Finite Group Databasebeta

← #7628124

Subgroups — #7628124

Order 512.

5678 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34953C211yesmaximal, characteristic, complemented
2#34952C211yesmaximal, characteristic
3#34951C212yesmaximal, complemented
4#34950C212yesmaximal, complemented
5#34947C211yesmaximal, characteristic
6#34941C212yesmaximal, complemented
7#34938C211yesmaximal, characteristic, complemented
8#34929C212yesmaximal, complemented
9#34920C214yesmaximal, complemented
10#34916C214yesmaximal, complemented
11#34893C214yesmaximal, complemented
12#34882C214yesmaximal, complemented
13#34840C218yesmaximal, complemented
14#34815C212yesmaximal, complemented
15#34772C214yesmaximal, complemented
16#34745C212yesmaximal
17#34691C214yesmaximal, complemented
18#34552C214yesmaximal, complemented
19C4×#533C214yesmaximal, complemented
20C4×#533C211yesmaximal, characteristic, complemented
21C4×#533C212yesmaximal, complemented
22#34026C212yesmaximal
23C42×#41C211yesmaximal, characteristic
24C2×C42×Q8C211yesmaximal, characteristic, complemented
25C2×#533C2214yes—
26C2×#533C2212yes—
27C2×#533C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C22×C4×Q8C2212yes—
32C22×C4×Q8C2211yescharacteristic
33#2590C2218yes—
34#2589C2218yes—
35#2588C2218yes—
36#2587C2218yes—
37#2586C2218yes—
38#2585C2218yes—
39#2584C2214yes—
40#2583C2214yes—
41#2582C2212yes—
42#2581C2212yes—
43#2580C2212yes—
44#2579C2214yes—
45#2574C2218yes—
46#2568C2211yescharacteristic
47#2567C2212yes—
48#2567C2211yescharacteristic
49#2566C2212yes—
50#2565C2212yes—
51#2564C2214yes—
52#2563C2211yescharacteristic
53#2556C2218yes—
54#2552C2212yes—
55#2551C2212yes—
56#2550C2214yes—
57#2549C2214yes—
58#2546C2212yes—
59#2542C2211yescharacteristic
60#2538C2212yes—
61#2522C2218yes—
62#2520C2218yes—
63#2511C2214yes—
64#2509C2214yes—
65#2508C2214yes—
66#2507C2214yes—
67#2507C2214yes—
68#2506C2214yes—
69#2505C2218yes—
70#2502C2212yes—
71#2497C2214yes—
72#2492C2214yes—
73#2487C2212yes—
74#2473C2218yes—
75#2465C2218yes—
76#2462C2218yes—
77#2454C2214yes—
78#2453C2214yes—
79#2452C2214yes—
80#2451C2214yes—
81#2451C2214yes—
82#2450C2218yes—
83#2449C2218yes—
84#2446C2214yes—
85#2440C2214yes—
86#2434C2212yes—
87#2429C2214yes—
88#2423C2214yes—
89#2417C2214yes—
90#2409C2212yes—
91#2402C2218yes—
92#2402C2218yes—
93#2402C2218yes—
94#2399C2218yes—
95#2399C2214yes—
96#2399C2214yes—
97#2399C2218yes—
98#2396C2218yes—
99#2396C2218yes—
100#2396C2214yes—
101#2396C2214yes—
102#2396C2218yes—
103#2396C2218yes—
104#2396C2218yes—
105C4×C4⋊Q8C2214yes—
106C4×C4⋊Q8C2214yes—
107C4×C4⋊Q8C2214yes—
108C4×C4⋊Q8C2214yes—
109C4×C4⋊Q8C2212yes—
110C4×C4⋊Q8C2212yes—
111C4×C4⋊Q8C2214yes—
112C4×C4⋊Q8C2214yes—
113C4×#125C2218yes—
114C4×#125C2218yes—
115C4×#125C2214yes—
116C4×#125C2214yes—
117C4×#125C2214yes—
118C4×C22⋊Q8C2214yes—
119C4×C22⋊Q8C2218yes—
120C4×C22⋊Q8C2218yes—
121C4×C22⋊Q8C2218yes—
122C4×C22⋊Q8C2218yes—
123C4×C22⋊Q8C2214yes—
124C4×C22⋊Q8C2214yes—
125C4×C22⋊Q8C2214yes—
126C4×C22⋊Q8C2214yes—
127C4×C22⋊Q8C2214yes—
128#2298C2218yes—
129#2297C2212yes—
130#2297C2212yes—
131#2296C2218yes—
132#2296C2212yes—
133#2296C2212yes—
134#2296C2212yes—
135#2296C2212yes—
136#2296C2212yes—
137#2295C2218yes—
138#2295C2212yes—
139#2295C2218yes—
140#2295C2212yes—
141#2295C2214yes—
142#2295C2214yes—
143#2295C2214yes—
144#2295C2214yes—
145#2293C2214yes—
146#2293C2214yes—
147#2290C2218yes—
148#2290C2218yes—
149#2285C2211yescharacteristic
150#2285C2214yes—
151#2285C2212yes—
152C42×Q8C2212yes—
153C42×Q8C2214yes—
154C42×Q8C2212yes—
155C42×Q8C2212yes—
156C42×Q8C2212yes—
157C42×Q8C2212yes—
158C42×Q8C2212yes—
159C42×Q8C2212yes—
