Finite Group Databasebeta

← #7682829

Subgroups — #7682829

Order 512.

5614 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59943C218yesmaximal, complemented
2#59905C214yesmaximal, complemented
3#59874C214yesmaximal, complemented
4#59638C214yesmaximal, complemented
5#59549C214yesmaximal, complemented
6#45392C214yesmaximal, complemented
7#45368C214yesmaximal, complemented
8#45148C214yesmaximal, complemented
9#44995C214yesmaximal, complemented
10#43643C214yesmaximal, complemented
11#43244C214yesmaximal, complemented
12#35676C211yesmaximal, characteristic
13#35630C212yesmaximal, complemented
14#35626C211yesmaximal, characteristic, complemented
15#35531C212yesmaximal, complemented
16#34952C212yesmaximal, complemented
17C2×#2592C211yesmaximal, characteristic, complemented
18#34269C212yesmaximal, complemented
19#34259C212yesmaximal, complemented
20#34252C212yesmaximal, complemented
21C22×2−1+4C2211yescharacteristic
22C2×#535C2212yes—
23C22×#124C2211yescharacteristic
24C2×#520C2212yes—
25C2×#518C2211yescharacteristic
26C2×C4×#41C2212yes—
27C22×C4×Q8C2211yescharacteristic
28#2798C2218yescomplemented
29#2778C2218yescomplemented
30#2764C2214yescomplemented
31#2763C2214yescomplemented
32#2760C2214yescomplemented
33#2759C2218yescomplemented
34#2754C2218yescomplemented
35#2749C2218yescomplemented
36#2746C2218yescomplemented
37#2743C2218yescomplemented
38#2740C2218yescomplemented
39#2737C2218yescomplemented
40#2696C2218yescomplemented
41#2693C2214yescomplemented
42#2607C2214yescomplemented
43#2600C2214yescomplemented
44#2598C2218yescomplemented
45#2592C2214yes—
46#2592C2214yes—
47#2592C2214yes—
48#2592C2214yes—
49#2589C2218yescomplemented
50#2582C2212yescomplemented
51#2582C2212yescomplemented
52#2581C2212yescomplemented
53#2581C2212yescomplemented
54#2580C2212yescomplemented
55#2580C2212yescomplemented
56#2579C2214yes—
57#2579C2214yes—
58#2576C2218yescomplemented
59#2572C2218yescomplemented
60#2564C2218yescomplemented
61#2538C2212yescomplemented
62#2538C2212yescomplemented
63#2532C2218yescomplemented
64#2527C2218yescomplemented
65#2526C2218yescomplemented
66#2523C2214yescomplemented
67#2516C2218yescomplemented
68#2514C2214yescomplemented
69#2514C2214yescomplemented
70#2514C2214yescomplemented
71#2514C2214yescomplemented
72#2511C2214yescomplemented
73#2511C2214yescomplemented
74#2511C2214yescomplemented
75#2511C2214yescomplemented
76#2510C2218yescomplemented
77#2510C2218yescomplemented
78#2504C2214yes—
79#2501C2214yes—
80#2500C2214yes—
81#2500C2214yes—
82#2498C2218yescomplemented
83#2493C2218yes—
84#2493C2218yes—
85#2488C2218yescomplemented
86#2487C2214yes—
87#2483C2214yes—
88#2483C2214yes—
89#2471C2218yescomplemented
90#2463C2214yescomplemented
91#2457C2218yescomplemented
92#2448C2214yes—
93#2448C2214yes—
94#2447C2214yes—
95#2447C2214yes—
96#2447C2214yes—
97#2447C2214yes—
98#2445C2214yes—
99#2445C2214yes—
100#2436C2214yes—
101#2436C2214yes—
102#2431C2214yes—
103#2431C2214yes—
104#2419C2218yescomplemented
105#2418C2218yes—
106#2418C2218yes—
107#2409C2214yes—
108#2404C2214yes—
109#2404C2214yes—
110#2396C2214yescomplemented
111#2396C2214yescomplemented
112C2×#397C2212yes—
113C2×#393C2212yes—
114#2367C2214yes—
115#2367C2214yes—
116#2366C2214yes—
117#2366C2214yes—
118#2359C2218yescomplemented
119#2358C2218yes—
120#2358C2218yes—
121#2357C2214yescomplemented
