Finite Group Databasebeta

← #7716067

Subgroups — #7716067

Order 512.

6804 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3538C212yesmaximal, complemented
2#49568C218yesmaximal, complemented
3#47860C218yesmaximal, complemented
4#45322C214yesmaximal, complemented
5#45321C214yesmaximal, complemented
6#45238C214yesmaximal, complemented
7#45237C214yesmaximal, complemented
8#39615C212yesmaximal, complemented
9#39487C212yesmaximal, complemented
10#39482C214yesmaximal, complemented
11#37866C214yesmaximal, complemented
12#36742C214yesmaximal, complemented
13Q8×#121C212yesmaximal, complemented
14#36186C212yesmaximal, complemented
15#35306C212yesmaximal, complemented
16#35167C212yesmaximal, complemented
17#35011C211yesmaximal, characteristic, complemented
18#35004C212yesmaximal, complemented
19#34575C211yesmaximal, characteristic
20C2×#2362C211yesmaximal, characteristic, complemented
21#3538—232no—
22C2×#563C2218yes—
23C2×#552C2214yes—
24C2×#552C2214yes—
25C2×#551C2218yes—
26C2×D4×Q8C2214yes—
27C2×D4×Q8C2214yes—
28C2×D4×Q8C2212yescomplemented
29C2×#544C2214yes—
30C2×#544C2214yes—
31C2×#541C2214yes—
32C2×#539C2214yes—
33C2×#539C2214yes—
34C2×#536C2214yes—
35C2×#536C2212yes—
36C2×#525C2212yes—
37C22×C22⋊Q8C2212yes—
38C22×C22⋊Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×#117C2211yescharacteristic
41#2857C2214yes—
42#2857C2212yes—
43#2857C2212yes—
44#2857C2214yes—
45#2854C2214yes—
46#2850C2214yes—
47#2734C2214yescomplemented
48#2732C2214yescomplemented
49#2729C2218yescomplemented
50#2727C2214yescomplemented
51#2726C2214yescomplemented
52#2725C2218yescomplemented
53#2721C2218yescomplemented
54#2719C2218yescomplemented
55#2718C2218yes—
56#2718C2218yes—
57#2716C2218yescomplemented
58#2713C2218yescomplemented
59#2710C2218yes—
60#2706C2218yes—
61#2698C2218yes—
62#2694C2218yescomplemented
63#2690C2218yescomplemented
64#2689C2218yes—
65#2680C2218yes—
66#2677C2218yescomplemented
67#2674C2218yes—
68#2674C2218yescomplemented
69#2663C2214yes—
70#2661C2214yes—
71#2659C2211yescharacteristic
72#2659C2212yes—
73#2659C2214yes—
74#2659C2212yes—
75#2656C2211yescharacteristic
76#2639C2212yes—
77#2621C2214yes—
78#2620C2214yes—
79#2618C2214yes—
80#2617C2212yes—
81#2617C2212yes—
82#2583C2218yes—
83#2564C2218yes—
84#2556C2218yescomplemented
85#2554C2218yescomplemented
86#2552C2212yescomplemented
87#2552C2218yescomplemented
88#2551C2218yescomplemented
89#2550C2218yescomplemented
90#2550C2218yescomplemented
91#2546C2212yescomplemented
92#2546C2214yescomplemented
93#2542C2212yescomplemented
94#2538C2212yescomplemented
95#2538C2214yescomplemented
96#2519C2218yescomplemented
97#2519C2218yescomplemented
98#2512C2214yescomplemented
99#2506C2214yescomplemented
100#2502C2214yes—
101#2498C2218yes—
102#2498C2218yes—
103#2489C2214yescomplemented
104#2478C2218yes—
105#2478C2218yes—
106#2474C2218yes—
107#2470C2218yes—
108#2468C2218yes—
109#2466C2218yes—
110#2461C2218yes—
111#2461C2218yescomplemented
112#2455C2218yes—
113#2453C2214yescomplemented
114#2446C2214yescomplemented
115#2441C2214yescomplemented
116#2434C2214yes—
117#2434C2214yescomplemented
118#2429C2214yescomplemented
119#2429C2214yescomplemented
120#2429C2218yescomplemented
121#2423C2214yescomplemented
122#2417C2214yes—
123#2417C2214yes—
