Finite Group Databasebeta

← #7697424

Subgroups — #7697424

Order 512.

5861 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59836C212yesmaximal, complemented
2#59816C211yesmaximal, characteristic
3#59802C214yesmaximal, complemented
4#59375C212yesmaximal, complemented
5#52301C212yesmaximal, complemented
6#52273C211yesmaximal, characteristic, complemented
7#45140C214yesmaximal, complemented
8#45088C212yesmaximal, complemented
9#43790C214yesmaximal, complemented
10#43365C218yesmaximal, complemented
11#39628C212yesmaximal, complemented
12#39258C214yesmaximal, complemented
13#38768C214yesmaximal, complemented
14#38508C218yesmaximal, complemented
15#36534C211yesmaximal, characteristic, complemented
16#36528C212yesmaximal, complemented
17#36075C212yesmaximal, complemented
18#35947C214yesmaximal, complemented
19#34331C212yesmaximal, complemented
20#34290C214yesmaximal, complemented
21C2×#559C2212yes—
22C2×#556C2211yescharacteristic, complemented
23C2×#554C2211yescharacteristic, complemented
24C2×#551C2214yescomplemented
25C2×D42C2214yes—
26C2×D42C2212yes—
27C2×#518C2212yescomplemented
28C22×C4×D4C2212yescomplemented
29#2862C2211yescharacteristic, complemented
30#2861C2212yescomplemented
31#2855C2212yescomplemented
32#2848C2214yescomplemented
33#2808C2212yescomplemented
34#2804C2211yescharacteristic, complemented
35#2804C2214yescomplemented
36#2804C2214yescomplemented
37#2796C2214yescomplemented
38#2794C2212yescomplemented
39#2782C2214yescomplemented
40#2782C2218yescomplemented
41#2781C2218yescomplemented
42#2751C2214yescomplemented
43#2747C2218yescomplemented
44#2736C2214yescomplemented
45#2732C2214yescomplemented
46#2732C2214yescomplemented
47#2724C2211yescharacteristic, complemented
48#2709C2212yes—
49#2708C2218yescomplemented
50#2708C2218yescomplemented
51#2696C2218yescomplemented
52#2693C2214yescomplemented
53#2691C2218yescomplemented
54#2684C2218yescomplemented
55#2684C2214yescomplemented
56#2684C2218yescomplemented
57#2679C2212yes—
58#2679C2212yes—
59#2649C2218yescomplemented
60#2647C2214yescomplemented
61#2636C2214yescomplemented
62#2625C2212yescomplemented
63#2609C2214yescomplemented
64#2603C2214yescomplemented
65#2600C2214yescomplemented
66#2595C2218yescomplemented
67#2580C2214yescomplemented
68#2569C2218yescomplemented
69#2565C2212yescomplemented
70#2563C2211yescharacteristic, complemented
71#2561C2214yescomplemented
72#2560C2218yescomplemented
73#2559C2218yescomplemented
74#2553C2218yescomplemented
75#2547C2211yescharacteristic, complemented
76#2544C2212yes—
77#2537C2212yes—
78#2537C2214yes—
79#2536C2214yescomplemented
80#2536C2214yescomplemented
81#2534C2214yescomplemented
82#2530C2218yescomplemented
83#2505C2218yescomplemented
84#2497C2214yescomplemented
85#2496C2214yescomplemented
86#2480C2218yescomplemented
87#2480C2218yescomplemented
88#2477C2218yescomplemented
89#2472C2218yescomplemented
90#2468C2218yescomplemented
91#2463C2218yescomplemented
92#2460C2218yescomplemented
93#2458C2218yescomplemented
94#2452C2214yescomplemented
95#2452C2214yescomplemented
96#2450C2218yescomplemented
97#2450C2218yescomplemented
98#2444C2218yescomplemented
99#2437C2214yescomplemented
100#2435C2212yescomplemented
101#2435C2212yescomplemented
102#2427C2214yescomplemented
103#2427C2214yescomplemented
104#2425C2218yescomplemented
105#2422C2214yescomplemented
106#2422C2214yescomplemented
107#2418C2218yescomplemented
108#2418C2218yescomplemented
109#2411C2218yescomplemented
110#2408C2212yes—
111#2408C2218yes—
112#2408C2212yes—
113#2405C2218yescomplemented
114#2405C2218yescomplemented
115#2398C2214yescomplemented
116#2398C2214yescomplemented
117#2398C2218yescomplemented
118#2395C2212yescomplemented
119#2367C2214yescomplemented
120#2367C2214yescomplemented
121#2366C2212yes—
122#2364C2218yescomplemented
