Finite Group Databasebeta

← #7673905

Subgroups — #7673905

Order 512.

4634 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#45329C214yesmaximal, complemented
2#45256C214yesmaximal, complemented
3#45124C214yesmaximal, complemented
4#44911C214yesmaximal, complemented
5#39515C214yesmaximal, complemented
6#39509C214yesmaximal, complemented
7#39291C218yesmaximal, complemented
8#39289C218yesmaximal, complemented
9#37961C214yesmaximal, complemented
10#37960C214yesmaximal, complemented
11#35544C212yesmaximal, complemented
12#35542C212yesmaximal
13#35334C211yesmaximal, characteristic, complemented
14#35330C211yesmaximal, characteristic, complemented
15#35160C212yesmaximal, complemented
16#34634C211yesmaximal, characteristic, complemented
17#34271C212yesmaximal, complemented
18#34214C211yesmaximal, characteristic, complemented
19#34188C211yesmaximal, characteristic, complemented
20#34065C211yesmaximal, characteristic
21C2×#2314C211yesmaximal, characteristic, complemented
22C2×#544C2212yes—
23C2×#533C2211yescharacteristic
24C2×#525C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2862C2212yescomplemented
28#2859C2212yescomplemented
29#2852C2218yes—
30#2851C2212yescomplemented
31#2851C2212yescomplemented
32#2810C2218yescomplemented
33#2808C2218yes—
34#2805C2218yescomplemented
35#2798C2218yes—
36#2798C2218yescomplemented
37#2789C2218yescomplemented
38#2788C2218yescomplemented
39#2787C2218yescomplemented
40#2786C2218yes—
41#2783C2218yes—
42#2775C2218yes—
43#2767C2218yescomplemented
44#2759C2218yes—
45#2759C2218yescomplemented
46#2727C2218yes—
47#2715C2218yes—
48#2660C2214yescomplemented
49#2643C2218yes—
50#2629C2212yes—
51#2629C2212yes—
52#2628C2212yes—
53#2628C2212yes—
54#2628C2214yescomplemented
55#2627C2214yes—
56#2626C2214yes—
57#2601C2218yes—
58#2599C2218yescomplemented
59#2596C2218yes—
60#2596C2218yescomplemented
61#2594C2218yes—
62#2592C2218yes—
63#2588C2218yescomplemented
64#2581C2214yescomplemented
65#2581C2218yescomplemented
66#2580C2214yescomplemented
67#2564C2218yes—
68#2563C2214yes—
69#2562C2214yes—
70#2562C2214yes—
71#2550C2214yescomplemented
72#2550C2214yescomplemented
73#2549C2218yes—
74#2547C2214yes—
75#2524C2218yescomplemented
76#2514C2214yescomplemented
77#2514C2218yescomplemented
78#2513C2214yescomplemented
79#2512C2214yescomplemented
80#2511C2214yescomplemented
81#2497C2214yes—
82#2497C2214yes—
83#2497C2214yescomplemented
84#2496C2214yes—
85#2496C2214yes—
86#2496C2214yescomplemented
87#2495C2214yes—
88#2495C2214yes—
89#2495C2214yescomplemented
90#2494C2214yes—
91#2494C2214yes—
92#2494C2214yescomplemented
93#2493C2218yes—
94#2492C2214yes—
95#2491C2214yes—
96#2490C2214yes—
97#2489C2214yes—
98#2488C2218yes—
99#2480C2218yes—
100#2478C2218yescomplemented
101#2474C2218yes—
102#2472C2218yes—
103#2469C2218yes—
104#2469C2218yes—
105#2469C2218yescomplemented
106#2448C2218yes—
107#2396C2214yes—
108#2396C2214yes—
109#2370C2214yescomplemented
110#2370C2214yescomplemented
111#2370C2214yescomplemented
112#2370C2214yescomplemented
113#2369C2214yescomplemented
114#2369C2214yescomplemented
115#2365C2214yescomplemented
116#2365C2214yescomplemented
117#2360C2218yes—
118#2355C2214yescomplemented
119#2355C2214yescomplemented
120#2354C2214yescomplemented
121#2352C2218yes—
122Q8×C4⋊C4C2214yescomplemented
123#2330C2212yescomplemented
124#2330C2212yescomplemented
125#2329C2218yes—
126#2324C2212yes—
127#2324C2212yes—
128#2323C2212yes—
129#2323C2212yes—
130#2322C2214yes—
131#2321C2214yes—
132#2317C2212yes—
133#2317C2212yes—
134#2316C2212yes—
135#2314C2214yes—
136#2314C2214yes—
137#2314C2214yes—
138#2314C2214yes—
139#2314C2212yescomplemented
140#2314C2212yescomplemented
141#2311C2212yes—
142#2311C2212yes—
143C4×C4⋊Q8C2214yescomplemented
144C4×C22⋊Q8C2218yes—
145#2297C2211yescharacteristic
146#2296C2211yescharacteristic
147#2296C2212yes—
148#2293C2214yes—
