Finite Group Databasebeta

← #7880302

Subgroups — #7880302

Order 512.

5903 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59683C214yesmaximal, complemented
2#59465C211yesmaximal, characteristic, complemented
3#59143C212yesmaximal, complemented
4#49969C218yesmaximal, complemented
5#46548C214yesmaximal, complemented
6#45013C214yesmaximal, complemented
7#44874C214yesmaximal, complemented
8#43005C214yesmaximal, complemented
9#42544C214yesmaximal, complemented
10#39770C212yesmaximal, complemented
11#39397C214yesmaximal, complemented
12#39351C212yesmaximal, complemented
13#39066C214yesmaximal, complemented
14#36460C212yesmaximal, complemented
15D4×#127C211yesmaximal, characteristic
16#35713C214yesmaximal, complemented
17#35536C214yesmaximal, complemented
18#34793C212yesmaximal, complemented
19#34498C211yesmaximal, characteristic, complemented
20#34210C212yesmaximal, complemented
21C2×#559C2211yescharacteristic
22C2×D42C2214yes—
23C2×D42C2212yes—
24C2×#542C2214yescomplemented
25C2×#539C2214yescomplemented
26C22×#127C2212yes—
27C2×#518C2214yescomplemented
28#2867C2211yescharacteristic
29#2860C2214yescomplemented
30#2856C2212yes—
31#2826C2214yescomplemented
32#2784C2214yescomplemented
33#2778C2218yescomplemented
34#2760C2214yescomplemented
35#2753C2218yescomplemented
36#2752C2214yescomplemented
37#2723C2218yescomplemented
38#2711C2218yescomplemented
39#2709C2218yescomplemented
40#2709C2218yescomplemented
41#2709C2218yescomplemented
42#2705C2218yescomplemented
43#2697C2218yescomplemented
44#2696C2218yescomplemented
45#2685C2218yescomplemented
46#2685C2218yescomplemented
47#2684C2218yescomplemented
48#2681C2218yescomplemented
49#2672C2218yescomplemented
50#2641C2214yescomplemented
51#2636C2218yescomplemented
52#2624C2214yescomplemented
53#2622C2218yescomplemented
54#2602C2218yescomplemented
55#2571C2211yescharacteristic, complemented
56#2564C2214yescomplemented
57#2563C2214yescomplemented
58#2559C2218yescomplemented
59#2559C2218yescomplemented
60#2551C2211yescharacteristic, complemented
61#2548C2212yescomplemented
62#2548C2212yescomplemented
63#2544C2214yescomplemented
64#2544C2214yescomplemented
65#2544C2214yescomplemented
66#2544C2214yescomplemented
67#2542C2214yescomplemented
68#2541C2214yes—
69#2541C2212yes—
70#2534C2218yescomplemented
71#2530C2214yescomplemented
72#2528C2214yescomplemented
73#2526C2218yescomplemented
74#2517C2214yescomplemented
75#2512C2214yescomplemented
76#2512C2214yescomplemented
77#2511C2212yescomplemented
78#2506C2212yescomplemented
79#2500C2214yescomplemented
80#2499C2212yescomplemented
81#2494C2212yescomplemented
82#2491C2214yescomplemented
83#2489C2212yescomplemented
84#2485C2212yes—
85#2472C2218yescomplemented
86#2472C2218yescomplemented
87#2467C2218yescomplemented
88#2467C2218yescomplemented
89#2463C2218yescomplemented
90#2463C2214yescomplemented
91#2460C2214yes—
92#2457C2218yescomplemented
93#2454C2214yescomplemented
94#2452C2214yescomplemented
95#2452C2214yescomplemented
96#2448C2214yescomplemented
97#2445C2214yescomplemented
98#2445C2214yescomplemented
99#2445C2214yescomplemented
100#2445C2214yescomplemented
101#2445C2214yescomplemented
102#2445C2214yescomplemented
103#2444C2218yescomplemented
104#2443C2218yescomplemented
105#2441C2212yescomplemented
106#2435C2214yes—
107#2435C2214yescomplemented
108#2435C2214yescomplemented
109#2433C2214yes—
110#2433C2214yes—
111#2433C2214yes—
112#2426C2214yescomplemented
113#2422C2214yescomplemented
114#2420C2214yescomplemented
115#2418C2218yescomplemented
116#2418C2218yescomplemented
