Finite Group Databasebeta

← #7683784

Subgroups — #7683784

Order 512.

7226 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C212yesmaximal, complemented
2#59819C214yesmaximal, complemented
3#59312C214yesmaximal, complemented
4#59059C214yesmaximal, complemented
5#59055C214yesmaximal, complemented
6#59054C214yesmaximal, complemented
7#59052C214yesmaximal, complemented
8#45217C214yesmaximal, complemented
9#45217C214yesmaximal, complemented
10#45112C214yesmaximal, complemented
11#45101C214yesmaximal, complemented
12#43528C218yesmaximal, complemented
13#35667C212yesmaximal, complemented
14#35634C212yesmaximal, complemented
15#35633C212yesmaximal, complemented
16C2×#2542C211yesmaximal, characteristic, complemented
17#34737C212yesmaximal, complemented
18#34274C211yesmaximal, characteristic, complemented
19#34271C211yesmaximal, characteristic, complemented
20#34203C212yesmaximal, complemented
21#3495—232no—
22C2×#556C2214yescomplemented
23C2×#554C2214yescomplemented
24C2×#552C2218yes—
25C2×#552C2214yescomplemented
26C2×#552C2214yescomplemented
27C2×#551C2218yes—
28C2×#544C2211yescharacteristic
29C2×#542C2214yescomplemented
30C2×#541C2214yescomplemented
31C2×#537C2211yescharacteristic
32C2×#536C2212yes—
33C2×#536C2212yes—
34C2×#533C2214yescomplemented
35C22×C4⋊Q8C2211yescharacteristic
36C2×#529C2214yescomplemented
37C2×#525C2212yes—
38C2×#525C2212yes—
39C22×C22⋊Q8C2212yes—
40C22×C22⋊Q8C2212yes—
41C2×#520C2212yes—
42C2×#519C2212yes—
43C22×C4×D4C2211yescharacteristic
44C22×#117C2212yes—
45#2733C2214yes—
46#2732C2214yes—
47#2732C2218yescomplemented
48#2730C2218yescomplemented
49#2727C2214yes—
50#2727C2218yescomplemented
51#2721C2218yescomplemented
52#2721C2218yescomplemented
53#2721C2218yescomplemented
54#2721C2218yescomplemented
55#2705C2218yescomplemented
56#2694C2218yescomplemented
57#2694C2218yescomplemented
58#2682C2214yes—
59#2554C2218yes—
60#2554C2218yes—
61#2552C2214yescomplemented
62#2552C2218yescomplemented
63#2546C2214yescomplemented
64#2546C2214yescomplemented
65#2545C2214yescomplemented
66#2545C2214yescomplemented
67#2542C2214yes—
68#2542C2214yes—
69#2542C2214yes—
70#2542C2214yes—
71#2542C2214yescomplemented
72#2542C2214yescomplemented
73#2542C2214yescomplemented
74#2542C2214yescomplemented
75#2540C2214yescomplemented
76#2540C2214yescomplemented
77#2540C2214yescomplemented
78#2540C2214yescomplemented
79#2539C2218yes—
80#2538C2214yescomplemented
81#2534C2218yes—
82#2512C2218yescomplemented
83#2501C2218yes—
84#2486C2218yes—
85#2479C2218yes—
86#2479C2218yescomplemented
87#2479C2218yescomplemented
88#2471C2218yescomplemented
89#2467C2218yescomplemented
90#2456C2218yes—
91#2454C2218yescomplemented
92#2448C2218yescomplemented
93#2441C2218yescomplemented
94#2441C2218yescomplemented
95#2429C2214yescomplemented
96#2429C2214yescomplemented
97#2429C2214yescomplemented
98#2429C2214yescomplemented
99#2429C2214yescomplemented
100#2429C2214yescomplemented
101#2427C2214yescomplemented
102#2427C2214yescomplemented
103#2426C2218yes—
104#2423C2218yescomplemented
105#2423C2218yescomplemented
106#2417C2212yes—
107#2417C2212yes—
108#2417C2214yescomplemented
109#2417C2214yescomplemented
110#2416C2212yes—
111#2416C2212yes—
112#2415C2212yes—
113#2415C2212yes—
114#2415C2214yescomplemented
115#2415C2214yescomplemented
116#2414C2212yes—
117#2414C2212yes—
118#2413C2218yes—
119#2413C2218yes—
120#2413C2214yes—
121#2412C2214yes—
122#2411C2214yes—
123#2410C2214yes—
124C2×#399C2214yes—
125#2392C2214yes—
126#2392C2214yes—
127#2370C2214yescomplemented
128#2370C2214yescomplemented
