Finite Group Databasebeta

← #7638598

Subgroups — #7638598

Order 512.

4704 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52283C218yesmaximal, complemented
2#39999C214yesmaximal, complemented
3#39997C214yesmaximal, complemented
4#39762C211yesmaximal, characteristic, complemented
5#39635C211yesmaximal, characteristic, complemented
6#39506C211yesmaximal, characteristic, complemented
7#39379C211yesmaximal, characteristic, complemented
8#39192C212yesmaximal, complemented
9#38976C212yesmaximal, complemented
10#38461C218yesmaximal, complemented
11#38113C214yesmaximal, complemented
12#37882C212yesmaximal, complemented
13#37695C212yesmaximal, complemented
14#36640C211yesmaximal, characteristic, complemented
15#34975C214yesmaximal, complemented
16#34952C212yesmaximal
17#34816C214yesmaximal
18#34815C214yesmaximal, complemented
19#34629C212yesmaximal, complemented
20Q8×#117C212yesmaximal, complemented
21C4×#541C212yesmaximal, complemented
22C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
23#34026C211yesmaximal, characteristic
24C2×#541C2212yes—
25C22×C4⋊Q8C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic
27C22×C4×Q8C2212yes—
28#2864C2214yes—
29#2859C2212yes—
30#2859C2211yescharacteristic
31#2859C2211yescharacteristic
32#2851C2214yes—
33#2851C2212yes—
34#2851C2212yes—
35#2802C2218yes—
36#2798C2218yes—
37#2794C2218yes—
38#2789C2218yes—
39#2783C2218yes—
40#2776C2218yes—
41#2772C2218yes—
42#2766C2218yes—
43#2758C2218yes—
44#2754C2218yes—
45#2725C2218yes—
46#2725C2218yes—
47#2721C2218yes—
48#2719C2218yes—
49#2716C2218yes—
50#2713C2218yes—
51#2655C2218yes—
52#2652C2218yes—
53#2647C2212yes—
54#2645C2214yes—
55#2642C2212yes—
56#2629C2212yes—
57#2625C2214yes—
58#2621C2212yes—
59#2582C2212yes—
60#2582C2212yes—
61#2581C2214yes—
62#2580C2214yes—
63#2579C2218yes—
64#2538C2212yes—
65#2538C2212yes—
66#2533C2218yes—
67#2528C2218yes—
68#2514C2214yes—
69#2514C2214yes—
70#2514C2214yes—
71#2513C2214yes—
72#2513C2214yes—
73#2512C2214yes—
74#2512C2214yes—
75#2511C2214yes—
76#2511C2214yes—
77#2510C2218yes—
78#2510C2218yes—
79#2509C2214yes—
80#2509C2214yes—
81#2508C2214yes—
82#2508C2214yes—
83#2507C2214yes—
84#2507C2214yes—
85#2506C2214yes—
86#2506C2214yes—
87#2506C2214yes—
88#2505C2218yes—
89#2505C2218yes—
90#2496C2214yes—
91#2489C2214yes—
92#2487C2214yes—
93#2481C2218yes—
94#2481C2218yes—
95#2478C2218yes—
96#2475C2218yes—
97#2473C2218yes—
98#2473C2218yes—
99#2453C2214yes—
100#2446C2214yes—
101#2429C2214yes—
102#2421C2214yes—
103#2409C2214yes—
104#2402C2218yes—
105#2402C2218yes—
106#2401C2218yes—
107#2401C2218yes—
108#2396C2218yes—
109#2355C2212yes—
110#2355C2214yes—
111#2355C2214yes—
112#2355C2212yes—
113Q8×C4⋊C4C2212yes—
114Q8×C4⋊C4C2212yes—
115#2345C2218yes—
116#2345C2214yes—
117Q8×C22⋊C4C2214yes—
118#2336C2218yes—
119#2334C2218yes—
120#2330C2212yes—
121#2327C2212yes—
122#2323C2214yes—
123#2320C2214yes—
124#2314C2212yes—
125C4×C4⋊Q8C2212yes—
126C4×C4⋊Q8C2211yescharacteristic
127C4×C4⋊Q8C2214yes—
128C4×C4⋊Q8C2214yes—
129C4×C4⋊Q8C2211yescharacteristic
130C4×C4⋊Q8C2211yescharacteristic
131C4×C4⋊Q8C2212yes—
132C4×C4⋊Q8C2211yescharacteristic
133C4×#125C2212yes—
134C4×#125C2214yes—
135C4×#125C2212yes—
136C4×#125C2218yes—
137C4×#125C2218yes—
138C4×#126C2218yes—