117#2418C2218yescomplemented
118#2415C2212yes—
119#2412C2218yescomplemented
120#2405C2218yes—
121#2405C2218yescomplemented
122#2401C2214yescomplemented
123#2395C2214yes—
124C2×#394C2214yes—
125#2376C2214yescomplemented
126#2367C2214yescomplemented
127#2366C2212yes—
128#2366C2211yescharacteristic
129#2366C2214yescomplemented
130#2366C2214yescomplemented
131#2366C2212yescomplemented
132#2366C2212yescomplemented
133#2364C2214yescomplemented
134#2363C2214yescomplemented
135#2357C2214yescomplemented
136Q8×C4⋊C4C2212yescomplemented
137#2349C2214yescomplemented
138D4×C4⋊C4C2214yescomplemented
139D4×C22⋊C4C2214yescomplemented
140D4×C22⋊C4C2214yescomplemented
141D4×C22⋊C4C2214yescomplemented
142D4×C22⋊C4C2218yescomplemented
143D4×C22⋊C4C2214yescomplemented
144#2328C2218yescomplemented
145#2328C2214yescomplemented
146#2326C2214yescomplemented
147#2322C2214yescomplemented
148#2319C2214yescomplemented
149#2309C2214yescomplemented
150C4×#127C2211yescharacteristic
151C4×#127C2214yescomplemented
152C4×#127C2214yescomplemented
153C4×#125C2214yescomplemented
154C4×#125C2212yescomplemented
155C4×#124C2214yescomplemented
156C4×C22⋊Q8C2212yescomplemented
157C4×C22⋊Q8C2212yescomplemented
158#2298C2214yescomplemented
159#2295C2212yescomplemented
160#2285C2212yescomplemented
161C42×D4C2211yescharacteristic
162C4×#117C2212yescomplemented
163C23×D4C2314yes—
164C23×D4C2314yes—
165C23×D4C2314yes—
166C23×D4C2314yes—
167#559—28no—
168D42—48no—
169D42—416no—
170#542—416no—
171#539—416no—
172C2×C4⋊Q8C2314yes—
173C2×#127—216no—
174C2×#127C2314yes—
175C2×#127C2314yes—
176C2×#127C2312yes—
177C2×#127C2314yes—
178C2×#127C2314yes—
179C2×#127C2314yes—
180C2×#127C2312yes—
181C2×#127C2312yes—
182C2×#127C2311yescharacteristic
183C2×#126C2318yes—
184C2×#126C2318yes—
185C2×#125C2314yes—
186C2×#125C2312yes—
187C2×#124C2314yes—
188C2×#124C2318yes—
189C2×#124C2314yes—
190C2×#124C2314yes—
191C2×#123C2314yes—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2318yes—
206C2×#120C2318yes—
207C2×#120C2318yes—
208C2×#120C2318yes—
209#518—416no—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2312yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2318yes—
220C2×C4×D4C2318yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2318yes—
228C2×#117C2314yes—
229C2×#117C2312yes—
230C2×#117C2312yes—
231C22×C4⋊C4C2314yes—
232C22×C22⋊C4C2318yes—
233C22×C22⋊C4C2318yes—
234C22×C22⋊C4C2318yes—
235C22×C42C2312yes—
236#401C2314yes—
237#400C2314yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2314yes—
242#399C2314yes—
243#399C2318yes—
244#399C2318yes—
245#399C2314yes—
246#398C2314yes—
247#397C2318yes—
248#397C2318yes—
249#397C2314yes—
250#397C2314yes—
251#397C2318yes—
252#397C2314yes—
253#397C2314yes—
254#397C2314yes—
255#397C2314yes—
256#396C2318yes—
257#396C2318yes—
258#396C2314yes—
259#396C2318yes—
260#395C2314yes—
261#394C2318yes—
262#394C2318yes—
263#394C2318yes—
264#394C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2314yes—
273#394C2318yes—
274#394C2318yes—
275#394C2314yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#393C2314yes—
284#393C2318yes—
285#393C2318yes—
286#392C2314yes—
287#392C2318yes—
288#392C2318yes—
289#392C2314yes—
290#391C2312yes—
291#391C2312yes—
292#391C2312yes—
293#391C2312yes—
294#390C2314yes—
295#390C2312yes—
296#390C2314yes—
297#390C2314yes—
298#390C2318yes—
299#390C2318yes—
300#390C2314yes—
301#390C2318yes—
302#390C2318yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2318yes—
317#389C2314yes—
318#389C2312yes—
319#389C2314yes—
320#389C2312yes—
321#389C2314yes—
