Finite Group Databasebeta

← #7643405

Subgroups — #7643405

Order 512.

4848 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40333C218yesmaximal, complemented
2#39677C214yesmaximal, complemented
3#39540C214yesmaximal
4#38748C218yesmaximal, complemented
5#37958C214yesmaximal, complemented
6#37934C214yesmaximal, complemented
7#37400C214yesmaximal, complemented
8#37369C214yesmaximal, complemented
9#36635C212yesmaximal, complemented
10#35671C214yesmaximal, complemented
11#35599C214yesmaximal, complemented
12#35310C212yesmaximal, complemented
13#35087C212yesmaximal, complemented
14#35084C212yesmaximal
15#35033C211yesmaximal, characteristic, complemented
16#35014C212yesmaximal, complemented
17#35011C211yesmaximal, characteristic, complemented
18#34203C212yesmaximal, complemented
19C2×#2293C211yesmaximal, characteristic
20C2×#541C2212yescomplemented
21C22×C22⋊Q8C2212yes—
22C2×#519C2212yescomplemented
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2864C2214yescomplemented
27#2863C2214yescomplemented
28#2863C2214yescomplemented
29#2862C2212yescomplemented
30#2859C2212yescomplemented
31#2857C2212yes—
32#2857C2212yes—
33#2857C2212yes—
34#2855C2214yes—
35#2855C2214yes—
36#2851C2212yes—
37#2851C2214yes—
38#2848C2214yes—
39#2806C2218yescomplemented
40#2802C2218yescomplemented
41#2783C2218yescomplemented
42#2777C2218yescomplemented
43#2775C2218yescomplemented
44#2774C2218yescomplemented
45#2765C2218yescomplemented
46#2764C2218yescomplemented
47#2761C2218yes—
48#2759C2218yescomplemented
49#2751C2218yes—
50#2744C2218yescomplemented
51#2738C2218yescomplemented
52#2726C2218yescomplemented
53#2707C2218yes—
54#2694C2218yes—
55#2659C2214yes—
56#2655C2218yescomplemented
57#2646C2214yes—
58#2638C2218yes—
59#2629C2212yescomplemented
60#2626C2214yes—
61#2626C2214yes—
62#2625C2214yescomplemented
63#2621C2212yescomplemented
64#2611C2218yescomplemented
65#2608C2214yescomplemented
66#2607C2214yescomplemented
67#2604C2218yescomplemented
68#2601C2218yes—
69#2594C2218yescomplemented
70#2590C2218yescomplemented
71#2589C2218yescomplemented
72#2587C2218yescomplemented
73#2584C2218yescomplemented
74#2583C2214yes—
75#2583C2214yescomplemented
76#2583C2214yescomplemented
77#2573C2218yescomplemented
78#2561C2214yes—
79#2558C2218yes—
80#2532C2218yescomplemented
81#2527C2218yescomplemented
82#2514C2214yescomplemented
83#2506C2214yescomplemented
84#2502C2214yescomplemented
85#2497C2214yescomplemented
86#2493C2218yes—
87#2492C2214yescomplemented
88#2486C2214yes—
89#2483C2214yes—
90#2480C2218yes—
91#2479C2218yes—
92#2478C2218yescomplemented
93#2475C2218yescomplemented
94#2475C2218yescomplemented
95#2473C2218yes—
96#2473C2218yes—
97#2469C2218yescomplemented
98#2462C2218yescomplemented
99#2458C2218yes—
100#2453C2214yescomplemented
101#2453C2218yescomplemented
102#2446C2214yescomplemented
103#2441C2214yescomplemented
104#2439C2214yescomplemented
105#2434C2214yescomplemented
106#2429C2214yescomplemented
107#2423C2214yescomplemented
108#2415C2214yes—
109#2415C2214yes—
110#2409C2214yes—
111#2405C2214yes—
112#2362C2218yescomplemented
113#2360C2218yes—
114#2344C2218yescomplemented
115#2342C2218yes—
116#2336C2218yescomplemented
117#2329C2214yes—
118#2329C2214yes—
119#2323C2214yescomplemented
120#2323C2214yescomplemented
121#2323C2214yescomplemented
122#2322C2218yes—
123#2316C2212yescomplemented
124#2315C2214yes—
125#2314C2212yescomplemented
126#2312C2214yes—
127#2310C2212yescomplemented
128C4×C4⋊Q8C2212yescomplemented
129C4×C4⋊Q8C2212yescomplemented
130C4×#125C2214yescomplemented
131C4×C22⋊Q8C2214yes—
132C4×C22⋊Q8C2214yes—
133C4×C22⋊Q8C2214yes—
134#2295C2214yescomplemented
135#2295C2214yescomplemented
136#2293C2214yes—
137#2293C2214yes—
138#2293C2214yes—
139#2293C2214yes—
140C2×#390C2212yes—
141C2×#389C2212yes—
142C2×#388C2212yes—
143C2×#388C2212yes—
144#2283C2214yes—
145#2280C2212yes—
146#2274C2212yescomplemented