124#2417C2218yes—
125#2415C2214yes—
126#2415C2214yes—
127#2415C2214yescomplemented
128#2413C2218yes—
129#2412C2218yes—
130#2409C2214yescomplemented
131#2395C2214yes—
132#2388C2214yes—
133#2365C2212yescomplemented
134#2362C2214yes—
135#2362C2214yes—
136#2362C2218yes—
137#2362C2214yescomplemented
138#2354C2212yescomplemented
139Q8×C4⋊C4C2212yescomplemented
140Q8×C22⋊C4C2214yescomplemented
141#2325C2214yes—
142#2317C2212yes—
143#2316C2214yes—
144#2315C2212yes—
145#2315C2212yes—
146#2311C2212yes—
147#2310C2212yes—
148C4×#121C2212yes—
149C4×#121C2212yes—
150C4×#121C2214yes—
151C2×#391C2211yescharacteristic
152C2×#389C2211yescharacteristic
153C2×#388C2212yes—
154C2×#388C2212yes—
155C2×#387C2212yes—
156#2285C2214yes—
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C4⋊C4C2212yes—
159C2×C4×C22⋊C4C2211yescharacteristic
160C22×#41C2312yes—
161C23×Q8C2312yes—
162C23×Q8C2314yes—
163C23×Q8C2311yescharacteristic
164C24×C4C2311yescharacteristic
165#563—264no—
166#552—232no—
167#552—232no—
168#551—264no—
169D4×Q8—232no—
170D4×Q8—232no—
171D4×Q8—48no—
172#544—232no—
173#544—232no—
174#541—232no—
175#539—232no—
176#539—232no—
177#536—232no—
178#536—48no—
179C2×C4⋊Q8C2318yes—
180C2×C4⋊Q8C2318yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2318yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2312yes—
187C2×#126C2318yes—
188C2×#126C2318yes—
189C2×#126C2318yes—
190C2×#126C2318yes—
191C2×#125C2318yes—
192C2×#125C2318yes—
193C2×#125C2314yes—
194C2×#125C2318yes—
195C2×#125C2318yes—
196C2×#124C2318yes—
197C2×#124C2314yes—
198#525—216no—
199C2×#123C2318yes—
200C2×#123C2314yes—
201C2×#123C2318yes—
202C2×#123C2318yes—
203C2×#123C2318yes—
204C2×#123C2318yes—
205C2×C22⋊Q8—216no—
206C2×C22⋊Q8D4116yescomplemented
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#120C2314yes—
229C2×C4×Q8—44no—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×#117—44no—
243C2×#117C2312yes—
244C2×#117C2318yes—
245C2×#117C2312yes—
246C2×#117C2314yes—
247C2×#117C2318yes—
248C2×#117C2312yes—
249C2×#117C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2311yescharacteristic
258C22×C22⋊C4C2311yescharacteristic
259C22×C22⋊C4C2311yescharacteristic
260C22×C22⋊C4C2314yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2312yes—
263C22×C42C2312yes—
264C22×C42C2312yes—
265C22×C42C2311yescharacteristic
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2318yes—
272#399C2318yes—
273#399C2314yes—
274#399C2318yes—
275#399C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#397C2314yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2314yes—
293#397C2318yes—
294#397C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2314yes—
305#395C2318yes—
306#395C2318yes—
307#394C2314yes—
308#394C2314yes—
309#394C2314yes—
310#394C2314yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2314yes—
315#393C2318yes—
316#393C2314yes—
317#392C2314yes—
318#392C2314yes—
319#392C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2312yes—
336#390C2314yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#386C2314yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2314yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#384C2314yes—
400#384C2312yes—
401#384C2314yes—
402#384C2312yes—
403#384C2314yes—
