Finite Group Databasebeta

← #7718468

Subgroups — #7718468

Order 512.

5576 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51921C218yesmaximal, complemented
2#51918C218yesmaximal, complemented
3#44102C214yesmaximal, complemented
4#43963C214yesmaximal, complemented
5#43509C214yesmaximal, complemented
6#43080C214yesmaximal, complemented
7#39807C214yesmaximal, complemented
8#37770C214yesmaximal, complemented
9#37693C214yesmaximal, complemented
10#36978C212yesmaximal, complemented
11#36731C212yesmaximal, complemented
12#36107C214yesmaximal, complemented
13#35119C212yesmaximal, complemented
14#35076C212yesmaximal, complemented
15#35052C211yesmaximal, characteristic, complemented
16#35003C212yesmaximal, complemented
17C2×#2656C211yesmaximal, characteristic, complemented
18#34379C212yesmaximal, complemented
19C2×#2353C211yesmaximal, characteristic, complemented
20C2×#538C2214yescomplemented
21C2×#529C2214yescomplemented
22C22×#121C2212yes—
23C22×#121C2214yes—
24C22×C4×D4C2211yescharacteristic
25#2854C2214yescomplemented
26#2854C2214yescomplemented
27#2850C2214yescomplemented
28#2848C2214yes—
29#2847C2214yescomplemented
30#2803C2218yescomplemented
31#2798C2218yescomplemented
32#2797C2218yescomplemented
33#2777C2218yescomplemented
34#2771C2218yescomplemented
35#2756C2218yescomplemented
36#2749C2218yescomplemented
37#2743C2218yescomplemented
38#2740C2218yescomplemented
39#2738C2218yescomplemented
40#2733C2218yescomplemented
41#2727C2218yescomplemented
42#2714C2218yescomplemented
43#2714C2218yescomplemented
44#2703C2218yescomplemented
45#2699C2218yescomplemented
46#2694C2218yescomplemented
47#2688C2218yescomplemented
48#2688C2218yescomplemented
49#2676C2218yescomplemented
50#2659C2212yescomplemented
51#2656C2212yes—
52#2656C2212yes—
53#2656C2214yes—
54#2656C2218yescomplemented
55#2646C2212yescomplemented
56#2639C2214yescomplemented
57#2635C2214yescomplemented
58#2635C2214yescomplemented
59#2617C2214yescomplemented
60#2611C2218yescomplemented
61#2610C2218yescomplemented
62#2604C2218yescomplemented
63#2603C2218yescomplemented
64#2600C2218yescomplemented
65#2596C2218yescomplemented
66#2591C2214yescomplemented
67#2575C2218yescomplemented
68#2569C2214yescomplemented
69#2559C2218yescomplemented
70#2555C2218yescomplemented
71#2553C2218yescomplemented
72#2549C2214yescomplemented
73#2539C2214yescomplemented
74#2521C2218yescomplemented
75#2490C2214yescomplemented
76#2487C2212yes—
77#2487C2212yes—
78#2481C2218yes—
79#2480C2218yescomplemented
80#2479C2218yescomplemented
81#2476C2218yescomplemented
82#2472C2218yes—
83#2464C2218yescomplemented
84#2459C2218yescomplemented
85#2456C2218yescomplemented
86#2448C2218yescomplemented
87#2444C2218yescomplemented
88#2444C2218yescomplemented
89#2442C2214yescomplemented
90#2438C2218yescomplemented
91#2435C2214yescomplemented
92#2427C2214yescomplemented
93#2426C2214yescomplemented
94#2425C2218yescomplemented
95#2424C2218yescomplemented
96#2420C2214yescomplemented
97#2414C2214yescomplemented
98#2414C2214yescomplemented
99#2414C2218yescomplemented
100#2412C2218yes—
101#2410C2218yes—
102#2408C2212yes—
103#2408C2212yes—
104#2405C2214yes—
105#2403C2214yes—
106C2×#399C2214yescomplemented
107C2×#392C2214yescomplemented
108#2377C2218yescomplemented
109#2361C2218yescomplemented
110#2360C2214yescomplemented
111#2353C2214yes—
112#2353C2214yes—
113#2353C2214yescomplemented
114#2353C2214yescomplemented
115#2345C2214yescomplemented
116#2342C2218yescomplemented
117D4×C22⋊C4C2218yes—
118D4×C22⋊C4C2214yescomplemented
119D4×C22⋊C4C2214yescomplemented
120#2329C2214yescomplemented
121#2325C2214yescomplemented
122#2325C2214yescomplemented