139C4×#126C2218yes—
140C4×C22⋊Q8C2214yes—
141C4×C22⋊Q8C2214yes—
142#2298C2214yes—
143#2297C2214yes—
144#2297C2212yes—
145#2296C2214yes—
146#2296C2214yes—
147#2296C2212yes—
148#2295C2218yes—
149#2295C2212yes—
150#2295C2211yescharacteristic
151#2295C2214yes—
152#2295C2211yescharacteristic
153C2×#391C2212yes—
154#2293C2211yescharacteristic
155#2293C2212yes—
156#2293C2211yescharacteristic
157C2×#389C2214yes—
158#2290C2214yes—
159#2290C2212yes—
160#2290C2212yes—
161#2285C2214yes—
162#2285C2212yes—
163C2×#384C2211yescharacteristic
164C42×Q8C2214yes—
165C4×#117C2214yes—
166C4×#117C2212yes—
167C4×#117C2211yescharacteristic
168C4×#117C2212yes—
169C2×C4×C4⋊C4C2214yes—
170C2×C43C2211yescharacteristic
171C22×#41C2311yescharacteristic
172C23×Q8C2312yes—
173#541—216no—
174C2×C4⋊Q8—28no—
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2311yescharacteristic
179C2×#126C2318yes—
180C2×#126C2318yes—
181C2×#125C2312yes—
182C2×#125C2318yes—
183C2×#125C2312yes—
184C2×#125C2314yes—
185C2×#125C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C4×#41—28no—
189C2×C4×Q8—216no—
190C2×C4×Q8C2314yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2314yes—
200C2×C4×D4C2312yes—
201C2×C4×D4C2311yescharacteristic
202C2×C4×D4C2312yes—
203C2×C4×D4C2311yescharacteristic
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2311yescharacteristic
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2312yes—
210C2×#117C2314yes—
211C22×C4⋊C4C2314yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2314yes—
214C22×C4⋊C4C2314yes—
215C22×C42C2311yescharacteristic
216C22×C42C2314yes—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222#401C2318yes—
223#401C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#395C2318yes—
261#393C2318yes—
262#391C2312yes—
263#391C2312yes—
264#391C2312yes—
265#391C2312yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2314yes—
273#391C2314yes—
274#391C2318yes—
275#391C2318yes—
276#391C2312yes—
277#391C2312yes—
278#390C2314yes—
279#390C2314yes—
280#390C2312yes—
281#390C2312yes—
282#389C2314yes—
283#389C2318yes—
284#389C2318yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2312yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2314yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2314yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#386C2318yes—
357#386C2318yes—
358#386C2314yes—
359#386C2314yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#384C2311yescharacteristic
369#384C2311yescharacteristic
370#384C2314yes—
371#384C2312yes—
372#384C2312yes—
373#384C2312yes—
374#384C2314yes—
375#384C2314yes—
376#383C2318yes—
377#383C2318yes—
378#382C2312yes—
379#382C2318yes—
380#382C2312yes—
381#382C2314yes—
382#382C2318yes—
383#382C2314yes—
384#382C2314yes—
385#382C2314yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2318yes—
390#380C2318yes—
391#380C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2318yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2312yes—
434C4×C22⋊C4C2312yes—
435#376C2312yes—
436#376C2312yes—
437#376C2318yes—
438#376C2314yes—
439#376C2312yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C43C2318yes—
443C43C2311yescharacteristic
444C43C2311yescharacteristic
445C43C2312yes—