122#2356C2214yescomplemented
123#2355C2214yescomplemented
124#2354C2214yescomplemented
125#2353C2218yescomplemented
126#2347C2214yescomplemented
127#2346C2214yescomplemented
128#2345C2214yescomplemented
129#2344C2214yescomplemented
130Q8×C22⋊C4C2214yescomplemented
131Q8×C22⋊C4C2214yescomplemented
132#2339C2218yes—
133#2339C2218yes—
134#2339C2214yescomplemented
135#2339C2214yescomplemented
136#2324C2214yes—
137#2324C2214yes—
138#2318C2218yes—
139#2317C2212yes—
140#2311C2212yes—
141#2311C2214yescomplemented
142#2310C2212yes—
143#2310C2211yescharacteristic
144#2310C2214yescomplemented
145#2309C2211yescharacteristic
146C4×C22⋊Q8C2214yescomplemented
147C4×C22⋊Q8C2214yescomplemented
148C4×#121C2214yes—
149C4×#121C2214yes—
150#2297C2212yes—
151#2297C2212yes—
152#2297C2214yescomplemented
153#2296C2212yes—
154#2296C2212yes—
155C2×#391C2212yes—
156C2×#391C2214yescomplemented
157C2×#390C2212yes—
158#2290C2218yes—
159C2×#388C2214yes—
160#2285C2212yes—
161#2274C2212yes—
162C2×C4×C4⋊C4C2211yescharacteristic
163C2×2−1+4—216no—
164C2×2−1+4—44no—
165C22×#41C2314yes—
166C22×#41C2314yes—
167C22×#41C2312yes—
168C23×Q8C2311yescharacteristic
169C23×Q8C2314yes—
170C23×Q8C2311yescharacteristic
171C23×D4C2311yescharacteristic
172#535—216no—
173C2×#127C2314yes—
174C2×#124—44no—
175C2×#124C2314yes—
176C2×#124C2314yes—
177C2×#124C2314yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×#121C2314yes—
183C2×#121C2314yes—
184C2×#120C2318yes—
185#520—216no—
186#518—44no—
187C4×#41—48no—
188C2×C4×Q8—44no—
189C2×C4×Q8C2314yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2312yes—
196C2×C4×D4C2318yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2318yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2318yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2314yes—
210C2×#117C2314yes—
211C2×#117C2318yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2314yes—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2312yes—
216C22×C22⋊C4C2314yes—
217C22×C22⋊C4C2314yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2314yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2314yes—
224C22×C42C2312yes—
225#401C2318yes—
226#401C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2314yes—
230#400C2314yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#399C2318yes—
236#399C2314yes—
237#399C2314yes—
238#399C2318yes—
239#398C2314yes—
240#398C2314yes—
241#398C2314yes—
242#398C2314yes—
243#397C2318yes—
244#397C2314yes—
245#397C2314yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#396C2314yes—
253#396C2314yes—
254#396C2314yes—
255#396C2314yes—
256#395C2314yes—
257#395C2314yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#393C2318yes—
263#393C2314yes—
264#393C2314yes—
265#393C2318yes—
266#393C2314yes—
267#393C2314yes—
268#393C2314yes—
269#393C2314yes—
270#392C2318yes—
271#392C2314yes—
272#392C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2312yes—
280#391C2314yes—
281#391C2314yes—
282#391C2318yes—
283#391C2318yes—
284#391C2314yes—
285#391C2312yes—
286#391C2312yes—
287#391C2312yes—
288#391C2314yes—
289#391C2318yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2318yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2312yes—
298#390C2314yes—
299#390C2318yes—
300#390C2318yes—
301#390C2312yes—
302#390C2312yes—
303#390C2312yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2312yes—