147C2×C4×C4⋊C4C2211yescharacteristic
148C2×C4×C22⋊C4C2211yescharacteristic
149C2×C4×C22⋊C4C2211yescharacteristic
150C2×C43C2211yescharacteristic
151C23×Q8C2312yes—
152C23×D4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155#541—48no—
156C2×C4⋊Q8C2312yes—
157C2×C4⋊Q8C2312yes—
158C2×C4⋊Q8C2312yes—
159C2×#126C2318yes—
160C2×#125C2314yes—
161C2×#125C2318yes—
162C2×#125C2318yes—
163C2×#125C2312yes—
164C2×#123C2318yes—
165C2×C22⋊Q8—216no—
166C2×C22⋊Q8C2314yes—
167C2×C22⋊Q8C2314yes—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2314yes—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173#519—48no—
174C2×C4×Q8C2314yes—
175C2×C4×Q8C2314yes—
176C2×C4×Q8C2314yes—
177C2×C4×Q8C2318yes—
178C2×C4×D4—28no—
179C2×C4×D4C2314yes—
180C2×C4×D4C2314yes—
181C2×#117—44no—
182C2×#117—44no—
183C2×#117C2312yes—
184C2×#117C2312yes—
185C2×#117C2312yes—
186C2×#117C2312yes—
187C2×#117C2312yes—
188C2×#117C2318yes—
189C2×#117C2314yes—
190C2×#117C2312yes—
191C2×#117C2314yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2314yes—
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2314yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C42C2311yescharacteristic
206C22×C42C2312yes—
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212#401C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#399C2318yes—
221#399C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#396C2318yes—
240#396C2318yes—
241#396C2318yes—
242#396C2318yes—
243#396C2318yes—
244#395C2318yes—
245#395C2318yes—
246#395C2318yes—
247#394C2318yes—
248#394C2318yes—
249#393C2318yes—
250#393C2318yes—
251#393C2318yes—
252#391C2314yes—
253#391C2314yes—
254#391C2314yes—
255#391C2314yes—
256#391C2318yes—
257#391C2314yes—
258#391C2318yes—
259#391C2318yes—
260#391C2314yes—
261#391C2314yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#390C2314yes—
266#390C2314yes—
267#390C2314yes—
268#390C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2318yes—
278#389C2318yes—
279#389C2318yes—
280#389C2318yes—
281#389C2318yes—
282#389C2314yes—
283#389C2318yes—
284#389C2314yes—
285#389C2318yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2314yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2314yes—
312#388C2314yes—
313#388C2314yes—
314#388C2314yes—
315#388C2314yes—
316#388C2314yes—
317#388C2314yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#386C2318yes—
342#385C2318yes—
343#385C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#384C2312yes—
355#384C2312yes—
356#384C2312yes—
357#383C2318yes—
358#383C2318yes—
359#382C2314yes—
360#382C2312yes—
361#382C2314yes—
362#382C2314yes—
363#381C2318yes—
364#381C2318yes—
365#381C2318yes—
366#381C2314yes—
367#380C2314yes—
368#380C2314yes—
369#380C2314yes—
370#380C2314yes—
371#380C2318yes—
372#380C2318yes—
373#380C2314yes—
374#380C2314yes—
375#380C2314yes—
376#379C2318yes—
377#379C2314yes—
378C4×C4⋊C4C2314yes—
379C4×C4⋊C4C2314yes—
380C4×C4⋊C4C2318yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2314yes—
389C4×C22⋊C4C2314yes—
390C4×C22⋊C4C2318yes—
391C4×C22⋊C4C2318yes—
392C4×C22⋊C4C2314yes—
393C4×C22⋊C4C2312yes—
394C4×C22⋊C4C2312yes—
395C4×C22⋊C4C2312yes—
396C4×C22⋊C4C2312yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2314yes—
399C4×C22⋊C4C2314yes—
400#376C2318yes—
401C2×#95C2312yes—
402C2×#95C2312yes—
403C2×#95C2312yes—
404C43C2312yes—
405C43C2312yes—
406C43C2312yes—
407C43C2312yes—
408C25C2411yescharacteristic
409C25C2411yescharacteristic
410C22×Q8—28no—
411C22×Q8—44no—
412C22×Q8—44no—
413C22×Q8C2414yes—
414C22×Q8C2414yes—
415C22×Q8C2414yes—
416C22×D4—24no—
417C22×D4—44no—
418C22×D4C2414yes—
419C23×C4—24no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4#4118yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2414yes—
435C23×C4C2414yes—
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C4⋊Q8—44no—
441C4⋊Q8—44no—
442C4⋊Q8—44no—
443#126—416no—
444#125—48no—
445#125—44no—
446#125—416no—