149#2290C2214yes—
150C2×#388C2214yes—
151C2×#387C2214yes—
152#2285C2211yescharacteristic
153#2285C2214yescomplemented
154C2×#384C2211yescharacteristic
155C2×#382C2211yescharacteristic
156#2280C2211yescharacteristic
157#2280C2212yes—
158C2×#380C2212yes—
159#2274C2212yes—
160#2274C2212yes—
161C4×#117C2211yescharacteristic
162C2×C4×C4⋊C4C2212yes—
163C22×#41C2311yescharacteristic
164C24×C4C2311yescharacteristic
165#544—216no—
166#533—28no—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2314yes—
170C2×#126C2318yes—
171C2×#126C2318yes—
172C2×#125C2314yes—
173C2×#125C2311yescharacteristic
174C2×#125C2311yescharacteristic
175C2×#125C2314yes—
176C2×#124C2318yes—
177#525—28no—
178C2×#123C2312yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2312yes—
181C2×C22⋊Q8C2318yes—
182C2×#121C2312yes—
183C2×#120C2312yes—
184C4×#41—28no—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2318yes—
188C2×C4×Q8C2318yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2312yes—
192C2×#117—28no—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2318yes—
203C2×#117C2311yescharacteristic
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2314yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2314yes—
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2314yes—
213C22×C42C2311yescharacteristic
214#401C2318yes—
215#401C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2314yes—
224#400C2318yes—
225#400C2314yes—
226#400C2318yes—
227#399C2318yes—
228#399C2314yes—
229#399C2314yes—
230#398C2314yes—
231#398C2318yes—
232#398C2314yes—
233#398C2318yes—
234#398C2314yes—
235#398C2314yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#396C2314yes—
245#396C2314yes—
246#396C2318yes—
247#396C2314yes—
248#396C2314yes—
249#396C2318yes—
250#395C2318yes—
251#395C2314yes—
252#395C2318yes—
253#395C2318yes—
254#395C2314yes—
255#394C2318yes—
256#394C2318yes—
257#393C2318yes—
258#393C2318yes—
259#393C2318yes—
260#393C2314yes—
261#393C2314yes—
262#391C2318yes—
263#391C2314yes—
264#391C2314yes—
265#391C2311yescharacteristic
266#391C2311yescharacteristic
267#391C2318yes—
268#391C2318yes—
269#391C2318yes—
270#391C2318yes—
271#391C2318yes—
272#391C2318yes—
273#390C2318yes—
274#390C2314yes—
275#390C2314yes—
276#390C2314yes—
277#390C2314yes—
278#390C2311yescharacteristic
279#390C2311yescharacteristic
280#389C2314yes—
281#389C2314yes—
282#389C2318yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2312yes—
292#389C2312yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2312yes—
300#389C2312yes—
301#389C2312yes—
302#389C2312yes—
303#389C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2314yes—
315#388C2314yes—
316#388C2314yes—
317#388C2314yes—
318#388C2314yes—
319#388C2314yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2314yes—
335#387C2314yes—
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#386C2318yes—
351#386C2318yes—
352#386C2314yes—
353#386C2314yes—
354#386C2314yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2314yes—
360#385C2314yes—
361#385C2314yes—
362#385C2314yes—
363#385C2314yes—
364#384C2312yes—
365#384C2312yes—
366#384C2314yes—
367#384C2314yes—
368#384C2314yes—
369#384C2312yes—
370#383C2318yes—
371#383C2318yes—
372#382C2318yes—
373#382C2314yes—
374#382C2312yes—
375#382C2312yes—
376#382C2311yescharacteristic
377#382C2311yescharacteristic
378#382C2314yes—
379#382C2314yes—
380#382C2318yes—
381#381C2312yes—
382#381C2314yes—
383#380C2314yes—
384#380C2312yes—
385#380C2312yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2312yes—
391#380C2314yes—
392#380C2318yes—
393#380C2314yes—
394#380C2314yes—
395#380C2312yes—
396#380C2312yes—
397#380C2314yes—
398#380C2318yes—
399#380C2312yes—
400#379C2312yes—
401#379C2314yes—
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⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432#376C2312yes—
433C2×#95C2314yes—