310#389C2312yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2314yes—
318#389C2314yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2314yes—
339#387C2318yes—
340#387C2314yes—
341#387C2314yes—
342#387C2314yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2314yes—
356#386C2318yes—
357#386C2318yes—
358#386C2314yes—
359#386C2314yes—
360#386C2314yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#385C2314yes—
369#385C2318yes—
370#385C2318yes—
371#385C2314yes—
372#385C2314yes—
373#385C2314yes—
374#385C2314yes—
375#385C2314yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#385C2314yes—
380#385C2318yes—
381#385C2318yes—
382#384C2314yes—
383#384C2312yes—
384#384C2312yes—
385#383C2318yes—
386#383C2318yes—
387#383C2318yes—
388#382C2314yes—
389#382C2318yes—
390#382C2312yes—
391#382C2312yes—
392#381C2318yes—
393#381C2314yes—
394#381C2318yes—
395#381C2318yes—
396#381C2314yes—
397#381C2318yes—
398#381C2314yes—
399#381C2318yes—
400#380C2318yes—
401#380C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2318yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#379C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433#376C2318yes—
434C2×#95C2318yes—
435C2×#95C2312yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C2×#95C2318yes—
439C25C2412yes—
4402−1+4—464no—
441C2×#41—216no—
442C2×#41—232no—
443C2×#41—28no—
444C2×#41—216no—
445C2×#41—28no—
446C2×#41—48no—
447C2×#41—48no—
448C2×#41#41116yes—
449C22×Q8—216no—
450C22×Q8—216no—
451C22×Q8—28no—
452C22×Q8—24no—
453C22×Q8—42no—
454C22×Q8—44no—
455C22×Q8—48no—
456C22×Q8C2414yes—
457C22×Q8C2411yescharacteristic
458C22×Q8C2414yes—
459C22×Q8C2412yes—
460C22×Q8C2412yes—
461C22×Q8C2411yescharacteristic
462C22×D4—28no—
463C22×D4—24no—
464C22×D4C2414yes—
465C22×D4C2414yes—
466C22×D4C2414yes—
467C22×D4C2412yes—
468C22×D4C2418yes—
469C22×D4C2418yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2418yes—
473C23×C4C2414yes—
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2414yes—
477C23×C4C2411yescharacteristic
478C23×C4C2418yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2411yescharacteristic
484#127—216no—
485#124—216no—
486#124—48no—
487#124—48no—
488#123—416no—
489#123—88no—
490C22⋊Q8—48no—
491C22⋊Q8—48no—
492#121—216no—
493#121—216no—
494#120—232no—
495C4×Q8—216no—
496C4×Q8—44no—
497C4×Q8—44no—
498C4×Q8—44no—
499C4×Q8—44no—
500C4×Q8—44no—
501C4×Q8—44no—
502C4×D4—232no—
503C4×D4—216no—
504C4×D4—44no—
505C4×D4—44no—
506C4×D4—48no—
507C4×D4—48no—
508C4×D4—416no—
509C4×D4—48no—
510C4×D4—48no—
511C4×D4—88no—
512#117—216no—
513#117—28no—
514#117—28no—
515#117—28no—
516#117—48no—
517#117—88no—
518C2×C4⋊C4—216no—
519C2×C4⋊C4—28no—
520C2×C4⋊C4—44no—
521C2×C4⋊C4—42no—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2411yescharacteristic
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C22⋊C4—48no—
555C2×C22⋊C4—48no—
556C2×C22⋊C4—44no—
557C2×C22⋊C4—44no—
558C2×C22⋊C4—84no—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C42—28no—
589C2×C42—24no—
590C2×C42—48no—
591C2×C42—82no—
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2418yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2418yes—
603C2×C42C2418yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2418yes—
612#95C2418yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2414yes—
646C24—28no—
647C24—24no—
648C24—44no—
