Finite Group Databasebeta

← #8096594

Subgroups — #8096594

Order 512.

5671 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53099C212yesmaximal, complemented
2#53000C214yesmaximal, complemented
3#52480C218yesmaximal, complemented
4#52420C214yesmaximal, complemented
5#52304C211yesmaximal, characteristic, complemented
6#52103C212yesmaximal, complemented
7#46280C212yesmaximal, complemented
8#45997C212yesmaximal, complemented
9#45996C211yesmaximal, characteristic, complemented
10#45962C214yesmaximal, complemented
11#45653C214yesmaximal, complemented
12#45487C212yesmaximal, complemented
13#45477C214yesmaximal, complemented
14#45451C218yesmaximal, complemented
15#36528C212yesmaximal, complemented
16#36496C211yesmaximal, characteristic, complemented
17#36300C212yesmaximal, complemented
18#36101C214yesmaximal, complemented
19#35930C212yesmaximal, complemented
20#35916C214yesmaximal, complemented
21C2×#562C2214yescomplemented
22C2×H(3,𝔽4)C2212yes—
23C2×#560C2214yes—
24C2×#559C2211yescharacteristic, complemented
25C2×#554C2211yescharacteristic
26C2×#550C2212yes—
27C2×#525C2218yescomplemented
28C22×C4×D4C2212yescomplemented
29#2861C2212yescomplemented
30#2860C2214yescomplemented
31#2858C2212yes—
32#2858C2211yescharacteristic, complemented
33#2856C2214yes—
34#2855C2212yescomplemented
35#2848C2214yescomplemented
36#2847C2218yescomplemented
37#2830C2214yescomplemented
38#2830C2218yescomplemented
39#2828C2218yescomplemented
40#2825C2218yescomplemented
41#2823C2214yescomplemented
42#2819C2212yes—
43#2819C2214yescomplemented
44#2815C2214yes—
45#2814C2218yescomplemented
46#2813C2218yescomplemented
47#2812C2218yescomplemented
48#2805C2212yescomplemented
49#2800C2218yescomplemented
50#2789C2212yescomplemented
51#2765C2214yescomplemented
52#2733C2212yes—
53#2724C2211yescharacteristic
54#2717C2212yes—
55#2715C2218yescomplemented
56#2714C2218yescomplemented
57#2703C2218yescomplemented
58#2701C2218yescomplemented
59#2692C2218yescomplemented
60#2690C2214yescomplemented
61#2686C2218yescomplemented
62#2683C2211yescharacteristic
63#2683C2214yescomplemented
64#2682C2214yescomplemented
65#2682C2214yescomplemented
66#2681C2218yescomplemented
67#2680C2214yescomplemented
68#2679C2212yes—
69#2678C2218yescomplemented
70#2678C2218yescomplemented
71#2678C2218yescomplemented
72#2676C2218yescomplemented
73#2676C2218yescomplemented
74#2675C2214yes—
75#2672C2218yescomplemented
76#2670C2218yes—
77#2669C2214yes—
78#2668C2218yescomplemented
79#2661C2214yescomplemented
80#2657C2212yes—
81#2653C2218yescomplemented
82#2644C2214yescomplemented
83#2595C2218yescomplemented
84#2592C2212yescomplemented
85#2567C2212yescomplemented
86#2567C2211yescharacteristic, complemented
87#2566C2212yescomplemented
88#2561C2214yescomplemented
89#2557C2218yescomplemented
90#2555C2218yescomplemented
91#2548C2212yes—
92#2548C2212yes—
93#2544C2212yes—
94#2544C2214yescomplemented
95#2543C2214yescomplemented
96#2541C2214yes—
97#2541C2211yescharacteristic
98#2541C2214yescomplemented
99#2538C2214yescomplemented
100#2534C2214yes—
101#2521C2218yescomplemented
102#2513C2214yescomplemented
103#2512C2214yescomplemented
104#2507C2214yescomplemented
105#2491C2214yes—
106#2474C2218yescomplemented
107#2470C2218yescomplemented
108#2464C2218yescomplemented
109#2463C2218yes—
110#2461C2218yescomplemented
111#2460C2218yescomplemented
112#2456C2218yescomplemented
113#2456C2218yescomplemented
114#2454C2214yescomplemented
115#2452C2214yescomplemented
116#2452C2214yescomplemented
117#2450C2218yescomplemented
118#2448C2214yescomplemented
119#2445C2214yes—
120#2445C2214yescomplemented
121#2445C2214yescomplemented
122#2435C2212yescomplemented
123#2433C2214yes—
124#2433C2214yescomplemented