404#384C2314yes—
405#382C2314yes—
406#382C2318yes—
407#381C2318yes—
408#380C2314yes—
409#380C2318yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2312yes—
416#380C2318yes—
417#380C2318yes—
418#380C2312yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C2×#95C2312yes—
436C2×#95C2312yes—
437C2×#95C2311yescharacteristic
438C2×#95C2311yescharacteristic
439C2×#95C2312yes—
440C2×#95C2312yes—
441C25C2411yescharacteristic
442C2×#41—28no—
443C2×#41—44no—
444C2×#41—44no—
445C22×Q8—216no—
446C22×Q8—28no—
447C22×Q8—42no—
448C22×Q8—42no—
449C22×Q8—44no—
450C22×Q8—48no—
451C22×Q8—44no—
452C22×Q8—48no—
453C22×Q8C2×D418yes—
454C22×Q8C2414yes—
455C22×Q8C2412yes—
456C22×Q8C2414yes—
457C22×Q8C2418yes—
458C22×Q8C2412yes—
459C22×Q8C2412yes—
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2412yes—
463C22×D4C2412yes—
464C22×D4C2414yes—
465C22×D4C2412yes—
466C23×C4—42no—
467C23×C4—42no—
468C23×C4C2×D418yes—
469C23×C4C2414yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2414yes—
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C23×C4C2414yes—
478C23×C4C2411yescharacteristic
479C23×C4C2418yes—
480C23×C4C2412yes—
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C4⋊Q8—216no—
486C4⋊Q8—232no—
487C4⋊Q8—232no—
488C4⋊Q8—232no—
489C4⋊Q8—48no—
490C4⋊Q8—48no—
491C4⋊Q8—44no—
492C4⋊Q8—44no—
493#126—232no—
494#126—232no—
495#126—232no—
496#126—232no—
497#125—232no—
498#125—232no—
499#125—216no—
500#125—232no—
501#125—232no—
502#124—232no—
503#124—48no—
504#123—216no—
505#123—232no—
506#123—232no—
507#123—232no—
508#123—232no—
509#123—416no—
510C22⋊Q8—216no—
511C22⋊Q8—232no—
512C22⋊Q8—216no—
513C22⋊Q8—216no—
514C22⋊Q8—216no—
515C22⋊Q8—216no—
516C22⋊Q8—28no—
517C22⋊Q8—28no—
518C22⋊Q8—232no—
519C22⋊Q8—216no—
520C22⋊Q8—232no—
521C22⋊Q8—216no—
522C22⋊Q8—232no—
523C22⋊Q8—416no—
524C22⋊Q8—48no—
525C22⋊Q8C2×D4132yes—
526C22⋊Q8C2×D4132yes—
527#121—28no—
528#121—28no—
529#121—28no—
530#121—28no—
531#120—216no—
532C4×Q8—216no—
533C4×Q8—216no—
534C4×Q8—28no—
535C4×Q8—48no—
536C4×Q8—44no—
537C4×D4—216no—
538C4×D4—216no—
539C4×D4—232no—
540C4×D4—232no—
541C4×D4—48no—
542C4×D4—44no—
543C4×D4—44no—
544#117—28no—
545#117—232no—
546#117—216no—
547#117—28no—
548#117—232no—
549#117—48no—
550#117—44no—
551C2×C4⋊C4—216no—
552C2×C4⋊C4—28no—
553C2×C4⋊C4—28no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—42no—
556C2×C4⋊C4—44no—
557C2×C4⋊C4C2×D4116yes—
558C2×C4⋊C4C2×D418yes—
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—216no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—44no—
608C2×C22⋊C4C2×D4116yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C42—28no—
635C2×C42—44no—
636C2×C42—42no—
637C2×C42—44no—
638C2×C42—42no—
639C2×C42C2418yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2418yes—
643C2×C42C2418yes—
644C2×C42C2412yes—
645C2×C42C2414yes—
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2414yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2414yes—
657#95C2414yes—
658#95C2418yes—
659#95C2418yes—
660#95C2414yes—
661#95C2418yes—
662#95C2414yes—
663#95C2418yes—
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2414yes—
671#95C2414yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678C24—22no—
679C24—22no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24C22×D414yes—
