Finite Group Databasebeta

← #8109891

Subgroups — #8109891

Order 512.

5962 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59885C212yesmaximal, complemented
2#59814C212yesmaximal, complemented
3#53204C214yesmaximal, complemented
4#53181C214yesmaximal, complemented
5#46232C214yesmaximal, complemented
6#46225C214yesmaximal, complemented
7#45991C212yesmaximal, complemented
8#45977C212yesmaximal, complemented
9#39499C214yesmaximal, complemented
10#39354C214yesmaximal, complemented
11#38838C218yesmaximal, complemented
12#38358C218yesmaximal, complemented
13#36918C218yesmaximal, complemented
14#36717C212yesmaximal, complemented
15#36707C212yesmaximal, complemented
16#36624C212yesmaximal, complemented
17C2×#2850C211yesmaximal, characteristic, complemented
18C2×H(3,𝔽4)C2212yescomplemented
19C2×#546C2218yescomplemented
20C2×#537C2212yes—
21C2×#534C2212yescomplemented
22C2×#532C2212yescomplemented
23C22×#124C2211yescharacteristic
24C2×#525C2214yescomplemented
25C22×C22⋊Q8C2211yescharacteristic, complemented
26C22×#121C2211yescharacteristic
27C23×C42C2211yescharacteristic, complemented
28#2857C2212yescomplemented
29#2857C2212yescomplemented
30#2856C2212yes—
31#2856C2212yescomplemented
32#2854C2214yescomplemented
33#2854C2214yescomplemented
34#2850C2214yescomplemented
35#2850C2214yescomplemented
36#2850C2214yescomplemented
37#2850C2214yescomplemented
38#2850C2214yescomplemented
39#2850C2214yescomplemented
40#2847C2214yescomplemented
41#2847C2214yescomplemented
42#2844C2212yescomplemented
43#2819C2212yescomplemented
44#2819C2214yescomplemented
45#2809C2212yescomplemented
46#2808C2214yescomplemented
47#2803C2218yescomplemented
48#2795C2218yescomplemented
49#2785C2214yescomplemented
50#2783C2218yescomplemented
51#2782C2214yescomplemented
52#2763C2218yescomplemented
53#2753C2218yescomplemented
54#2733C2214yescomplemented
55#2733C2212yescomplemented
56#2731C2218yescomplemented
57#2712C2218yescomplemented
58#2706C2218yescomplemented
59#2703C2218yescomplemented
60#2703C2218yescomplemented
61#2703C2218yescomplemented
62#2696C2218yescomplemented
63#2692C2218yescomplemented
64#2692C2218yescomplemented
65#2692C2218yescomplemented
66#2684C2214yescomplemented
67#2683C2212yescomplemented
68#2682C2214yescomplemented
69#2681C2218yescomplemented
70#2680C2218yescomplemented
71#2679C2212yescomplemented
72#2678C2218yescomplemented
73#2678C2218yescomplemented
74#2676C2218yescomplemented
75#2676C2218yescomplemented
76#2676C2218yescomplemented
77#2673C2218yescomplemented
78#2670C2218yescomplemented
79#2669C2218yescomplemented
80#2669C2218yescomplemented
81#2669C2218yescomplemented
82#2669C2218yescomplemented
83#2635C2218yescomplemented
84#2631C2218yescomplemented
85#2618C2214yescomplemented
86#2617C2214yes—
87#2610C2218yescomplemented
88#2598C2218yescomplemented
89#2591C2214yescomplemented
90#2572C2214yescomplemented
91#2555C2214yescomplemented
92#2543C2218yescomplemented
93#2539C2214yescomplemented
94#2534C2218yescomplemented
95#2532C2218yescomplemented
96#2532C2218yescomplemented
97#2526C2218yescomplemented
98#2518C2218yescomplemented
