Finite Group Databasebeta

← #7989582

Subgroups — #7989582

Order 512.

5383 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59465C211yesmaximal, characteristic, complemented
2#59381C214yesmaximal, complemented
3#59035C212yesmaximal, complemented
4#48117C218yesmaximal, complemented
5#45693C214yesmaximal, complemented
6#45171C214yesmaximal, complemented
7#45049C214yesmaximal, complemented
8#42591C214yesmaximal, complemented
9#42543C214yesmaximal, complemented
10#39350C212yesmaximal, complemented
11#39258C214yesmaximal, complemented
12#38930C212yesmaximal, complemented
13#38924C214yesmaximal, complemented
14#36454C212yesmaximal, complemented
15#36155C214yesmaximal, complemented
16#36149C211yesmaximal, characteristic, complemented
17#35225C214yesmaximal, complemented
18#34917C212yesmaximal, complemented
19#34393C212yesmaximal, complemented
20C4×D42C211yesmaximal, characteristic, complemented
21C2×#546C2214yes—
22C2×D42C2211yescharacteristic
23C2×#542C2214yes—
24C2×#532C2212yes—
25C22×C4×D4C2214yes—
26#2862C2211yescharacteristic, complemented
27#2857C2212yescomplemented
28#2855C2214yescomplemented
29#2849C2218yescomplemented
30#2848C2214yescomplemented
31#2835C2214yescomplemented
32#2826C2214yescomplemented
33#2784C2214yescomplemented
34#2782C2218yescomplemented
35#2781C2218yescomplemented
36#2761C2218yescomplemented
37#2750C2218yescomplemented
38#2747C2218yescomplemented
39#2745C2218yescomplemented
40#2743C2218yescomplemented
41#2743C2218yescomplemented
42#2738C2218yescomplemented
43#2735C2214yescomplemented
44#2717C2218yescomplemented
45#2703C2218yescomplemented
46#2698C2218yescomplemented
47#2691C2218yescomplemented
48#2687C2218yescomplemented
49#2670C2214yescomplemented
50#2668C2218yes—
51#2647C2214yescomplemented
52#2646C2218yescomplemented
53#2638C2218yescomplemented
54#2630C2218yescomplemented
55#2625C2214yescomplemented
56#2595C2218yescomplemented
57#2578C2214yescomplemented
58#2576C2214yescomplemented
59#2576C2218yescomplemented
60#2575C2218yescomplemented
61#2571C2211yescharacteristic, complemented
62#2570C2212yescomplemented
63#2569C2214yescomplemented
64#2566C2212yes—
65#2564C2214yescomplemented
66#2563C2214yescomplemented
67#2562C2212yescomplemented
68#2557C2218yescomplemented
69#2551C2211yescharacteristic, complemented
70#2547C2212yes—
71#2547C2214yescomplemented
72#2542C2212yes—
73#2537C2214yes—
74#2536C2214yescomplemented
75#2535C2212yes—
76#2535C2212yescomplemented
77#2517C2218yescomplemented
78#2515C2214yescomplemented
79#2511C2214yescomplemented
80#2503C2214yescomplemented
81#2497C2214yescomplemented
82#2497C2212yescomplemented
83#2496C2214yescomplemented
84#2494C2212yescomplemented
85#2489C2214yescomplemented
86#2486C2214yescomplemented
87#2483C2218yescomplemented
88#2480C2218yescomplemented
89#2480C2218yescomplemented
90#2472C2218yescomplemented
91#2468C2218yescomplemented
92#2461C2218yescomplemented
93#2457C2214yescomplemented
94#2454C2214yescomplemented
95#2452C2214yescomplemented
96#2451C2214yescomplemented
97#2447C2214yes—
98#2447C2214yes—
99#2447C2214yescomplemented
100#2444C2218yescomplemented
101#2444C2218yescomplemented
102#2440C2214yescomplemented
103#2435C2214yes—
104#2427C2214yes—
105#2427C2214yescomplemented
106#2422C2214yes—
107#2422C2212yes—
108#2421C2214yescomplemented
109#2421C2214yescomplemented
110#2420C2214yes—
111#2420C2212yes—
112#2420C2214yescomplemented
113#2419C2218yescomplemented
114#2419C2218yescomplemented
115#2418C2218yes—
116#2417C2214yescomplemented
117#2412C2218yescomplemented
118#2408C2214yes—
119#2407C2214yes—