125#2430C2214yescomplemented
126#2428C2214yes—
127#2427C2214yes—
128#2427C2218yescomplemented
129#2426C2214yescomplemented
130#2425C2218yescomplemented
131#2424C2218yescomplemented
132#2424C2218yescomplemented
133#2422C2214yescomplemented
134#2414C2218yescomplemented
135#2408C2212yes—
136#2407C2218yescomplemented
137#2401C2214yescomplemented
138#2399C2212yescomplemented
139#2392C2218yescomplemented
140#2388C2214yescomplemented
141#2376C2218yescomplemented
142#2369C2212yescomplemented
143#2367C2214yescomplemented
144#2366C2212yes—
145#2366C2214yescomplemented
146#2361C2214yes—
147#2361C2214yescomplemented
148#2354C2214yescomplemented
149#2345C2212yescomplemented
150C4×#127C2212yes—
151C4×#125C2212yescomplemented
152C4×#124C2211yescharacteristic
153C4×C22⋊Q8C2214yescomplemented
154C4×#123C2212yes—
155C4×#120C2214yes—
156#2293C2214yescomplemented
157#2275C2212yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C22×#41C2314yes—
160C23×D4C2312yes—
161C24×C4C2314yes—
162#562—416no—
163H(3,𝔽4)—48no—
164#560—416no—
165#559—44no—
166#554—44no—
167#550—48no—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2311yescharacteristic
170C2×#127C2312yes—
171C2×#127C2314yes—
172C2×#127C2312yes—
173C2×#127C2311yescharacteristic
174C2×#127C2314yes—
175C2×#127C2312yes—
176C2×#126C2318yes—
177C2×#125C2312yes—
178C2×#125C2312yes—
179C2×#124C2311yescharacteristic
180C2×#124C2314yes—
181C2×#124C2314yes—
182C2×#124C2314yes—
183C2×#124C2312yes—
184C2×#124C2312yes—
185C2×#124C2314yes—
186C2×#124C2318yes—
187C2×#124C2314yes—
188#525—432no—
189C2×#123C2318yes—
190C2×#123C2312yes—
191C2×#123C2314yes—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×#123C2318yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×#121C2318yes—
202C2×#121C2318yes—
203C2×#121C2318yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2318yes—
209C2×#121C2318yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#120C2314yes—
213C2×#120C2318yes—
214C2×#120C2318yes—
215C2×#120C2318yes—
216C2×#120C2318yes—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×D4—48no—
222C2×C4×D4C2314yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2318yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2314yes—
234C2×#117C2318yes—
235C22×C4⋊C4C2312yes—
236C22×C22⋊C4C2314yes—
237C22×C42C2312yes—
238#401C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2314yes—
242#399C2318yes—
243#398C2312yes—
244#398C2318yes—
245#398C2312yes—
246#398C2318yes—
247#398C2314yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2314yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2314yes—
257#397C2314yes—
258#397C2314yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2314yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#395C2318yes—
268#395C2314yes—
269#395C2312yes—
270#395C2312yes—
271#395C2314yes—
272#394C2314yes—
273#394C2314yes—
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#394C2314yes—
288#394C2318yes—
289#394C2318yes—
290#393C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2314yes—
294#392C2318yes—
295#392C2318yes—
296#392C2318yes—
297#392C2314yes—
298#392C2318yes—
299#392C2318yes—
300#392C2318yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2314yes—
305#392C2318yes—
306#392C2314yes—
307#392C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2311yescharacteristic
311#391C2318yes—
312#391C2314yes—
313#390C2311yescharacteristic
314#390C2312yes—
315#390C2318yes—
316#390C2312yes—
317#390C2312yes—
318#390C2314yes—
319#390C2318yes—
320#390C2314yes—
321#390C2314yes—
322#390C2318yes—
323#390C2314yes—
324#390C2318yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#389C2312yes—