99#2488C2218yescomplemented
100#2472C2218yescomplemented
101#2472C2218yescomplemented
102#2464C2218yescomplemented
103#2461C2218yescomplemented
104#2461C2218yescomplemented
105#2459C2218yescomplemented
106#2459C2218yescomplemented
107#2436C2214yescomplemented
108#2433C2214yes—
109#2431C2218yescomplemented
110#2430C2218yescomplemented
111#2424C2218yescomplemented
112#2424C2218yescomplemented
113#2410C2218yescomplemented
114#2406C2214yescomplemented
115#2404C2214yescomplemented
116#2404C2218yescomplemented
117#2403C2214yes—
118#2403C2214yescomplemented
119#2379C2214yescomplemented
120#2379C2212yescomplemented
121#2372C2214yescomplemented
122#2358C2214yescomplemented
123#2353C2218yescomplemented
124#2328C2218yescomplemented
125#2321C2218yescomplemented
126#2313C2212yescomplemented
127#2312C2212yescomplemented
128C4×#121C2214yescomplemented
129C4×#121C2214yescomplemented
130C4×#121C2214yescomplemented
131C4×#121C2214yescomplemented
132#2297C2214yescomplemented
133C2×#391C2211yescharacteristic, complemented
134C2×#390C2211yescharacteristic
135C2×#388C2214yescomplemented
136C2×#386C2214yescomplemented
137#2285C2212yescomplemented
138C2×#382C2211yescharacteristic, complemented
139C22×#41C2314yes—
140C22×#41C2314yes—
141C23×Q8C2311yescharacteristic
142C23×D4C2311yescharacteristic
143C23×D4C2314yes—
144C23×D4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147H(3,𝔽4)—48no—
148#546—432no—
149#537—48no—
150#534—48no—
151#532—48no—
152C2×C4⋊Q8C2312yes—
153C2×#127C2318yes—
154C2×#127C2312yes—
155C2×#124—44no—
156C2×#124C2312yes—
157C2×#124C2314yes—
158C2×#124C2314yes—
159C2×#124C2312yes—
160C2×#124C2318yes—
161C2×#124C2314yes—
162C2×#124C2314yes—
163C2×#124C2318yes—
164#525—416no—
165C2×#123C2318yes—
166C2×#123C2318yes—
167C2×#123C2318yes—
168C2×#123C2318yes—
169C2×C22⋊Q8—44no—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2318yes—
175C2×C22⋊Q8C2318yes—
176C2×#121—44no—
177C2×#121C2314yes—
178C2×#121C2314yes—
179C2×#121C2314yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2314yes—
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2318yes—
189C2×#121C2314yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#120C2318yes—
193C2×#120C2318yes—
194C2×#120C2314yes—
195C2×#120C2318yes—
196C2×#120C2314yes—
197C2×#120C2318yes—
198C2×#120C2318yes—
199C2×#120C2318yes—
200C2×C4×D4C2318yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2314yes—
205C2×#117C2314yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2314yes—
211C22×C22⋊C4C2318yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2314yes—
214C22×C42—44no—
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222#400C2314yes—
223#400C2314yes—
224#400C2318yes—
225#400C2318yes—
226#399C2318yes—
227#398C2318yes—
228#398C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#397C2318yes—
233#396C2318yes—
234#396C2318yes—
235#396C2318yes—
236#396C2318yes—
237#395C2318yes—
238#395C2314yes—
239#395C2314yes—
240#394C2314yes—
241#394C2318yes—
242#394C2318yes—
243#394C2314yes—
244#394C2314yes—
245#394C2318yes—
246#394C2318yes—
247#394C2318yes—
