Finite Group Databasebeta

← #7715024

Subgroups — #7715024

Order 512.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51940C214yesmaximal, complemented
2#51930C214yesmaximal, complemented
3#51831C214yesmaximal, complemented
4#51815C214yesmaximal, complemented
5#46600C218yesmaximal, complemented
6#46504C218yesmaximal, complemented
7#39565C214yesmaximal, complemented
8#39434C214yesmaximal, complemented
9#37857C214yesmaximal, complemented
10#37662C214yesmaximal, complemented
11#37515C212yesmaximal, complemented
12#37425C211yesmaximal, characteristic, complemented
13#37317C212yesmaximal, complemented
14#37297C211yesmaximal, characteristic, complemented
15#35261C212yesmaximal, complemented
16#35261C212yesmaximal, complemented
17#35250C212yesmaximal, complemented
18#34415C212yesmaximal, complemented
19#34044C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C2×#540C2212yes—
22C2×#540C2212yescomplemented
23C2×#535C2212yes—
24C2×#535C2212yescomplemented
25C22×#121C2212yescomplemented
26C22×#117C2211yescharacteristic, complemented
27C22×#117C2211yescharacteristic, complemented
28#2856C2212yescomplemented
29#2856C2212yescomplemented
30#2851C2212yescomplemented
31#2851C2212yescomplemented
32#2847C2214yes—
33#2847C2214yescomplemented
34#2825C2218yescomplemented
35#2809C2214yescomplemented
36#2797C2218yescomplemented
37#2780C2218yescomplemented
38#2778C2218yescomplemented
39#2754C2218yescomplemented
40#2753C2218yescomplemented
41#2751C2218yescomplemented
42#2748C2214yescomplemented
43#2746C2218yescomplemented
44#2740C2218yescomplemented
45#2733C2214yescomplemented
46#2714C2218yescomplemented
47#2714C2218yescomplemented
48#2710C2218yescomplemented
49#2703C2218yescomplemented
50#2699C2218yescomplemented
51#2697C2218yescomplemented
52#2688C2218yescomplemented
53#2688C2218yescomplemented
54#2685C2218yescomplemented
55#2679C2214yescomplemented
56#2678C2218yescomplemented
57#2673C2218yescomplemented
58#2671C2218yescomplemented
59#2669C2218yescomplemented
60#2668C2218yescomplemented
61#2661C2218yescomplemented
62#2653C2218yescomplemented
63#2629C2212yescomplemented
64#2629C2212yescomplemented
65#2624C2214yescomplemented
66#2624C2214yescomplemented
67#2619C2212yes—
68#2619C2212yescomplemented
69#2615C2214yes—
70#2615C2214yescomplemented
71#2603C2218yescomplemented
72#2600C2218yescomplemented
73#2576C2218yescomplemented
74#2557C2218yescomplemented
75#2553C2218yescomplemented
76#2539C2218yescomplemented
77#2531C2218yescomplemented
78#2527C2218yescomplemented
79#2526C2218yescomplemented
80#2500C2214yescomplemented
81#2496C2214yescomplemented
82#2494C2214yescomplemented
83#2490C2214yescomplemented
84#2490C2214yescomplemented
85#2476C2218yescomplemented
86#2476C2218yescomplemented
87#2471C2218yescomplemented
88#2471C2218yescomplemented
89#2467C2218yescomplemented
90#2456C2218yescomplemented
91#2443C2218yescomplemented
92#2443C2218yescomplemented
93#2442C2214yescomplemented
94#2441C2214yescomplemented
95#2436C2214yescomplemented
96#2433C2214yes—
97#2433C2214yescomplemented
98#2431C2214yes—
99#2431C2214yescomplemented
100#2428C2214yescomplemented
101#2428C2214yescomplemented
102#2428C2218yescomplemented
103#2424C2218yescomplemented
104#2424C2218yescomplemented
105#2424C2218yescomplemented
106#2422C2214yescomplemented
107#2420C2214yescomplemented
108#2418C2218yescomplemented
109#2412C2218yescomplemented
110#2410C2218yescomplemented
111#2408C2218yescomplemented
112#2404C2214yes—
113#2404C2214yescomplemented
114#2403C2214yes—
115#2403C2214yescomplemented