123#2325C2214yescomplemented
124#2324C2218yescomplemented
125#2321C2214yes—
126#2321C2214yes—
127#2315C2214yescomplemented
128#2312C2214yescomplemented
129C4×#121C2214yescomplemented
130C2×#388C2212yescomplemented
131C2×#387C2212yescomplemented
132C2×#386C2212yes—
133C2×#383C2211yescharacteristic, complemented
134#2280C2212yes—
135C2×#381C2211yescharacteristic, complemented
136C2×#380C2211yescharacteristic
137C2×C4×C22⋊C4C2212yes—
138C2×C4×C22⋊C4C2211yescharacteristic, complemented
139C2×#376C2211yescharacteristic, complemented
140C22×#95C2211yescharacteristic
141C23×D4C2314yes—
142C23×D4C2311yescharacteristic
143C23×D4C2312yes—
144C23×D4C2314yes—
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148#538—416no—
149#529—416no—
150C2×#126C2318yes—
151C2×#126C2318yes—
152C2×#125C2314yes—
153C2×#124C2314yes—
154C2×#124C2318yes—
155C2×#124C2314yes—
156C2×#123C2318yes—
157C2×#123C2318yes—
158C2×C22⋊Q8C2314yes—
159C2×C22⋊Q8C2314yes—
160C2×C22⋊Q8C2314yes—
161C2×#121—216no—
162C2×#121—416no—
163C2×#121C2314yes—
164C2×#121C2314yes—
165C2×#121C2314yes—
166C2×#121C2314yes—
167C2×#121C2314yes—
168C2×#121C2314yes—
169C2×#121C2318yes—
170C2×#121C2314yes—
171C2×#121C2318yes—
172C2×#121C2314yes—
173C2×#121C2318yes—
174C2×#121C2314yes—
175C2×#121C2314yes—
176C2×#121C2318yes—
177C2×#120C2314yes—
178C2×#120C2314yes—
179C2×#120C2318yes—
180C2×C4×Q8C2314yes—
181C2×C4×D4—28no—
182C2×C4×D4C2312yes—
183C2×C4×D4C2312yes—
184C2×C4×D4C2312yes—
185C2×C4×D4C2312yes—
186C2×C4×D4C2318yes—
187C2×C4×D4C2318yes—
188C2×C4×D4C2314yes—
189C2×C4×D4C2318yes—
190C2×C4×D4C2314yes—
191C2×#117C2318yes—
192C2×#117C2314yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2314yes—
196C22×C4⋊C4C2312yes—
197C22×C22⋊C4C2314yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2318yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2318yes—
204C22×C22⋊C4C2312yes—
205C22×C42C2311yescharacteristic
206C22×C42C2312yes—
207C22×C42C2312yes—
208#400C2318yes—
209#400C2314yes—
210#400C2318yes—
211#400C2314yes—
212#400C2318yes—
213#400C2318yes—
214#399C2318yes—
215#399C2318yes—
216#399C2318yes—
217#399C2314yes—
218#399C2314yes—
219#399C2318yes—
220#398C2318yes—
221#398C2318yes—
222#398C2318yes—
223#397C2318yes—
224#397C2318yes—
225#397C2318yes—
226#397C2318yes—
227#397C2318yes—
228#397C2318yes—
229#397C2318yes—
230#396C2318yes—
231#396C2318yes—
232#395C2318yes—
233#394C2314yes—
234#394C2314yes—
235#394C2318yes—
236#394C2318yes—
237#394C2318yes—
238#394C2318yes—
239#394C2318yes—
240#394C2318yes—
241#394C2318yes—
242#394C2318yes—
243#394C2318yes—
244#394C2318yes—
245#393C2318yes—
246#392C2318yes—
247#392C2318yes—
248#392C2318yes—
249#392C2318yes—
250#392C2318yes—
251#392C2314yes—
252#392C2314yes—
253#392C2318yes—
254#392C2318yes—
255#392C2318yes—
256#391C2318yes—
257#391C2314yes—
258#390C2318yes—
259#390C2318yes—
260#390C2318yes—
261#390C2318yes—
262#390C2318yes—
263#390C2314yes—
264#390C2314yes—
265#390C2314yes—
266#390C2314yes—
267#390C2314yes—
268#390C2318yes—
269#390C2314yes—
270#389C2318yes—
271#389C2318yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2318yes—
277#389C2314yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#386C2318yes—
308#386C2318yes—
309#386C2314yes—
310#386C2314yes—
311#386C2318yes—
312#386C2318yes—
313#386C2318yes—
314#386C2318yes—
315#386C2318yes—
316#386C2318yes—
317#386C2318yes—
318#386C2318yes—
319#386C2318yes—
320#386C2318yes—
321#386C2318yes—
322#386C2318yes—
323#386C2318yes—
324#386C2318yes—
325#386C2318yes—
326#385C2318yes—
327#385C2318yes—
328#385C2318yes—
329#385C2318yes—
330#385C2318yes—
331#385C2314yes—
332#385C2314yes—
333#385C2318yes—
334#385C2318yes—
335#385C2318yes—