322#389C2312yes—
323#389C2314yes—
324#389C2318yes—
325#389C2312yes—
326#389C2312yes—
327#389C2314yes—
328#389C2312yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2314yes—
338#388C2314yes—
339#388C2314yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#387C2314yes—
349#387C2314yes—
350#387C2314yes—
351#387C2314yes—
352#387C2314yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#386C2318yes—
359#386C2318yes—
360#386C2314yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#385C2318yes—
379#385C2314yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#384C2311yescharacteristic
387#384C2312yes—
388#384C2312yes—
389#384C2314yes—
390#382C2312yes—
391#382C2314yes—
392#382C2314yes—
393#382C2314yes—
394#381C2314yes—
395#381C2318yes—
396#380C2318yes—
397#380C2318yes—
398#380C2318yes—
399#380C2312yes—
400#380C2312yes—
401#380C2314yes—
402#380C2312yes—
403#380C2312yes—
404#379C2318yes—
405#379C2318yes—
406#379C2318yes—
407#379C2318yes—
408#379C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2311yescharacteristic
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2312yes—
433#376C2314yes—
434#376C2314yes—
435C2×#95C2314yes—
436C43C2311yescharacteristic
437C43C2314yes—
438C25C2418yes—
439C22×Q8C2412yes—
440C22×Q8C2414yes—
441C22×D4—216no—
442C22×D4—216no—
443C22×D4—216no—
444C22×D4—216no—
445C22×D4—48no—
446C22×D4—48no—
447C22×D4—48no—
448C22×D4—48no—
449C22×D4—48no—
450C22×D4—416no—
451C22×D4—84no—
452C22×D4C2411yescharacteristic
453C22×D4C2414yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C22×D4C2418yes—
457C22×D4C2414yes—
458C22×D4C2418yes—
459C22×D4C2418yes—
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2418yes—
463C22×D4C2414yes—
464C22×D4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2418yes—
472C23×C4C2418yes—
473C23×C4C2418yes—
474C4⋊Q8—48no—
475#127—216no—
476#127—216no—
477#127—216no—
478#127—28no—
479#127—48no—
480#127—48no—
481#127—44no—
482#127—82no—
483#127#4118yes—
484#126—416no—
485#126—416no—
486#125—216no—
487#125—44no—
488#124—216no—
489#124—48no—
490#124—48no—
491#124—416no—
492#123—216no—
493#123—416no—
494#123—416no—
495#123—416no—
496#123—88no—
497C22⋊Q8—28no—
498C22⋊Q8—416no—
499C22⋊Q8—416no—
500C22⋊Q8—48no—
501C22⋊Q8—44no—
502#121—216no—
503#121—216no—
504#121—48no—
505#121—416no—
506#121—48no—
507#120—416no—
508#120—416no—
509#120—416no—
510C4×Q8—28no—
511C4×Q8—48no—
512C4×D4—216no—
513C4×D4—28no—
514C4×D4—24no—
515C4×D4—48no—
516C4×D4—48no—
517C4×D4—416no—
518C4×D4—416no—
519C4×D4—48no—
520C4×D4—48no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—416no—
524C4×D4—48no—
525C4×D4—48no—
526C4×D4—44no—
527C4×D4—88no—
528#117—28no—
529#117—216no—
530#117—44no—
531C2×C4⋊C4—48no—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2411yescharacteristic
562C2×C22⋊C4—416no—
563C2×C22⋊C4—416no—
564C2×C22⋊C4—88no—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C42—28no—
603C2×C42C2414yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2411yescharacteristic
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2418yes—
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2412yes—
633#95C2414yes—
634#95C2414yes—
635#95C2411yescharacteristic
636#95C2412yes—
637#95C2411yescharacteristic
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653C24—216no—
654C24—216no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24C2518yes—
661C24C2514yes—
662C24C2512yes—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—44no—
667C2×Q8—48no—
668C2×D4—24no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—216no—