116#2379C2214yescomplemented
117#2375C2214yescomplemented
118#2372C2214yescomplemented
119#2363C2214yescomplemented
120#2361C2214yescomplemented
121#2358C2214yescomplemented
122#2346C2214yescomplemented
123D4×C22⋊C4C2214yescomplemented
124#2328C2218yescomplemented
125#2324C2214yescomplemented
126#2324C2214yescomplemented
127#2321C2218yescomplemented
128#2314C2212yescomplemented
129#2314C2212yescomplemented
130#2311C2212yes—
131#2311C2212yes—
132#2311C2214yescomplemented
133#2311C2212yescomplemented
134#2311C2212yescomplemented
135#2310C2212yescomplemented
136#2309C2212yes—
137#2308C2214yescomplemented
138C4×#121C2214yescomplemented
139C4×#121C2214yescomplemented
140#2297C2211yescharacteristic
141#2297C2211yescharacteristic
142#2297C2214yescomplemented
143#2297C2211yescharacteristic, complemented
144#2297C2211yescharacteristic, complemented
145#2280C2214yescomplemented
146#2280C2212yescomplemented
147C22×#41—28no—
148C22×#41—44no—
149C22×#41—44no—
150C22×#41C2312yes—
151C22×#41C2311yescharacteristic
152C22×#41C2312yes—
153C22×#41C2311yescharacteristic
154C22×#41C2311yescharacteristic
155C22×#41C2311yescharacteristic
156C23×Q8C2311yescharacteristic
157C23×D4C2312yes—
158C23×D4C2311yescharacteristic
159C23×D4C2312yes—
160C23×D4C2314yes—
161C24×C4C2311yescharacteristic
162C24×C4C2312yes—
163#540—48no—
164#540—48no—
165#535—216no—
166#535—48no—
167C2×#127C2314yes—
168C2×#127C2312yes—
169C2×#127C2312yes—
170C2×#127C2314yes—
171C2×#126C2318yes—
172C2×#125C2312yes—
173C2×#125C2312yes—
174C2×#124C2314yes—
175C2×#124C2314yes—
176C2×#123C2318yes—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×#121—48no—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2314yes—
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2318yes—
187C2×#121C2314yes—
188C2×#121C2314yes—
189C2×#121C2318yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#121C2318yes—
193C2×#121C2318yes—
194C2×#120C2314yes—
195C2×#120C2314yes—
196C2×#120C2314yes—
197C2×#120C2314yes—
198C2×#120C2318yes—
199C2×#120C2318yes—
200C2×#120C2318yes—
201C2×#120C2318yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2318yes—
207C2×#117—44no—
208C2×#117—44no—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2312yes—
219C2×#117C2311yescharacteristic
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2318yes—
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229C22×C42C2311yescharacteristic
230#401C2318yes—
231#400C2318yes—
232#400C2318yes—
233#399C2318yes—
234#399C2318yes—
235#399C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2318yes—
264#393C2318yes—
265#393C2318yes—
266#392C2318yes—
267#392C2318yes—
268#392C2318yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#392C2318yes—
273#392C2318yes—
274#392C2318yes—
275#392C2318yes—
276#392C2318yes—
277#392C2318yes—
278#391C2312yes—
279#391C2312yes—
280#391C2312yes—
281#391C2314yes—
282#391C2312yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#390C2312yes—
287#390C2312yes—
288#390C2312yes—
289#390C2314yes—
290#390C2312yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2318yes—
295#390C2314yes—
296#390C2314yes—
297#390C2318yes—
298#390C2318yes—
299#390C2314yes—
300#390C2318yes—
301#390C2318yes—
302#390C2318yes—
303#390C2314yes—
304#390C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#386C2314yes—
333#386C2314yes—
334#386C2314yes—
335#386C2314yes—
336#386C2314yes—
337#386C2314yes—
338#386C2314yes—
339#386C2314yes—
340#386C2314yes—
341#386C2314yes—
342#386C2314yes—
343#386C2314yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#384C2312yes—