120#2407C2214yescomplemented
121#2401C2214yescomplemented
122#2392C2214yescomplemented
123#2377C2218yescomplemented
124#2368C2214yescomplemented
125#2367C2214yes—
126#2366C2212yes—
127#2366C2211yescharacteristic
128#2365C2212yescomplemented
129#2365C2212yescomplemented
130#2361C2214yes—
131#2358C2214yes—
132#2357C2214yescomplemented
133#2355C2214yescomplemented
134#2349C2212yescomplemented
135#2349C2214yescomplemented
136#2349C2214yescomplemented
137D4×C4⋊C4C2212yes—
138#2341C2214yescomplemented
139#2339C2214yescomplemented
140#2339C2214yescomplemented
141D4×C22⋊C4C2214yes—
142D4×C22⋊C4C2214yes—
143#2326C2214yescomplemented
144#2326C2214yescomplemented
145#2324C2214yescomplemented
146#2324C2214yescomplemented
147#2319C2214yes—
148#2318C2218yescomplemented
149C4×#127C2211yescharacteristic
150C4×#125C2212yescomplemented
151C4×C22⋊Q8C2214yescomplemented
152C4×#123C2214yescomplemented
153C4×#121C2212yes—
154C4×#121C2214yes—
155C4×#121C2212yes—
156C4×#120C2214yes—
157#2290C2214yescomplemented
158#2285C2212yescomplemented
159#2283C2212yescomplemented
160C2×#381C2214yescomplemented
161C42×D4C2212yes—
162C42×D4C2211yescharacteristic, complemented
163C22×#41C2314yes—
164C23×D4C2314yes—
165C24×C4C2314yes—
166#546—416no—
167D42—28no—
168#542—416no—
169#532—216no—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2314yes—
172C2×#127C2311yescharacteristic
173C2×#126C2318yes—
174C2×#125C2312yes—
175C2×#124C2314yes—
176C2×#124C2314yes—
177C2×#124C2318yes—
178C2×#123C2314yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2314yes—
189C2×#121C2312yes—
190C2×#121C2312yes—
191C2×#121C2318yes—
192C2×#120C2314yes—
193C2×#120C2318yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×D4—416no—
197C2×C4×D4C2314yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2312yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2311yescharacteristic
214C2×#117C2314yes—
215C22×C4⋊C4C2314yes—
216C22×C22⋊C4C2318yes—
217C22×C22⋊C4C2318yes—
218C22×C42C2312yes—
219C22×C42C2314yes—
220#401C2314yes—
221#400C2314yes—
222#400C2314yes—
223#400C2318yes—
224#400C2314yes—
225#400C2318yes—
226#400C2318yes—
227#400C2314yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#399C2314yes—
232#399C2318yes—
233#398C2318yes—
234#398C2314yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2314yes—
241#397C2318yes—
242#397C2314yes—
243#397C2314yes—
244#397C2318yes—
245#397C2314yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2314yes—
251#397C2318yes—
252#397C2318yes—
253#396C2314yes—
254#396C2314yes—
255#396C2318yes—
256#396C2318yes—
257#396C2314yes—
258#395C2314yes—
259#395C2318yes—
260#394C2314yes—
261#394C2318yes—
262#394C2314yes—
263#394C2318yes—
264#394C2314yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#393C2314yes—
270#393C2318yes—
271#392C2314yes—
272#392C2318yes—
273#392C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2314yes—
280#391C2318yes—
281#390C2314yes—
282#390C2312yes—
283#390C2314yes—
284#390C2312yes—
285#390C2312yes—
286#390C2314yes—
287#390C2314yes—
288#390C2318yes—
289#390C2318yes—
290#390C2314yes—
291#389C2312yes—
292#389C2312yes—
293#389C2312yes—
294#389C2312yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#388C2314yes—
303#388C2314yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2314yes—
312#388C2314yes—
313#388C2318yes—
314#388C2314yes—
315#388C2314yes—
316#388C2318yes—
317#388C2318yes—
318#387C2314yes—
319#387C2314yes—
320#387C2314yes—
321#387C2318yes—
322#387C2314yes—
323#387C2314yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2314yes—
331#387C2318yes—
