Finite Group Databasebeta

← #7641857

Subgroups — #7641857

Order 512.

5378 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37525C218yesmaximal, complemented
2#37505C214yesmaximal, complemented
3#37504C214yesmaximal, complemented
4#37503C214yesmaximal, complemented
5#37502C214yesmaximal, complemented
6#35267C212yesmaximal, complemented
7#35265C212yesmaximal, complemented
8#35257C212yesmaximal, complemented
9#35255C212yesmaximal, complemented
10#35227C212yesmaximal, complemented
11#35224C211yesmaximal, characteristic, complemented
12#35223C211yesmaximal, characteristic
13#35029C214yesmaximal, complemented
14#35026C214yesmaximal, complemented
15#35017C214yesmaximal, complemented
16#35008C214yesmaximal, complemented
17#34997C214yesmaximal, complemented
18#34989C214yesmaximal, complemented
19C4×#525C212yesmaximal, complemented
20C22×#389C211yesmaximal, characteristic, complemented
21C2×#544C2211yescharacteristic
22C2×#539C2214yes—
23C2×#537C2211yescharacteristic
24C2×#525C2212yes—
25C2×C4×#41C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2212yes—
29C23×C42C2211yescharacteristic
30#2864C2214yescomplemented
31#2863C2214yescomplemented
32#2860C2214yescomplemented
33#2859C2214yescomplemented
34#2857C2214yescomplemented
35#2855C2214yescomplemented
36#2854C2214yescomplemented
37#2851C2214yescomplemented
38#2849C2218yes—
39#2848C2214yes—
40#2847C2214yes—
41#2839C2218yescomplemented
42#2838C2218yescomplemented
43#2837C2218yescomplemented
44#2836C2218yescomplemented
45#2667C2218yescomplemented
46#2666C2218yescomplemented
47#2664C2218yescomplemented
48#2663C2218yescomplemented
49#2655C2218yescomplemented
50#2654C2218yescomplemented
51#2652C2218yescomplemented
52#2649C2218yescomplemented
53#2647C2214yescomplemented
54#2647C2214yescomplemented
55#2646C2214yes—
56#2645C2214yescomplemented
57#2644C2214yescomplemented
58#2643C2218yes—
59#2639C2214yes—
60#2629C2214yescomplemented
61#2628C2214yescomplemented
62#2627C2214yes—
63#2627C2214yes—
64#2625C2214yescomplemented
65#2624C2214yescomplemented
66#2623C2218yes—
67#2623C2218yes—
68#2618C2214yes—
69#2618C2214yes—
70#2585C2218yescomplemented
71#2573C2218yescomplemented
72#2556C2218yescomplemented
73#2553C2218yescomplemented
74#2510C2218yes—
75#2509C2214yescomplemented
76#2508C2214yescomplemented
77#2507C2214yescomplemented
78#2506C2214yescomplemented
79#2505C2218yes—
80#2504C2214yes—
81#2503C2214yes—
82#2502C2214yes—
83#2501C2214yes—
84#2497C2214yescomplemented
85#2496C2214yescomplemented
86#2495C2214yescomplemented
87#2494C2214yescomplemented
88#2493C2218yes—
89#2488C2218yes—
90#2487C2214yes—
91#2487C2214yes—
92#2486C2214yes—
93#2486C2214yes—
94#2481C2218yes—
95#2481C2218yes—
96#2473C2218yes—
97#2473C2218yes—
98#2454C2214yescomplemented
99#2453C2214yescomplemented
100#2452C2214yescomplemented
101#2451C2214yescomplemented
102#2450C2218yes—
103#2449C2218yes—
104#2449C2218yes—
105#2444C2218yes—
106#2443C2218yes—
107#2443C2218yes—
108#2442C2214yes—
109#2442C2214yes—
110#2440C2214yes—
111#2440C2214yes—
112#2425C2218yes—
113#2423C2214yescomplemented
114#2422C2214yescomplemented
115#2421C2214yescomplemented
116#2420C2214yescomplemented
117#2419C2218yes—
118#2417C2214yes—
119#2417C2214yes—
120#2416C2214yes—
121#2416C2214yes—
122#2329C2214yes—
123#2325C2214yes—
124#2322C2218yes—
125#2318C2218yes—
126#2317C2212yes—
127#2317C2212yes—
128#2317C2212yes—
129#2316C2211yescharacteristic
130#2316C2211yescharacteristic
131#2313C2214yes—
132#2311C2212yes—
133#2311C2212yes—