369#384C2312yes—
370#382C2312yes—
371#382C2312yes—
372#382C2318yes—
373#381C2314yes—
374#381C2314yes—
375#381C2318yes—
376#381C2314yes—
377#380C2314yes—
378#380C2314yes—
379#380C2314yes—
380#380C2314yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2314yes—
387#380C2318yes—
388#379C2314yes—
389#379C2314yes—
390#379C2318yes—
391#379C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2318yes—
396C4×C22⋊C4C2314yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2314yes—
399C4×C22⋊C4C2314yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2318yes—
403#376C2318yes—
404C25C2411yescharacteristic
405C25C2412yes—
406C25C2414yes—
407C2×#41—24no—
408C2×#41—28no—
409C2×#41—24no—
410C2×#41—28no—
411C2×#41—24no—
412C2×#41—28no—
413C2×#41—44no—
414C2×#41—42no—
415C2×#41—42no—
416C2×#41—42no—
417C2×#41—42no—
418C2×#41—42no—
419C2×#41—44no—
420C2×#41—42no—
421C2×#41—42no—
422C2×#41—42no—
423C2×#41—44no—
424C2×#41—464no—
425C2×#41#4118yes—
426C22×Q8—24no—
427C22×Q8—42no—
428C22×Q8—42no—
429C22×Q8C2412yes—
430C22×Q8C2411yescharacteristic
431C22×Q8C2411yescharacteristic
432C22×D4—24no—
433C22×D4—28no—
434C22×D4—28no—
435C22×D4—42no—
436C22×D4—44no—
437C22×D4—44no—
438C22×D4—42no—
439C22×D4—44no—
440C22×D4—44no—
441C22×D4—48no—
442C22×D4—88no—
443C22×D4C2414yes—
444C22×D4C2412yes—
445C22×D4C2412yes—
446C22×D4C2412yes—
447C22×D4C2418yes—
448C22×D4C2418yes—
449C22×D4C2418yes—
450C22×D4C2418yes—
451C22×D4C2414yes—
452C22×D4C2412yes—
453C22×D4C2411yescharacteristic
454C22×D4C2418yes—
455C22×D4C2418yes—
456C22×D4C2418yes—
457C22×D4C2418yes—
458C22×D4C2411yescharacteristic
459C22×D4C2412yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—28no—
464C23×C4—28no—
465C23×C4—44no—
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2414yes—
480C23×C4C2412yes—
481C23×C4C2418yes—
482C23×C4C2418yes—
483#127—216no—
484#127—44no—
485#127—44no—
486#127—48no—
487#126—88no—
488#125—44no—
489#125—44no—
490#124—216no—
491#124—48no—
492#123—416no—
493#123—416no—
494#123—88no—
495#121—216no—
496#121—216no—
497#121—216no—
498#121—216no—
499#121—48no—
500#121—416no—
501#121—416no—
502#121—48no—
503#121—48no—
504#121—48no—
505#121—88no—
506#121—88no—
507#121—88no—
508#121—88no—
509#120—216no—
510#120—216no—
511#120—48no—
512#120—48no—
513#120—88no—
514#120—88no—
515#120—88no—
516#120—88no—
517C4×D4—48no—
518C4×D4—48no—
519C4×D4—88no—
520C4×D4—88no—
521C4×D4—88no—
522#117—28no—
523#117—28no—
524#117—28no—
525#117—42no—
526#117—44no—
527#117—42no—
528#117—44no—
529#117—44no—
530#117—44no—
531#117—44no—
532#117—44no—
533C2×C4⋊C4—44no—
534C2×C4⋊C4—44no—
535C2×C4⋊C4—44no—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C22⋊C4—48no—
554C2×C22⋊C4—44no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4—88no—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2414yes—
594C2×C42—42no—
595C2×C42—44no—
596C2×C42—42no—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2418yes—
607C2×C42C2418yes—
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—24no—
634C24—24no—
635C24—28no—
636C24—42no—
637C24—44no—
638C24—44no—
639C24—44no—
640C24—44no—
641C24—48no—
642C24—48no—
643C24—44no—
644C24C2518yes—
645C24C2512yes—
646C24C2512yes—
647C24C2511yescharacteristic
648C24C2511yescharacteristic
649C24C2511yescharacteristic
650#41—416no—
651#41—432no—
652#41—416no—
653#41—432no—
654#41—416no—
655#41—416no—
656C2×Q8—24no—
657C2×Q8—22no—
658C2×Q8—24no—
659C2×Q8—41no—
660C2×Q8—42no—
661C2×Q8—41no—
662C2×Q8—41no—
663C2×Q8—41no—
664C2×Q8—416no—
