Finite Group Databasebeta

← #8701557

Subgroups — #8701557

Order 512.

5465 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59814C212yesmaximal, complemented
2#59199C212yesmaximal, complemented
3#59015C214yesmaximal, complemented
4#57725C214yesmaximal, complemented
5#55046C218yesmaximal, complemented
6#52301C211yesmaximal, characteristic, complemented
7#48113C214yesmaximal, complemented
8#47938C218yesmaximal, complemented
9#46152C211yesmaximal, characteristic, complemented
10#45995C212yesmaximal, complemented
11#45378C212yesmaximal, complemented
12#45377C214yesmaximal, complemented
13#42514C214yesmaximal, complemented
14#42482C212yesmaximal, complemented
15#39144C214yesmaximal, complemented
16#38904C212yesmaximal, complemented
17#37165C214yesmaximal, complemented
18#37134C212yesmaximal, complemented
19#36453C212yesmaximal, complemented
20#36289C211yesmaximal, characteristic, complemented
21C2×#562C2214yescomplemented
22C2×#554C2211yescharacteristic, complemented
23C2×#547C2212yes—
24C2×#546C2218yescomplemented
25C2×D42C2211yescharacteristic
26C22×#121C2212yescomplemented
27#2859C2212yescomplemented
28#2858C2211yescharacteristic, complemented
29#2855C2214yescomplemented
30#2850C2212yescomplemented
31#2847C2212yescomplemented
32#2844C2212yescomplemented
33#2838C2218yescomplemented
34#2820C2214yescomplemented
35#2817C2214yescomplemented
36#2809C2212yescomplemented
37#2804C2211yescharacteristic
38#2804C2212yescomplemented
39#2795C2214yescomplemented
40#2784C2214yescomplemented
41#2782C2214yescomplemented
42#2782C2212yescomplemented
43#2780C2218yescomplemented
44#2779C2218yescomplemented
45#2778C2218yescomplemented
46#2750C2218yescomplemented
47#2750C2218yescomplemented
48#2748C2214yes—
49#2746C2218yescomplemented
50#2742C2214yescomplemented
51#2735C2218yescomplemented
52#2732C2214yescomplemented
53#2720C2218yescomplemented
54#2717C2218yescomplemented
55#2708C2218yescomplemented
56#2706C2218yescomplemented
57#2693C2218yescomplemented
58#2692C2218yescomplemented
59#2688C2218yescomplemented
60#2687C2218yescomplemented
61#2687C2218yescomplemented
62#2686C2218yescomplemented
63#2684C2212yes—
64#2684C2214yescomplemented
65#2683C2212yes—
66#2682C2214yescomplemented
67#2680C2218yescomplemented
68#2679C2211yescharacteristic
69#2672C2218yescomplemented
70#2672C2218yescomplemented
71#2671C2218yescomplemented
72#2668C2218yes—
73#2660C2212yescomplemented
74#2654C2218yescomplemented
75#2643C2218yescomplemented
76#2630C2218yescomplemented
77#2627C2214yescomplemented
78#2622C2214yescomplemented
79#2616C2214yescomplemented
80#2576C2218yescomplemented
81#2567C2212yescomplemented
82#2564C2218yescomplemented
83#2563C2211yescharacteristic
84#2562C2212yescomplemented
85#2555C2214yescomplemented
86#2548C2211yescharacteristic, complemented
87#2538C2214yescomplemented
88#2538C2212yescomplemented
89#2537C2212yes—
90#2537C2214yescomplemented
91#2535C2214yes—
92#2534C2218yescomplemented
93#2534C2218yescomplemented
94#2505C2218yescomplemented
95#2504C2212yescomplemented
96#2504C2212yescomplemented
97#2501C2214yescomplemented
98#2497C2214yescomplemented
99#2497C2214yescomplemented
100#2494C2214yescomplemented
101#2494C2214yescomplemented
102#2491C2214yescomplemented
103#2490C2214yescomplemented
104#2487C2212yes—
105#2487C2214yescomplemented
106#2472C2218yescomplemented
107#2463C2218yescomplemented
108#2461C2218yescomplemented
109#2460C2218yescomplemented
110#2459C2218yescomplemented
111#2442C2214yescomplemented
112#2440C2214yescomplemented
113#2440C2214yescomplemented
114#2437C2218yescomplemented
115#2437C2218yescomplemented
116#2437C2214yescomplemented
117#2435C2212yes—
118#2430C2218yescomplemented
119#2428C2214yescomplemented
120#2427C2214yescomplemented
121#2425C2218yescomplemented
122#2424C2218yescomplemented
123#2422C2214yescomplemented