123#2363C2214yescomplemented
124#2361C2214yescomplemented
125#2359C2218yescomplemented
126#2358C2218yescomplemented
127#2358C2218yescomplemented
128#2355C2212yescomplemented
129#2354C2214yescomplemented
130#2352C2214yescomplemented
131Q8×C4⋊C4C2212yescomplemented
132#2349C2214yescomplemented
133#2349C2214yescomplemented
134#2346C2212yescomplemented
135#2345C2212yescomplemented
136D4×C22⋊C4C2214yescomplemented
137D4×C22⋊C4C2214yescomplemented
138D4×C22⋊C4C2218yescomplemented
139#2335C2218yescomplemented
140#2328C2214yes—
141#2326C2214yescomplemented
142#2325C2218yescomplemented
143#2324C2214yescomplemented
144#2321C2218yescomplemented
145C4×#127C2212yes—
146C4×#127C2211yescharacteristic
147C4×#124C2214yescomplemented
148C4×#124C2212yescomplemented
149C4×#123C2212yescomplemented
150C4×#121C2214yescomplemented
151C4×#120C2218yescomplemented
152C4×#120C2214yescomplemented
153#2295C2212yescomplemented
154#2293C2214yescomplemented
155#2290C2214yescomplemented
156C2×#386C2218yescomplemented
157#2275C2214yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C23×D4C2312yes—
160C23×D4C2312yes—
161C23×D4C2318yes—
162C24×C4C2314yes—
163#559—216no—
164#556—44no—
165#554—44no—
166#551—416no—
167D42—232no—
168D42—48no—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2311yescharacteristic
171C2×#127C2311yescharacteristic
172C2×#127C2312yes—
173C2×#126C2314yes—
174C2×#126C2318yes—
175C2×#125C2312yes—
176C2×#124C2314yes—
177C2×#124C2314yes—
178C2×#124C2312yes—
179C2×#124C2312yes—
180C2×#123C2318yes—
181C2×#123C2312yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2312yes—
186C2×C22⋊Q8C2312yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×#121C2314yes—
190C2×#121C2318yes—
191C2×#121C2314yes—
192C2×#121C2318yes—
193C2×#120C2318yes—
194C2×#120C2318yes—
195C2×#120C2314yes—
196C2×#120C2314yes—
197#518—48no—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2311yescharacteristic
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2314yes—
203C2×C4×D4—48no—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2314yes—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2318yes—
221C2×C4×D4C2314yes—
222C2×#117C2312yes—
223C2×#117C2312yes—
224C2×#117C2318yes—
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2318yes—
228C22×C22⋊C4C2318yes—
229C22×C22⋊C4C2318yes—
230C22×C42C2312yes—
231#400C2314yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2312yes—
236#400C2318yes—
237#400C2314yes—
238#400C2314yes—
239#399C2318yes—
240#399C2312yes—
241#398C2318yes—
242#398C2318yes—
243#398C2314yes—
244#398C2312yes—
245#398C2318yes—
246#397C2314yes—
247#397C2318yes—
248#397C2318yes—
249#397C2312yes—
250#397C2314yes—
251#397C2318yes—
252#397C2314yes—
253#397C2314yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2314yes—
264#394C2314yes—
265#394C2318yes—
266#394C2314yes—
267#394C2318yes—
268#394C2314yes—
269#394C2314yes—
270#394C2314yes—
271#394C2318yes—
272#394C2318yes—
273#394C2314yes—
274#394C2318yes—
275#393C2314yes—
276#393C2318yes—
277#393C2318yes—
278#393C2314yes—
279#393C2314yes—
280#393C2318yes—
281#392C2314yes—
282#392C2314yes—
283#391C2314yes—
284#391C2312yes—
285#391C2312yes—
286#391C2314yes—
287#391C2312yes—
288#391C2312yes—
289#391C2312yes—
290#390C2314yes—
291#390C2314yes—
292#390C2311yescharacteristic
293#390C2314yes—
294#390C2311yescharacteristic
295#390C2314yes—
296#390C2312yes—
297#390C2314yes—
298#390C2318yes—
299#390C2314yes—
300#390C2318yes—
301#390C2314yes—
302#390C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2318yes—
307#389C2312yes—
308#389C2314yes—
309#389C2314yes—
310#389C2312yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2314yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2318yes—
328#388C2314yes—
329#387C2318yes—
330#387C2314yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2314yes—