134#2311C2212yes—
135C4×C22⋊Q8C2212yes—
136C4×C22⋊Q8C2212yes—
137C4×C22⋊Q8C2212yes—
138C4×C22⋊Q8C2212yes—
139C4×#123C2214yes—
140C4×#123C2214yes—
141C4×#121C2212yes—
142C4×#121C2212yes—
143C4×#121C2212yes—
144C4×#121C2212yes—
145C4×#120C2214yes—
146C4×#120C2214yes—
147#2297C2212yes—
148#2296C2212yes—
149C2×#389C2214yes—
150C2×#389C2214yes—
151C2×#389C2214yes—
152C2×#389C2212yes—
153C2×#389C2212yes—
154C2×#389C2214yes—
155C2×#389C2214yes—
156#2290C2214yes—
157#2290C2214yes—
158#2280C2212yes—
159C42×D4C2214yes—
160C42×D4C2214yes—
161C4×#117C2212yes—
162C22×#95C2212yes—
163C22×#41C2312yes—
164C24×C4C2311yescharacteristic
165C24×C4C2312yes—
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168C24×C4C2312yes—
169#544—44no—
170#539—416no—
171#537—44no—
172C2×C4⋊Q8C2314yes—
173C2×#126C2318yes—
174C2×#125C2314yes—
175C2×#125C2318yes—
176#525—216no—
177C2×#123C2314yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×C22⋊Q8C2312yes—
182C2×C22⋊Q8C2312yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×#121C2312yes—
189C2×#121C2312yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#120C2314yes—
195C4×#41—48no—
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2312yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2314yes—
212C22×C4⋊C4—28no—
213C22×C4⋊C4—44no—
214C22×C4⋊C4—48no—
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2314yes—
225C22×C4⋊C4C2314yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2318yes—
228C22×C4⋊C4C2314yes—
229C22×C42—44no—
230C22×C42C2312yes—
231C22×C42C2314yes—
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2312yes—
236C22×C42C2312yes—
237#401C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2318yes—
251#399C2318yes—
252#399C2318yes—
253#399C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#395C2318yes—
280#395C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#393C2318yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2318yes—
289#391C2312yes—
290#391C2312yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2312yes—
295#390C2312yes—
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#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2312yes—
312#389C2314yes—
313#389C2314yes—
314#389C2312yes—
315#389C2314yes—
316#389C2312yes—
317#389C2314yes—
318#389C2312yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2314yes—
330#388C2318yes—
331#388C2314yes—
332#388C2314yes—
333#388C2314yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#387C2318yes—
346#387C2318yes—
347#387C2314yes—
348#387C2314yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2314yes—
358#386C2314yes—
359#386C2314yes—
360#386C2314yes—
361#386C2314yes—
362#386C2314yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2314yes—
375#385C2314yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#384C2314yes—
380#384C2314yes—
381#384C2314yes—
382#383C2318yes—
383#382C2314yes—
384#382C2314yes—
385#382C2314yes—
386#382C2318yes—
387#381C2318yes—
388#381C2318yes—
389#381C2318yes—
390#381C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2312yes—
408#379C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433#376C2314yes—
434C2×#95C2314yes—
435C2×#95C2314yes—
436C2×#95C2318yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C43C2314yes—
440C25C2411yescharacteristic
441C2×#41—28no—
442C2×#41—28no—
443C2×#41—28no—
444C22×Q8C2412yes—
445C22×Q8C2414yes—
446C22×D4C2414yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C22×D4C2412yes—