649C24—42no—
650C24—42no—
651C24C2514yes—
652C24C2514yes—
653C24C2511yescharacteristic
654#41—264no—
655#41—464no—
656#41—464no—
657C2×Q8—24no—
658C2×Q8—216no—
659C2×Q8—28no—
660C2×Q8—28no—
661C2×Q8—24no—
662C2×Q8—28no—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—41no—
666C2×Q8—42no—
667C2×Q8—41no—
668C2×Q8—44no—
669C2×Q8—42no—
670C2×Q8—42no—
671C2×Q8—464no—
672C2×Q8—416no—
673C2×Q8—416no—
674C2×Q8C2×#4118yes—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—216no—
678C2×D4—216no—
679C2×D4—216no—
680C2×D4—24no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—24no—
684C2×D4—28no—
685C2×D4—44no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—416no—
691C2×D4C2×#41116yes—
692C2×D4C2×#4118yes—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—216no—
696C22×C4—28no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—216no—
702C22×C4—28no—
703C22×C4—24no—
704C22×C4—216no—
705C22×C4—24no—
706C22×C4—28no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—48no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—42no—
717C22×C4—48no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—48no—
721C22×C4—42no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—48no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4C2×#41116yes—
729C22×C4C2×#4118yes—
730C22×C4H(5,𝔽2)14yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2518yes—
734C22×C4C2512yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2514yes—
738C22×C4C2514yes—
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C22×C4C2512yes—
742C22×C4C2514yes—
743C22×C4C2512yes—
744C22×C4C2512yes—
745C22×C4C2514yes—
746C22×C4C2512yes—
747C22×C4C2512yes—
748C4⋊C4—28no—
749C4⋊C4—24no—
750C4⋊C4—216no—
751C4⋊C4—28no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—42no—
760C4⋊C4—42no—
761C4⋊C4—41no—
762C4⋊C4—42no—
763C4⋊C4—42no—
764C4⋊C4—42no—
765C4⋊C4—41no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—48no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—48no—
779C4⋊C4—44no—
780C22⋊C4—216no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—216no—
787C22⋊C4—28no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C42—216no—
810C42—28no—
811C42—28no—
812C42—24no—
813C42—24no—
814C42—24no—
815C42—24no—
816C42—24no—
817C42—24no—
818C42—28no—
819C42—44no—
820C42—44no—
821C42—48no—
822C42—48no—
823C42—48no—
824C23—22no—
825C23—21no—
826C23—21no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—28no—
834C23—24no—
835C23—28no—
836C23—24no—
837C23—24no—
838C23—48no—
839C23—88no—
840C23—88no—
841C23—84no—
842C23—84no—
843C23C22×#4118yes—
844C23C22×#4114yes—
845C23C2×H(5,𝔽2)12yes—
846C23C2611yescharacteristic
847Q8—216no—
848Q8—44no—
849Q8—416no—
850Q8—48no—
851Q8—44no—
852Q8—416no—
853D4—232no—
854D4—216no—
855D4—416no—
856D4—416no—
857D4—816no—
858D4—816no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—232no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—28no—
868C2×C4—24no—
869C2×C4—28no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—28no—
882C2×C4—24no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—48no—
904C2×C4—432no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—48no—
908C2×C4—88no—
909C2×C4—88no—
910C2×C4—816no—
911C2×C4—84no—
912C2×C4—88no—
913C2×C4—164no—
914C2×C4—164no—
915C2×C4#551116yes—
916C2×C4C22×#4118yes—
917C2×C4C22×#4114yes—