338#387C2314yes—
339#387C2314yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2312yes—
357#386C2318yes—
358#386C2314yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2312yes—
368#385C2314yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2314yes—
373#385C2318yes—
374#385C2318yes—
375#385C2314yes—
376#384C2311yescharacteristic
377#384C2312yes—
378#384C2314yes—
379#382C2312yes—
380#382C2314yes—
381#382C2314yes—
382#382C2314yes—
383#381C2312yes—
384#381C2314yes—
385#380C2314yes—
386#380C2318yes—
387#380C2318yes—
388#380C2318yes—
389#380C2318yes—
390#380C2318yes—
391#380C2314yes—
392#380C2314yes—
393#380C2312yes—
394#380C2312yes—
395#379C2314yes—
396#379C2314yes—
397#379C2318yes—
398#379C2314yes—
399#379C2318yes—
400#379C2318yes—
401#379C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2314yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423#376C2314yes—
424#376C2314yes—
425C2×#95C2318yes—
426C2×#95C2318yes—
427C43C2311yescharacteristic
428C43C2312yes—
429C25C2414yes—
430C25C2414yes—
431C22×Q8C2411yescharacteristic
432C22×Q8C2412yes—
433C22×Q8C2412yes—
434C22×Q8C2412yes—
435C22×D4—216no—
436C22×D4—216no—
437C22×D4—232no—
438C22×D4—44no—
439C22×D4—44no—
440C22×D4—416no—
441C22×D4—88no—
442C22×D4C2418yes—
443C22×D4C2414yes—
444C22×D4C2414yes—
445C22×D4C2414yes—
446C22×D4C2414yes—
447C22×D4C2411yescharacteristic
448C22×D4C2418yes—
449C22×D4C2414yes—
450C22×D4C2414yes—
451C22×D4C2411yescharacteristic
452C23×C4—48no—
453C23×C4—88no—
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2418yes—
457C23×C4C2412yes—
458C23×C4C2414yes—
459C23×C4C2418yes—
460C23×C4C2418yes—
461C23×C4C2418yes—
462C23×C4C2418yes—
463C23×C4C2412yes—
464C4⋊Q8—42no—
465C4⋊Q8—42no—
466#127—24no—
467#127#41116yes—
468#126—48no—
469#126—416no—
470#125—44no—
471#124—216no—
472#124—216no—
473#124—28no—
474#124—44no—
475#123—232no—
476#123—28no—
477#123—416no—
478#123—88no—
479C22⋊Q8—416no—
480C22⋊Q8—48no—
481C22⋊Q8—44no—
482C22⋊Q8—44no—
483C22⋊Q8—88no—
484#121—216no—
485#121—216no—
486#121—232no—
487#121—416no—
488#120—232no—
489#120—232no—
490#120—216no—
491#120—48no—
492C4×Q8—24no—
493C4×Q8—28no—
494C4×Q8—28no—
495C4×Q8—44no—
496C4×Q8—84no—
497C4×D4—216no—
498C4×D4—216no—
499C4×D4—216no—
500C4×D4—216no—
501C4×D4—216no—
502C4×D4—48no—
503C4×D4—48no—
504C4×D4—48no—
505C4×D4—48no—
506C4×D4—48no—
507C4×D4—42no—
508C4×D4—44no—
509C4×D4—42no—
510C4×D4—416no—
511C4×D4—416no—
512C4×D4—84no—
513C4×D4—84no—
514C4×D4—88no—
515#117—28no—
516#117—44no—
517#117—416no—
518C2×C4⋊C4—28no—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2411yescharacteristic
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2411yescharacteristic
550C2×C22⋊C4—48no—
551C2×C22⋊C4—416no—
552C2×C22⋊C4—416no—
553C2×C22⋊C4—88no—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C42—44no—
591C2×C42C2412yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596C2×C42C2412yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2418yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2418yes—
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2412yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2412yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2412yes—
633#95C2418yes—
634#95C2414yes—
635#95C2414yes—
636C24—216no—
637C24—28no—
638C24—216no—
639C24—44no—
640C24—48no—
641C24—44no—
642C24—44no—
643C24—48no—
644C24—44no—
645C24—44no—
646C24C2512yes—
647C24C2518yes—
648C24C2512yes—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—22no—
652C2×Q8—24no—
653C2×Q8—42no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8—42no—
657C2×Q8—42no—
658C2×Q8—44no—
659C2×D4—216no—
660C2×D4—216no—
661C2×D4—216no—
662C2×D4—216no—
663C2×D4—28no—
664C2×D4—216no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—22no—