129#2369C2214yescomplemented
130#2365C2214yescomplemented
131#2363C2218yes—
132#2363C2214yescomplemented
133#2362C2214yescomplemented
134#2362C2214yescomplemented
135#2362C2214yescomplemented
136#2361C2214yescomplemented
137#2360C2214yescomplemented
138#2360C2214yescomplemented
139#2360C2214yescomplemented
140#2354C2214yescomplemented
141Q8×C4⋊C4C2214yescomplemented
142#2344C2218yes—
143#2342C2218yes—
144#2329C2214yes—
145#2325C2214yes—
146#2323C2214yescomplemented
147#2323C2214yescomplemented
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2310C2212yes—
151C4×C22⋊Q8C2214yes—
152C4×C22⋊Q8C2214yescomplemented
153C4×C22⋊Q8C2214yescomplemented
154C4×#121C2214yes—
155C4×#121C2214yes—
156C4×#121C2214yes—
157#2297C2212yes—
158#2296C2212yes—
159C2×#390C2212yes—
160C2×#384C2212yes—
161#2280C2212yes—
162#2274C2212yes—
163C2×C4×C4⋊C4C2211yescharacteristic
164C22×#41C2312yes—
165C23×Q8C2312yes—
166C23×D4C2311yescharacteristic
167C24×C4C2312yes—
168#556—232no—
169#554—232no—
170#552—232no—
171#552—232no—
172#552—264no—
173#551—264no—
174#544D4116yescomplemented
175#542—232no—
176#541—232no—
177#537—28no—
178#536—216no—
179#536—48no—
180#533—232no—
181C2×C4⋊Q8—44no—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187#529—232no—
188C2×#126C2318yes—
189C2×#126C2318yes—
190C2×#126C2318yes—
191C2×#126C2318yes—
192C2×#125C2318yes—
193C2×#125C2318yes—
194C2×#125C2318yes—
195C2×#125C2314yes—
196C2×#124C2314yes—
197C2×#124C2318yes—
198C2×#124C2314yes—
199#525—216no—
200#525—48no—
201C2×#123C2314yes—
202C2×#123C2318yes—
203C2×#123C2318yes—
204C2×#123C2318yes—
205C2×#123C2314yes—
206C2×#123C2318yes—
207C2×C22⋊Q8—216no—
208C2×C22⋊Q8—216no—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#120C2314yes—
238C2×#120C2314yes—
239#520—216no—
240#519—216no—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2318yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×D4—44no—
249C2×C4×D4C2318yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×#117—216no—
262C2×#117C2312yes—
263C2×#117C2312yes—
264C2×#117C2314yes—
265C2×#117C2318yes—
266C2×#117C2314yes—
267C2×#117C2318yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2318yes—
272C2×#117C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2314yes—
285C22×C22⋊C4C2314yes—
286C22×C22⋊C4C2312yes—
287C22×C42C2314yes—
288C22×C42C2311yescharacteristic
289C22×C42C2312yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2318yes—
294#399C2318yes—
295#399C2318yes—
296#399C2318yes—
297#399C2318yes—
298#399C2318yes—
299#399C2318yes—
300#398C2314yes—
301#398C2314yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#397C2314yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#396C2314yes—
313#396C2314yes—
314#396C2314yes—
315#396C2314yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#394C2314yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#394C2318yes—
329#394C2318yes—
330#392C2314yes—
331#392C2314yes—
332#392C2318yes—
333#392C2318yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2318yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#390C2318yes—
343#390C2312yes—
344#390C2314yes—
345#390C2318yes—
346#390C2318yes—
347#390C2312yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2318yes—
352#390C2318yes—
353#390C2318yes—
354#390C2314yes—
355#390C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2314yes—
364#389C2318yes—
365#389C2318yes—
366#389C2314yes—
367#389C2318yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#386C2314yes—
402#386C2318yes—
403#386C2314yes—
404#386C2318yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2318yes—