918C2×C4C22×#4114yes—
919C2×C4C2×H(5,𝔽2)14yes—
920C2×C4#58514yes—
921C22—24no—
922C22—24no—
923C22—22no—
924C22—22no—
925C22—28no—
926C22—28no—
927C22—28no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—48no—
933C22—48no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—168no—
938C22C2×#55114yes—
939C22C23×#4112yes—
940C22C22×H(5,𝔽2)11yescharacteristic
941C22C2×#58512yes—
942C22H(7,𝔽2)11yescharacteristic
943C222−1+611yescharacteristic
944C4—24no—
945C4—28no—
946C4—44no—
947C4—44no—
948C4—48no—
949C4—44no—
950C4—44no—
951C4—41no—
952C4—41no—
953C4—42no—
954C4—44no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—44no—
959C4—44no—
960C4C2×#55118yes—
961C2—24no—
962C2—48no—
963C2—84no—
964C2C22×#55111yescharacteristic
965C2#6282111yescharacteristic
966C2#6287511yescharacteristic
967C2#6299512yes—
968C2#6301012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35676C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59943C2semidirect
2. #59905C2semidirect
3. #59874C2semidirect
4. #59638C2semidirect
5. #59549C2semidirect
6. #45392C2semidirect
7. #45368C2semidirect
8. #45148C2semidirect
9. #44995C2semidirect
10. #43643C2semidirect
11. #43244C2semidirect
13. #35630C2semidirect
14. #35626C2semidirect
15. #35531C2semidirect
16. #34952C2semidirect
17. C2×#2592C2semidirect
18. #34269C2semidirect
19. #34259C2semidirect
20. #34252C2semidirect
28. #2798C22semidirect
29. #2778C22semidirect
30. #2764C22semidirect
31. #2763C22semidirect
32. #2760C22semidirect
33. #2759C22semidirect
34. #2754C22semidirect
35. #2749C22semidirect
36. #2746C22semidirect
37. #2743C22semidirect
38. #2740C22semidirect
39. #2737C22semidirect
40. #2696C22semidirect
41. #2693C22semidirect
42. #2607C22semidirect
43. #2600C22semidirect
44. #2598C22semidirect
49. #2589C22semidirect
50. #2582C22semidirect
51. #2582C22semidirect
52. #2581C22semidirect
53. #2581C22semidirect
54. #2580C22semidirect
55. #2580C22semidirect
58. #2576C22semidirect
59. #2572C22semidirect
60. #2564C22semidirect
61. #2538C22semidirect
62. #2538C22semidirect
63. #2532C22semidirect
64. #2527C22semidirect
65. #2526C22semidirect
66. #2523C22semidirect
67. #2516C22semidirect
68. #2514C22semidirect
69. #2514C22semidirect
70. #2514C22semidirect
71. #2514C22semidirect
72. #2511C22semidirect
73. #2511C22semidirect
74. #2511C22semidirect
75. #2511C22semidirect
76. #2510C22semidirect
77. #2510C22semidirect
82. #2498C22semidirect
85. #2488C22semidirect
89. #2471C22semidirect
90. #2463C22semidirect
91. #2457C22semidirect
104. #2419C22semidirect
110. #2396C22semidirect
111. #2396C22semidirect
118. #2359C22semidirect
121. #2357C22semidirect
122. #2356C22semidirect
123. #2355C22semidirect
124. #2354C22semidirect
125. #2353C22semidirect
126. #2347C22semidirect
127. #2346C22semidirect
128. #2345C22semidirect
129. #2344C22semidirect
130. Q8×C22⋊C4C22semidirect
131. Q8×C22⋊C4C22semidirect
134. #2339C22semidirect
135. #2339C22semidirect
141. #2311C22semidirect
144. #2310C22semidirect
146. C4×C22⋊Q8C22semidirect
147. C4×C22⋊Q8C22semidirect
152. #2297C22semidirect
156. C2×#391C22semidirect

Maximal subgroups

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

subgroupindex
#599432
#599052
#598742
#596382
#595492
#453922
#453682
#451482
#449952
#436432
#432442
#356762
#356302
#356262
#355312
#349522
C2×#25922
#342692
#342592
#342522