336#383C2314yes—
337#383C2314yes—
338#382C2314yes—
339#381C2318yes—
340#381C2318yes—
341#381C2314yes—
342#381C2314yes—
343#381C2314yes—
344#380C2312yes—
345#380C2314yes—
346#380C2312yes—
347#380C2314yes—
348#380C2318yes—
349#380C2314yes—
350#380C2314yes—
351#380C2314yes—
352#380C2314yes—
353#380C2314yes—
354#380C2314yes—
355#380C2318yes—
356#379C2318yes—
357#379C2314yes—
358#379C2314yes—
359#379C2314yes—
360C4×C4⋊C4C2318yes—
361C4×C4⋊C4C2314yes—
362C4×C22⋊C4C2318yes—
363C4×C22⋊C4C2314yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2314yes—
366C4×C22⋊C4C2314yes—
367C4×C22⋊C4C2314yes—
368C4×C22⋊C4C2314yes—
369C4×C22⋊C4C2314yes—
370C4×C22⋊C4C2314yes—
371C4×C22⋊C4C2314yes—
372#376C2314yes—
373#376C2314yes—
374C2×#95C2314yes—
375C2×#95C2311yescharacteristic
376C2×#95C2311yescharacteristic
377C2×#95C2312yes—
378C2×#95C2312yes—
379C2×#95C2314yes—
380C2×#95C2311yescharacteristic
381C2×#95C2311yescharacteristic
382C2×#95C2312yes—
383C2×#95C2312yes—
384C2×#95C2312yes—
385C25C2411yescharacteristic
386C25C2411yescharacteristic
387C25C2414yes—
388C22×Q8C2414yes—
389C22×D4—24no—
390C22×D4—216no—
391C22×D4—28no—
392C22×D4—48no—
393C22×D4—48no—
394C22×D4—42no—
395C22×D4—42no—
396C22×D4—416no—
397C22×D4—84no—
398C22×D4—84no—
399C22×D4C2412yes—
400C22×D4C2418yes—
401C22×D4C2414yes—
402C22×D4C2414yes—
403C22×D4C2412yes—
404C22×D4C2418yes—
405C22×D4C2414yes—
406C22×D4C2414yes—
407C22×D4C2418yes—
408C22×D4C2418yes—
409C22×D4C2418yes—
410C23×C4—24no—
411C23×C4—28no—
412C23×C4—44no—
413C23×C4—82no—
414C23×C4—82no—
415C23×C4—82no—
416C23×C4#4118yes—
417C23×C4C2411yescharacteristic
418C23×C4C2414yes—
419C23×C4C2414yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2414yes—
428C23×C4C2418yes—
429C23×C4C2418yes—
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435#126—416no—
436#126—416no—
437#125—48no—
438#124—48no—
439#124—416no—
440#124—84no—
441#123—416no—
442#123—416no—
443C22⋊Q8—216no—
444C22⋊Q8—48no—
445C22⋊Q8—84no—
446#121—216no—
447#121—216no—
448#121—216no—
449#121—216no—
450#121—216no—
451#121—216no—
452#121—416no—
453#121—416no—
454#121—48no—
455#121—48no—
456#121—416no—
457#121—88no—
458#121—84no—
459#121—84no—
460#120—48no—
461#120—48no—
462#120—416no—
463C4×Q8—48no—
464C4×D4—28no—
465C4×D4—28no—
466C4×D4—28no—
467C4×D4—28no—
468C4×D4—48no—
469C4×D4—416no—
470C4×D4—416no—
471C4×D4—84no—
472C4×D4—88no—
473#117—416no—
474#117—84no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—28no—
477C2×C4⋊C4—48no—
478C2×C4⋊C4—82no—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2418yes—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—216no—
502C2×C22⋊C4—28no—
503C2×C22⋊C4—416no—
504C2×C22⋊C4—44no—
505C2×C22⋊C4—416no—
506C2×C22⋊C4—82no—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2411yescharacteristic
511C2×C22⋊C4C2411yescharacteristic
512C2×C22⋊C4C2411yescharacteristic
513C2×C22⋊C4C2411yescharacteristic
514C2×C22⋊C4C2412yes—
515C2×C22⋊C4C2412yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2414yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2418yes—
541C2×C42—24no—
542C2×C42—28no—
543C2×C42—82no—
544C2×C42C2414yes—
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2414yes—
548C2×C42C2418yes—
549C2×C42C2418yes—
550C2×C42C2418yes—
551C2×C42C2414yes—
552C2×C42C2414yes—
553#95C2414yes—
554#95C2414yes—
555#95C2418yes—
556#95C2414yes—
557#95C2418yes—
558#95C2414yes—
559#95C2414yes—
560#95C2414yes—
561#95C2414yes—
562#95C2414yes—
563#95C2418yes—
564#95C2418yes—
565#95C2414yes—
566#95C2418yes—
567#95C2414yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576#95C2418yes—
577#95C2418yes—
578C24—24no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—28no—