410#385C2318yes—
411#385C2314yes—
412#385C2318yes—
413#385C2318yes—
414#385C2314yes—
415#384C2314yes—
416#384C2318yes—
417#384C2318yes—
418#384C2318yes—
419#384C2314yes—
420#381C2318yes—
421#381C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2312yes—
425#380C2312yes—
426#380C2318yes—
427#380C2314yes—
428#380C2314yes—
429#380C2312yes—
430#380C2312yes—
431#380C2318yes—
432#379C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2318yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2318yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C22⋊C4C2318yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C2×#95C2312yes—
455C25C2412yes—
456C2×#41—28no—
457C2×#41—28no—
458C2×#41—28no—
459C22×Q8—28no—
460C22×Q8—28no—
461C22×Q8—28no—
462C22×Q8C2414yes—
463C22×Q8C2414yes—
464C22×Q8C2412yes—
465C22×Q8C2414yes—
466C22×D4—24no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4C2414yes—
470C22×D4C2412yes—
471C22×D4C2414yes—
472C22×D4C2412yes—
473C22×D4C2411yescharacteristic
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C22×D4C2414yes—
478C22×D4C2411yescharacteristic
479C23×C4—28no—
480C23×C4—28no—
481C23×C4—28no—
482C23×C4C2414yes—
483C23×C4C2412yes—
484C23×C4C2411yescharacteristic
485C23×C4C2412yes—
486C23×C4C2414yes—
487C23×C4C2412yes—
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2414yes—
491C23×C4C2411yescharacteristic
492C23×C4C2414yes—
493C23×C4C2418yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C4⋊Q8—216no—
498C4⋊Q8—48no—
499C4⋊Q8—48no—
500C4⋊Q8—48no—
501C4⋊Q8C2×D4132yescomplemented
502#126—232no—
503#126—232no—
504#126—232no—
505#126—232no—
506#125—232no—
507#125—232no—
508#125—232no—
509#125C2×D4132yescomplemented
510#124—232no—
511#124—216no—
512#124—48no—
513#123—232no—
514#123—232no—
515#123—216no—
516#123—232no—
517#123—48no—
518#123—416no—
519C22⋊Q8—232no—
520C22⋊Q8—232no—
521C22⋊Q8—216no—
522C22⋊Q8—216no—
523C22⋊Q8—216no—
524C22⋊Q8—216no—
525C22⋊Q8—28no—
526C22⋊Q8—28no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—216no—
530C22⋊Q8—216no—
531C22⋊Q8—216no—
532C22⋊Q8—216no—
533C22⋊Q8—216no—
534C22⋊Q8—44no—
535C22⋊Q8—44no—
536C22⋊Q8—48no—
537C22⋊Q8—48no—
538C22⋊Q8C2×D4132yes—
539#121—216no—
540#121—216no—
541#121—28no—
542#121—28no—
543#121—216no—
544#121—48no—
545#121—44no—
546#121—44no—
547#120—216no—
548#120—48no—
549C4×Q8—232no—
550C4×Q8—216no—
551C4×Q8—216no—
552C4×Q8—216no—
553C4×Q8—216no—
554C4×Q8—216no—
555C4×Q8—48no—
556C4×D4—232no—
557C4×D4—216no—
558C4×D4—232no—
559C4×D4—216no—
560C4×D4—216no—
561C4×D4—48no—
562C4×D4—44no—
563C4×D4—44no—
564C4×D4—44no—
565C4×D4—44no—
566C4×D4—48no—
567C4×D4—48no—
568#117—28no—
569#117—28no—
570#117—28no—
571#117—28no—
572#117—216no—
573#117—232no—
574#117—232no—
575#117—216no—
576#117—232no—
577#117—216no—
578#117C2×D4116yes—
579C2×C4⋊C4—216no—
580C2×C4⋊C4—216no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—42no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4—44no—
587C2×C4⋊C4C2×D418yes—
588C2×C4⋊C4#4118yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C22⋊C4—216no—
632C2×C22⋊C4—216no—
633C2×C22⋊C4—216no—
634C2×C22⋊C4—44no—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C42—24no—
671C2×C42—216no—
672C2×C42—44no—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2418yes—
676C2×C42C2418yes—
677C2×C42C2418yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2418yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2418yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708C24—24no—
709C24—24no—
710C24—24no—
711C24—24no—
712C24—42no—
713C24—42no—