450C22×D4C2414yes—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—28no—
454C23×C4—24no—
455C23×C4—24no—
456C23×C4—44no—
457C23×C4—42no—
458C23×C4—42no—
459C23×C4—44no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—44no—
463C23×C4—44no—
464C23×C4—44no—
465C23×C4#4118yes—
466C23×C4C2414yes—
467C23×C4C2414yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2412yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2411yescharacteristic
482C23×C4C2414yes—
483C23×C4C2414yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C4⋊Q8—48no—
489#126—416no—
490#125—416no—
491#125—48no—
492#123—216no—
493#123—416no—
494#123—416no—
495#123—416no—
496C22⋊Q8—28no—
497C22⋊Q8—28no—
498C22⋊Q8—48no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501C22⋊Q8—416no—
502C22⋊Q8—48no—
503#121—28no—
504#121—28no—
505#121—48no—
506#121—48no—
507#121—48no—
508#121—48no—
509#120—216no—
510C4×Q8—44no—
511C4×Q8—44no—
512C4×D4—216no—
513C4×D4—216no—
514C4×D4—216no—
515C4×D4—216no—
516C4×D4—44no—
517C4×D4—44no—
518C4×D4—48no—
519C4×D4—48no—
520C4×D4—48no—
521C4×D4—48no—
522#117—28no—
523#117—28no—
524#117—28no—
525#117—48no—
526C2×C4⋊C4—216no—
527C2×C4⋊C4—216no—
528C2×C4⋊C4—28no—
529C2×C4⋊C4—28no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—216no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—48no—
534C2×C4⋊C4—48no—
535C2×C4⋊C4—48no—
536C2×C4⋊C4—416no—
537C2×C4⋊C4—48no—
538C2×C4⋊C4—44no—
539C2×C4⋊C4—48no—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C42—28no—
602C2×C42—48no—
603C2×C42—44no—
604C2×C42—44no—
605C2×C42—44no—
606C2×C42—44no—
607C2×C42—44no—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2412yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24C2×#4114yes—
666C24C2514yes—
667C24C2511yescharacteristic
668C24C2511yescharacteristic
669C24C2511yescharacteristic
670#41—432no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—232no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—28no—
710C22×C4—24no—
711C22×C4—28no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—42no—
744C22×C4—44no—
745C22×C4—42no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—42no—
749C22×C4—44no—
750C22×C4—42no—
751C22×C4—416no—
752C22×C4—416no—
753C22×C4—432no—
754C22×C4—816no—
755C22×C4C2×#4118yes—
756C22×C4C2×#4118yes—
757C22×C4C2×#4114yes—
758C22×C4C2×#4114yes—
759C22×C4H(5,𝔽2)14yes—
760C22×C4H(5,𝔽2)14yes—
761C22×C42−1+414yes—
762C22×C42−1+414yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2518yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2512yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C4⋊C4—216no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—216no—
788C4⋊C4—216no—
789C4⋊C4—28no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—28no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—48no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—48no—
816C22⋊C4—28no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C42—28no—
841C42—24no—
842C42—24no—
843C42—24no—
844C42—24no—
845C42—28no—
846C42—28no—
847C42—28no—
848C42—28no—
849C42—42no—
850C42—42no—
851C42—42no—
852C42—42no—
853C42—44no—
854C42—44no—
855C42—44no—
856C42—44no—
857C23—28no—
858C23—28no—
859C23—28no—
860C23—28no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—28no—
874C23—28no—
875C23—28no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23C22×#4112yes—
884C23C22×#4112yes—
885C23C22×#4112yes—
886C23C2×H(5,𝔽2)12yes—
887C23C2×H(5,𝔽2)12yes—
888C23C2×2−1+412yes—
889C23C2×2−1+412yes—
890C23#58512yes—
891C23#58512yes—