336#389C2312yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2314yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2314yes—
359#388C2318yes—
360#387C2314yes—
361#387C2314yes—
362#387C2314yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2314yes—
367#387C2314yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2312yes—
381#385C2318yes—
382#385C2312yes—
383#385C2314yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2314yes—
390#385C2314yes—
391#384C2312yes—
392#384C2314yes—
393#382C2312yes—
394#382C2311yescharacteristic
395#381C2312yes—
396#381C2314yes—
397#380C2314yes—
398#380C2318yes—
399#380C2318yes—
400#380C2314yes—
401#380C2318yes—
402#380C2312yes—
403#379C2314yes—
404#379C2314yes—
405#379C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425#376C2312yes—
426C2×#95C2314yes—
427C43C2311yescharacteristic
428C43C2312yes—
429C25C2414yes—
430C2×#41—48no—
431C2×#41—416no—
432C22×Q8C2411yescharacteristic
433C22×Q8C2412yes—
434C22×Q8C2411yescharacteristic
435C22×Q8C2412yes—
436C22×Q8C2414yes—
437C22×D4—44no—
438C22×D4—48no—
439C22×D4C2412yes—
440C22×D4C2414yes—
441C22×D4C2418yes—
442C22×D4C2418yes—
443C22×D4C2414yes—
444C22×D4C2412yes—
445C22×D4C2418yes—
446C22×D4C2414yes—
447C22×D4C2418yes—
448C22×D4C2414yes—
449C22×D4C2414yes—
450C22×D4C2414yes—
451C22×D4C2418yes—
452C22×D4C2418yes—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C23×C4—48no—
456C23×C4—416no—
457C23×C4C2412yes—
458C23×C4C2418yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2414yes—
462C23×C4C2414yes—
463C23×C4C2418yes—
464C23×C4C2418yes—
465C4⋊Q8—44no—
466C4⋊Q8—42no—
467#127—28no—
468#127—48no—
469#127—44no—
470#127—48no—
471#127—44no—
472#127—42no—
473#126—416no—
474#125—28no—
475#125—44no—
476#124—24no—
477#124—44no—
478#124—48no—
479#124—48no—
480#124—48no—
481#124—48no—
482#124—44no—
483#124—416no—
484#124—48no—
485#123—28no—
486#123—232no—
487#123—416no—
488#123—416no—
489#123—416no—
490#123—48no—
491C22⋊Q8—216no—
492C22⋊Q8—416no—
493C22⋊Q8—416no—
494C22⋊Q8—48no—
495C22⋊Q8—416no—
496C22⋊Q8—44no—
497#121—416no—
498#121—48no—
499#121—416no—
500#121—416no—
501#121—416no—
502#121—416no—
503#121—416no—
504#121—48no—
505#121—48no—
506#121—416no—
507#121—416no—
508#120—216no—
509#120—416no—
510#120—416no—
511#120—416no—
512#120—416no—
513C4×Q8—24no—
514C4×Q8—44no—
515C4×Q8—42no—
516C4×Q8—44no—
517C4×D4—216no—
518C4×D4—216no—
519C4×D4—28no—
520C4×D4—416no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—44no—
524C4×D4—42no—
525C4×D4—44no—
526C4×D4—416no—
527C4×D4—416no—
528C4×D4—416no—
529#117—416no—
530C2×C4⋊C4—28no—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2411yescharacteristic
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2411yescharacteristic
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2412yes—
562C2×C22⋊C4—48no—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2412yes—
598C2×C42—44no—
599C2×C42C2414yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2412yes—
603C2×C42C2411yescharacteristic
604C2×C42C2414yes—
605C2×C42C2412yes—
606C2×C42C2411yescharacteristic
607C2×C42C2412yes—
608C2×C42C2412yes—
609C2×C42C2418yes—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2414yes—
613C2×C42C2411yescharacteristic
614#95C2412yes—
615#95C2418yes—
616#95C2414yes—
617#95C2412yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2412yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641C24—28no—
642C24—44no—
643C24—48no—
644C24—48no—
645C24—44no—
646C24C2518yes—
647C24C2514yes—
648C24C2512yes—
649#41—832no—
650C2×Q8—22no—
651C2×Q8—28no—
652C2×Q8—22no—
653C2×Q8—24no—
654C2×Q8—42no—
655C2×Q8—41no—
656C2×Q8—41no—
657C2×Q8—44no—
658C2×Q8—44no—
659C2×Q8—42no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×D4—216no—
