Finite Group Databasebeta

← #8094526

Subgroups — #8094526

Order 512.

4998 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53101C214yesmaximal, complemented
2#53094C214yesmaximal, complemented
3#53054C214yesmaximal, complemented
4#53019C214yesmaximal, complemented
5#52412C218yesmaximal, complemented
6#46088C214yesmaximal, complemented
7#45990C214yesmaximal, complemented
8#45717C214yesmaximal, complemented
9#45641C214yesmaximal, complemented
10#45609C214yesmaximal, complemented
11#45498C214yesmaximal, complemented
12#35574C212yesmaximal, complemented
13#35518C212yesmaximal, complemented
14#35516C212yesmaximal, complemented
15#35263C212yesmaximal, complemented
16#35253C212yesmaximal, complemented
17#35159C211yesmaximal, characteristic, complemented
18#35158C211yesmaximal, characteristic, complemented
19C2×#2563C211yesmaximal, characteristic, complemented
20#34737C212yesmaximal, complemented
21C2×#544C2211yescharacteristic
22C2×#537C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#525C2212yes—
25C2×#525C2212yes—
26C2×#520C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×#117C2212yes—
29#2857C2214yescomplemented
30#2855C2214yescomplemented
31#2854C2214yescomplemented
32#2851C2214yes—
33#2851C2214yescomplemented
34#2850C2214yes—
35#2845C2214yescomplemented
36#2841C2218yescomplemented
37#2832C2218yescomplemented
38#2832C2218yescomplemented
39#2831C2218yescomplemented
40#2830C2218yescomplemented
41#2829C2218yes—
42#2824C2218yescomplemented
43#2820C2214yescomplemented
44#2816C2218yescomplemented
45#2814C2218yescomplemented
46#2808C2214yes—
47#2798C2218yescomplemented
48#2788C2218yescomplemented
49#2783C2218yescomplemented
50#2772C2218yescomplemented
51#2768C2218yescomplemented
52#2761C2218yes—
53#2761C2218yescomplemented
54#2755C2218yescomplemented
55#2751C2218yescomplemented
56#2744C2218yescomplemented
57#2732C2214yes—
58#2711C2218yes—
59#2706C2218yes—
60#2696C2218yescomplemented
61#2692C2218yescomplemented
62#2692C2218yescomplemented
63#2687C2218yescomplemented
64#2682C2214yes—
65#2682C2214yes—
66#2681C2218yescomplemented
67#2676C2218yes—
68#2646C2214yes—
69#2639C2214yes—
70#2629C2214yescomplemented
71#2628C2214yescomplemented
72#2625C2214yescomplemented
73#2624C2214yescomplemented
74#2579C2218yes—
75#2563C2214yes—
76#2563C2214yes—
77#2563C2214yes—
78#2563C2214yes—
79#2538C2214yescomplemented
80#2537C2214yescomplemented
81#2536C2214yescomplemented
82#2535C2214yescomplemented
83#2509C2214yescomplemented
84#2508C2214yescomplemented
85#2507C2214yescomplemented
86#2506C2214yescomplemented
87#2498C2218yes—
88#2492C2214yescomplemented
89#2491C2214yescomplemented
90#2490C2214yescomplemented
91#2489C2214yescomplemented
92#2487C2214yescomplemented
93#2487C2214yescomplemented
94#2486C2214yescomplemented
95#2486C2214yescomplemented
96#2485C2214yescomplemented
97#2485C2214yescomplemented
98#2485C2214yescomplemented
99#2485C2214yescomplemented
100#2452C2214yescomplemented
101#2452C2214yescomplemented
102#2451C2214yescomplemented
103#2451C2214yescomplemented
104#2442C2214yescomplemented
105#2441C2214yescomplemented
106#2440C2214yescomplemented
107#2440C2214yescomplemented
108#2440C2214yescomplemented
109#2439C2214yescomplemented
110#2439C2214yescomplemented
111#2439C2214yescomplemented
112#2438C2218yes—
113#2437C2218yes—
114#2425C2218yes—
115#2424C2218yes—
116#2423C2214yescomplemented
117#2422C2214yescomplemented
118#2421C2214yescomplemented
119#2420C2214yescomplemented
120#2419C2218yes—
121#2418C2218yes—
122#2417C2212yes—
123#2417C2212yes—
124#2417C2214yescomplemented
125#2416C2212yes—
126#2416C2212yes—
127#2416C2214yescomplemented
128#2415C2212yes—
129#2415C2212yes—
130#2415C2214yescomplemented
131#2414C2212yes—
132#2414C2212yes—
133#2414C2214yescomplemented
134#2413C2214yes—
135#2412C2218yes—
136#2412C2214yes—
137#2411C2214yes—
138#2410C2214yes—
139#2409C2218yes—
140#2392C2214yes—
141#2392C2214yes—
142C2×#393C2214yes—