332#386C2318yes—
333#386C2318yes—
334#386C2314yes—
335#386C2318yes—
336#386C2318yes—
337#386C2314yes—
338#386C2314yes—
339#386C2314yes—
340#386C2314yes—
341#386C2318yes—
342#386C2314yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#385C2318yes—
349#385C2314yes—
350#385C2314yes—
351#385C2318yes—
352#385C2314yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2314yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#384C2311yescharacteristic
365#384C2312yes—
366#384C2312yes—
367#384C2314yes—
368#383C2314yes—
369#382C2312yes—
370#382C2314yes—
371#382C2312yes—
372#382C2312yes—
373#382C2314yes—
374#382C2312yes—
375#382C2318yes—
376#382C2312yes—
377#381C2318yes—
378#381C2318yes—
379#381C2318yes—
380#381C2318yes—
381#381C2314yes—
382#381C2318yes—
383#381C2314yes—
384#381C2318yes—
385#380C2312yes—
386#380C2312yes—
387#380C2312yes—
388#380C2312yes—
389#380C2318yes—
390#380C2318yes—
391#380C2314yes—
392#380C2318yes—
393#380C2318yes—
394#380C2318yes—
395#380C2314yes—
396#380C2312yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2312yes—
401#380C2314yes—
402#380C2314yes—
403#379C2318yes—
404#379C2318yes—
405#379C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2312yes—
431#376C2314yes—
432C2×#95C2314yes—
433C2×#95C2318yes—
434C2×#95C2314yes—
435C43C2311yescharacteristic
436C25C2414yes—
437C2×#41—216no—
438C2×#41—48no—
439C2×#41—48no—
440C22×Q8C2414yes—
441C22×Q8C2414yes—
442C22×D4—216no—
443C22×D4—216no—
444C22×D4—48no—
445C22×D4C2418yes—
446C22×D4C2414yes—
447C22×D4C2412yes—
448C22×D4C2414yes—
449C22×D4C2414yes—
450C22×D4C2418yes—
451C22×D4C2411yescharacteristic
452C22×D4C2412yes—
453C23×C4—48no—
454C23×C4—416no—
455C23×C4C2414yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2414yes—
459C23×C4C2418yes—
460C23×C4C2418yes—
461C23×C4C2414yes—
462C23×C4C2412yes—
463C23×C4C2414yes—
464C23×C4C2418yes—
465C23×C4C2414yes—
466C4⋊Q8—28no—
467C4⋊Q8—48no—
468#127#4118yes—
469#126—416no—
470#125—44no—
471#124—216no—
472#124—216no—
473#124—416no—
474#123—416no—
475#123—48no—
476#123—416no—
477C22⋊Q8—416no—
478C22⋊Q8—48no—
479C22⋊Q8—48no—
480C22⋊Q8—48no—
481C22⋊Q8—48no—
482#121—216no—
483#121—216no—
484#121—216no—
485#121—28no—
486#121—28no—
487#121—416no—
488#120—216no—
489#120—416no—
490C4×Q8—48no—
491C4×Q8—48no—
492C4×D4—216no—
493C4×D4—216no—
494C4×D4—28no—
495C4×D4—216no—
496C4×D4—28no—
497C4×D4—42no—
498C4×D4—48no—
499C4×D4—48no—
500C4×D4—48no—
501C4×D4—44no—
502C4×D4—48no—
503C4×D4—44no—
504C4×D4—48no—
505C4×D4—44no—
506C4×D4—48no—
507C4×D4—416no—
508C4×D4—416no—
509#117—48no—
510C2×C4⋊C4—48no—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2411yescharacteristic
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C22⋊C4—416no—
543C2×C22⋊C4—416no—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C42—28no—
579C2×C42—48no—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2411yescharacteristic
583C2×C42C2412yes—
584C2×C42C2414yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2418yes—
592C2×C42C2418yes—
593C2×C42C2411yescharacteristic
594C2×C42C2411yescharacteristic
595#95C2411yescharacteristic
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2418yes—
602#95C2418yes—
603#95C2414yes—
604#95C2418yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2411yescharacteristic
611#95C2414yes—
612#95C2414yes—
613#95C2412yes—
614#95C2414yes—
615#95C2414yes—
616#95C2412yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2418yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2414yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2414yes—