665C2×Q8C2×#4114yes—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—216no—
672C2×D4—216no—
673C2×D4—216no—
674C2×D4—216no—
675C2×D4—28no—
676C2×D4—24no—
677C2×D4—22no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—41no—
683C2×D4—42no—
684C2×D4—41no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—416no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—432no—
717C2×D4—816no—
718C2×D4—832no—
719C2×D4C2×#4114yes—
720C2×D4C2×#4118yes—
721C22×C4—232no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—432no—
752C22×C4—42no—
753C22×C4—44no—
754C22×C4—42no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—48no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4C2×#4118yes—
768C22×C4C2×#4114yes—
769C22×C4H(5,𝔽2)14yes—
770C22×C4H(5,𝔽2)14yes—
771C22×C4C2512yes—
772C22×C4C2518yes—
773C22×C4C2518yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2518yes—
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—44no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—44no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—216no—
805C22⋊C4—216no—
806C22⋊C4—216no—
807C22⋊C4—216no—
808C22⋊C4—42no—
809C22⋊C4—44no—
810C22⋊C4—42no—
811C22⋊C4—48no—
812C22⋊C4—44no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—44no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—44no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C42—28no—
839C42—24no—
840C42—24no—
841C42—24no—
842C42—24no—
843C42—42no—
844C42—44no—
845C42—42no—
846C42—44no—
847C42—48no—
848C42—48no—
849C23—28no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—22no—
855C23—21no—
856C23—21no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—28no—
864C23—22no—
865C23—28no—
866C23—28no—
867C23—22no—
868C23—22no—
869C23—24no—
870C23—28no—
871C23—28no—
872C23—28no—
873C23—24no—
874C23—28no—
875C23—48no—
876C23—48no—
877C23—84no—
878C23—88no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—88no—
883C23—816no—
884C23—88no—
885C23—88no—
886C23—88no—
887C23—168no—
888C23C22×#4114yes—
889C23C22×#4112yes—
890C23C2×H(5,𝔽2)12yes—
891C23C2×H(5,𝔽2)12yes—
892C23C2611yescharacteristic
893Q8—44no—
894Q8—48no—
895Q8—44no—
896D4—44no—
897D4—48no—
898D4—48no—
899D4—48no—
900D4—44no—
901D4—48no—
902D4—48no—
903D4—416no—
904D4—88no—
905D4—816no—
906D4—816no—
907D4—816no—
908D4—816no—
909D4—816no—
910D4—168no—
911D4—168no—
912D4—168no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—216no—
928C2×C4—28no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—28no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—24no—
952C2×C4—48no—
953C2×C4—48no—
954C2×C4—48no—
955C2×C4—48no—
956C2×C4—88no—
957C2×C4—84no—
958C2×C4—84no—
959C2×C4—88no—
960C2×C4—168no—
961C2×C4—168no—
962C2×C4C22×#4114yes—
963C2×C4C22×#4112yes—
964C2×C4C22×#4112yes—
965C2×C4C2×H(5,𝔽2)12yes—
966C2×C4C2×H(5,𝔽2)12yes—
967C2×C4C2×H(5,𝔽2)12yes—
968C2×C4C2×H(5,𝔽2)12yes—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—24no—
973C22—24no—
974C22—28no—
975C22—24no—
976C22—24no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—44no—
986C22—42no—
987C22—48no—
988C22—48no—
989C22—48no—
990C22—44no—
991C22—48no—
992C22—42no—
993C22—48no—
994C22—42no—
995C22—48no—
996C22—48no—
997C22—44no—
998C22—88no—
999C22—816no—
1000C22—1616no—
1001C22C23×#4111yescharacteristic
1002C22C22×H(5,𝔽2)11yescharacteristic
1003C22C22×H(5,𝔽2)11yescharacteristic
1004C22H(7,𝔽2)14yes—
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—24no—
1009C4—42no—
1010C4—48no—
1011C4—44no—
1012C4—48no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—48no—
1017C4#349014yes—
1018C2—42no—