143#2382C2214yescomplemented
144#2379C2214yescomplemented
145#2377C2218yes—
146#2317C2212yes—
147#2317C2212yes—
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2212yes—
151#2311C2212yes—
152#2311C2212yes—
153C4×#121C2214yes—
154C4×#121C2214yes—
155#2297C2212yes—
156#2296C2212yes—
157C2×#390C2212yes—
158C2×#382C2212yes—
159#2280C2212yes—
160C2×#380C2212yes—
161C2×#380C2212yes—
162C2×C4×C4⋊C4C2211yescharacteristic
163C22×#41C2312yes—
164C23×Q8C2312yes—
165C23×D4C2311yescharacteristic
166C24×C4C2312yes—
167#544—44no—
168#537—44no—
169C2×C4⋊Q8—44no—
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2314yes—
173C2×#125C2314yes—
174C2×#125C2314yes—
175C2×#124C2314yes—
176#525—48no—
177#525—48no—
178C2×#123C2314yes—
179C2×#123C2314yes—
180C2×#123C2318yes—
181C2×#123C2318yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2312yes—
184C2×C22⋊Q8C2312yes—
185C2×C22⋊Q8C2312yes—
186C2×C22⋊Q8C2312yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2318yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2312yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×#121C2312yes—
197C2×#121C2312yes—
198C2×#121C2314yes—
199C2×#121C2318yes—
200C2×#120C2314yes—
201C2×#120C2314yes—
202#520—48no—
203C2×C4×Q8C2314yes—
204C2×C4×D4—44no—
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×#117—48no—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2314yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2314yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2314yes—
234C22×C22⋊C4C2314yes—
235C22×C22⋊C4C2314yes—
236C22×C42C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2314yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#399C2318yes—
246#399C2318yes—
247#399C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2314yes—
257#398C2318yes—
258#398C2314yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2314yes—
267#397C2318yes—
268#397C2318yes—
269#396C2314yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2314yes—
276#396C2314yes—
277#396C2318yes—
278#396C2314yes—
279#395C2318yes—
280#395C2318yes—
281#395C2318yes—
282#394C2314yes—
283#394C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2314yes—
289#394C2318yes—
290#394C2314yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2314yes—
295#394C2314yes—
296#393C2318yes—
297#393C2318yes—
298#393C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2318yes—
302#393C2318yes—
303#393C2318yes—
304#392C2318yes—
305#392C2314yes—
306#392C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2318yes—
310#391C2318yes—
311#391C2318yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#390C2314yes—
316#390C2314yes—
317#390C2318yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2318yes—
323#390C2314yes—
324#390C2312yes—
325#390C2312yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2318yes—
341#389C2314yes—
342#389C2318yes—
343#389C2314yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#388C2318yes—
349#388C2318yes—
350#388C2314yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2314yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2314yes—
380#386C2314yes—
381#386C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2314yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2314yes—
392#384C2314yes—
393#384C2314yes—
394#382C2314yes—
395#382C2314yes—
396#382C2318yes—
397#382C2314yes—
398#382C2314yes—
399#382C2314yes—
400#382C2314yes—
401#381C2318yes—
402#381C2318yes—
403#381C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2318yes—
421#380C2312yes—
422#380C2312yes—
423#380C2312yes—
424#380C2312yes—
425#380C2314yes—
426#380C2318yes—
427#379C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C2×#95C2312yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C25C2412yes—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—28no—
443C22×Q8—44no—
444C22×Q8—82no—
445C22×Q8—82no—
446C22×Q8C2412yes—
447C22×Q8C2414yes—
448C22×Q8C2418yes—
449C22×D4—24no—
450C22×D4—42no—
451C22×D4—42no—