685C24C2514yes—
686C24C2512yes—
687C24C2511yescharacteristic
688#41—816no—
689C2×Q8—28no—
690C2×Q8—28no—
691C2×Q8—216no—
692C2×Q8—24no—
693C2×Q8—24no—
694C2×Q8—28no—
695C2×Q8—24no—
696C2×Q8—28no—
697C2×Q8—42no—
698C2×Q8—42no—
699C2×Q8—48no—
700C2×Q8—44no—
701C2×Q8—42no—
702C2×Q8—44no—
703C2×Q8—48no—
704C2×Q8—42no—
705C2×Q8—416no—
706C2×Q8—816no—
707C2×Q8—832no—
708C2×Q8C22×D418yes—
709C2×Q8C22×D418yes—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—42no—
723C2×D4—44no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—22no—
731C22×C4—24no—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—28no—
735C22×C4—24no—
736C22×C4—28no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—216no—
745C22×C4—416no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—42no—
749C22×C4—41no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—41no—
753C22×C4—42no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—48no—
763C22×C4—44no—
764C22×C4—42no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—48no—
768C22×C4—44no—
769C22×C4C22×D418yes—
770C22×C4C22×D418yes—
771C22×C4C22×D414yes—
772C22×C4C22×D418yes—
773C22×C4C22×D418yes—
774C22×C4C22×D414yes—
775C22×C42−1+414yes—
776C22×C42−1+414yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2518yes—
784C22×C4C2514yes—
785C22×C4C2518yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C4⋊C4—28no—
795C4⋊C4—216no—
796C4⋊C4—216no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—216no—
801C4⋊C4—216no—
802C4⋊C4—216no—
803C4⋊C4—216no—
804C4⋊C4—216no—
805C4⋊C4—216no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—216no—
809C4⋊C4—216no—
810C4⋊C4—24no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—42no—
819C4⋊C4—44no—
820C4⋊C4—48no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—42no—
824C4⋊C4—42no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—42no—
829C4⋊C4—44no—
830C4⋊C4—42no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4C22×D418yes—
836C4⋊C4C22×D4132yes—
837C4⋊C4C22×D418yes—
838C4⋊C4H(5,𝔽2)14yes—
839C22⋊C4—216no—
840C22⋊C4—216no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—216no—
845C22⋊C4—28no—
846C22⋊C4—28no—
847C22⋊C4—216no—
848C22⋊C4—216no—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—44no—
856C22⋊C4—48no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—48no—
863C22⋊C4C22×D4132yes—
864C42—216no—
865C42—28no—
866C42—216no—
867C42—216no—
868C42—28no—
869C42—28no—
870C42—24no—
871C42—28no—
872C42—28no—
873C42—24no—
874C42—42no—
875C42—44no—
876C42—44no—
877C42—42no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—28no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—24no—
896C23—44no—
897C23—44no—
898C23—82no—
899C23—82no—
900C23—82no—
901C23—82no—
902C23C23×D414yes—
903C23C23×D412yes—
904C23C2×2−1+412yes—
905C23C2×2−1+412yes—
906C23C2611yescharacteristic
907Q8—216no—
908Q8—48no—
909Q8—416no—
910Q8—88no—
911Q8—816no—
912Q8—84no—
913D4—48no—
914D4—416no—
915D4—416no—
916D4—84no—
917D4—84no—
918D4—88no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—21no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—216no—
934C2×C4—28no—
935C2×C4—216no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—28no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—28no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—24no—