446C43C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2312yes—
449C43C2312yes—
450C2×#41—24no—
451C2×#41—28no—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8—44no—
455C22×Q8C2412yes—
456C22×Q8C2411yescharacteristic
457C22×Q8C2414yes—
458C22×Q8C2412yes—
459C22×D4C2412yes—
460C22×D4C2411yescharacteristic
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2414yes—
465C23×C4C2411yescharacteristic
466C23×C4C2414yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C4⋊Q8—28no—
472C4⋊Q8—216no—
473C4⋊Q8—24no—
474C4⋊Q8#4118yescomplemented
475#126—232no—
476#126—416no—
477#125—232no—
478#125—28no—
479#125—44no—
480#125—48no—
481#125—416no—
482C22⋊Q8—216no—
483C22⋊Q8—48no—
484C4×Q8—216no—
485C4×Q8—28no—
486C4×Q8—28no—
487C4×Q8—216no—
488C4×Q8—28no—
489C4×Q8—216no—
490C4×Q8—28no—
491C4×Q8—24no—
492C4×Q8—24no—
493C4×Q8—48no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—24no—
497C4×D4—24no—
498#117—24no—
499#117—28no—
500#117—216no—
501#117—28no—
502#117—28no—
503#117—44no—
504#117—48no—
505C2×C4⋊C4—216no—
506C2×C4⋊C4—28no—
507C2×C4⋊C4—216no—
508C2×C4⋊C4—48no—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2411yescharacteristic
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C42—216no—
566C2×C42—28no—
567C2×C42—28no—
568C2×C42—24no—
569C2×C42—44no—
570C2×C42—42no—
571C2×C42#4118yes—
572C2×C42C2412yes—
573C2×C42C2411yescharacteristic
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2414yes—
579C2×C42C2414yes—
580C2×C42C2418yes—
581C2×C42C2411yescharacteristic
582C2×C42C2412yes—
583C2×C42C2411yescharacteristic
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2414yes—
589C2×C42C2418yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2414yes—
595C2×C42C2418yes—
596C2×C42C2418yes—
597C2×C42C2418yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2412yes—
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2412yes—
623#95C2412yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647C24C2512yes—
648C24C2511yescharacteristic
649#41—416no—
650C2×Q8—24no—
651C2×Q8—28no—
652C2×Q8—24no—
653C2×Q8—22no—
654C2×Q8—28no—
655C2×Q8—24no—
656C2×Q8—24no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—44no—
660C2×Q8—432no—
661C2×Q8C2×#4118yes—
662C2×D4—24no—
663C2×D4—28no—
664C2×D4—22no—
665C2×D4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—22no—
671C22×C4—28no—
672C22×C4—24no—
673C22×C4—28no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—28no—
678C22×C4—24no—
679C22×C4—28no—
680C22×C4—24no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4C2×#4114yes—
689C22×C4C2×#4114yes—
690C22×C4C2×#4114yes—
691C22×C42−1+418yes—
692C22×C4C2512yes—
693C22×C4C2512yes—
694C22×C4C2512yes—
695C22×C4C2514yes—
696C22×C4C2514yes—
697C22×C4C2514yes—
698C22×C4C2518yes—
699C22×C4C2518yes—
700C22×C4C2514yes—
701C22×C4C2512yes—
702C22×C4C2512yes—
703C22×C4C2514yes—
704C22×C4C2511yescharacteristic
705C22×C4C2511yescharacteristic
706C22×C4C2512yes—
707C22×C4C2514yes—
708C22×C4C2511yescharacteristic
709C22×C4C2512yes—
710C22×C4C2511yescharacteristic
711C22×C4C2511yescharacteristic
712C22×C4C2511yescharacteristic
713C4⋊C4—28no—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—216no—
730C4⋊C4—216no—