892C23C2611yescharacteristic
893Q8—48no—
894Q8—164no—
895D4—416no—
896D4—416no—
897D4—416no—
898D4—48no—
899D4—164no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—28no—
907C2×C4—216no—
908C2×C4—216no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—28no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—48no—
950C2×C4—48no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—416no—
954C2×C4—416no—
955C2×C4—416no—
956C2×C4—416no—
957C2×C4—88no—
958C2×C4—88no—
959C2×C4—84no—
960C2×C4—88no—
961C2×C4—88no—
962C2×C4—84no—
963C2×C4#539116yescomplemented
964C2×C4C22×#4114yes—
965C2×C4C22×#4114yes—
966C2×C4C2×H(5,𝔽2)14yes—
967C2×C4C2×H(5,𝔽2)14yes—
968C2×C4C2×2−1+414yes—
969C2×C4C2×2−1+414yes—
970C22—232no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22—44no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22C2×#53914yes—
997C22#346014yes—
998C22#346114yes—
999C22C23×#4111yescharacteristic
1000C22C22×H(5,𝔽2)11yescharacteristic
1001C22C22×H(5,𝔽2)11yescharacteristic
1002C22C22×2−1+411yescharacteristic
1003C22C22×2−1+411yescharacteristic
1004C22C2×#58511yescharacteristic
1005C22C2×#58511yescharacteristic
1006C4—24no—
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4—44no—
1016C4—44no—
1017C4—44no—
1018C4—48no—
1019C4—44no—
1020C4—44no—
1021C4C2×#53918yes—
1022C2—24no—
1023C2—24no—
1024C2—24no—
1025C2—84no—
1026C2C22×#53911yescharacteristic
1027C2C2×#346011yescharacteristic
1028C2C2×#346111yescharacteristic
1029C2#6281811yescharacteristic
1030C2#6281911yescharacteristic
1031C2#6282511yescharacteristic
1032C2#6283311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35223C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37525C2semidirect
2. #37505C2semidirect
3. #37504C2semidirect
4. #37503C2semidirect
5. #37502C2semidirect
6. #35267C2semidirect
7. #35265C2semidirect
8. #35257C2semidirect
9. #35255C2semidirect
10. #35227C2semidirect
11. #35224C2semidirect
13. #35029C2semidirect
14. #35026C2semidirect
15. #35017C2semidirect
16. #35008C2semidirect
17. #34997C2semidirect
18. #34989C2semidirect
19. C4×#525C2semidirect
20. C22×#389C2semidirect
30. #2864C22semidirect
31. #2863C22semidirect
32. #2860C22semidirect
33. #2859C22semidirect
34. #2857C22semidirect
35. #2855C22semidirect
36. #2854C22semidirect
37. #2851C22semidirect
41. #2839C22semidirect
42. #2838C22semidirect
43. #2837C22semidirect
44. #2836C22semidirect
45. #2667C22semidirect
46. #2666C22semidirect
47. #2664C22semidirect
48. #2663C22semidirect
49. #2655C22semidirect
50. #2654C22semidirect
51. #2652C22semidirect
52. #2649C22semidirect
53. #2647C22semidirect
54. #2647C22semidirect
56. #2645C22semidirect
57. #2644C22semidirect
60. #2629C22semidirect
61. #2628C22semidirect
64. #2625C22semidirect
65. #2624C22semidirect
70. #2585C22semidirect
71. #2573C22semidirect
72. #2556C22semidirect
73. #2553C22semidirect
75. #2509C22semidirect
76. #2508C22semidirect
77. #2507C22semidirect
78. #2506C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2495C22semidirect
87. #2494C22semidirect
98. #2454C22semidirect
99. #2453C22semidirect
100. #2452C22semidirect
101. #2451C22semidirect
113. #2423C22semidirect
114. #2422C22semidirect
115. #2421C22semidirect
116. #2420C22semidirect
963. C2×C4#539semidirect

Maximal subgroups

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

subgroupindex
#375252
#375052
#375042
#375032
#375022
#352672
#352652
#352572
#352552
#352272
#352242
#352232
#350292
#350262
#350172
#350082
#349972
#349892
C4×#5252
C22×#3892