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#394C2314yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#393C2318yes—
256#393C2318yes—
257#393C2318yes—
258#393C2318yes—
259#393C2318yes—
260#393C2318yes—
261#392C2318yes—
262#392C2318yes—
263#392C2318yes—
264#392C2318yes—
265#392C2318yes—
266#392C2318yes—
267#392C2318yes—
268#392C2318yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#392C2318yes—
273#392C2318yes—
274#391C2312yes—
275#391C2314yes—
276#391C2312yes—
277#391C2314yes—
278#391C2314yes—
279#391C2314yes—
280#391C2318yes—
281#391C2314yes—
282#390C2318yes—
283#390C2318yes—
284#390C2318yes—
285#390C2318yes—
286#390C2312yes—
287#390C2312yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#386C2318yes—
326#386C2318yes—
327#386C2318yes—
328#386C2318yes—
329#386C2318yes—
330#386C2318yes—
331#386C2318yes—
332#386C2318yes—
333#386C2318yes—
334#386C2318yes—
335#386C2318yes—
336#386C2318yes—
337#386C2318yes—
338#386C2318yes—
339#386C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2314yes—
346#386C2318yes—
347#386C2314yes—
348#386C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#384C2312yes—
355#384C2312yes—
356#383C2318yes—
357#382C2312yes—
358#382C2314yes—
359#382C2318yes—
360#382C2314yes—
361#382C2312yes—
362#381C2314yes—
363#381C2318yes—
364#380C2314yes—
365#380C2314yes—
366#380C2314yes—
367#380C2314yes—
368#380C2314yes—
369#380C2314yes—
370#379C2314yes—
371#379C2318yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2314yes—
374C4×C22⋊C4C2314yes—
375C4×C22⋊C4C2314yes—
376C4×C22⋊C4C2318yes—
377C4×C22⋊C4C2318yes—
378C4×C22⋊C4C2318yes—
379#376C2318yes—
380C2×#95C2314yes—
381C2×#95C2314yes—
382C25C2411yescharacteristic
383C25C2412yes—
384C25C2414yes—
385C2×#41—48no—
386C2×#41—48no—
387C2×#41—416no—
388C2×#41—48no—
389C2×#41—48no—
390C22×Q8—42no—
391C22×Q8—42no—
392C22×Q8—42no—
393C22×Q8C2412yes—
394C22×Q8C2412yes—
395C22×Q8C2414yes—
396C22×Q8C2414yes—
397C22×D4—42no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4—44no—
401C22×D4—48no—
402C22×D4—416no—
403C22×D4—48no—
404C22×D4C2418yes—
405C22×D4C2414yes—
406C22×D4C2414yes—
407C22×D4C2418yes—
408C22×D4C2418yes—
409C22×D4C2412yes—
410C22×D4C2412yes—
411C22×D4C2414yes—
412C22×D4C2418yes—
413C22×D4C2418yes—
414C22×D4C2418yes—
415C22×D4C2414yes—
416C22×D4C2414yes—
417C22×D4C2414yes—
418C22×D4C2418yes—
419C23×C4—24no—
420C23×C4—28no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—44no—
424C23×C4—44no—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2418yes—
436C23×C4C2412yes—
437C23×C4C2418yes—
438C23×C4C2414yes—
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C4⋊Q8—44no—
442#127—44no—
443#127—416no—
444#124—28no—
445#124—216no—
446#124—48no—
447#124—416no—
448#124—44no—
449#124—48no—
450#124—416no—
451#124—48no—
452#123—416no—
453#123—416no—
454#123—416no—
455#123—416no—
456C22⋊Q8—48no—
457C22⋊Q8—416no—
458C22⋊Q8—416no—
459C22⋊Q8—48no—
460C22⋊Q8—48no—
461C22⋊Q8—48no—
462#121—216no—
463#121—216no—
464#121—48no—
465#121—48no—
466#121—48no—
467#121—48no—
468#121—48no—
469#121—48no—
470#121—416no—
471#121—416no—
472#121—416no—