452C22×D4C2414yes—
453C22×D4C2412yes—
454C22×D4C2412yes—
455C22×D4C2411yescharacteristic
456C22×D4C2414yes—
457C22×D4C2414yes—
458C22×D4C2414yes—
459C22×D4C2414yes—
460C22×D4C2414yes—
461C22×D4C2411yescharacteristic
462C23×C4—28no—
463C23×C4—28no—
464C23×C4—28no—
465C23×C4C2412yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2414yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2418yes—
479C23×C4C2411yescharacteristic
480C4⋊Q8—48no—
481C4⋊Q8—48no—
482C4⋊Q8—48no—
483#125—48no—
484#125—48no—
485#124—48no—
486#123—48no—
487#123—48no—
488#123—88no—
489#123—88no—
490C22⋊Q8—48no—
491C22⋊Q8—44no—
492C22⋊Q8—44no—
493C22⋊Q8—44no—
494C22⋊Q8—44no—
495C22⋊Q8—48no—
496C22⋊Q8—88no—
497C22⋊Q8—88no—
498C22⋊Q8—88no—
499#121—216no—
500#121—48no—
501#121—44no—
502#121—44no—
503#121—44no—
504#121—44no—
505#121—48no—
506#121—48no—
507#121—88no—
508#120—48no—
509#120—48no—
510C4×Q8—48no—
511C4×D4—48no—
512C4×D4—44no—
513C4×D4—44no—
514C4×D4—44no—
515C4×D4—44no—
516C4×D4—48no—
517C4×D4—48no—
518C4×D4—48no—
519C4×D4—48no—
520C4×D4—416no—
521#117—28no—
522#117—28no—
523#117—28no—
524#117—48no—
525#117—48no—
526#117—44no—
527#117—44no—
528#117—48no—
529C2×C4⋊C4—28no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—44no—
533C2×C4⋊C4—44no—
534C2×C4⋊C4—48no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4—44no—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2411yescharacteristic
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C22⋊C4—48no—
577C2×C22⋊C4—44no—
578C2×C22⋊C4—84no—
579C2×C22⋊C4—84no—
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⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C42—24no—
616C2×C42—48no—
617C2×C42—44no—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2418yes—
627C2×C42C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
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#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—
657C24—24no—
658C24—24no—
659C24—24no—
660C24—24no—
661C24—42no—
662C24—42no—
663C24—42no—
664C24C2512yes—
665C24C2514yes—
666C24C2512yes—
667C24C2511yescharacteristic
668#41—432no—
669C2×Q8—24no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—48no—
673C2×Q8—48no—
674C2×Q8—48no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—816no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—22no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—41no—
693C2×D4—41no—
694C2×D4—41no—
695C2×D4—416no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D42−1+414yes—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—28no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—28no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—28no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4—432no—
753C22×C4H(5,𝔽2)14yes—
754C22×C4H(5,𝔽2)14yes—
755C22×C42−1+414yes—
756C22×C4C2514yes—
757C22×C4C2512yes—
758C22×C4C2514yes—
759C22×C4C2512yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2512yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2518yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2511yescharacteristic
771C22×C4C2512yes—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—41no—
787C4⋊C4—42no—
788C4⋊C4—41no—
789C4⋊C4—48no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—48no—
798C4⋊C4—44no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—48no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—44no—
845C22⋊C4—48no—
846C42—24no—
847C42—24no—
848C42—28no—
849C42—28no—
850C42—28no—
851C42—28no—
852C42—44no—
853C42—44no—
854C42—44no—
855C42—48no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—22no—
872C23—24no—
873C23—22no—
874C23—24no—
875C23—22no—
876C23—22no—
877C23—24no—
878C23—22no—
879C23—24no—
880C23—48no—
881C23—48no—
882C23—48no—
883C23—48no—
884C23—84no—
885C23—84no—
886C23—84no—
887C23C2×H(5,𝔽2)12yes—
888C23C2×H(5,𝔽2)12yes—
889C23C2×2−1+414yes—
890C23C2×2−1+412yes—
891C23C2611yescharacteristic
892Q8—48no—
893Q8—816no—
894Q8—164no—