160C42×Q8C2212yes—
161C42×Q8C2212yes—
162C42×Q8C2218yes—
163C42×Q8C2212yes—
164C42×D4C2214yes—
165C42×D4C2212yes—
166C42×D4C2212yes—
167C42×D4C2214yes—
168C4×#117C2212yes—
169C4×#117C2212yes—
170C4×#117C2211yescharacteristic
171C4×#117C2211yescharacteristic
172C4×#117C2212yes—
173C4×#117C2211yescharacteristic
174C4×#117C2212yes—
175C4×#117C2218yes—
176C2×C4×C4⋊C4C2214yes—
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×C4×C4⋊C4C2212yes—
179C2×C4×C4⋊C4C2212yes—
180C2×C43C2211yescharacteristic
181C2×C43C2212yes—
182C2×C43C2212yes—
183C22×#41C2311yescharacteristic
184C23×Q8C2311yescharacteristic
185#533—232no—
186#533—216no—
187#533—28no—
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2314yes—
193C2×#125C2312yes—
194C2×#125C2314yes—
195C2×#125C2318yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2318yes—
202C4×#41—28no—
203C4×#41—28no—
204C4×#41Q8116yescomplemented
205C2×C4×Q8—216no—
206C2×C4×Q8—28no—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2312yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2318yes—
212C2×C4×Q8C2318yes—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2318yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2312yes—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×#117C2312yes—
237C2×#117C2312yes—
238C2×#117C2318yes—
239C2×#117C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2318yes—
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2311yescharacteristic
250C22×C42C2312yes—
251C22×C42C2314yes—
252C22×C42C2312yes—
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2314yes—
258C22×C42C2312yes—
259C22×C42C2314yes—
260C22×C42C2314yes—
261C22×C42C2311yescharacteristic
262C22×C42C2312yes—
263C22×C42C2311yescharacteristic
264#400C2314yes—
265#400C2314yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#399C2314yes—
272#399C2314yes—
273#399C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#395C2314yes—
291#395C2318yes—
292#395C2314yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#393C2314yes—
298#393C2314yes—
299#393C2318yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2318yes—
305#391C2318yes—
306#391C2318yes—
307#391C2318yes—
308#391C2314yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#390C2312yes—
314#390C2312yes—
315#390C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2318yes—
320#389C2314yes—
321#389C2318yes—
322#389C2318yes—
323#389C2318yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2314yes—
330#389C2318yes—
331#389C2318yes—
332#389C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#386C2318yes—
363#386C2314yes—
364#386C2314yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#384C2312yes—
378#384C2312yes—
379#384C2314yes—
380#384C2312yes—
381#384C2314yes—
382#382C2312yes—
383#382C2312yes—
384#382C2318yes—
385#382C2312yes—
386#380C2314yes—
387#380C2318yes—
388#380C2318yes—
389#380C2312yes—
390#380C2312yes—
391#380C2314yes—
392C4×C4⋊C4C2312yes—
393C4×C4⋊C4C2312yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2318yes—
465#376C2312yes—
466#376C2318yes—
467#376C2312yes—
468#376C2318yes—
469#376C2312yes—
470#376C2314yes—
471C2×#95C2312yes—
472C2×#95C2314yes—
473C43C2312yes—
474C43C2312yes—
475C43C2314yes—
476C43C2314yes—
477C43C2312yes—
478C43C2312yes—
479C43C2314yes—
480C43C2314yes—
481C43C2311yescharacteristic
482C43C2311yescharacteristic
483C43C2314yes—
484C43C2311yescharacteristic
485C43C2311yescharacteristic
486C43C2314yes—
487C43C2312yes—
488C43C2314yes—
489C2×#41—24no—
490C2×#41—24no—
491C2×#41C2×Q818yes—
492C22×Q8—28no—
493C22×Q8—24no—
494C22×Q8C2412yes—
495C22×Q8C2412yes—
496C22×Q8C2418yes—