124#2422C2214yescomplemented
125#2420C2214yescomplemented
126#2418C2218yescomplemented
127#2418C2218yescomplemented
128#2416C2214yescomplemented
129#2416C2214yescomplemented
130#2410C2214yescomplemented
131#2408C2214yes—
132#2406C2214yescomplemented
133#2405C2218yescomplemented
134#2403C2214yes—
135#2398C2214yescomplemented
136#2398C2212yescomplemented
137#2379C2212yes—
138#2361C2214yescomplemented
139#2361C2214yescomplemented
140#2358C2214yes—
141#2355C2212yescomplemented
142D4×C4⋊C4C2214yescomplemented
143D4×C4⋊C4C2212yescomplemented
144#2345C2214yescomplemented
145D4×C22⋊C4C2212yescomplemented
146D4×C22⋊C4C2214yescomplemented
147#2325C2218yescomplemented
148#2319C2214yescomplemented
149#2319C2212yescomplemented
150#2308C2214yes—
151C4×#124C2211yescharacteristic
152C4×#124C2212yescomplemented
153C4×#121C2214yescomplemented
154C4×#120C2212yes—
155C4×#120C2214yescomplemented
156C2×#390C2212yes—
157C2×#380C2214yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2314yes—
160C23×D4C2312yes—
161C23×D4C2312yes—
162C23×D4C2314yes—
163C24×C4C2312yes—
164#562—416no—
165#554—44no—
166#547—48no—
167#546—432no—
168D42—44no—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2312yes—
171C2×#127C2311yescharacteristic
172C2×#125C2312yes—
173C2×#125C2314yes—
174C2×#124C2311yescharacteristic
175C2×#124C2312yes—
176C2×#124C2314yes—
177C2×#124C2318yes—
178C2×#124C2312yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2312yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2314yes—
191C2×#121—48no—
192C2×#121C2318yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2312yes—
197C2×#121C2312yes—
198C2×#121C2318yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#121C2318yes—
202C2×#120C2312yes—
203C2×#120C2314yes—
204C2×#120C2314yes—
205C2×#120C2318yes—
206C2×#120C2314yes—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2312yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2311yescharacteristic
211C2×C4×D4C2312yes—
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2318yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2318yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2318yes—
227C22×C22⋊C4C2318yes—
228C22×C22⋊C4C2314yes—
229C22×C42C2312yes—
230#401C2318yes—
231#400C2312yes—
232#400C2314yes—
233#400C2318yes—
234#400C2318yes—
235#400C2314yes—
236#400C2318yes—
237#400C2314yes—
238#400C2312yes—
239#400C2318yes—
240#400C2314yes—
241#399C2318yes—
242#399C2318yes—
243#399C2318yes—
244#399C2314yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2314yes—
257#397C2314yes—
258#397C2314yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#395C2318yes—
267#395C2314yes—
268#395C2314yes—
269#395C2314yes—
270#395C2318yes—
271#395C2314yes—
272#394C2314yes—
273#394C2318yes—
274#394C2318yes—
275#394C2312yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2314yes—
280#394C2318yes—
281#394C2318yes—
282#394C2312yes—
283#394C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2314yes—
288#393C2314yes—
289#393C2318yes—
290#393C2314yes—
291#393C2314yes—
292#393C2314yes—
293#392C2318yes—
294#392C2318yes—
295#392C2318yes—
296#391C2314yes—
297#391C2311yescharacteristic
298#391C2312yes—
299#391C2314yes—
300#390C2312yes—
301#390C2314yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2312yes—
306#390C2312yes—
307#390C2312yes—
308#390C2311yescharacteristic
309#390C2318yes—
310#390C2312yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2318yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2314yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2314yes—
332#388C2318yes—
333#388C2314yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#386C2312yes—
341#386C2314yes—
342#386C2314yes—
343#386C2314yes—
344#386C2318yes—
345#386C2318yes—
346#386C2314yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2314yes—
