no—
583C4×D4—216no—
584C4×D4—232no—
585C4×D4—84no—
586#117—28no—
587#117—216no—
588#117—28no—
589#117—216no—
590#117—28no—
591#117—216no—
592#117—216no—
593#117—232no—
594C2×C4⋊C4—24no—
595C2×C4⋊C4—28no—
596C2×C4⋊C4—28no—
597C2×C4⋊C4—216no—
598C2×C4⋊C4—28no—
599C2×C4⋊C4—216no—
600C2×C4⋊C4—216no—
601C2×C4⋊C4—216no—
602C2×C4⋊C4—82no—
603C2×C4⋊C4—88no—
604C2×C4⋊C4C2×D418yes—
605C2×C4⋊C4#4118yescomplemented
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C22⋊C4—28no—
647C2×C22⋊C4—24no—
648C2×C22⋊C4—42no—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2411yescharacteristic
653C2×C22⋊C4C2411yescharacteristic
654C2×C22⋊C4C2411yescharacteristic
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2411yescharacteristic
679C2×C42—24no—
680C2×C42—28no—
681C2×C42—216no—
682C2×C42—24no—
683C2×C42—82no—
684C2×C42C2418yes—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2418yes—
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2412yes—
703#95C2412yes—
704#95C2414yes—
705#95C2412yes—
706#95C2414yes—
707#95C2412yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734C24—22no—
735C24—22no—
736C24—22no—
737C24—22no—
738C24—22no—
739C24—41no—
740C24—41no—
741C24C2514yes—
742C24C2511yescharacteristic
743C24C2511yescharacteristic
744C24C2511yescharacteristic
745#41—264no—
746#41—832no—
747C2×Q8—28no—
748C2×Q8—28no—
749C2×Q8—28no—
750C2×Q8—24no—
751C2×Q8—28no—
752C2×Q8—24no—
753C2×Q8—28no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—44no—
758C2×Q8—416no—
759C2×Q8C22×D418yes—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4C22×D4116yes—
773C2×D4C22×D418yes—
774C2×D4C22×D4116yes—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—22no—
778C22×C4—24no—
779C22×C4—28no—
780C22×C4—22no—
781C22×C4—24no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—28no—
787C22×C4—22no—
788C22×C4—28no—
789C22×C4—24no—
790C22×C4—216no—
791C22×C4—22no—
792C22×C4—28no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—28no—
803C22×C4—216no—
804C22×C4—41no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—44no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—44no—
815C22×C4—41no—
816C22×C4—48no—
817C22×C4—42no—
818C22×C4—48no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—42no—
823C22×C4—48no—
824C22×C4—41no—
825C22×C4—48no—
826C22×C4—416no—
827C22×C4—816no—
828C22×C4C22×D4116yes—
829C22×C4C22×D418yes—
830C22×C4C22×D414yes—
831C22×C4C2×#4118yes—
832C22×C4C2×#4114yes—
833C22×C42−1+414yes—
834C22×C4C2511yescharacteristic
835C22×C4C2512yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2511yescharacteristic
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2512yes—
853C4⋊C4—28no—
854C4⋊C4—216no—
855C4⋊C4—24no—
856C4⋊C4—216no—
857C4⋊C4—216no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—216no—
865C4⋊C4—216no—
866C4⋊C4—28no—
867C4⋊C4—216no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—216no—
871C4⋊C4—24no—
872C4⋊C4—216no—
873C4⋊C4—216no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4C22×D4116yes—
891C4⋊C4C22×D4116yes—
892C4⋊C4C2×#41116yes—
893C22⋊C4—28no—
894C22⋊C4—216no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—216no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—216no—
902C22⋊C4—28no—
903C22⋊C4—22no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—216no—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—28no—
915C22⋊C4—42no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4C22×D4132yes—
922C22⋊C42−1+414yes—
923C42—24no—
924C42—28no—
925C42—28no—
926C42—24no—
927C42—28no—
928C42—28no—
929C42—28no—
930C42—216no—
931C42—28no—
932C42—216no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—44no—
937C42—44no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—28no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—24no—
948C23—21no—
949C23—24no—
950C23—21no—
951C23—21no—
952C23—24no—
953C23—21no—
954C23—24no—
955C23—21no—
956C23—24no—
957C23—21no—
958C23—21no—
959C23—24no—
960C23—21no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23C23×D418yes—
968C23C23×D412yes—