895D4—44no—
896D4—48no—
897D4—44no—
898D4—416no—
899D4—48no—
900D4—88no—
901D4—88no—
902D4—88no—
903D4—88no—
904D4—164no—
905C2×C4—28no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—44no—
950C2×C4—48no—
951C2×C4—48no—
952C2×C4—48no—
953C2×C4—48no—
954C2×C4—48no—
955C2×C4—416no—
956C2×C4—84no—
957C2×C4—84no—
958C2×C4—88no—
959C2×C4—88no—
960C2×C4—88no—
961C2×C4—168no—
962C2×C4#562116yes—
963C2×C4C2×H(5,𝔽2)14yes—
964C2×C4C2×H(5,𝔽2)14yes—
965C2×C4C2×2−1+412yes—
966C2×C4C2×2−1+414yes—
967C2×C4#58512yes—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—24no—
975C22—24no—
976C22—24no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—44no—
990C22—42no—
991C22—42no—
992C22—44no—
993C22—44no—
994C22—42no—
995C22—816no—
996C22C2×#56214yes—
997C22C22×H(5,𝔽2)11yescharacteristic
998C22C22×H(5,𝔽2)11yescharacteristic
999C22C22×2−1+411yescharacteristic
1000C22C22×2−1+411yescharacteristic
1001C22C2×#58511yescharacteristic
1002C22H(7,𝔽2)11yescharacteristic
1003C22H(7,𝔽2)11yescharacteristic
1004C4—22no—
1005C4—22no—
1006C4—44no—
1007C4—42no—
1008C4—48no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—42no—
1017C4—42no—
1018C4—44no—
1019C4C2×#56218yes—
1020C2—24no—
1021C2—44no—
1022C2—84no—
1023C2—82no—
1024C2C22×#56211yescharacteristic
1025C2#6281911yescharacteristic
1026C2#6287411yescharacteristic
1027C2#6292911yescharacteristic
1028C2#6293011yescharacteristic
1029C2#6294411yescharacteristic
1030C2#6294511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53101C2semidirect
2. #53094C2semidirect
3. #53054C2semidirect
4. #53019C2semidirect
5. #52412C2semidirect
6. #46088C2semidirect
7. #45990C2semidirect
8. #45717C2semidirect
9. #45641C2semidirect
10. #45609C2semidirect
11. #45498C2semidirect
12. #35574C2semidirect
13. #35518C2semidirect
14. #35516C2semidirect
15. #35263C2semidirect
16. #35253C2semidirect
17. #35159C2semidirect
18. #35158C2semidirect
19. C2×#2563C2semidirect
20. #34737C2semidirect
29. #2857C22semidirect
30. #2855C22semidirect
31. #2854C22semidirect
33. #2851C22semidirect
35. #2845C22semidirect
36. #2841C22semidirect
37. #2832C22semidirect
38. #2832C22semidirect
39. #2831C22semidirect
40. #2830C22semidirect
42. #2824C22semidirect
43. #2820C22semidirect
44. #2816C22semidirect
45. #2814C22semidirect
47. #2798C22semidirect
48. #2788C22semidirect
49. #2783C22semidirect
50. #2772C22semidirect
51. #2768C22semidirect
53. #2761C22semidirect
54. #2755C22semidirect
55. #2751C22semidirect
56. #2744C22semidirect
60. #2696C22semidirect
61. #2692C22semidirect
62. #2692C22semidirect
63. #2687C22semidirect
66. #2681C22semidirect
70. #2629C22semidirect
71. #2628C22semidirect
72. #2625C22semidirect
73. #2624C22semidirect
79. #2538C22semidirect
80. #2537C22semidirect
81. #2536C22semidirect
82. #2535C22semidirect
83. #2509C22semidirect
84. #2508C22semidirect
85. #2507C22semidirect
86. #2506C22semidirect
88. #2492C22semidirect
89. #2491C22semidirect
90. #2490C22semidirect
91. #2489C22semidirect
92. #2487C22semidirect
93. #2487C22semidirect
94. #2486C22semidirect
95. #2486C22semidirect
96. #2485C22semidirect
97. #2485C22semidirect
98. #2485C22semidirect
99. #2485C22semidirect
100. #2452C22semidirect
101. #2452C22semidirect
102. #2451C22semidirect
103. #2451C22semidirect
104. #2442C22semidirect
105. #2441C22semidirect
106. #2440C22semidirect
107. #2440C22semidirect
108. #2440C22semidirect
109. #2439C22semidirect
110. #2439C22semidirect
111. #2439C22semidirect
116. #2423C22semidirect
117. #2422C22semidirect
118. #2421C22semidirect
119. #2420C22semidirect
124. #2417C22semidirect
127. #2416C22semidirect
130. #2415C22semidirect
133. #2414C22semidirect
143. #2382C22semidirect
144. #2379C22semidirect

Maximal subgroups

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

subgroupindex
#531012
#530942
#530542
#530192
#524122
#460882
#459902
#457172
#456412
#456092
#454982
#355742
#355182
#355162
#352632
#352532
#351592
#351582
C2×#25632
#347372