473#121—48no—
474#121—48no—
475#121—48no—
476#121—48no—
477#120—48no—
478#120—416no—
479#120—416no—
480#120—416no—
481#120—48no—
482#120—416no—
483#120—416no—
484#120—416no—
485C4×D4—232no—
486C4×D4—48no—
487C4×D4—48no—
488C4×D4—416no—
489C4×D4—416no—
490#117—48no—
491C2×C4⋊C4—28no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—216no—
515C2×C22⋊C4—48no—
516C2×C22⋊C4—416no—
517C2×C22⋊C4—44no—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
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⋊C4C2414yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C42—24no—
549C2×C42—28no—
550C2×C42—42no—
551C2×C42—44no—
552C2×C42—44no—
553C2×C42—44no—
554C2×C42—44no—
555C2×C42C2418yes—
556C2×C42C2412yes—
557C2×C42C2412yes—
558C2×C42C2411yescharacteristic
559C2×C42C2412yes—
560C2×C42C2412yes—
561C2×C42C2414yes—
562C2×C42C2414yes—
563C2×C42C2418yes—
564C2×C42C2411yescharacteristic
565C2×C42C2412yes—
566C2×C42C2412yes—
567C2×C42C2411yescharacteristic
568C2×C42C2411yescharacteristic
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576#95C2418yes—
577#95C2418yes—
578#95C2418yes—
579#95C2414yes—
580#95C2418yes—
581#95C2414yes—
582#95C2418yes—
583#95C2418yes—
584#95C2414yes—
585#95C2418yes—
586#95C2414yes—
587#95C2418yes—
588#95C2418yes—
589C24—22no—
590C24—24no—
591C24—24no—
592C24—28no—
593C24—24no—
594C24—41no—
595C24—41no—
596C24—42no—
597C24—42no—
598C24—44no—
599C24—48no—
600C24—44no—
601C24—44no—
602C24—48no—
603C24—44no—
604C24C2514yes—
605C24C2518yes—
606C24C2512yes—
607C24C2511yescharacteristic
608#41—832no—
609#41—832no—
610C2×Q8—24no—
611C2×Q8—28no—
612C2×Q8—24no—
613C2×Q8—42no—
614C2×Q8—42no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—48no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—44no—
621C2×Q8—88no—
622C2×D4—216no—
623C2×D4—216no—
624C2×D4—216no—
625C2×D4—216no—
626C2×D4—216no—
627C2×D4—216no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—24no—
631C2×D4—28no—
632C2×D4—24no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—48no—
638C2×D4—48no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—48no—
644C2×D4—44no—
645C2×D4—48no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—48no—
649C2×D4—44no—
650C2×D4—44no—
651C2×D4—48no—
652C2×D4—42no—
653C2×D4—48no—
654C2×D4—42no—
655C2×D4—48no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—48no—
664C2×D4—48no—
665C2×D4—88no—
666C2×D4—832no—
667C2×D4—816no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—216no—
690C22×C4—41no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—41no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—42no—
710C22×C4—48no—
711C22×C4—416no—
712C22×C4—432no—
713C22×C4H(5,𝔽2)14yes—
714C22×C4H(5,𝔽2)18yes—
715C22×C4C2514yes—
716C22×C4C2518yes—
717C22×C4C2514yes—
718C22×C4C2518yes—
719C22×C4C2512yes—
720C22×C4C2518yes—
721C22×C4C2514yes—
722C22×C4C2512yes—
723C22×C4C2512yes—
724C22×C4C2511yescharacteristic
725C22×C4C2512yes—
726C22×C4C2512yes—
727C22×C4C2511yescharacteristic
728C4⋊C4—216no—
729C4⋊C4—216no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—48no—