497C22×Q8C2411yescharacteristic
498C22×Q8C2412yes—
499C22×Q8C2412yes—
500C22×D4C2412yes—
501C22×D4C2411yescharacteristic
502C23×C4C2412yes—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2414yes—
506C23×C4C2414yes—
507C23×C4C2414yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C4⋊Q8—216no—
516C4⋊Q8—216no—
517C4⋊Q8—216no—
518C4⋊Q8—24no—
519C4⋊Q8—24no—
520#125—232no—
521#125—216no—
522#125—28no—
523C22⋊Q8—216no—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—216no—
527C22⋊Q8—232no—
528C22⋊Q8—232no—
529C4×Q8—28no—
530C4×Q8—216no—
531C4×Q8—28no—
532C4×Q8—28no—
533C4×Q8—28no—
534C4×Q8—28no—
535C4×Q8—216no—
536C4×Q8—28no—
537C4×Q8—28no—
538C4×Q8—28no—
539C4×Q8—24no—
540C4×Q8—24no—
541C4×Q8—232no—
542C4×Q8—232no—
543C4×Q8—216no—
544C4×Q8—28no—
545C4×Q8—28no—
546C4×Q8—416no—
547C4×Q8—48no—
548C4×Q8C2×Q8116yescomplemented
549C4×Q8#41116yescomplemented
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—28no—
553C4×D4—216no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4C2×Q8132yes—
557C4×D4C2×Q8116yescomplemented
558#117—24no—
559#117—28no—
560#117—28no—
561#117—28no—
562#117—28no—
563#117—232no—
564#117—416no—
565#117C2×Q818yes—
566#117C2×Q8116yescomplemented
567#117#4118yes—
568C2×C4⋊C4—28no—
569C2×C4⋊C4—24no—
570C2×C4⋊C4—216no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2412yes—
628C2×C42—28no—
629C2×C42—24no—
630C2×C42—28no—
631C2×C42—28no—
632C2×C42—216no—
633C2×C42—28no—
634C2×C42—28no—
635C2×C42—216no—
636C2×C42—44no—
637C2×C42—48no—
638C2×C42—48no—
639C2×C42C2×Q818yes—
640C2×C42C2×Q8116yescomplemented
641C2×C42#4118yes—
642C2×C42C2411yescharacteristic
643C2×C42C2412yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2418yes—
648C2×C42C2418yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2414yes—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2414yes—
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2412yes—
694#95C2414yes—
695#95C2412yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723C24C2512yes—
724C24C2511yescharacteristic
725#41—232no—
726C2×Q8—232no—
727C2×Q8—28no—
728C2×Q8—24no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—216no—
734C2×Q8—216no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—24no—
738C2×Q8—48no—
739C2×Q8—44no—
740C2×Q8C22×Q814yes—
741C2×Q8C2×#4118yes—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4C22×Q818yes—
747C2×D4C22×Q814yes—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—24no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—42no—
768C22×C4—44no—
769C22×C4—42no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4C22×Q818yes—
774C22×C4C22×Q818yes—
775C22×C4C22×Q8116yes—
776C22×C4C22×Q814yes—
777C22×C4C2×#4114yes—
778C22×C4C2×#4114yes—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2518yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2514yes—
795C22×C4C2511yescharacteristic
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—216no—
818C4⋊C4—216no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—216no—
823C4⋊C4—216no—
824C4⋊C4—216no—
825C4⋊C4—216no—
826C4⋊C4—216no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—216no—
830C4⋊C4—216no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4C22×Q818yes—
842C4⋊C4C22×Q8116yes—
843C4⋊C4C2×#41116yes—
844C4⋊C4C2×#4118yes—
845C4⋊C4C2×#4118yes—
846C22⋊C4—24no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—216no—
853C22⋊C4—216no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4C22×Q818yes—
857C22⋊C4C22×Q8116yes—
858C22⋊C4C2×#4118yes—
859C42—22no—
860C42—22no—
861C42—24no—
862C42—28no—
863C42—24no—
864C42—24no—
865C42—24no—
866C42—24no—
867C42—28no—