672C2×D4—216no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—22no—
677C2×D4—28no—
678C2×D4—216no—
679C2×D4—28no—
680C2×D4—216no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—464no—
687C2×D4—42no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—42no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—44no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—832no—
704C2×D4—832no—
705C2×D4—832no—
706C2×D4C2×#41116yes—
707C2×D4C2×#4118yes—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—28no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—28no—
717C22×C4—42no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—48no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4H(5,𝔽2)18yes—
733C22×C4C2512yes—
734C22×C4C2511yescharacteristic
735C22×C4C2514yes—
736C22×C4C2512yes—
737C22×C4C2514yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2514yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2511yescharacteristic
746C22×C4C2512yes—
747C22×C4C2511yescharacteristic
748C22×C4C2512yes—
749C22×C4C2512yes—
750C4⋊C4—24no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—48no—
769C4⋊C4—42no—
770C4⋊C4—44no—
771C4⋊C4—48no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4H(5,𝔽2)14yes—
780C22⋊C4—216no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—24no—
786C22⋊C4—28no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—216no—
790C22⋊C4—216no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—44no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C42—24no—
818C42—24no—
819C42—24no—
820C42—28no—
821C42—28no—
822C42—28no—
823C42—28no—
824C42—24no—
825C42—22no—
826C42—28no—
827C42—28no—
828C42—24no—
829C42—44no—
830C42—44no—
831C42—48no—
832C42—41no—
833C42C2×#4114yes—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—24no—
838C23—28no—
839C23—22no—
840C23—22no—
841C23—28no—
842C23—22no—
843C23—24no—
844C23—28no—
845C23—28no—
846C23—28no—
847C23—28no—
848C23—28no—
849C23—28no—
850C23—28no—
851C23—432no—
852C23—816no—
853C23—816no—
854C23—816no—
855C23—816no—
856C23—168no—
857C23—168no—
858C23C22×#4118yes—
859C23C2×H(5,𝔽2)14yes—
860C23C2611yescharacteristic
861Q8—48no—
862Q8—164no—
863D4—28no—
864D4—232no—
865D4—48no—
866D4—432no—
867D4—432no—
868D4—416no—
869D4—416no—
870D4—88no—
871D4—88no—
872D4—816no—
873D4—816no—
874D4—164no—
875D4—168no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—216no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—48no—
919C2×C4—48no—
920C2×C4—88no—
921C2×C4—88no—
922C2×C4—164no—
923C2×C4—168no—
924C2×C4—168no—
925C2×C4—168no—
926C2×C4C22×#4112yes—
927C2×C4C22×#4114yes—
928C2×C4C2×H(5,𝔽2)14yes—
929C2×C4C2×H(5,𝔽2)14yes—
930C2×C4C2×H(5,𝔽2)12yes—
931C2×C4C2×H(5,𝔽2)14yes—
932C2×C4#58514yes—
933C22—28no—
934C22—24no—
935C22—216no—
936C22—24no—
937C22—24no—
938C22—42no—
939C22—42no—
940C22—44no—
941C22—42no—
942C22—44no—
943C22—48no—
944C22—42no—
945C22—48no—
946C22—48no—
947C22—48no—
948C22—48no—
949C22—48no—
950C22—48no—
951C22—48no—
952C22—1632no—
953C22C23×#4111yescharacteristic
954C22C22×H(5,𝔽2)11yescharacteristic
955C22C22×H(5,𝔽2)12yes—
956C22C2×#58512yes—
957C22H(7,𝔽2)11yescharacteristic
958C4—22no—
959C4—24no—
960C4—24no—
961C4—22no—
962C4—44no—
963C4—42no—
964C4—44no—
965C4—44no—
966C4—41no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—42no—
974C4#351318yes—
975C2—48no—
976C2—44no—
977C2—88no—
978C2C2×#351312yes—
979C2#6283211yescharacteristic
980C2#6296112yes—
981C2#6298311yescharacteristic
982C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalD4×#127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59683C2semidirect