663C2×D4—216no—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—28no—
667C2×D4—216no—
668C2×D4—24no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—41no—
673C2×D4—44no—
674C2×D4—48no—
675C2×D4—41no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—42no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—44no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—48no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—48no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—42no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—44no—
705C2×D4—432no—
706C2×D4H(5,𝔽2)14yes—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—216no—
710C22×C4—216no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—216no—
716C22×C4—42no—
717C22×C4—48no—
718C22×C4—42no—
719C22×C4—48no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—42no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—832no—
728C22×C4C2514yes—
729C22×C4C2512yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2512yes—
735C22×C4C2518yes—
736C22×C4C2512yes—
737C22×C4C2514yes—
738C22×C4C2511yescharacteristic
739C22×C4C2514yes—
740C22×C4C2512yes—
741C22×C4C2514yes—
742C22×C4C2512yes—
743C22×C4C2511yescharacteristic
744C22×C4C2511yescharacteristic
745C4⋊C4—28no—
746C4⋊C4—24no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—216no—
750C4⋊C4—24no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—24no—
755C4⋊C4—28no—
756C4⋊C4—24no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—41no—
762C4⋊C4—48no—
763C4⋊C4—41no—
764C4⋊C4—42no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—42no—
768C4⋊C4—42no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—48no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4H(5,𝔽2)14yes—
775C4⋊C4H(5,𝔽2)18yes—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—24no—
780C22⋊C4—216no—
781C22⋊C4—216no—
782C22⋊C4—216no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—216no—
787C22⋊C4—216no—
788C22⋊C4—216no—
789C22⋊C4—48no—
790C22⋊C4—42no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—44no—
796C22⋊C4—42no—
797C22⋊C4—44no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—44no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C42—28no—
812C42—28no—
813C42—24no—
814C42—24no—
815C42—22no—
816C42—22no—
817C42—24no—
818C42—24no—
819C42—28no—
820C42—24no—
821C42—44no—
822C42—41no—
823C42—48no—
824C42—44no—
825C42—44no—
826C23—24no—
827C23—22no—
828C23—24no—
829C23—22no—
830C23—28no—
831C23—28no—
832C23—28no—
833C23—28no—
834C23—24no—
835C23—28no—
836C23—24no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—24no—
841C23—28no—
842C23—416no—
843C23—816no—
844C23—88no—
845C23—88no—
846C23—816no—
847C23C2×H(5,𝔽2)14yes—
848C23C2611yescharacteristic
849Q8—48no—
850Q8—44no—
851Q8—82no—
852Q8—162no—
853Q8—164no—
854D4—44no—
855D4—416no—
856D4—48no—
857D4—416no—
858D4—84no—
859D4—88no—
860D4—816no—
861D4—816no—
862D4—816no—
863D4—816no—
864D4—88no—
865D4—162no—
866D4—168no—
867D4—164no—
868D4—168no—
869D4—164no—
870C2×C4—21no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—24no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—28no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—28no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—48no—
909C2×C4—432no—
910C2×C4—48no—
911C2×C4—88no—
912C2×C4—816no—
913C2×C4—88no—
914C2×C4—84no—
915C2×C4—168no—
916C2×C4C2×H(5,𝔽2)14yes—
917C2×C4C2×H(5,𝔽2)12yes—
918C2×C4C2×H(5,𝔽2)14yes—
919C2×C4C2×H(5,𝔽2)18yes—
920C2×C4C2×H(5,𝔽2)12yes—
921C2×C4#58514yes—
922C22—28no—
923C22—24no—
924C22—42no—
925C22—42no—
926C22—44no—
927C22—48no—
928C22—44no—
929C22—48no—
930C22—48no—
931C22—48no—
932C22—44no—
933C22—48no—
934C22—48no—
935C22—44no—
