Finite Group Databasebeta

← #8196402

Subgroups — #8196402

Order 512.

5332 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#59476C214yesmaximal, complemented
2#59143C212yesmaximal, complemented
3#59084C211yesmaximal, characteristic, complemented
4#59070C211yesmaximal, characteristic, complemented
5#56590C218yesmaximal, complemented
6#52995C214yesmaximal, complemented
7#50165C214yesmaximal, complemented
8#46359C214yesmaximal, complemented
9#46061C214yesmaximal, complemented
10#44970C214yesmaximal, complemented
11#42575C214yesmaximal, complemented
12#42544C214yesmaximal, complemented
13#40026C214yesmaximal, complemented
14#39770C212yesmaximal, complemented
15#39397C214yesmaximal, complemented
16#39168C212yesmaximal, complemented
17#36595C212yesmaximal, complemented
18#36300C212yesmaximal, complemented
19#35274C211yesmaximal, characteristic
20#34975C212yesmaximal, complemented
21C2×#559C2212yes—
22C2×#559C2211yescharacteristic, complemented
23C2×Q82C2211yescharacteristic, complemented
24C2×#551C2214yes—
25C2×#539C2214yescomplemented
26C2×#535C2212yes—
27C2×#535C2212yes—
28C2×#532C2211yescharacteristic
29C22×#127C2211yescharacteristic
30#2867C2212yes—
31#2860C2214yescomplemented
32#2858C2212yes—
33#2858C2214yescomplemented
34#2829C2218yescomplemented
35#2826C2218yescomplemented
36#2824C2218yescomplemented
37#2816C2214yescomplemented
38#2803C2218yescomplemented
39#2778C2218yescomplemented
40#2778C2218yescomplemented
41#2756C2218yescomplemented
42#2753C2218yescomplemented
43#2731C2214yescomplemented
44#2717C2214yescomplemented
45#2711C2218yescomplemented
46#2709C2218yes—
47#2709C2218yescomplemented
48#2709C2218yescomplemented
49#2708C2218yescomplemented
50#2705C2218yescomplemented
51#2701C2218yescomplemented
52#2697C2218yes—
53#2697C2214yes—
54#2696C2218yescomplemented
55#2696C2218yescomplemented
56#2685C2218yes—
57#2685C2218yes—
58#2684C2214yes—
59#2681C2218yescomplemented
60#2674C2218yescomplemented
61#2674C2218yescomplemented
62#2657C2214yes—
63#2648C2218yescomplemented
64#2641C2214yescomplemented
65#2640C2214yescomplemented
66#2636C2218yescomplemented
67#2622C2218yes—
68#2598C2218yescomplemented
69#2591C2214yescomplemented
70#2567C2212yescomplemented
71#2548C2212yes—
72#2548C2212yes—
73#2548C2214yescomplemented
74#2548C2214yescomplemented
75#2548C2212yescomplemented
76#2545C2214yescomplemented
77#2544C2214yes—
78#2544C2214yes—
79#2544C2214yescomplemented
80#2544C2214yescomplemented
81#2544C2214yescomplemented
82#2544C2214yescomplemented
83#2542C2214yescomplemented
84#2541C2214yes—
85#2541C2214yes—
86#2533C2214yescomplemented
87#2528C2214yescomplemented
88#2521C2218yescomplemented
89#2514C2212yescomplemented
90#2513C2214yescomplemented
91#2512C2214yescomplemented
92#2506C2212yescomplemented
93#2496C2212yes—
94#2491C2214yes—
95#2489C2212yes—
96#2478C2214yes—
97#2476C2218yescomplemented
98#2475C2214yes—
99#2474C2218yescomplemented
100#2472C2218yes—
101#2471C2218yescomplemented
102#2463C2218yescomplemented
103#2454C2214yescomplemented
104#2453C2212yescomplemented
105#2452C2214yescomplemented
106#2452C2214yescomplemented
107#2452C2214yescomplemented
108#2448C2214yescomplemented
109#2448C2214yescomplemented
110#2448C2214yescomplemented
111#2447C2214yescomplemented
112#2446C2212yescomplemented
113#2445C2214yes—
114#2445C2214yes—
115#2445C2214yescomplemented
116#2445C2218yescomplemented
117#2445C2218yescomplemented
118#2445C2214yescomplemented
119#2445C2214yescomplemented
120#2445C2214yescomplemented
121#2443C2218yescomplemented
122#2435C2214yes—
123#2435C2214yes—
124#2433C2214yes—
125#2433C2214yes—
126#2432C2214yes—
127#2429C2212yes—
128#2427C2214yes—
129#2426C2214yes—
130#2422C2214yes—
131#2421C2212yes—
132#2418C2218yes—
133#2406C2214yes—
134#2405C2218yes—
135#2402C2214yescomplemented
136#2401C2214yes—
137#2375C2214yes—
138#2369C2211yescharacteristic, complemented
139#2367C2214yescomplemented