583C24—24no—
584C24—28no—
585C24—28no—
586C24—42no—
587C24—42no—
588C24—41no—
589C24—41no—
590C24—48no—
591C24—48no—
592C24C2×#4114yes—
593C24C2512yes—
594C24C2518yes—
595C24C2511yescharacteristic
596C24C2511yescharacteristic
597C24C2511yescharacteristic
598C2×Q8—28no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—216no—
604C2×D4—216no—
605C2×D4—216no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—216no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—48no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—48no—
619C2×D4—48no—
620C2×D4—48no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—48no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—48no—
627C2×D4—48no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—48no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—416no—
634C2×D4—816no—
635C2×D4—832no—
636C2×D4—832no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—28no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—28no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—44no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—42no—
661C22×C4—48no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—48no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—42no—
674C22×C4—48no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—88no—
678C22×C4—816no—
679C22×C4—88no—
680C22×C4C2×#4114yes—
681C22×C4C2×#4118yes—
682C22×C4C2×#4114yes—
683C22×C4C2×#4118yes—
684C22×C4H(5,𝔽2)18yes—
685C22×C4C2512yes—
686C22×C4C2514yes—
687C22×C4C2511yescharacteristic
688C22×C4C2511yescharacteristic
689C22×C4C2514yes—
690C22×C4C2514yes—
691C22×C4C2518yes—
692C22×C4C2518yes—
693C22×C4C2518yes—
694C22×C4C2511yescharacteristic
695C22×C4C2511yescharacteristic
696C22×C4C2512yes—
697C22×C4C2512yes—
698C22×C4C2514yes—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—216no—
706C4⋊C4—28no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—48no—
713C4⋊C4—48no—
714C4⋊C4—44no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—216no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—216no—
730C22⋊C4—216no—
731C22⋊C4—216no—
732C22⋊C4—216no—
733C22⋊C4—216no—
734C22⋊C4—44no—
735C22⋊C4—48no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C22⋊C4—48no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C42—24no—
754C42—24no—
755C42—28no—
756C42—28no—
757C42—44no—
758C42—44no—
759C42—48no—
760C42—48no—
761C42—48no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—28no—
772C23—28no—
773C23—22no—
774C23—28no—
775C23—24no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—28no—
784C23—28no—
785C23—44no—
786C23—48no—
787C23—48no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—416no—
792C23—84no—
793C23—84no—
794C23—88no—
795C23—88no—
796C23—816no—
797C23—816no—
798C23C22×#4112yes—
799C23C22×#4112yes—
800C23C22×#4112yes—
801C23C2×H(5,𝔽2)14yes—
802C23#58512yes—
803C23#58512yes—
804C23C2611yescharacteristic
805Q8—88no—
806D4—416no—
807D4—416no—
808D4—48no—
809D4—48no—
810D4—432no—
811D4—88no—
812D4—88no—
813D4—816no—
814D4—816no—
815D4—168no—
816D4—168no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—28no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—44no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—48no—
854C2×C4—48no—
855C2×C4—416no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—84no—
860C2×C4—84no—
861C2×C4—88no—
862C2×C4—84no—
863C2×C4—84no—
864C2×C4—84no—
865C2×C4—88no—
866C2×C4—816no—
867C2×C4—168no—
868C2×C4C22×#4114yes—
869C2×C4C22×#4114yes—
870C2×C4C2×H(5,𝔽2)18yes—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—416no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—48no—