447#125—416no—
448#123—416no—
449C22⋊Q8—216no—
450C22⋊Q8—216no—
451C22⋊Q8—216no—
452C22⋊Q8—216no—
453C22⋊Q8—216no—
454C22⋊Q8—48no—
455C22⋊Q8—48no—
456C4×Q8—216no—
457C4×Q8—48no—
458C4×Q8—416no—
459C4×Q8—48no—
460C4×D4—216no—
461C4×D4—216no—
462#117—28no—
463#117—28no—
464#117—44no—
465#117—44no—
466#117—48no—
467#117—48no—
468#117—416no—
469#117—44no—
470#117—44no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—216no—
473C2×C4⋊C4—28no—
474C2×C4⋊C4—44no—
475C2×C4⋊C4—44no—
476C2×C4⋊C4—44no—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—216no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—28no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4—44no—
517C2×C22⋊C4C2414yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2414yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2414yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C42—24no—
538C2×C42—28no—
539C2×C42—24no—
540C2×C42—42no—
541C2×C42—42no—
542C2×C42—44no—
543C2×C42—42no—
544C2×C42C2412yes—
545C2×C42C2411yescharacteristic
546C2×C42C2412yes—
547C2×C42C2412yes—
548C2×C42C2418yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2412yes—
553C2×C42C2412yes—
554C2×C42C2412yes—
555C2×C42C2412yes—
556C2×C42C2412yes—
557C2×C42C2412yes—
558C2×C42C2412yes—
559C2×C42C2412yes—
560C2×C42C2414yes—
561C2×C42C2418yes—
562C2×C42C2414yes—
563C2×C42C2418yes—
564C2×C42C2418yes—
565C2×C42C2411yescharacteristic
566C2×C42C2411yescharacteristic
567C2×C42C2412yes—
568C2×C42C2412yes—
569C2×C42C2411yescharacteristic
570#95C2414yes—
571#95C2414yes—
572#95C2414yes—
573#95C2414yes—
574#95C2414yes—
575#95C2414yes—
576#95C2418yes—
577#95C2418yes—
578#95C2418yes—
579#95C2418yes—
580#95C2418yes—
581#95C2418yes—
582#95C2418yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601C24—24no—
602C24—22no—
603C24—24no—
604C24—41no—
605C24—41no—
606C24—41no—
607C24—41no—
608C24—42no—
609C24—42no—
610C24C2×#4114yes—
611C24C2512yes—
612C24C2512yes—
613C24C2511yescharacteristic
614C2×Q8—28no—
615C2×Q8—28no—
616C2×Q8—28no—
617C2×Q8—28no—
618C2×Q8—28no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—432no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—416no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—28no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—28no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—416no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—44no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—44no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—48no—
666C22×C4—416no—
667C22×C4C2×#4114yes—
668C22×C4C2×#4118yes—
669C22×C4C2×#4114yes—
670C22×C4C2×#4118yes—
671C22×C42−1+418yes—
672C22×C4C2512yes—
673C22×C4C2518yes—
674C22×C4C2512yes—
675C22×C4C2514yes—
676C22×C4C2518yes—
677C22×C4C2514yes—
678C22×C4C2518yes—
679C22×C4C2512yes—
680C22×C4C2518yes—
681C22×C4C2511yescharacteristic
682C22×C4C2512yes—
683C22×C4C2512yes—
684C22×C4C2512yes—
685C22×C4C2512yes—
686C22×C4C2512yes—
687C22×C4C2511yescharacteristic
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—216no—
692C4⋊C4—216no—
693C4⋊C4—28no—
694C4⋊C4—28no—
695C4⋊C4—28no—
696C4⋊C4—216no—
697C4⋊C4—28no—
698C4⋊C4—216no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—216no—
702C4⋊C4—216no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—48no—
707C4⋊C4—44no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—48no—
713C4⋊C4—48no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C22⋊C4—28no—
722C22⋊C4—216no—
723C22⋊C4—216no—
724C22⋊C4—216no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C42—24no—
742C42—24no—
743C42—24no—
744C42—22no—
745C42—24no—
746C42—24no—
747C42—216no—
748C42—24no—
749C42—24no—
750C42—24no—
751C42—24no—
752C42—24no—
753C42—24no—
754C42—24no—
755C42—42no—
756C42—41no—
757C42—41no—
758C42—42no—
759C42—42no—
760C42—42no—
761C42—44no—
762C42—44no—
763C42—48no—
764C42—48no—
765C42—48no—
766C42H(5,𝔽2)14yes—
767C23—21no—