669C2×D4—41no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—48no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—41no—
679C2×D4—41no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—41no—
683C2×D4—432no—
684C2×D4—432no—
685C2×D4—864no—
686C2×D4C2×#41116yes—
687C2×D4C2×#41116yes—
688C2×D4C2×#41116yes—
689C2×D4H(5,𝔽2)14yes—
690C22×C4—216no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—216no—
697C22×C4—28no—
698C22×C4—216no—
699C22×C4—42no—
700C22×C4—44no—
701C22×C4—42no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—48no—
712C22×C4—42no—
713C22×C4—48no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—832no—
717C22×C4C2514yes—
718C22×C4C2512yes—
719C22×C4C2512yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2518yes—
723C22×C4C2514yes—
724C22×C4C2514yes—
725C22×C4C2514yes—
726C22×C4C2512yes—
727C22×C4C2514yes—
728C22×C4C2511yescharacteristic
729C22×C4C2512yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2511yescharacteristic
733C22×C4C2511yescharacteristic
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—28no—
744C4⋊C4—24no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—42no—
748C4⋊C4—48no—
749C4⋊C4—41no—
750C4⋊C4—44no—
751C4⋊C4—48no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C4⋊C4—42no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—44no—
762C4⋊C4—48no—
763C4⋊C4—42no—
764C4⋊C4H(5,𝔽2)14yes—
765C22⋊C4—216no—
766C22⋊C4—216no—
767C22⋊C4—216no—
768C22⋊C4—216no—
769C22⋊C4—216no—
770C22⋊C4—28no—
771C22⋊C4—216no—
772C22⋊C4—28no—
773C22⋊C4—24no—
774C22⋊C4—28no—
775C22⋊C4—216no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—216no—
779C22⋊C4—216no—
780C22⋊C4—44no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—42no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—42no—
793C22⋊C4—44no—
794C22⋊C4—42no—
795C22⋊C4—44no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C42—28no—
802C42—28no—
803C42—28no—
804C42—28no—
805C42—24no—
806C42—22no—
807C42—22no—
808C42—24no—
809C42—44no—
810C42—41no—
811C42—48no—
812C42—42no—
813C42—44no—
814C42—48no—
815C42C2×#4118yes—
816C23—24no—
817C23—28no—
818C23—28no—
819C23—28no—
820C23—22no—
821C23—28no—
822C23—28no—
823C23—24no—
824C23—28no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—22no—
831C23—416no—
832C23—432no—
833C23—416no—
834C23—816no—
835C23—88no—
836C23—816no—
837C23—816no—
838C23—88no—
839C23—164no—
840C23—164no—
841C23C22×#41116yes—
842C23C2×H(5,𝔽2)14yes—
843C23C2611yescharacteristic
844Q8—48no—
845Q8—44no—
846Q8—84no—
847Q8—162no—
848D4—232no—
849D4—416no—
850D4—416no—
851D4—44no—
852D4—416no—
853D4—416no—
854D4—416no—
855D4—432no—
856D4—82no—
857D4—816no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—28no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—24no—
880C2×C4—22no—
881C2×C4—28no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—28no—
889C2×C4—24no—
890C2×C4—28no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—48no—
897C2×C4—48no—
898C2×C4—48no—
899C2×C4—816no—
900C2×C4—88no—
901C2×C4—816no—
902C2×C4—816no—
903C2×C4—84no—
904C2×C4—816no—
905C2×C4—168no—
906C2×C4C22×#4114yes—
907C2×C4C22×#4114yes—
908C2×C4C22×#4114yes—
909C2×C4C2×H(5,𝔽2)12yes—
910C2×C4C2×H(5,𝔽2)14yes—
911C2×C4C2×H(5,𝔽2)12yes—
912C22—216no—
913C22—28no—
914C22—216no—
915C22—24no—
916C22—216no—
917C22—48no—
918C22—42no—
919C22—48no—
920C22—44no—
921C22—48no—
922C22—48no—
923C22—42no—
924C22—44no—
925C22—42no—
926C22—44no—
927C22—42no—
928C22—42no—
929C22—832no—
930C22—1616no—
931C22C23×#4112yes—
932C22C22×H(5,𝔽2)11yescharacteristic
933C22C22×H(5,𝔽2)11yescharacteristic
934C22H(7,𝔽2)12yes—
935C222−1+611yescharacteristic
936C4—24no—
937C4—24no—
938C4—24no—
939C4—22no—
940C4—44no—
941C4—44no—
942C4—48no—
943C4—44no—
944C4—44no—
945C4—41no—
946C4—44no—
947C4—44no—
948C4—44no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4#348114yes—