2. #59465C2semidirect
3. #59143C2semidirect
4. #49969C2semidirect
5. #46548C2semidirect
6. #45013C2semidirect
7. #44874C2semidirect
8. #43005C2semidirect
9. #42544C2semidirect
10. #39770C2semidirect
11. #39397C2semidirect
12. #39351C2semidirect
13. #39066C2semidirect
14. #36460C2semidirect
16. #35713C2semidirect
17. #35536C2semidirect
18. #34793C2semidirect
19. #34498C2semidirect
20. #34210C2semidirect
24. C2×#542C22semidirect
25. C2×#539C22semidirect
27. C2×#518C22semidirect
29. #2860C22semidirect
31. #2826C22semidirect
32. #2784C22semidirect
33. #2778C22semidirect
34. #2760C22semidirect
35. #2753C22semidirect
36. #2752C22semidirect
37. #2723C22semidirect
38. #2711C22semidirect
39. #2709C22semidirect
40. #2709C22semidirect
41. #2709C22semidirect
42. #2705C22semidirect
43. #2697C22semidirect
44. #2696C22semidirect
45. #2685C22semidirect
46. #2685C22semidirect
47. #2684C22semidirect
48. #2681C22semidirect
49. #2672C22semidirect
50. #2641C22semidirect
51. #2636C22semidirect
52. #2624C22semidirect
53. #2622C22semidirect
54. #2602C22semidirect
55. #2571C22semidirect
56. #2564C22semidirect
57. #2563C22semidirect
58. #2559C22semidirect
59. #2559C22semidirect
60. #2551C22semidirect
61. #2548C22semidirect
62. #2548C22semidirect
63. #2544C22semidirect
64. #2544C22semidirect
65. #2544C22semidirect
66. #2544C22semidirect
67. #2542C22semidirect
70. #2534C22semidirect
71. #2530C22semidirect
72. #2528C22semidirect
73. #2526C22semidirect
74. #2517C22semidirect
75. #2512C22semidirect
76. #2512C22semidirect
77. #2511C22semidirect
78. #2506C22semidirect
79. #2500C22semidirect
80. #2499C22semidirect
81. #2494C22semidirect
82. #2491C22semidirect
83. #2489C22semidirect
85. #2472C22semidirect
86. #2472C22semidirect
87. #2467C22semidirect
88. #2467C22semidirect
89. #2463C22semidirect
90. #2463C22semidirect
92. #2457C22semidirect
93. #2454C22semidirect
94. #2452C22semidirect
95. #2452C22semidirect
96. #2448C22semidirect
97. #2445C22semidirect
98. #2445C22semidirect
99. #2445C22semidirect
100. #2445C22semidirect
101. #2445C22semidirect
102. #2445C22semidirect
103. #2444C22semidirect
104. #2443C22semidirect
105. #2441C22semidirect
107. #2435C22semidirect
108. #2435C22semidirect
112. #2426C22semidirect
113. #2422C22semidirect
114. #2420C22semidirect
115. #2418C22semidirect
116. #2418C22semidirect
117. #2418C22semidirect
119. #2412C22semidirect
121. #2405C22semidirect
122. #2401C22semidirect
125. #2376C22semidirect
126. #2367C22semidirect
129. #2366C22semidirect
130. #2366C22semidirect
131. #2366C22semidirect
132. #2366C22semidirect
133. #2364C22semidirect
134. #2363C22semidirect
135. #2357C22semidirect
136. Q8×C4⋊C4C22semidirect
137. #2349C22semidirect
138. D4×C4⋊C4C22semidirect
139. D4×C22⋊C4C22semidirect
140. D4×C22⋊C4C22semidirect
141. D4×C22⋊C4C22semidirect
142. D4×C22⋊C4C22semidirect
143. D4×C22⋊C4C22semidirect
144. #2328C22semidirect
145. #2328C22semidirect
146. #2326C22semidirect
147. #2322C22semidirect
148. #2319C22semidirect
149. #2309C22semidirect
151. C4×#127C22semidirect
152. C4×#127C22semidirect
153. C4×#125C22semidirect
154. C4×#125C22semidirect
155. C4×#124C22semidirect
156. C4×C22⋊Q8C22semidirect
157. C4×C22⋊Q8C22semidirect
158. #2298C22semidirect
159. #2295C22semidirect
160. #2285C22semidirect
162. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#596832
#594652
#591432
#499692
#465482
#450132
#448742
#430052
#425442
#397702
#393972
#393512
#390662
#364602
D4×#1272
#357132
#355362
#347932
#344982
#342102