936C22—48no—
937C22—48no—
938C22—48no—
939C22—832no—
940C22C22×H(5,𝔽2)12yes—
941C22C22×H(5,𝔽2)11yescharacteristic
942C22C22×H(5,𝔽2)11yescharacteristic
943C22C2×#58512yes—
944C222−1+611yescharacteristic
945C4—24no—
946C4—28no—
947C4—22no—
948C4—24no—
949C4—44no—
950C4—42no—
951C4—41no—
952C4—44no—
953C4—48no—
954C4—44no—
955C4—42no—
956C4—44no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—44no—
961C4#352914yes—
962C2—44no—
963C2—84no—
964C2—88no—
965C2C2×#352911yescharacteristic
966C2#6289511yescharacteristic
967C2#6296012yes—
968C2#6301111yescharacteristic
969C2#6301412yes—
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. #53099C2semidirect
2. #53000C2semidirect
3. #52480C2semidirect
4. #52420C2semidirect
5. #52304C2semidirect
6. #52103C2semidirect
7. #46280C2semidirect
8. #45997C2semidirect
9. #45996C2semidirect
10. #45962C2semidirect
11. #45653C2semidirect
12. #45487C2semidirect
13. #45477C2semidirect
14. #45451C2semidirect
15. #36528C2semidirect
16. #36496C2semidirect
17. #36300C2semidirect
18. #36101C2semidirect
19. #35930C2semidirect
20. #35916C2semidirect
21. C2×#562C22semidirect
24. C2×#559C22semidirect
27. C2×#525C22semidirect
28. C22×C4×D4C22semidirect
29. #2861C22semidirect
30. #2860C22semidirect
32. #2858C22semidirect
34. #2855C22semidirect
35. #2848C22semidirect
36. #2847C22semidirect
37. #2830C22semidirect
38. #2830C22semidirect
39. #2828C22semidirect
40. #2825C22semidirect
41. #2823C22semidirect
43. #2819C22semidirect
45. #2814C22semidirect
46. #2813C22semidirect
47. #2812C22semidirect
48. #2805C22semidirect
49. #2800C22semidirect
50. #2789C22semidirect
51. #2765C22semidirect
55. #2715C22semidirect
56. #2714C22semidirect
57. #2703C22semidirect
58. #2701C22semidirect
59. #2692C22semidirect
60. #2690C22semidirect
61. #2686C22semidirect
63. #2683C22semidirect
64. #2682C22semidirect
65. #2682C22semidirect
66. #2681C22semidirect
67. #2680C22semidirect
69. #2678C22semidirect
70. #2678C22semidirect
71. #2678C22semidirect
72. #2676C22semidirect
73. #2676C22semidirect
75. #2672C22semidirect
78. #2668C22semidirect
79. #2661C22semidirect
81. #2653C22semidirect
82. #2644C22semidirect
83. #2595C22semidirect
84. #2592C22semidirect
85. #2567C22semidirect
86. #2567C22semidirect
87. #2566C22semidirect
88. #2561C22semidirect
89. #2557C22semidirect
90. #2555C22semidirect
94. #2544C22semidirect
95. #2543C22semidirect
98. #2541C22semidirect
99. #2538C22semidirect
101. #2521C22semidirect
102. #2513C22semidirect
103. #2512C22semidirect
104. #2507C22semidirect
106. #2474C22semidirect
107. #2470C22semidirect
108. #2464C22semidirect
110. #2461C22semidirect
111. #2460C22semidirect
112. #2456C22semidirect
113. #2456C22semidirect
114. #2454C22semidirect
115. #2452C22semidirect
116. #2452C22semidirect
117. #2450C22semidirect
118. #2448C22semidirect
120. #2445C22semidirect
121. #2445C22semidirect
122. #2435C22semidirect
124. #2433C22semidirect
125. #2430C22semidirect
128. #2427C22semidirect
129. #2426C22semidirect
130. #2425C22semidirect
131. #2424C22semidirect
132. #2424C22semidirect
133. #2422C22semidirect
134. #2414C22semidirect
136. #2407C22semidirect
137. #2401C22semidirect
138. #2399C22semidirect
139. #2392C22semidirect
140. #2388C22semidirect
141. #2376C22semidirect
142. #2369C22semidirect
143. #2367C22semidirect
145. #2366C22semidirect
147. #2361C22semidirect
148. #2354C22semidirect
149. #2345C22semidirect
151. C4×#125C22semidirect
153. C4×C22⋊Q8C22semidirect
156. #2293C22semidirect
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
#530992
#530002
#524802
#524202
#523042
#521032
#462802
#459972
#459962
#459622
#456532
#454872
#454772
#454512
#365282
#364962
#363002
#361012
#359302
#359162