359#386C2318yes—
360#386C2314yes—
361#386C2314yes—
362#385C2314yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2312yes—
372#385C2318yes—
373#385C2318yes—
374#385C2314yes—
375#385C2318yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#384C2314yes—
380#384C2312yes—
381#384C2312yes—
382#384C2314yes—
383#382C2312yes—
384#382C2312yes—
385#382C2314yes—
386#382C2311yescharacteristic
387#382C2314yes—
388#381C2314yes—
389#381C2318yes—
390#381C2318yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2318yes—
395#380C2318yes—
396#380C2314yes—
397#380C2318yes—
398#380C2318yes—
399#380C2312yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2318yes—
404#380C2318yes—
405#380C2314yes—
406#379C2318yes—
407#379C2314yes—
408#379C2318yes—
409#379C2314yes—
410#379C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424#376C2312yes—
425C2×#95C2318yes—
426C43C2311yescharacteristic
427C25C2412yes—
428C25C2414yes—
429C2×#41—416no—
430C2×#41—48no—
431C22×Q8C2412yes—
432C22×Q8C2411yescharacteristic
433C22×Q8C2412yes—
434C22×Q8C2414yes—
435C22×D4—28no—
436C22×D4—28no—
437C22×D4—48no—
438C22×D4—44no—
439C22×D4—48no—
440C22×D4—416no—
441C22×D4—82no—
442C22×D4C2412yes—
443C22×D4C2414yes—
444C22×D4C2412yes—
445C22×D4C2418yes—
446C22×D4C2411yescharacteristic
447C22×D4C2418yes—
448C22×D4C2414yes—
449C22×D4C2414yes—
450C22×D4C2418yes—
451C22×D4C2412yes—
452C22×D4C2412yes—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C23×C4—44no—
456C23×C4—48no—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2418yes—
463C23×C4C2412yes—
464C23×C4C2418yes—
465C23×C4C2414yes—
466C23×C4C2418yes—
467C23×C4C2414yes—
468C4⋊Q8—44no—
469C4⋊Q8—42no—
470#127—42no—
471#125—44no—
472#125—48no—
473#124—28no—
474#124—24no—
475#124—48no—
476#124—416no—
477#124—82no—
478#123—416no—
479#123—416no—
480#123—416no—
481#123—416no—
482#123—416no—
483C22⋊Q8—48no—
484C22⋊Q8—48no—
485C22⋊Q8—44no—
486C22⋊Q8—416no—
487C22⋊Q8—416no—
488C22⋊Q8—416no—
489C22⋊Q8—84no—
490#121—216no—
491#121—216no—
492#121—232no—
493#121—416no—
494#121—416no—
495#121—416no—
496#121—48no—
497#121—48no—
498#121—44no—
499#121—44no—
500#120—216no—
501#120—28no—
502#120—48no—
503#120—416no—
504#120—84no—
505C4×Q8—44no—
506C4×Q8—42no—
507C4×D4—24no—
508C4×D4—28no—
509C4×D4—44no—
510C4×D4—48no—
511C4×D4—48no—
512C4×D4—44no—
513C4×D4—42no—
514C4×D4—44no—
515C4×D4—416no—
516C4×D4—416no—
517C4×D4—84no—
518C4×D4—88no—
519C2×C4⋊C4—48no—
520C2×C4⋊C4—44no—
521C2×C4⋊C4—48no—
522C2×C4⋊C4—44no—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2411yescharacteristic
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2411yescharacteristic
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2411yescharacteristic
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C22⋊C4—416no—
555C2×C22⋊C4—48no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—84no—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C42—82no—
596C2×C42C2412yes—
597C2×C42C2411yescharacteristic
598C2×C42C2412yes—
599C2×C42C2414yes—
600C2×C42C2412yes—
601C2×C42C2411yescharacteristic
602C2×C42C2418yes—
603C2×C42C2414yes—
604C2×C42C2414yes—
605C2×C42C2412yes—
606C2×C42C2411yescharacteristic
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2412yes—
612#95C2414yes—
613#95C2412yes—
614#95C2412yes—
615#95C2414yes—
616#95C2418yes—
617#95C2414yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2418yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2414yes—
636C24—28no—
637C24—24no—
638C24—28no—
639C24—28no—
640C24—42no—
641C24—44no—
642C24—44no—
643C24—42no—
644C24—48no—
645C24—48no—
646C24C2514yes—
647C24C2512yes—
648C24C2514yes—
649C24C2512yes—
650#41—832no—
651C2×Q8—24no—
652C2×Q8—22no—
653C2×Q8—41no—
654C2×Q8—42no—
655C2×Q8—48no—
656C2×Q8—44no—
657C2×Q8—42no—
658C2×Q8—41no—
659C2×Q8—44no—