768C23—22no—
769C23—21no—
770C23—22no—
771C23—24no—
772C23—22no—
773C23—24no—
774C23—28no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—22no—
779C23—24no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23C22×#4114yes—
790C23C22×#4112yes—
791C23C2×2−1+414yes—
792C23C2611yescharacteristic
793Q8—416no—
794Q8—416no—
795Q8—88no—
796D4—416no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—28no—
811C2×C4—216no—
812C2×C4—22no—
813C2×C4—28no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—22no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—48no—
840C2×C4—44no—
841C2×C4—48no—
842C2×C4—48no—
843C2×C4—48no—
844C2×C4—44no—
845C2×C4—416no—
846C2×C4—44no—
847C2×C4—48no—
848C2×C4—88no—
849C2×C4—84no—
850C2×C4—84no—
851C2×C4C22×#4112yes—
852C2×C4C22×#4114yes—
853C2×C4C22×#4112yes—
854C2×C4C2×H(5,𝔽2)14yes—
855C2×C4C2×H(5,𝔽2)12yes—
856C2×C4C2×2−1+414yes—
857C2×C4C2×2−1+414yes—
858C2×C4#58514yes—
859C2×C4#58512yes—
860C22—22no—
861C22—24no—
862C22—24no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—44no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—88no—
875C22—88no—
876C22#350914yes—
877C22C23×#4111yescharacteristic
878C22C22×H(5,𝔽2)11yescharacteristic
879C22C22×2−1+412yes—
880C22C2×#58512yes—
881C22C2×#58511yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—22no—
887C4—24no—
888C4—42no—
889C4—48no—
890C4—48no—
891C4—48no—
892C4—42no—
893C4—44no—
894C4—44no—
895C4—42no—
896C4—48no—
897C4#345914yes—
898C2—24no—
899C2—44no—
900C2—82no—
901C2C2×#345911yescharacteristic
902C2C2×#350911yescharacteristic
903C2#6281411yescharacteristic
904C2#6282312yes—
905C2#6283512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40333C2semidirect
2. #39677C2semidirect
4. #38748C2semidirect
5. #37958C2semidirect
6. #37934C2semidirect
7. #37400C2semidirect
8. #37369C2semidirect
9. #36635C2semidirect
10. #35671C2semidirect
11. #35599C2semidirect
12. #35310C2semidirect
13. #35087C2semidirect
15. #35033C2semidirect
16. #35014C2semidirect
17. #35011C2semidirect
18. #34203C2semidirect
20. C2×#541C22semidirect
22. C2×#519C22semidirect
26. #2864C22semidirect
27. #2863C22semidirect
28. #2863C22semidirect
29. #2862C22semidirect
30. #2859C22semidirect
39. #2806C22semidirect
40. #2802C22semidirect
41. #2783C22semidirect
42. #2777C22semidirect
43. #2775C22semidirect
44. #2774C22semidirect
45. #2765C22semidirect
46. #2764C22semidirect
48. #2759C22semidirect
50. #2744C22semidirect
51. #2738C22semidirect
52. #2726C22semidirect
56. #2655C22semidirect
59. #2629C22semidirect
62. #2625C22semidirect
63. #2621C22semidirect
64. #2611C22semidirect
65. #2608C22semidirect
66. #2607C22semidirect
67. #2604C22semidirect
69. #2594C22semidirect
70. #2590C22semidirect
71. #2589C22semidirect
72. #2587C22semidirect
73. #2584C22semidirect
75. #2583C22semidirect
76. #2583C22semidirect
77. #2573C22semidirect
80. #2532C22semidirect
81. #2527C22semidirect
82. #2514C22semidirect
83. #2506C22semidirect
84. #2502C22semidirect
85. #2497C22semidirect
87. #2492C22semidirect
92. #2478C22semidirect
93. #2475C22semidirect
94. #2475C22semidirect
97. #2469C22semidirect
98. #2462C22semidirect
100. #2453C22semidirect
101. #2453C22semidirect
102. #2446C22semidirect
103. #2441C22semidirect
104. #2439C22semidirect
105. #2434C22semidirect
106. #2429C22semidirect
107. #2423C22semidirect
112. #2362C22semidirect
114. #2344C22semidirect
116. #2336C22semidirect
119. #2323C22semidirect
120. #2323C22semidirect
121. #2323C22semidirect
123. #2316C22semidirect
125. #2314C22semidirect
127. #2310C22semidirect
128. C4×C4⋊Q8C22semidirect
129. C4×C4⋊Q8C22semidirect
130. C4×#125C22semidirect
134. #2295C22semidirect
135. #2295C22semidirect
146. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#403332
#396772
#395402
#387482
#379582
#379342
#374002
#373692
#366352
#356712
#355992
#353102
#350872
#350842
#350332
#350142
#350112
#342032
C2×#22932