434C2×#95C2314yes—
435C2×#95C2314yes—
436C43C2312yes—
437C25C2411yescharacteristic
438C2×#41—24no—
439C2×#41—24no—
440C2×#41—24no—
441C22×Q8C2411yescharacteristic
442C22×Q8C2414yes—
443C22×Q8C2418yes—
444C22×D4C2412yes—
445C22×D4C2411yescharacteristic
446C22×D4C2414yes—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—24no—
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2414yes—
455C23×C4C2414yes—
456C23×C4C2412yes—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460C4⋊Q8—216no—
461C4⋊Q8—28no—
462C4⋊Q8—216no—
463#126—88no—
464#126—88no—
465#125—216no—
466#125—24no—
467#125—24no—
468#125—216no—
469#124—88no—
470#123—28no—
471C22⋊Q8—216no—
472C22⋊Q8—28no—
473C22⋊Q8—232no—
474#121—28no—
475#120—28no—
476C4×Q8—28no—
477C4×Q8—216no—
478C4×Q8—88no—
479C4×Q8—88no—
480C4×D4—216no—
481C4×D4—28no—
482C4×D4—216no—
483#117—24no—
484#117—28no—
485#117—28no—
486#117—24no—
487#117—28no—
488#117—28no—
489#117—28no—
490#117—28no—
491#117—28no—
492#117—88no—
493#117#4118yes—
494C2×C4⋊C4—28no—
495C2×C4⋊C4—28no—
496C2×C4⋊C4—28no—
497C2×C4⋊C4—84no—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2411yescharacteristic
513C2×C4⋊C4C2411yescharacteristic
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2412yes—
538C2×C22⋊C4—28no—
539C2×C22⋊C4—84no—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2412yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2412yes—
566C2×C42—24no—
567C2×C42—28no—
568C2×C42—84no—
569C2×C42#4118yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2411yescharacteristic
573C2×C42C2411yescharacteristic
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2418yes—
579C2×C42C2418yes—
580C2×C42C2414yes—
581C2×C42C2418yes—
582C2×C42C2418yes—
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2414yes—
586C2×C42C2411yescharacteristic
587C2×C42C2412yes—
588C2×C42C2411yescharacteristic
589C2×C42C2412yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2414yes—
597#95C2414yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—42no—
632C24—42no—
633C24C2512yes—
634C24C2512yes—
635C24C2511yescharacteristic
636#41—416no—
637C2×Q8—22no—
638C2×Q8—28no—
639C2×Q8—22no—
640C2×Q8—216no—
641C2×Q8—22no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8—48no—
645C2×Q8—48no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—28no—
652C2×D4—22no—
653C2×D4—44no—
654C2×D4—44no—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—24no—
662C22×C4—28no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—44no—
674C22×C4—42no—
675C22×C4—44no—
676C22×C4—42no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—416no—
682C22×C4C2×#4118yes—
683C22×C4C2×#4114yes—
684C22×C4C2×#4114yes—
685C22×C42−1+414yes—
686C22×C4C2512yes—
687C22×C4C2512yes—
688C22×C4C2512yes—
689C22×C4C2514yes—
690C22×C4C2518yes—
691C22×C4C2512yes—
692C22×C4C2514yes—
693C22×C4C2512yes—
694C22×C4C2518yes—
695C22×C4C2514yes—
696C22×C4C2514yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C22×C4C2514yes—
700C22×C4C2512yes—
701C22×C4C2512yes—
702C22×C4C2511yescharacteristic
703C22×C4C2511yescharacteristic
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—24no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—24no—
711C4⋊C4—28no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—216no—
721C4⋊C4—216no—
722C4⋊C4—216no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—48no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—48no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—48no—
741C4⋊C4—44no—
742C4⋊C4—48no—
743C4⋊C4C2×#4118yes—
744C22⋊C4—24no—
745C22⋊C4—28no—
746C22⋊C4—28no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—28no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—48no—
756C22⋊C4—48no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—48no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—44no—