140#2367C2214yescomplemented
141#2366C2212yes—
142#2366C2214yescomplemented
143#2366C2214yescomplemented
144#2366C2211yescharacteristic, complemented
145#2354C2214yescomplemented
146D4×C4⋊C4C2214yescomplemented
147D4×C22⋊C4C2214yes—
148D4×C22⋊C4C2214yes—
149#2333C2214yescomplemented
150#2328C2214yescomplemented
151#2326C2214yescomplemented
152C4×C4⋊Q8C2212yescomplemented
153C4×#127C2214yescomplemented
154C4×#125C2212yescomplemented
155C4×#125C2214yescomplemented
156C4×#126C2214yes—
157C4×C22⋊Q8C2212yes—
158C4×C22⋊Q8C2212yes—
159#2295C2212yescomplemented
160#2293C2214yescomplemented
161C42×Q8C2212yescomplemented
162C4×#117C2211yescharacteristic
163C22×#41C2312yes—
164C23×D4C2314yes—
165C23×D4C2312yes—
166#559—48no—
167#559—44no—
168Q82—44no—
169#551—416no—
170#539—416no—
171#535—48no—
172#535—48no—
173#532—44no—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×#127—44no—
179C2×#127C2312yes—
180C2×#127C2311yescharacteristic
181C2×#127C2314yes—
182C2×#127C2314yes—
183C2×#127C2314yes—
184C2×#127C2314yes—
185C2×#127C2314yes—
186C2×#127C2314yes—
187C2×#127C2312yes—
188C2×#127C2314yes—
189C2×#126C2314yes—
190C2×#126C2318yes—
191C2×#125C2314yes—
192C2×#125C2312yes—
193C2×#124C2314yes—
194C2×#124C2314yes—
195C2×#124C2314yes—
196C2×#124C2314yes—
197C2×#124C2314yes—
198C2×#124C2314yes—
199C2×#124C2314yes—
200C2×#124C2314yes—
201C2×#124C2312yes—
202C2×#124C2314yes—
203C2×#123C2318yes—
204C2×#123C2318yes—
205C2×#123C2314yes—
206C2×#123C2314yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2318yes—
218C2×#120C2314yes—
219C2×#120C2314yes—
220C2×#120C2318yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2318yes—
238C22×C4⋊C4C2314yes—
239C22×C22⋊C4C2318yes—
240C22×C42C2311yescharacteristic
241#401C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#399C2318yes—
250#399C2318yes—
251#399C2318yes—
252#398C2314yes—
253#398C2314yes—
254#398C2314yes—
255#398C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2314yes—
262#397C2314yes—
263#397C2318yes—
264#397C2314yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2314yes—
270#395C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#393C2318yes—
295#393C2318yes—
296#393C2318yes—
297#392C2318yes—
298#392C2318yes—
299#392C2318yes—
300#392C2318yes—
301#391C2312yes—
302#391C2312yes—
303#391C2314yes—
304#391C2312yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#390C2314yes—
310#390C2318yes—
311#390C2318yes—
312#390C2314yes—
313#390C2318yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2318yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2318yes—
325#390C2318yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#389C2312yes—
333#389C2314yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2314yes—
389#386C2318yes—
390#386C2314yes—
391#386C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2314yes—
399#385C2314yes—
400#384C2312yes—
401#384C2314yes—
402#383C2314yes—
403#382C2312yes—
404#382C2314yes—
405#381C2314yes—
406#380C2312yes—
407#380C2312yes—
408#380C2318yes—
409#380C2318yes—
410#379C2318yes—
411#379C2318yes—
412#379C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2312yes—
436#376C2314yes—
437#376C2312yes—
438C43C2314yes—
439C43C2312yes—
440C25C2414yes—
441C2×#41—44no—
442C2×#41—44no—
443C2×#41—44no—
444C22×Q8C2412yes—
445C22×Q8C2412yes—
446C22×Q8C2412yes—
447C22×Q8C2414yes—
448C22×D4—44no—
449C22×D4—48no—
450C22×D4—44no—
451C22×D4—48no—
452C22×D4—48no—
453C22×D4—44no—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2418yes—
458C22×D4C2418yes—
459C22×D4C2414yes—
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2412yes—
463C22×D4C2418yes—
464C22×D4C2418yes—
465C22×D4C2418yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2418yes—
470C23×C4C2418yes—
471C23×C4C2414yes—
472C23×C4C2414yes—
473C4⋊Q8—24no—
474C4⋊Q8—48no—
475C4⋊Q8—44no—
476C4⋊Q8—48no—
477#127—28no—
478#127—24no—
479#127—48no—
480#127—44no—