635C24—28no—
636C24—216no—
637C24—44no—
638C24—48no—
639C24—44no—
640C24C2512yes—
641C24C2514yes—
642C24C2514yes—
643#41—832no—
644C2×Q8—28no—
645C2×Q8—28no—
646C2×Q8—28no—
647C2×Q8—48no—
648C2×Q8—44no—
649C2×D4—216no—
650C2×D4—216no—
651C2×D4—216no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—24no—
655C2×D4—28no—
656C2×D4—24no—
657C2×D4—28no—
658C2×D4—42no—
659C2×D4—41no—
660C2×D4—42no—
661C2×D4—48no—
662C2×D4—42no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—48no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—48no—
669C2×D4—464no—
670C2×D4C2×#41116yes—
671C2×D4C2×#4118yes—
672C2×D4H(5,𝔽2)18yes—
673C22×C4—28no—
674C22×C4—216no—
675C22×C4—216no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—28no—
684C22×C4—24no—
685C22×C4—28no—
686C22×C4—24no—
687C22×C4—28no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—48no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—42no—
695C22×C4—44no—
696C22×C4—48no—
697C22×C4—44no—
698C22×C4—42no—
699C22×C4—44no—
700C22×C4—48no—
701C22×C4—48no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—832no—
705C22×C4C2512yes—
706C22×C4C2512yes—
707C22×C4C2514yes—
708C22×C4C2512yes—
709C22×C4C2511yescharacteristic
710C22×C4C2518yes—
711C22×C4C2514yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2512yes—
719C22×C4C2511yescharacteristic
720C22×C4C2511yescharacteristic
721C22×C4C2512yes—
722C4⋊C4—24no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—24no—
726C4⋊C4—28no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—28no—
732C4⋊C4—24no—
733C4⋊C4—48no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—42no—
739C4⋊C4—41no—
740C4⋊C4—42no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—44no—
748C4⋊C4—48no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C22⋊C4—216no—
754C22⋊C4—216no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—216no—
759C22⋊C4—216no—
760C22⋊C4—216no—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—24no—
764C22⋊C4—44no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—48no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—48no—
781C22⋊C4—44no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C42—24no—
788C42—24no—
789C42—24no—
790C42—24no—
791C42—28no—
792C42—28no—
793C42—22no—
794C42—28no—
795C42—24no—
796C42—44no—
797C42—44no—
798C42—41no—
799C42—48no—
800C42—48no—
801C42C2×#4114yes—
802C23—24no—
803C23—24no—
804C23—28no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—28no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—416no—
820C23—432no—
821C23—88no—
822C23—816no—
823C23—88no—
824C23C22×#4118yes—
825C23C2×H(5,𝔽2)18yes—
826C23C2611yescharacteristic
827Q8—416no—
828Q8—164no—
829D4—216no—
830D4—232no—
831D4—48no—
832D4—432no—
833D4—44no—
834D4—88no—
835D4—88no—
836D4—816no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—28no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—21no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—416no—
881C2×C4—48no—
882C2×C4—416no—
883C2×C4—48no—
884C2×C4—84no—
885C2×C4—88no—
886C2×C4—816no—
887C2×C4—816no—
888C2×C4—88no—
889C2×C4—88no—
890C2×C4—168no—
891C2×C4C22×#4112yes—
892C2×C4C22×#4114yes—
893C2×C4C2×H(5,𝔽2)14yes—
894C2×C4#58512yes—
895C2×C4#58514yes—
896C22—28no—
897C22—28no—
898C22—216no—
899C22—28no—
900C22—28no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—48no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—832no—
916C22C23×#4111yescharacteristic
917C22C22×H(5,𝔽2)12yes—
918C22C2×#58511yescharacteristic
919C22C2×#58512yes—
920C222−1+611yescharacteristic
921C4—22no—
922C4—22no—