765C22⋊C4—48no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4C2×#4118yes—
770C42—22no—
771C42—22no—
772C42—24no—
773C42—24no—
774C42—28no—
775C42—28no—
776C42—28no—
777C42—24no—
778C42—48no—
779C42—48no—
780C42—44no—
781C42—48no—
782C42—48no—
783C42—44no—
784C42—48no—
785C42—48no—
786C42C2×#4114yes—
787C42C2×#4114yes—
788C42C2×#4118yes—
789C42C2×#4118yes—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—24no—
800C23—22no—
801C23—22no—
802C23—24no—
803C23—22no—
804C23—48no—
805C23—44no—
806C23—84no—
807C23—82no—
808C23—82no—
809C23C22×#4112yes—
810C23C22×#4112yes—
811C23C2×2−1+412yes—
812C23C2611yescharacteristic
813Q8—416no—
814Q8—44no—
815Q8—816no—
816D4—48no—
817D4—44no—
818D4—88no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—28no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—28no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—48no—
863C2×C4—416no—
864C2×C4—48no—
865C2×C4—44no—
866C2×C4—48no—
867C2×C4—48no—
868C2×C4—48no—
869C2×C4—88no—
870C2×C4—88no—
871C2×C4#556116yes—
872C2×C4C22×#4114yes—
873C2×C4C22×#4114yes—
874C2×C4C22×#4118yes—
875C2×C4C22×#4112yes—
876C2×C4C22×#4112yes—
877C2×C4C22×#4112yes—
878C2×C4C22×#4112yes—
879C2×C4C2×2−1+412yes—
880C2×C4C2×2−1+412yes—
881C22—24no—
882C22—24no—
883C22—22no—
884C22—22no—
885C22—44no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—44no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—88no—
898C22C2×#55614yes—
899C22C23×#4111yescharacteristic
900C22C23×#4111yescharacteristic
901C22C22×2−1+411yescharacteristic
902C22H(7,𝔽2)12yes—
903C222−1+612yes—
904C4—24no—
905C4—24no—
906C4—28no—
907C4—42no—
908C4—44no—
909C4—42no—
910C4—44no—
911C4—44no—
912C4—44no—
913C4—48no—
914C4—44no—
915C4—42no—
916C4—48no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4C2×#55614yes—
921C4C2×#55614yes—
922C2—24no—
923C2—82no—
924C2—82no—
925C2C22×#55611yescharacteristic
926C2#6284512yes—
927C2#6285712yes—
928C2#6288111yescharacteristic
929C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45329C2semidirect
2. #45256C2semidirect
3. #45124C2semidirect
4. #44911C2semidirect
5. #39515C2semidirect
6. #39509C2semidirect
7. #39291C2semidirect
8. #39289C2semidirect
9. #37961C2semidirect
10. #37960C2semidirect
11. #35544C2semidirect
13. #35334C2semidirect
14. #35330C2semidirect
15. #35160C2semidirect
16. #34634C2semidirect
17. #34271C2semidirect
18. #34214C2semidirect
19. #34188C2semidirect
21. C2×#2314C2semidirect
27. #2862C22semidirect
28. #2859C22semidirect
30. #2851C22semidirect
31. #2851C22semidirect
32. #2810C22semidirect
34. #2805C22semidirect
36. #2798C22semidirect
37. #2789C22semidirect
38. #2788C22semidirect
39. #2787C22semidirect
43. #2767C22semidirect
45. #2759C22semidirect
48. #2660C22semidirect
54. #2628C22semidirect
58. #2599C22semidirect
60. #2596C22semidirect
63. #2588C22semidirect
64. #2581C22semidirect
65. #2581C22semidirect
66. #2580C22semidirect
71. #2550C22semidirect
72. #2550C22semidirect
75. #2524C22semidirect
76. #2514C22semidirect
77. #2514C22semidirect
78. #2513C22semidirect
79. #2512C22semidirect
80. #2511C22semidirect
83. #2497C22semidirect
86. #2496C22semidirect
89. #2495C22semidirect
92. #2494C22semidirect
100. #2478C22semidirect
105. #2469C22semidirect
109. #2370C22semidirect
110. #2370C22semidirect
111. #2370C22semidirect
112. #2370C22semidirect
113. #2369C22semidirect
114. #2369C22semidirect
115. #2365C22semidirect
116. #2365C22semidirect
118. #2355C22semidirect
119. #2355C22semidirect
120. #2354C22semidirect
122. Q8×C4⋊C4C22semidirect
123. #2330C22semidirect
124. #2330C22semidirect
139. #2314C22semidirect
140. #2314C22semidirect
143. C4×C4⋊Q8C22semidirect
153. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#453292
#452562
#451242
#449112
#395152
#395092
#392912
#392892
#379612
#379602
#355442
#355422
#353342
#353302
#351602
#346342
#342712
#342142
#341882
#340652
C2×#23142