1019C2—42no—
1020C2—42no—
1021C2—44no—
1022C2—82no—
1023C2—88no—
1024C2C2×#349011yescharacteristic
1025C2#6285812yes—
1026C2#6287412yes—
1027C2#6288012yes—
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. #51940C2semidirect
2. #51930C2semidirect
3. #51831C2semidirect
4. #51815C2semidirect
5. #46600C2semidirect
6. #46504C2semidirect
7. #39565C2semidirect
8. #39434C2semidirect
9. #37857C2semidirect
10. #37662C2semidirect
11. #37515C2semidirect
12. #37425C2semidirect
13. #37317C2semidirect
14. #37297C2semidirect
15. #35261C2semidirect
16. #35261C2semidirect
17. #35250C2semidirect
18. #34415C2semidirect
19. #34044C2semidirect
22. C2×#540C22semidirect
24. C2×#535C22semidirect
25. C22×#121C22semidirect
26. C22×#117C22semidirect
27. C22×#117C22semidirect
28. #2856C22semidirect
29. #2856C22semidirect
30. #2851C22semidirect
31. #2851C22semidirect
33. #2847C22semidirect
34. #2825C22semidirect
35. #2809C22semidirect
36. #2797C22semidirect
37. #2780C22semidirect
38. #2778C22semidirect
39. #2754C22semidirect
40. #2753C22semidirect
41. #2751C22semidirect
42. #2748C22semidirect
43. #2746C22semidirect
44. #2740C22semidirect
45. #2733C22semidirect
46. #2714C22semidirect
47. #2714C22semidirect
48. #2710C22semidirect
49. #2703C22semidirect
50. #2699C22semidirect
51. #2697C22semidirect
52. #2688C22semidirect
53. #2688C22semidirect
54. #2685C22semidirect
55. #2679C22semidirect
56. #2678C22semidirect
57. #2673C22semidirect
58. #2671C22semidirect
59. #2669C22semidirect
60. #2668C22semidirect
61. #2661C22semidirect
62. #2653C22semidirect
63. #2629C22semidirect
64. #2629C22semidirect
65. #2624C22semidirect
66. #2624C22semidirect
68. #2619C22semidirect
70. #2615C22semidirect
71. #2603C22semidirect
72. #2600C22semidirect
73. #2576C22semidirect
74. #2557C22semidirect
75. #2553C22semidirect
76. #2539C22semidirect
77. #2531C22semidirect
78. #2527C22semidirect
79. #2526C22semidirect
80. #2500C22semidirect
81. #2496C22semidirect
82. #2494C22semidirect
83. #2490C22semidirect
84. #2490C22semidirect
85. #2476C22semidirect
86. #2476C22semidirect
87. #2471C22semidirect
88. #2471C22semidirect
89. #2467C22semidirect
90. #2456C22semidirect
91. #2443C22semidirect
92. #2443C22semidirect
93. #2442C22semidirect
94. #2441C22semidirect
95. #2436C22semidirect
97. #2433C22semidirect
99. #2431C22semidirect
100. #2428C22semidirect
101. #2428C22semidirect
102. #2428C22semidirect
103. #2424C22semidirect
104. #2424C22semidirect
105. #2424C22semidirect
106. #2422C22semidirect
107. #2420C22semidirect
108. #2418C22semidirect
109. #2412C22semidirect
110. #2410C22semidirect
111. #2408C22semidirect
113. #2404C22semidirect
115. #2403C22semidirect
116. #2379C22semidirect
117. #2375C22semidirect
118. #2372C22semidirect
119. #2363C22semidirect
120. #2361C22semidirect
121. #2358C22semidirect
122. #2346C22semidirect
123. D4×C22⋊C4C22semidirect
124. #2328C22semidirect
125. #2324C22semidirect
126. #2324C22semidirect
127. #2321C22semidirect
128. #2314C22semidirect
129. #2314C22semidirect
132. #2311C22semidirect
133. #2311C22semidirect
134. #2311C22semidirect
135. #2310C22semidirect
137. #2308C22semidirect
138. C4×#121C22semidirect
139. C4×#121C22semidirect
142. #2297C22semidirect
143. #2297C22semidirect
144. #2297C22semidirect
145. #2280C22semidirect
146. #2280C22semidirect

Maximal subgroups

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

subgroupindex
#519402
#519302
#518312
#518152
#466002
#465042
#395652
#394342
#378572
#376622
#375152
#374252
#373172
#372972
#352612
#352502
#344152
#340442