660C2×Q8—42no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—216no—
664C2×D4—216no—
665C2×D4—28no—
666C2×D4—216no—
667C2×D4—28no—
668C2×D4—216no—
669C2×D4—28no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—28no—
674C2×D4—41no—
675C2×D4—48no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—41no—
681C2×D4—48no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—42no—
687C2×D4—48no—
688C2×D4—42no—
689C2×D4—48no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—816no—
693C2×D4—816no—
694C2×D4—832no—
695C2×D4H(5,𝔽2)14yes—
696C2×D4H(5,𝔽2)18yes—
697C2×D42−1+414yes—
698C22×C4—24no—
699C22×C4—28no—
700C22×C4—216no—
701C22×C4—28no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—42no—
709C22×C4—44no—
710C22×C4—42no—
711C22×C4—44no—
712C22×C4—48no—
713C22×C4—48no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—48no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—816no—
728C22×C4C2512yes—
729C22×C4C2512yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2512yes—
734C22×C4C2512yes—
735C22×C4C2514yes—
736C22×C4C2518yes—
737C22×C4C2512yes—
738C22×C4C2518yes—
739C22×C4C2511yescharacteristic
740C22×C4C2514yes—
741C22×C4C2512yes—
742C22×C4C2511yescharacteristic
743C22×C4C2511yescharacteristic
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—22no—
747C4⋊C4—216no—
748C4⋊C4—28no—
749C4⋊C4—24no—
750C4⋊C4—28no—
751C4⋊C4—41no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—42no—
757C4⋊C4—42no—
758C4⋊C4—44no—
759C4⋊C4—41no—
760C4⋊C4—42no—
761C4⋊C4—48no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C4⋊C4—42no—
765C4⋊C4—44no—
766C4⋊C4—42no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C22⋊C4—216no—
776C22⋊C4—216no—
777C22⋊C4—216no—
778C22⋊C4—24no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—24no—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—216no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—42no—
794C22⋊C4—44no—
795C22⋊C4—48no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—42no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C42—24no—
813C42—22no—
814C42—24no—
815C42—22no—
816C42—24no—
817C42—28no—
818C42—41no—
819C42—44no—
820C42—42no—
821C42—48no—
822C42—44no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—22no—
828C23—24no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—22no—
835C23—24no—
836C23—22no—
837C23—28no—
838C23—24no—
839C23—24no—
840C23—28no—
841C23—24no—
842C23—48no—
843C23—416no—
844C23—416no—
845C23—84no—
846C23—88no—
847C23—88no—
848C23—88no—
849C23—816no—
850C23—84no—
851C23—168no—
852C23C2×H(5,𝔽2)14yes—
853C23C2×H(5,𝔽2)18yes—
854C23C2×2−1+414yes—
855C23C2611yescharacteristic
856Q8—82no—
857Q8—84no—
858Q8—88no—
859Q8—162no—
860D4—28no—
861D4—44no—
862D4—48no—
863D4—416no—
864D4—432no—
865D4—48no—
866D4—48no—
867D4—84no—
868D4—816no—
869D4—88no—
870D4—816no—
871D4—88no—
872D4—162no—
873C2×C4—21no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—28no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—28no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—28no—
911C2×C4—24no—
912C2×C4—48no—
913C2×C4—416no—
914C2×C4—48no—
915C2×C4—88no—
916C2×C4—816no—
917C2×C4—88no—
918C2×C4—84no—
919C2×C4—88no—
920C2×C4—88no—
921C2×C4—168no—
922C2×C4—168no—
923C2×C4C2×H(5,𝔽2)14yes—
924C2×C4C2×H(5,𝔽2)12yes—
925C2×C4C2×2−1+412yes—
926C2×C4#58514yes—
927C22—24no—
928C22—24no—
929C22—28no—
930C22—28no—
931C22—28no—
932C22—24no—
933C22—24no—
934C22—28no—
935C22—44no—
936C22—42no—
937C22—42no—
938C22—44no—
939C22—44no—
940C22—44no—
941C22—44no—
942C22—44no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—48no—
947C22—44no—
948C22—48no—
949C22—816no—
950C22—1616no—
951C22C22×H(5,𝔽2)11yescharacteristic
952C22C22×H(5,𝔽2)12yes—
953C22C22×2−1+411yescharacteristic
954C22C2×#58512yes—
955C22H(7,𝔽2)11yescharacteristic
956C4—22no—
957C4—24no—
958C4—44no—
959C4—42no—