923C4—42no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4—44no—
928C4—41no—
929C4—42no—
930C4—42no—
931C4—44no—
932C4—48no—
933C4—44no—
934C4—42no—
935C4—44no—
936C4—44no—
937C4#351318yes—
938C2—48no—
939C2—48no—
940C2—82no—
941C2#6276211yescharacteristic
942C2C2×#351312yes—
943C2#6292112yes—
944C2#6299111yescharacteristic
945C2#6301211yescharacteristic
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. #59465C2semidirect
2. #59381C2semidirect
3. #59035C2semidirect
4. #48117C2semidirect
5. #45693C2semidirect
6. #45171C2semidirect
7. #45049C2semidirect
8. #42591C2semidirect
9. #42543C2semidirect
10. #39350C2semidirect
11. #39258C2semidirect
12. #38930C2semidirect
13. #38924C2semidirect
14. #36454C2semidirect
15. #36155C2semidirect
16. #36149C2semidirect
17. #35225C2semidirect
18. #34917C2semidirect
19. #34393C2semidirect
20. C4×D42C2semidirect
26. #2862C22semidirect
27. #2857C22semidirect
28. #2855C22semidirect
29. #2849C22semidirect
30. #2848C22semidirect
31. #2835C22semidirect
32. #2826C22semidirect
33. #2784C22semidirect
34. #2782C22semidirect
35. #2781C22semidirect
36. #2761C22semidirect
37. #2750C22semidirect
38. #2747C22semidirect
39. #2745C22semidirect
40. #2743C22semidirect
41. #2743C22semidirect
42. #2738C22semidirect
43. #2735C22semidirect
44. #2717C22semidirect
45. #2703C22semidirect
46. #2698C22semidirect
47. #2691C22semidirect
48. #2687C22semidirect
49. #2670C22semidirect
51. #2647C22semidirect
52. #2646C22semidirect
53. #2638C22semidirect
54. #2630C22semidirect
55. #2625C22semidirect
56. #2595C22semidirect
57. #2578C22semidirect
58. #2576C22semidirect
59. #2576C22semidirect
60. #2575C22semidirect
61. #2571C22semidirect
62. #2570C22semidirect
63. #2569C22semidirect
65. #2564C22semidirect
66. #2563C22semidirect
67. #2562C22semidirect
68. #2557C22semidirect
69. #2551C22semidirect
71. #2547C22semidirect
74. #2536C22semidirect
76. #2535C22semidirect
77. #2517C22semidirect
78. #2515C22semidirect
79. #2511C22semidirect
80. #2503C22semidirect
81. #2497C22semidirect
82. #2497C22semidirect
83. #2496C22semidirect
84. #2494C22semidirect
85. #2489C22semidirect
86. #2486C22semidirect
87. #2483C22semidirect
88. #2480C22semidirect
89. #2480C22semidirect
90. #2472C22semidirect
91. #2468C22semidirect
92. #2461C22semidirect
93. #2457C22semidirect
94. #2454C22semidirect
95. #2452C22semidirect
96. #2451C22semidirect
99. #2447C22semidirect
100. #2444C22semidirect
101. #2444C22semidirect
102. #2440C22semidirect
105. #2427C22semidirect
108. #2421C22semidirect
109. #2421C22semidirect
112. #2420C22semidirect
113. #2419C22semidirect
114. #2419C22semidirect
116. #2417C22semidirect
117. #2412C22semidirect
120. #2407C22semidirect
121. #2401C22semidirect
122. #2392C22semidirect
123. #2377C22semidirect
124. #2368C22semidirect
128. #2365C22semidirect
129. #2365C22semidirect
132. #2357C22semidirect
133. #2355C22semidirect
134. #2349C22semidirect
135. #2349C22semidirect
136. #2349C22semidirect
138. #2341C22semidirect
139. #2339C22semidirect
140. #2339C22semidirect
143. #2326C22semidirect
144. #2326C22semidirect
145. #2324C22semidirect
146. #2324C22semidirect
148. #2318C22semidirect
150. C4×#125C22semidirect
151. C4×C22⋊Q8C22semidirect
152. C4×#123C22semidirect
157. #2290C22semidirect
158. #2285C22semidirect
159. #2283C22semidirect
160. C2×#381C22semidirect
162. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#594652
#593812
#590352
#481172
#456932
#451712
#450492
#425912
#425432
#393502
#392582
#389302
#389242
#364542
#361552
#361492
#352252
#349172
#343932
C4×D422