963C2×C4—44no—
964C2×C4—48no—
965C2×C4—48no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—48no—
969C2×C4—416no—
970C2×C4—416no—
971C2×C4—816no—
972C2×C4—84no—
973C2×C4—82no—
974C2×C4—82no—
975C2×C4—88no—
976C2×C4C23×D418yes—
977C2×C4C23×D418yes—
978C2×C4C23×D412yes—
979C2×C4C23×D414yes—
980C2×C4C23×D412yes—
981C2×C4C2×H(5,𝔽2)14yes—
982C2×C4C2×H(5,𝔽2)12yes—
983C2×C4C2×2−1+414yes—
984C2×C4C2×2−1+414yes—
985C2×C4#58512yes—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—88no—
1007C22#349914yes—
1008C22C24×D411yescharacteristic
1009C22C22×H(5,𝔽2)11yescharacteristic
1010C22C22×2−1+411yescharacteristic
1011C22C22×2−1+411yescharacteristic
1012C22C2×#58511yescharacteristic
1013C222−1+611yescharacteristic
1014C222−1+611yescharacteristic
1015C4—24no—
1016C4—22no—
1017C4—28no—
1018C4—28no—
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—44no—
1023C4—48no—
1024C4—44no—
1025C4—48no—
1026C4—44no—
1027C4—44no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4#349614yes—
1032C2—24no—
1033C2—44no—
1034C2—84no—
1035C2C2×#349611yescharacteristic
1036C2C2×#349911yescharacteristic
1037C2#6284811yescharacteristic
1038C2#6289311yescharacteristic
1039C2#6290411yescharacteristic
1040C2#6291511yescharacteristic
1041C2#6293211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34575C2
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×#3538C2semidirect
2. #49568C2semidirect
3. #47860C2semidirect
4. #45322C2semidirect
5. #45321C2semidirect
6. #45238C2semidirect
7. #45237C2semidirect
8. #39615C2semidirect
9. #39487C2semidirect
10. #39482C2semidirect
11. #37866C2semidirect
12. #36742C2semidirect
13. Q8×#121C2semidirect
14. #36186C2semidirect
15. #35306C2semidirect
16. #35167C2semidirect
17. #35011C2semidirect
18. #35004C2semidirect
20. C2×#2362C2semidirect
28. C2×D4×Q8C22semidirect
47. #2734C22semidirect
48. #2732C22semidirect
49. #2729C22semidirect
50. #2727C22semidirect
51. #2726C22semidirect
52. #2725C22semidirect
53. #2721C22semidirect
54. #2719C22semidirect
57. #2716C22semidirect
58. #2713C22semidirect
62. #2694C22semidirect
63. #2690C22semidirect
66. #2677C22semidirect
68. #2674C22semidirect
84. #2556C22semidirect
85. #2554C22semidirect
86. #2552C22semidirect
87. #2552C22semidirect
88. #2551C22semidirect
89. #2550C22semidirect
90. #2550C22semidirect
91. #2546C22semidirect
92. #2546C22semidirect
93. #2542C22semidirect
94. #2538C22semidirect
95. #2538C22semidirect
96. #2519C22semidirect
97. #2519C22semidirect
98. #2512C22semidirect
99. #2506C22semidirect
103. #2489C22semidirect
111. #2461C22semidirect
113. #2453C22semidirect
114. #2446C22semidirect
115. #2441C22semidirect
117. #2434C22semidirect
118. #2429C22semidirect
119. #2429C22semidirect
120. #2429C22semidirect
121. #2423C22semidirect
127. #2415C22semidirect
130. #2409C22semidirect
133. #2365C22semidirect
137. #2362C22semidirect
138. #2354C22semidirect
139. Q8×C4⋊C4C22semidirect
140. Q8×C22⋊C4C22semidirect
206. C2×C22⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35382
#495682
#478602
#453222
#453212
#452382
#452372
#396152
#394872
#394822
#378662
#367422
Q8×#1212
#361862
#353062
#351672
#350112
#350042
#345752
C2×#23622