714C24—42no—
715C24C2512yes—
716C24C2514yes—
717C24C2512yes—
718C24C2511yescharacteristic
719#41—432no—
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—24no—
723C2×Q8—28no—
724C2×Q8—28no—
725C2×Q8—24no—
726C2×Q8—28no—
727C2×Q8—24no—
728C2×Q8—28no—
729C2×Q8—44no—
730C2×Q8—44no—
731C2×Q8—432no—
732C2×Q8C22×D4116yes—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—24no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—24no—
741C2×D4—28no—
742C2×D4—24no—
743C2×D4—28no—
744C2×D4—24no—
745C2×D4—22no—
746C2×D4—24no—
747C2×D4—41no—
748C2×D4—42no—
749C2×D4—41no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—44no—
753C2×D4—416no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D42−1+414yes—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—22no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—24no—
776C22×C4—28no—
777C22×C4—24no—
778C22×C4—28no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—28no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—216no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—44no—
797C22×C4—42no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—48no—
801C22×C4—44no—
802C22×C4—48no—
803C22×C4—44no—
804C22×C4—432no—
805C22×C4C22×D418yes—
806C22×C4C22×D414yes—
807C22×C4C2×#4118yes—
808C22×C4C2×#4114yes—
809C22×C4H(5,𝔽2)14yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2518yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—216no—
831C4⋊C4—216no—
832C4⋊C4—216no—
833C4⋊C4—216no—
834C4⋊C4—216no—
835C4⋊C4—216no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—216no—
839C4⋊C4—216no—
840C4⋊C4—216no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—41no—
847C4⋊C4—42no—
848C4⋊C4—41no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4C22×D4116yes—
863C4⋊C4C22×D418yes—
864C4⋊C4C22×D418yes—
865C4⋊C4C22×D4116yes—
866C4⋊C4C22×D4132yes—
867C4⋊C4C2×#41116yes—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—216no—
874C22⋊C4—216no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—216no—
878C22⋊C4—216no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—216no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4C22×D4116yes—
903C42—28no—
904C42—28no—
905C42—28no—
906C42—216no—
907C42—216no—
908C42—216no—
909C42—24no—
910C42—24no—
911C42—28no—
912C42—28no—
913C42—44no—
914C42—48no—
915C42—48no—
916C42C22×D4116yes—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—22no—
930C23—24no—
931C23—24no—
932C23—22no—
933C23—24no—
934C23—22no—
935C23—24no—
936C23—22no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—22no—
941C23—48no—
942C23—48no—
943C23—48no—
944C23—48no—
945C23—84no—
946C23—84no—
947C23—84no—
948C23C23×D412yes—
949C23C22×#4112yes—
950C23C2×H(5,𝔽2)12yes—
951C23C2×2−1+414yes—
952C23C2611yescharacteristic
953Q8—416no—
954Q8—416no—
955Q8—416no—
956Q8—48no—
957D4—44no—
958D4—416no—
959D4—48no—
960D4—44no—
961D4—416no—
962D4—48no—
963D4—88no—
964D4—88no—
965D4—88no—
966D4—88no—
967C2×C4—28no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—24no—
971C2×C4—21no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—21no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—48no—
1008C2×C4—48no—
1009C2×C4—416no—
1010C2×C4—44no—
1011C2×C4—48no—
1012C2×C4—416no—
1013C2×C4—48no—
1014C2×C4—48no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—416no—
1018C2×C4—816no—
1019C2×C4—88no—
1020C2×C4#550116yes—
1021C2×C4C23×D418yes—
1022C2×C4C23×D418yes—
1023C2×C4C23×D418yes—
1024C2×C4C23×D414yes—
1025C2×C4C22×#4118yes—
1026C2×C4C22×#4114yes—
1027C2×C4C2×H(5,𝔽2)14yes—
1028C2×C4C2×2−1+412yes—