481#127—48no—
482#127—48no—
483#127—48no—
484#127—48no—
485#127—48no—
486#127—48no—
487#126—216no—
488#126—416no—
489#125—216no—
490#125—44no—
491#124—48no—
492#124—48no—
493#124—48no—
494#124—48no—
495#124—48no—
496#124—44no—
497#124—48no—
498#124—48no—
499#124—48no—
500#124—48no—
501#123—48no—
502#123—416no—
503#123—416no—
504#123—416no—
505#123—48no—
506#123—416no—
507C22⋊Q8—416no—
508C22⋊Q8—416no—
509C22⋊Q8—48no—
510C22⋊Q8—44no—
511C22⋊Q8—44no—
512#121—216no—
513#121—416no—
514#121—48no—
515#121—48no—
516#120—216no—
517#120—416no—
518#120—48no—
519C4×Q8—28no—
520C4×Q8—28no—
521C4×Q8—44no—
522C4×Q8—44no—
523C4×Q8—48no—
524C4×D4—48no—
525C4×D4—48no—
526C4×D4—48no—
527C4×D4—48no—
528C4×D4—416no—
529C4×D4—416no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533#117—24no—
534#117—24no—
535#117—416no—
536C2×C4⋊C4—48no—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2411yescharacteristic
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C22⋊C4—416no—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2411yescharacteristic
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2411yescharacteristic
604C2×C42—24no—
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2412yes—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2411yescharacteristic
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2411yescharacteristic
624#95C2412yes—
625#95C2412yes—
626#95C2412yes—
627#95C2412yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657C24—28no—
658C24—44no—
659C24—48no—
660C24—48no—
661C24—44no—
662C24C2518yes—
663C24C2514yes—
664C24C2511yescharacteristic
665#41—816no—
666C2×Q8—24no—
667C2×Q8—24no—
668C2×Q8—24no—
669C2×Q8—24no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—216no—
683C2×D4—216no—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—48no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—816no—
715C2×D4—832no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—28no—
723C22×C4—48no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—48no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—44no—
730C22×C4—48no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—48no—
735C22×C4—48no—
736C22×C4C2512yes—
737C22×C4C2512yes—
738C22×C4C2512yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2514yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2514yes—
746C22×C4C2514yes—
747C22×C4C2514yes—
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C22×C4C2512yes—
751C22×C4C2512yes—
752C22×C4C2512yes—
753C4⋊C4—28no—
754C4⋊C4—24no—
755C4⋊C4—22no—
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—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—48no—
773C4⋊C4—48no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4H(5,𝔽2)14yes—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—22no—
788C22⋊C4—24no—
789C22⋊C4—216no—
790C22⋊C4—216no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—48no—
808C22⋊C4—44no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—44no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4H(5,𝔽2)14yes—
819C42—24no—
820C42—22no—
821C42—24no—
822C42—24no—
823C42—28no—
824C42—28no—
825C42—28no—
826C42—28no—
827C42—28no—
828C42—28no—
829C42—24no—
830C42—24no—
831C42—24no—
832C42—24no—
833C42—44no—
834C42—44no—
835C42—44no—
836C42—44no—
837C42H(5,𝔽2)14yes—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—28no—
843C23—28no—
844C23—24no—
845C23—24no—
846C23—28no—
847C23—24no—
848C23—28no—
849C23—28no—
850C23—28no—
851C23—28no—
852C23—28no—
853C23—28no—
854C23—88no—
855C23—816no—
856C23—816no—
857C23—164no—
858C23—164no—
859C23C2×H(5,𝔽2)12yes—
860C23C2611yescharacteristic
861Q8—48no—
862Q8—48no—
863Q8—84no—
864Q8—164no—
865D4—416no—
866D4—416no—
867D4—416no—
868D4—816no—
869D4—816no—
870D4—88no—
871D4—88no—
872D4—84no—
873D4—88no—
874D4—816no—
875D4—168no—
876D4—168no—
877C2×C4—28no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—48no—