868C42—28no—
869C42—24no—
870C42—28no—
871C42—28no—
872C42—28no—
873C42—24no—
874C42—28no—
875C42—28no—
876C42—28no—
877C42—24no—
878C42—28no—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—216no—
883C42—24no—
884C42—28no—
885C42—24no—
886C42—28no—
887C42—28no—
888C42—216no—
889C42—42no—
890C42—44no—
891C42—42no—
892C42—44no—
893C42—44no—
894C42—44no—
895C42C22×Q814yes—
896C42C22×Q814yes—
897C42C22×Q818yes—
898C42C22×Q818yes—
899C42C22×Q8116yes—
900C42C2×#4118yes—
901C42C2×#4114yes—
902C42C2×#41116yes—
903C42C2×#4118yes—
904C42C2×#4114yes—
905C42C2×#4114yes—
906C42C2×#4114yes—
907C23—22no—
908C23—22no—
909C23—24no—
910C23—22no—
911C23—22no—
912C23—24no—
913C23C23×Q814yes—
914C23C23×Q812yes—
915C23C22×#4112yes—
916C23C22×#4112yes—
917C23C2611yescharacteristic
918Q8—216no—
919Q8—28no—
920Q8—216no—
921Q8—432no—
922Q8—48no—
923Q8—48no—
924D4—216no—
925D4—28no—
926C2×C4—216no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—216no—
945C2×C4—28no—
946C2×C4—216no—
947C2×C4—232no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—24no—
959C2×C4—28no—
960C2×C4—28no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—28no—
967C2×C4—28no—
968C2×C4—44no—
969C2×C4—416no—
970C2×C4—48no—
971C2×C4—416no—
972C2×C4—48no—
973C2×C4—48no—
974C2×C4—48no—
975C2×C4#533116yescomplemented
976C2×C4C23×Q814yes—
977C2×C4C23×Q818yes—
978C2×C4C23×Q814yes—
979C2×C4C23×Q812yes—
980C2×C4C23×Q812yes—
981C2×C4C23×Q814yes—
982C2×C4C22×#4114yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4118yes—
985C2×C4C22×#4118yes—
986C2×C4C22×#4118yes—
987C2×C4C22×#4112yes—
988C2×C4C22×#4112yes—
989C2×C4C22×#4112yes—
990C2×C4C22×#4112yes—
991C2×C4C22×#4112yes—
992C2×C4C22×#4112yes—
993C2×C4C22×#4114yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4114yes—
996C2×C4#58514yes—
997C22—22no—
998C22—22no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—28no—
1003C22—42no—
1004C22—42no—
1005C22—44no—
1006C22C2×#53314yes—
1007C22C24×Q811yescharacteristic
1008C22C23×#4111yescharacteristic
1009C22C23×#4111yescharacteristic
1010C22C23×#4112yes—
1011C22C2×#58512yes—
1012C4—24no—
1013C4—28no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—24no—
1018C4—28no—
1019C4—24no—
1020C4—28no—
1021C4—28no—
1022C4—42no—
1023C4—44no—
1024C4—42no—
1025C4—44no—
1026C4—44no—
1027C4—42no—
1028C4—44no—
1029C4—48no—
1030C4C2×#53314yes—
1031C4C2×#53314yes—
1032C4#344414yes—
1033C4Q8×#4118yes—
1034C2—24no—
1035C2—44no—
1036C2C22×#53311yescharacteristic
1037C2C2×#344411yescharacteristic
1038C2#6268611yescharacteristic
1039C2C2×Q8×#4112yes—
1040C2#41212yes—
subgroupG/H
centerC2×C42C24
commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C2×C42 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34953C2semidirect
3. #34951C2semidirect
4. #34950C2semidirect
6. #34941C2semidirect
7. #34938C2semidirect
8. #34929C2semidirect
9. #34920C2semidirect
10. #34916C2semidirect
11. #34893C2semidirect
12. #34882C2semidirect
13. #34840C2semidirect
14. #34815C2semidirect
15. #34772C2semidirect
17. #34691C2semidirect
18. #34552C2semidirect
19. C4×#533C2semidirect
20. C4×#533C2semidirect
21. C4×#533C2semidirect
24. C2×C42×Q8C2semidirect
204. C4×#41Q8semidirect
548. C4×Q8C2×Q8semidirect
549. C4×Q8#41semidirect
557. C4×D4C2×Q8semidirect
566. #117C2×Q8semidirect
640. C2×C42C2×Q8semidirect
975. C2×C4#533semidirect

Maximal subgroups

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

subgroupindex
#349532
#349522
#349512
#349502
#349472
#349412
#349382
#349292
#349202
#349162
#348932
#348822
#348402
#348152
#347722
#347452
#346912
#345522
C4×#5332
#340262
C42×#412
C2×C42×Q82