1029C2×C4#58512yes—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—44no—
1044C22—42no—
1045C22—44no—
1046C22—42no—
1047C22—44no—
1048C22—42no—
1049C22—44no—
1050C22—42no—
1051C22—42no—
1052C22—44no—
1053C22—42no—
1054C22—44no—
1055C22—42no—
1056C22—44no—
1057C22—816no—
1058C22C2×#55014yes—
1059C22C24×D411yescharacteristic
1060C22C23×#4111yescharacteristic
1061C22C22×H(5,𝔽2)11yescharacteristic
1062C22C22×2−1+411yescharacteristic
1063C22C2×#58511yescharacteristic
1064C222−1+611yescharacteristic
1065C222−1+611yescharacteristic
1066C4—28no—
1067C4—28no—
1068C4—28no—
1069C4—28no—
1070C4—22no—
1071C4—22no—
1072C4—44no—
1073C4—44no—
1074C4—44no—
1075C4—42no—
1076C4—44no—
1077C4—42no—
1078C4—42no—
1079C4—44no—
1080C4—48no—
1081C4C2×#55018yes—
1082C2—24no—
1083C2—44no—
1084C2—84no—
1085C2—82no—
1086C2C22×#55011yescharacteristic
1087C2#6281911yescharacteristic
1088C2#6288611yescharacteristic
1089C2#6298811yescharacteristic
1090C2#6299111yescharacteristic
1091C2D4×2−1+411yescharacteristic
1092C2#6299811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3495C2semidirect
2. #59819C2semidirect
3. #59312C2semidirect
4. #59059C2semidirect
5. #59055C2semidirect
6. #59054C2semidirect
7. #59052C2semidirect
8. #45217C2semidirect
9. #45217C2semidirect
10. #45112C2semidirect
11. #45101C2semidirect
12. #43528C2semidirect
13. #35667C2semidirect
14. #35634C2semidirect
15. #35633C2semidirect
16. C2×#2542C2semidirect
17. #34737C2semidirect
18. #34274C2semidirect
19. #34271C2semidirect
20. #34203C2semidirect
22. C2×#556C22semidirect
23. C2×#554C22semidirect
25. C2×#552C22semidirect
26. C2×#552C22semidirect
29. C2×#542C22semidirect
30. C2×#541C22semidirect
34. C2×#533C22semidirect
36. C2×#529C22semidirect
47. #2732C22semidirect
48. #2730C22semidirect
50. #2727C22semidirect
51. #2721C22semidirect
52. #2721C22semidirect
53. #2721C22semidirect
54. #2721C22semidirect
55. #2705C22semidirect
56. #2694C22semidirect
57. #2694C22semidirect
61. #2552C22semidirect
62. #2552C22semidirect
63. #2546C22semidirect
64. #2546C22semidirect
65. #2545C22semidirect
66. #2545C22semidirect
71. #2542C22semidirect
72. #2542C22semidirect
73. #2542C22semidirect
74. #2542C22semidirect
75. #2540C22semidirect
76. #2540C22semidirect
77. #2540C22semidirect
78. #2540C22semidirect
80. #2538C22semidirect
82. #2512C22semidirect
86. #2479C22semidirect
87. #2479C22semidirect
88. #2471C22semidirect
89. #2467C22semidirect
91. #2454C22semidirect
92. #2448C22semidirect
93. #2441C22semidirect
94. #2441C22semidirect
95. #2429C22semidirect
96. #2429C22semidirect
97. #2429C22semidirect
98. #2429C22semidirect
99. #2429C22semidirect
100. #2429C22semidirect
101. #2427C22semidirect
102. #2427C22semidirect
104. #2423C22semidirect
105. #2423C22semidirect
108. #2417C22semidirect
109. #2417C22semidirect
114. #2415C22semidirect
115. #2415C22semidirect
127. #2370C22semidirect
128. #2370C22semidirect
129. #2369C22semidirect
130. #2365C22semidirect
132. #2363C22semidirect
133. #2362C22semidirect
134. #2362C22semidirect
135. #2362C22semidirect
136. #2361C22semidirect
137. #2360C22semidirect
138. #2360C22semidirect
139. #2360C22semidirect
140. #2354C22semidirect
141. Q8×C4⋊C4C22semidirect
146. #2323C22semidirect
147. #2323C22semidirect
152. C4×C22⋊Q8C22semidirect
153. C4×C22⋊Q8C22semidirect
174. #544D4semidirect
501. C4⋊Q8C2×D4semidirect
509. #125C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
#598192
#593122
#590592
#590552
#590542
#590522
#452172
#451122
#451012
#435282
#356672
#356342
#356332
C2×#25422
#347372
#342742
#342712
#342032