887C22—48no—
888C22—42no—
889C22—42no—
890C22—48no—
891C22—48no—
892C22—48no—
893C22—44no—
894C22—48no—
895C22—48no—
896C22—44no—
897C22—88no—
898C22—1616no—
899C22#349314yes—
900C22#350814yes—
901C22C23×#4111yescharacteristic
902C22C22×H(5,𝔽2)12yes—
903C22C2×#58511yescharacteristic
904C22C2×#58511yescharacteristic
905C22H(7,𝔽2)12yes—
906C4—24no—
907C4—24no—
908C4—28no—
909C4—42no—
910C4—41no—
911C4—41no—
912C4—48no—
913C4—41no—
914C4—41no—
915C4—44no—
916C4—48no—
917C4—44no—
918C4—44no—
919C4—48no—
920C2—24no—
921C2—24no—
922C2—42no—
923C2—82no—
924C2—88no—
925C2C2×#349311yescharacteristic
926C2C2×#350811yescharacteristic
927C2#6284411yescharacteristic
928C2#6290012yes—
929C2#6295712yes—
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. #51921C2semidirect
2. #51918C2semidirect
3. #44102C2semidirect
4. #43963C2semidirect
5. #43509C2semidirect
6. #43080C2semidirect
7. #39807C2semidirect
8. #37770C2semidirect
9. #37693C2semidirect
10. #36978C2semidirect
11. #36731C2semidirect
12. #36107C2semidirect
13. #35119C2semidirect
14. #35076C2semidirect
15. #35052C2semidirect
16. #35003C2semidirect
17. C2×#2656C2semidirect
18. #34379C2semidirect
19. C2×#2353C2semidirect
20. C2×#538C22semidirect
21. C2×#529C22semidirect
25. #2854C22semidirect
26. #2854C22semidirect
27. #2850C22semidirect
29. #2847C22semidirect
30. #2803C22semidirect
31. #2798C22semidirect
32. #2797C22semidirect
33. #2777C22semidirect
34. #2771C22semidirect
35. #2756C22semidirect
36. #2749C22semidirect
37. #2743C22semidirect
38. #2740C22semidirect
39. #2738C22semidirect
40. #2733C22semidirect
41. #2727C22semidirect
42. #2714C22semidirect
43. #2714C22semidirect
44. #2703C22semidirect
45. #2699C22semidirect
46. #2694C22semidirect
47. #2688C22semidirect
48. #2688C22semidirect
49. #2676C22semidirect
50. #2659C22semidirect
54. #2656C22semidirect
55. #2646C22semidirect
56. #2639C22semidirect
57. #2635C22semidirect
58. #2635C22semidirect
59. #2617C22semidirect
60. #2611C22semidirect
61. #2610C22semidirect
62. #2604C22semidirect
63. #2603C22semidirect
64. #2600C22semidirect
65. #2596C22semidirect
66. #2591C22semidirect
67. #2575C22semidirect
68. #2569C22semidirect
69. #2559C22semidirect
70. #2555C22semidirect
71. #2553C22semidirect
72. #2549C22semidirect
73. #2539C22semidirect
74. #2521C22semidirect
75. #2490C22semidirect
79. #2480C22semidirect
80. #2479C22semidirect
81. #2476C22semidirect
83. #2464C22semidirect
84. #2459C22semidirect
85. #2456C22semidirect
86. #2448C22semidirect
87. #2444C22semidirect
88. #2444C22semidirect
89. #2442C22semidirect
90. #2438C22semidirect
91. #2435C22semidirect
92. #2427C22semidirect
93. #2426C22semidirect
94. #2425C22semidirect
95. #2424C22semidirect
96. #2420C22semidirect
97. #2414C22semidirect
98. #2414C22semidirect
99. #2414C22semidirect
106. C2×#399C22semidirect
107. C2×#392C22semidirect
108. #2377C22semidirect
109. #2361C22semidirect
110. #2360C22semidirect
113. #2353C22semidirect
114. #2353C22semidirect
115. #2345C22semidirect
116. #2342C22semidirect
118. D4×C22⋊C4C22semidirect
119. D4×C22⋊C4C22semidirect
120. #2329C22semidirect
121. #2325C22semidirect
122. #2325C22semidirect
123. #2325C22semidirect
124. #2324C22semidirect
127. #2315C22semidirect
128. #2312C22semidirect
129. C4×#121C22semidirect
130. C2×#388C22semidirect
131. C2×#387C22semidirect
133. C2×#383C22semidirect
135. C2×#381C22semidirect
138. C2×C4×C22⋊C4C22semidirect
139. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#519212
#519182
#441022
#439632
#435092
#430802
#398072
#377702
#376932
#369782
#367312
#361072
#351192
#350762
#350522
#350032
C2×#26562
#343792
C2×#23532