953C2—44no—
954C2—416no—
955C2—82no—
956C2C2×#348111yescharacteristic
957C2#6284712yes—
958C2#6289511yescharacteristic
959C2#6298312yes—
960C2#6304511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59816C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59836C2semidirect
3. #59802C2semidirect
4. #59375C2semidirect
5. #52301C2semidirect
6. #52273C2semidirect
7. #45140C2semidirect
8. #45088C2semidirect
9. #43790C2semidirect
10. #43365C2semidirect
11. #39628C2semidirect
12. #39258C2semidirect
13. #38768C2semidirect
14. #38508C2semidirect
15. #36534C2semidirect
16. #36528C2semidirect
17. #36075C2semidirect
18. #35947C2semidirect
19. #34331C2semidirect
20. #34290C2semidirect
22. C2×#556C22semidirect
23. C2×#554C22semidirect
24. C2×#551C22semidirect
27. C2×#518C22semidirect
28. C22×C4×D4C22semidirect
29. #2862C22semidirect
30. #2861C22semidirect
31. #2855C22semidirect
32. #2848C22semidirect
33. #2808C22semidirect
34. #2804C22semidirect
35. #2804C22semidirect
36. #2804C22semidirect
37. #2796C22semidirect
38. #2794C22semidirect
39. #2782C22semidirect
40. #2782C22semidirect
41. #2781C22semidirect
42. #2751C22semidirect
43. #2747C22semidirect
44. #2736C22semidirect
45. #2732C22semidirect
46. #2732C22semidirect
47. #2724C22semidirect
49. #2708C22semidirect
50. #2708C22semidirect
51. #2696C22semidirect
52. #2693C22semidirect
53. #2691C22semidirect
54. #2684C22semidirect
55. #2684C22semidirect
56. #2684C22semidirect
59. #2649C22semidirect
60. #2647C22semidirect
61. #2636C22semidirect
62. #2625C22semidirect
63. #2609C22semidirect
64. #2603C22semidirect
65. #2600C22semidirect
66. #2595C22semidirect
67. #2580C22semidirect
68. #2569C22semidirect
69. #2565C22semidirect
70. #2563C22semidirect
71. #2561C22semidirect
72. #2560C22semidirect
73. #2559C22semidirect
74. #2553C22semidirect
75. #2547C22semidirect
79. #2536C22semidirect
80. #2536C22semidirect
81. #2534C22semidirect
82. #2530C22semidirect
83. #2505C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2480C22semidirect
87. #2480C22semidirect
88. #2477C22semidirect
89. #2472C22semidirect
90. #2468C22semidirect
91. #2463C22semidirect
92. #2460C22semidirect
93. #2458C22semidirect
94. #2452C22semidirect
95. #2452C22semidirect
96. #2450C22semidirect
97. #2450C22semidirect
98. #2444C22semidirect
99. #2437C22semidirect
100. #2435C22semidirect
101. #2435C22semidirect
102. #2427C22semidirect
103. #2427C22semidirect
104. #2425C22semidirect
105. #2422C22semidirect
106. #2422C22semidirect
107. #2418C22semidirect
108. #2418C22semidirect
109. #2411C22semidirect
113. #2405C22semidirect
114. #2405C22semidirect
115. #2398C22semidirect
116. #2398C22semidirect
117. #2398C22semidirect
118. #2395C22semidirect
119. #2367C22semidirect
120. #2367C22semidirect
122. #2364C22semidirect
123. #2363C22semidirect
124. #2361C22semidirect
125. #2359C22semidirect
126. #2358C22semidirect
127. #2358C22semidirect
128. #2355C22semidirect
129. #2354C22semidirect
130. #2352C22semidirect
131. Q8×C4⋊C4C22semidirect
132. #2349C22semidirect
133. #2349C22semidirect
134. #2346C22semidirect
135. #2345C22semidirect
136. D4×C22⋊C4C22semidirect
137. D4×C22⋊C4C22semidirect
138. D4×C22⋊C4C22semidirect
139. #2335C22semidirect
141. #2326C22semidirect
142. #2325C22semidirect
143. #2324C22semidirect
144. #2321C22semidirect
147. C4×#124C22semidirect
148. C4×#124C22semidirect
149. C4×#123C22semidirect
150. C4×#121C22semidirect
151. C4×#120C22semidirect
152. C4×#120C22semidirect
153. #2295C22semidirect
154. #2293C22semidirect
155. #2290C22semidirect
156. C2×#386C22semidirect
157. #2275C22semidirect
158. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598362
#598162
#598022
#593752
#523012
#522732
#451402
#450882
#437902
#433652
#396282
#392582
#387682
#385082
#365342
#365282
#360752
#359472
#343312
#342902