731C4⋊C4—216no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—216no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4C2×#41116yes—
756C22⋊C4—24no—
757C22⋊C4—28no—
758C22⋊C4—216no—
759C22⋊C4—24no—
760C22⋊C4—24no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—28no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—48no—
769C42—24no—
770C42—24no—
771C42—24no—
772C42—28no—
773C42—28no—
774C42—28no—
775C42—28no—
776C42—22no—
777C42—24no—
778C42—24no—
779C42—216no—
780C42—24no—
781C42—24no—
782C42—24no—
783C42—24no—
784C42—28no—
785C42—216no—
786C42—24no—
787C42—22no—
788C42—24no—
789C42—22no—
790C42—24no—
791C42—42no—
792C42—42no—
793C42—42no—
794C42—44no—
795C42—48no—
796C42—48no—
797C42—48no—
798C42C2×#4114yes—
799C42C2×#4114yes—
800C42C2×#4114yes—
801C42C2×#4114yes—
802C42C2×#4114yes—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—24no—
809C23—24no—
810C23—22no—
811C23C22×#4112yes—
812C23C2×2−1+414yes—
813C23C2611yescharacteristic
814Q8—216no—
815Q8—416no—
816Q8—44no—
817Q8—48no—
818D4—48no—
819D4—44no—
820C2×C4—216no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—21no—
831C2×C4—28no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—28no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—28no—
846C2×C4—24no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—44no—
867C2×C4—416no—
868C2×C4—48no—
869C2×C4—48no—
870C2×C4—48no—
871C2×C4—48no—
872C2×C4—88no—
873C2×C4#541116yescomplemented
874C2×C4C22×#4112yes—
875C2×C4C22×#4118yes—
876C2×C4C22×#4114yes—
877C2×C4C22×#4112yes—
878C2×C4C22×#4112yes—
879C2×C4C22×#4112yes—
880C2×C4C22×#4112yes—
881C2×C4C22×#4112yes—
882C2×C4C22×#4112yes—
883C2×C4C2×2−1+414yes—
884C2×C4C2×2−1+414yes—
885C2×C4#58514yes—
886C2×C4#58512yes—
887C22—24no—
888C22—24no—
889C22—22no—
890C22—22no—
891C22—44no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22C2×#54114yes—
897C22C23×#4111yescharacteristic
898C22C23×#4111yescharacteristic
899C22C22×2−1+412yes—
900C22C2×#58511yescharacteristic
901C22C2×#58512yes—
902C4—24no—
903C4—24no—
904C4—22no—
905C4—22no—
906C4—22no—
907C4—28no—
908C4—44no—
909C4—48no—
910C4—42no—
911C4—42no—
912C4—44no—
913C4—48no—
914C4—42no—
915C4—44no—
916C4—44no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4C2×#54114yes—
921C4C2×#54114yes—
922C4#347514yes—
923C2—24no—
924C2—82no—
925C2C22×#54111yescharacteristic
926C2C2×#347511yescharacteristic
927C2#6276112yes—
928C2#6278812yes—
929C2#6281511yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52283C2semidirect
2. #39999C2semidirect
3. #39997C2semidirect
4. #39762C2semidirect
5. #39635C2semidirect
6. #39506C2semidirect
7. #39379C2semidirect
8. #39192C2semidirect
9. #38976C2semidirect
10. #38461C2semidirect
11. #38113C2semidirect
12. #37882C2semidirect
13. #37695C2semidirect
14. #36640C2semidirect
15. #34975C2semidirect
18. #34815C2semidirect
19. #34629C2semidirect
20. Q8×#117C2semidirect
21. C4×#541C2semidirect
22. C2×C4×C4⋊Q8C2semidirect
474. C4⋊Q8#41semidirect
873. C2×C4#541semidirect

Maximal subgroups

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

subgroupindex
#522832
#399992
#399972
#397622
#396352
#395062
#393792
#391922
#389762
#384612
#381132
#378822
#376952
#366402
#349752
#349522
#348162
#348152
#346292
Q8×#1172
C4×#5412
C2×C4×C4⋊Q82
#340262