741C4⋊C4—48no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C22⋊C4—216no—
748C22⋊C4—216no—
749C22⋊C4—216no—
750C22⋊C4—216no—
751C22⋊C4—216no—
752C22⋊C4—216no—
753C22⋊C4—216no—
754C22⋊C4—216no—
755C22⋊C4—216no—
756C22⋊C4—216no—
757C22⋊C4—216no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—44no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—48no—
772C22⋊C4—48no—
773C22⋊C4—44no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C42—24no—
778C42—24no—
779C42—24no—
780C42—22no—
781C42—24no—
782C42—216no—
783C42—41no—
784C42—42no—
785C42—42no—
786C42—41no—
787C42—44no—
788C42—44no—
789C42—48no—
790C42H(5,𝔽2)14yes—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—28no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—24no—
802C23—28no—
803C23—28no—
804C23—24no—
805C23—28no—
806C23—28no—
807C23—28no—
808C23—28no—
809C23—28no—
810C23—28no—
811C23—24no—
812C23—28no—
813C23—48no—
814C23—48no—
815C23—44no—
816C23—44no—
817C23—48no—
818C23—84no—
819C23—84no—
820C23—88no—
821C23—88no—
822C23—88no—
823C23—816no—
824C23—168no—
825C23—164no—
826C23—164no—
827C23C2×H(5,𝔽2)14yes—
828C23C2×H(5,𝔽2)12yes—
829C23#58514yes—
830C23C2611yescharacteristic
831Q8—84no—
832Q8—84no—
833Q8—88no—
834Q8—88no—
835D4—432no—
836D4—88no—
837D4—88no—
838D4—84no—
839D4—84no—
840D4—88no—
841D4—816no—
842D4—816no—
843D4—816no—
844D4—816no—
845D4—816no—
846D4—88no—
847D4—168no—
848D4—164no—
849D4—164no—
850C2×C4—28no—
851C2×C4—216no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—28no—
866C2×C4—28no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—28no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—28no—
880C2×C4—28no—
881C2×C4—24no—
882C2×C4—22no—
883C2×C4—48no—
884C2×C4—44no—
885C2×C4—48no—
886C2×C4—48no—
887C2×C4—48no—
888C2×C4—48no—
889C2×C4—48no—
890C2×C4—48no—
891C2×C4—48no—
892C2×C4—816no—
893C2×C4—84no—
894C2×C4—84no—
895C2×C4—88no—
896C2×C4—816no—
897C2×C4C2×H(5,𝔽2)14yes—
898C2×C4C2×H(5,𝔽2)12yes—
899C2×C4C2×H(5,𝔽2)14yes—
900C2×C4C2×H(5,𝔽2)14yes—
901C2×C4C2×H(5,𝔽2)14yes—
902C2×C4#58512yes—
903C22—24no—
904C22—22no—
905C22—24no—
906C22—22no—
907C22—24no—
908C22—24no—
909C22—24no—
910C22—416no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—48no—
916C22—48no—
917C22—48no—
918C22—48no—
919C22—44no—
920C22—48no—
921C22—44no—
922C22—48no—
923C22—48no—
924C22—48no—
925C22—44no—
926C22—48no—
927C22—168no—
928C22—1616no—
929C22#354914yes—
930C22C22×H(5,𝔽2)12yes—
931C22C22×H(5,𝔽2)11yescharacteristic
932C22C22×H(5,𝔽2)11yescharacteristic
933C22C2×#58511yescharacteristic
934C22C2×#58512yes—
935C4—24no—
936C4—22no—
937C4—24no—
938C4—22no—
939C4—24no—
940C4—24no—
941C4—48no—
942C4—44no—
943C4—48no—
944C4—42no—
945C4—48no—
946C4—44no—
947C4—44no—
948C2—24no—
949C2—44no—
950C2—88no—
951C2—84no—
952C2#6274812yes—
953C2C2×#354911yescharacteristic
954C2#6281811yescharacteristic
955C2#6281812yes—
956C2#6282411yescharacteristic
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. #59885C2semidirect
2. #59814C2semidirect
3. #53204C2semidirect
4. #53181C2semidirect
5. #46232C2semidirect
6. #46225C2semidirect
7. #45991C2semidirect