923C2×C4—88no—
924C2×C4—88no—
925C2×C4—816no—
926C2×C4—164no—
927C2×C4—168no—
928C2×C4C2×H(5,𝔽2)14yes—
929C2×C4C2×H(5,𝔽2)14yes—
930C2×C4C2×H(5,𝔽2)12yes—
931C2×C4C2×H(5,𝔽2)12yes—
932C2×C4C2×H(5,𝔽2)14yes—
933C2×C4#58514yes—
934C2×C4#58514yes—
935C22—24no—
936C22—22no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—48no—
941C22—48no—
942C22—48no—
943C22—44no—
944C22—48no—
945C22—48no—
946C22—48no—
947C22—48no—
948C22—44no—
949C22—48no—
950C22—44no—
951C22—48no—
952C22—1616no—
953C22C22×H(5,𝔽2)11yescharacteristic
954C22C22×H(5,𝔽2)11yescharacteristic
955C22C22×H(5,𝔽2)11yescharacteristic
956C22C2×#58512yes—
957C22C2×#58512yes—
958C4—24no—
959C4—24no—
960C4—22no—
961C4—22no—
962C4—42no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—42no—
969C4—44no—
970C4—42no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4#356218yes—
975C2—42no—
976C2—84no—
977C2—88no—
978C2C2×#356212yes—
979C2#6283211yescharacteristic
980C2#6302111yescharacteristic
981C2#6302112yes—
982C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35274C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59476C2semidirect
2. #59143C2semidirect
3. #59084C2semidirect
4. #59070C2semidirect
5. #56590C2semidirect
6. #52995C2semidirect
7. #50165C2semidirect
8. #46359C2semidirect
9. #46061C2semidirect
10. #44970C2semidirect
11. #42575C2semidirect
12. #42544C2semidirect
13. #40026C2semidirect
14. #39770C2semidirect
15. #39397C2semidirect
16. #39168C2semidirect
17. #36595C2semidirect
18. #36300C2semidirect
20. #34975C2semidirect
22. C2×#559C22semidirect
23. C2×Q82C22semidirect
25. C2×#539C22semidirect
31. #2860C22semidirect
33. #2858C22semidirect
34. #2829C22semidirect
35. #2826C22semidirect
36. #2824C22semidirect
37. #2816C22semidirect
38. #2803C22semidirect
39. #2778C22semidirect
40. #2778C22semidirect
41. #2756C22semidirect
42. #2753C22semidirect
43. #2731C22semidirect
44. #2717C22semidirect
45. #2711C22semidirect
47. #2709C22semidirect
48. #2709C22semidirect
49. #2708C22semidirect
50. #2705C22semidirect
51. #2701C22semidirect
54. #2696C22semidirect
55. #2696C22semidirect
59. #2681C22semidirect
60. #2674C22semidirect
61. #2674C22semidirect
63. #2648C22semidirect
64. #2641C22semidirect
65. #2640C22semidirect
66. #2636C22semidirect
68. #2598C22semidirect
69. #2591C22semidirect
70. #2567C22semidirect
73. #2548C22semidirect
74. #2548C22semidirect
75. #2548C22semidirect
76. #2545C22semidirect
79. #2544C22semidirect
80. #2544C22semidirect
81. #2544C22semidirect
82. #2544C22semidirect
83. #2542C22semidirect
86. #2533C22semidirect
87. #2528C22semidirect
88. #2521C22semidirect
89. #2514C22semidirect
90. #2513C22semidirect
91. #2512C22semidirect
92. #2506C22semidirect
97. #2476C22semidirect
99. #2474C22semidirect
101. #2471C22semidirect
102. #2463C22semidirect
103. #2454C22semidirect
104. #2453C22semidirect
105. #2452C22semidirect
106. #2452C22semidirect
107. #2452C22semidirect
108. #2448C22semidirect
109. #2448C22semidirect
110. #2448C22semidirect
111. #2447C22semidirect
112. #2446C22semidirect
115. #2445C22semidirect
116. #2445C22semidirect
117. #2445C22semidirect
118. #2445C22semidirect
119. #2445C22semidirect
120. #2445C22semidirect
121. #2443C22semidirect
135. #2402C22semidirect
138. #2369C22semidirect
139. #2367C22semidirect
140. #2367C22semidirect
142. #2366C22semidirect
143. #2366C22semidirect
144. #2366C22semidirect
145. #2354C22semidirect
146. D4×C4⋊C4C22semidirect
149. #2333C22semidirect
150. #2328C22semidirect
151. #2326C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×#127C22semidirect
154. C4×#125C22semidirect
155. C4×#125C22semidirect
159. #2295C22semidirect
160. #2293C22semidirect
161. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#594762
#591432
#590842
#590702
#565902
#529952
#501652
#463592
#460612
#449702
#425752
#425442
#400262
#397702
#393972
#391682
#365952
#363002
#352742
#349752