960C4—44no—
961C4—48no—
962C4—42no—
963C4—41no—
964C4—42no—
965C4—44no—
966C4—42no—
967C4—42no—
968C4—44no—
969C4—48no—
970C4—44no—
971C4#354514yes—
972C2—48no—
973C2—44no—
974C2—44no—
975C2—84no—
976C2C2×#354511yescharacteristic
977C2#6289411yescharacteristic
978C2#6290512yes—
979C2#6301111yescharacteristic
980C2#6301312yes—
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. #59814C2semidirect
2. #59199C2semidirect
3. #59015C2semidirect
4. #57725C2semidirect
5. #55046C2semidirect
6. #52301C2semidirect
7. #48113C2semidirect
8. #47938C2semidirect
9. #46152C2semidirect
10. #45995C2semidirect
11. #45378C2semidirect
12. #45377C2semidirect
13. #42514C2semidirect
14. #42482C2semidirect
15. #39144C2semidirect
16. #38904C2semidirect
17. #37165C2semidirect
18. #37134C2semidirect
19. #36453C2semidirect
20. #36289C2semidirect
21. C2×#562C22semidirect
22. C2×#554C22semidirect
24. C2×#546C22semidirect
26. C22×#121C22semidirect
27. #2859C22semidirect
28. #2858C22semidirect
29. #2855C22semidirect
30. #2850C22semidirect
31. #2847C22semidirect
32. #2844C22semidirect
33. #2838C22semidirect
34. #2820C22semidirect
35. #2817C22semidirect
36. #2809C22semidirect
38. #2804C22semidirect
39. #2795C22semidirect
40. #2784C22semidirect
41. #2782C22semidirect
42. #2782C22semidirect
43. #2780C22semidirect
44. #2779C22semidirect
45. #2778C22semidirect
46. #2750C22semidirect
47. #2750C22semidirect
49. #2746C22semidirect
50. #2742C22semidirect
51. #2735C22semidirect
52. #2732C22semidirect
53. #2720C22semidirect
54. #2717C22semidirect
55. #2708C22semidirect
56. #2706C22semidirect
57. #2693C22semidirect
58. #2692C22semidirect
59. #2688C22semidirect
60. #2687C22semidirect
61. #2687C22semidirect
62. #2686C22semidirect
64. #2684C22semidirect
66. #2682C22semidirect
67. #2680C22semidirect
69. #2672C22semidirect
70. #2672C22semidirect
71. #2671C22semidirect
73. #2660C22semidirect
74. #2654C22semidirect
75. #2643C22semidirect
76. #2630C22semidirect
77. #2627C22semidirect
78. #2622C22semidirect
79. #2616C22semidirect
80. #2576C22semidirect
81. #2567C22semidirect
82. #2564C22semidirect
84. #2562C22semidirect
85. #2555C22semidirect
86. #2548C22semidirect
87. #2538C22semidirect
88. #2538C22semidirect
90. #2537C22semidirect
92. #2534C22semidirect
93. #2534C22semidirect
94. #2505C22semidirect
95. #2504C22semidirect
96. #2504C22semidirect
97. #2501C22semidirect
98. #2497C22semidirect
99. #2497C22semidirect
100. #2494C22semidirect
101. #2494C22semidirect
102. #2491C22semidirect
103. #2490C22semidirect
105. #2487C22semidirect
106. #2472C22semidirect
107. #2463C22semidirect
108. #2461C22semidirect
109. #2460C22semidirect
110. #2459C22semidirect
111. #2442C22semidirect
112. #2440C22semidirect
113. #2440C22semidirect
114. #2437C22semidirect
115. #2437C22semidirect
116. #2437C22semidirect
118. #2430C22semidirect
119. #2428C22semidirect
120. #2427C22semidirect
121. #2425C22semidirect
122. #2424C22semidirect
123. #2422C22semidirect
124. #2422C22semidirect
125. #2420C22semidirect
126. #2418C22semidirect
127. #2418C22semidirect
128. #2416C22semidirect
129. #2416C22semidirect
130. #2410C22semidirect
132. #2406C22semidirect
133. #2405C22semidirect
135. #2398C22semidirect
136. #2398C22semidirect
138. #2361C22semidirect
139. #2361C22semidirect
141. #2355C22semidirect
142. D4×C4⋊C4C22semidirect
143. D4×C4⋊C4C22semidirect
144. #2345C22semidirect
145. D4×C22⋊C4C22semidirect
146. D4×C22⋊C4C22semidirect
147. #2325C22semidirect
148. #2319C22semidirect
149. #2319C22semidirect
152. C4×#124C22semidirect
153. C4×#121C22semidirect
155. C4×#120C22semidirect
157. C2×#380C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598142
#591992
#590152
#577252
#550462
#523012
#481132
#479382
#461522
#459952
#453782
#453772
#425142
#424822
#391442
#389042
#371652
#371342
#364532
#362892