969C23C22×#4112yes—
970C23C2×2−1+412yes—
971C23C2×2−1+412yes—
972C23#58512yes—
973C23C2611yescharacteristic
974Q8—216no—
975Q8—416no—
976Q8—88no—
977Q8—88no—
978D4—232no—
979D4—216no—
980D4—416no—
981D4—416no—
982D4—416no—
983C2×C4—21no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—21no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—21no—
993C2×C4—232no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—21no—
1032C2×C4—24no—
1033C2×C4—48no—
1034C2×C4—48no—
1035C2×C4—44no—
1036C2×C4—416no—
1037C2×C4—44no—
1038C2×C4—416no—
1039C2×C4—44no—
1040C2×C4—48no—
1041C2×C4—48no—
1042C2×C4—48no—
1043C2×C4—816no—
1044C2×C4—88no—
1045C2×C4—82no—
1046C2×C4—88no—
1047C2×C4—82no—
1048C2×C4—84no—
1049C2×C4—816no—
1050C2×C4#547116yes—
1051C2×C4C23×D418yes—
1052C2×C4C23×D418yes—
1053C2×C4C23×D414yes—
1054C2×C4C22×#4118yes—
1055C2×C4C22×#4114yes—
1056C2×C4C2×2−1+412yes—
1057C2×C4C2×2−1+412yes—
1058C2×C4C2×2−1+414yes—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—22no—
1066C22—28no—
1067C22—28no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—28no—
1074C22—416no—
1075C22—41no—
1076C22—41no—
1077C22—44no—
1078C22—44no—
1079C22—41no—
1080C22—41no—
1081C22—44no—
1082C22—41no—
1083C22—44no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22C2×#54714yes—
1088C22C24×D411yescharacteristic
1089C22C23×#4111yescharacteristic
1090C22C22×2−1+411yescharacteristic
1091C22C22×2−1+411yescharacteristic
1092C22C2×#58511yescharacteristic
1093C22H(7,𝔽2)11yescharacteristic
1094C222−1+611yescharacteristic
1095C4—28no—
1096C4—22no—
1097C4—28no—
1098C4—22no—
1099C4—28no—
1100C4—44no—
1101C4—42no—
1102C4—44no—
1103C4—44no—
1104C4—41no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—42no—
1110C4—41no—
1111C4—42no—
1112C4—44no—
1113C4C2×#54718yes—
1114C2—24no—
1115C2—48no—
1116C2—42no—
1117C2—42no—
1118C2C22×#54711yescharacteristic
1119C2#6278811yescharacteristic
1120C2#6284711yescharacteristic
1121C2#6292811yescharacteristic
1122C2#6294511yescharacteristic
1123C2#6298711yescharacteristic
1124C2D4×2−1+411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3492C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3461C2semidirect
3. #59121C2semidirect
4. #59116C2semidirect
5. #59113C2semidirect
6. #59031C2semidirect
7. #45185C2semidirect
8. #45177C2semidirect
9. #45107C2semidirect
10. #44875C2semidirect
11. #39376C2semidirect
12. #37763C2semidirect
13. #37760C2semidirect
14. #36143C2semidirect
15. #35633C2semidirect
16. #35619C2semidirect
17. #35224C2semidirect
18. #35167C2semidirect
19. #35154C2semidirect
20. #34742C2semidirect
21. #34274C2semidirect
22. #34250C2semidirect
23. C2×#2360C2semidirect
32. C2×#542C22semidirect
33. C2×#541C22semidirect
38. C2×#533C22semidirect
40. C2×#529C22semidirect
52. #2726C22semidirect
53. #2724C22semidirect
54. #2722C22semidirect
56. #2719C22semidirect
57. #2717C22semidirect
59. #2698C22semidirect
61. #2689C22semidirect
62. #2689C22semidirect
68. #2552C22semidirect
69. #2551C22semidirect
70. #2550C22semidirect
71. #2550C22semidirect
73. #2506C22semidirect
74. #2503C22semidirect
75. #2502C22semidirect
76. #2499C22semidirect
77. #2499C22semidirect
78. #2496C22semidirect
81. #2486C22semidirect
82. #2478C22semidirect
87. #2462C22semidirect
88. #2453C22semidirect
89. #2453C22semidirect
90. #2451C22semidirect
91. #2451C22semidirect
93. #2447C22semidirect
94. #2447C22semidirect
95. #2446C22semidirect
96. #2446C22semidirect
102. #2440C22semidirect
103. #2438C22semidirect
124. #2419C22semidirect
134. #2363C22semidirect
136. #2362C22semidirect
137. #2361C22semidirect
142. #2360C22semidirect
144. #2351C22semidirect
145. Q8×C4⋊C4C22semidirect
147. #2349C22semidirect
149. D4×C4⋊C4C22semidirect
153. #2317C22semidirect
156. #2316C22semidirect
163. #2296C22semidirect
167. C2×#389C22semidirect
605. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34922
C2×#34612
#591212
#591162
#591132
#590312
#451852
#451772
#451072
#448752
#393762
#377632
#377602
#361432
#356332
#356192
#352242
#351672
#351542
#347422
#342742
#342502
C2×#23602