8. #45977C2semidirect
9. #39499C2semidirect
10. #39354C2semidirect
11. #38838C2semidirect
12. #38358C2semidirect
13. #36918C2semidirect
14. #36717C2semidirect
15. #36707C2semidirect
16. #36624C2semidirect
17. C2×#2850C2semidirect
18. C2×H(3,𝔽4)C22semidirect
19. C2×#546C22semidirect
21. C2×#534C22semidirect
22. C2×#532C22semidirect
24. C2×#525C22semidirect
25. C22×C22⋊Q8C22semidirect
27. C23×C42C22semidirect
28. #2857C22semidirect
29. #2857C22semidirect
31. #2856C22semidirect
32. #2854C22semidirect
33. #2854C22semidirect
34. #2850C22semidirect
35. #2850C22semidirect
36. #2850C22semidirect
37. #2850C22semidirect
38. #2850C22semidirect
39. #2850C22semidirect
40. #2847C22semidirect
41. #2847C22semidirect
42. #2844C22semidirect
43. #2819C22semidirect
44. #2819C22semidirect
45. #2809C22semidirect
46. #2808C22semidirect
47. #2803C22semidirect
48. #2795C22semidirect
49. #2785C22semidirect
50. #2783C22semidirect
51. #2782C22semidirect
52. #2763C22semidirect
53. #2753C22semidirect
54. #2733C22semidirect
55. #2733C22semidirect
56. #2731C22semidirect
57. #2712C22semidirect
58. #2706C22semidirect
59. #2703C22semidirect
60. #2703C22semidirect
61. #2703C22semidirect
62. #2696C22semidirect
63. #2692C22semidirect
64. #2692C22semidirect
65. #2692C22semidirect
66. #2684C22semidirect
67. #2683C22semidirect
68. #2682C22semidirect
69. #2681C22semidirect
70. #2680C22semidirect
71. #2679C22semidirect
72. #2678C22semidirect
73. #2678C22semidirect
74. #2676C22semidirect
75. #2676C22semidirect
76. #2676C22semidirect
77. #2673C22semidirect
78. #2670C22semidirect
79. #2669C22semidirect
80. #2669C22semidirect
81. #2669C22semidirect
82. #2669C22semidirect
83. #2635C22semidirect
84. #2631C22semidirect
85. #2618C22semidirect
87. #2610C22semidirect
88. #2598C22semidirect
89. #2591C22semidirect
90. #2572C22semidirect
91. #2555C22semidirect
92. #2543C22semidirect
93. #2539C22semidirect
94. #2534C22semidirect
95. #2532C22semidirect
96. #2532C22semidirect
97. #2526C22semidirect
98. #2518C22semidirect
99. #2488C22semidirect
100. #2472C22semidirect
101. #2472C22semidirect
102. #2464C22semidirect
103. #2461C22semidirect
104. #2461C22semidirect
105. #2459C22semidirect
106. #2459C22semidirect
107. #2436C22semidirect
109. #2431C22semidirect
110. #2430C22semidirect
111. #2424C22semidirect
112. #2424C22semidirect
113. #2410C22semidirect
114. #2406C22semidirect
115. #2404C22semidirect
116. #2404C22semidirect
118. #2403C22semidirect
119. #2379C22semidirect
120. #2379C22semidirect
121. #2372C22semidirect
122. #2358C22semidirect
123. #2353C22semidirect
124. #2328C22semidirect
125. #2321C22semidirect
126. #2313C22semidirect
127. #2312C22semidirect
128. C4×#121C22semidirect
129. C4×#121C22semidirect
130. C4×#121C22semidirect
131. C4×#121C22semidirect
132. #2297C22semidirect
133. C2×#391C22semidirect
135. C2×#388C22semidirect
136. C2×#386C22semidirect
137. #2285C22semidirect
138. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#598852
#598142
#532042
#531812
#462322
#462252
#459912
#459772
#394992
#393542
#388382
#383582
#369182
#367172
#367072
#366242
C2×#28502