Finite Group Databasebeta

← #7716022

Subgroups — #7716022

Order 512.

4526 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50189C214yesmaximal, complemented
2#50185C214yesmaximal, complemented
3#48801C214yesmaximal, complemented
4#48797C214yesmaximal, complemented
5#45392C214yesmaximal, complemented
6#45119C214yesmaximal, complemented
7#44961C214yesmaximal, complemented
8#44958C214yesmaximal, complemented
9#39038C218yesmaximal, complemented
10#38982C214yesmaximal, complemented
11#36975C214yesmaximal, complemented
12#36487C214yesmaximal, complemented
13#35311C211yesmaximal, characteristic, complemented
14#35262C211yesmaximal, characteristic
15#35099C214yesmaximal, complemented
16#35019C211yesmaximal, characteristic
17#34578C211yesmaximal, characteristic, complemented
18#34380C211yesmaximal, characteristic, complemented
19#34379C211yesmaximal, characteristic
20C2×#2346C211yesmaximal, characteristic, complemented
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#117C2211yescharacteristic
24#2855C2214yescomplemented
25#2854C2214yes—
26#2853C2218yescomplemented
27#2850C2214yes—
28#2787C2218yescomplemented
29#2783C2218yescomplemented
30#2777C2218yescomplemented
31#2774C2218yescomplemented
32#2772C2218yescomplemented
33#2767C2218yescomplemented
34#2763C2218yescomplemented
35#2761C2218yescomplemented
36#2761C2218yescomplemented
37#2754C2218yescomplemented
38#2745C2218yes—
39#2744C2218yes—
40#2743C2218yescomplemented
41#2743C2218yescomplemented
42#2737C2218yescomplemented
43#2735C2218yes—
44#2735C2218yes—
45#2723C2218yescomplemented
46#2698C2218yescomplemented
47#2689C2218yescomplemented
48#2667C2212yes—
49#2667C2212yescomplemented
50#2665C2212yes—
51#2665C2212yescomplemented
52#2659C2212yescomplemented
53#2646C2212yescomplemented
54#2643C2218yescomplemented
55#2639C2212yes—
56#2639C2212yes—
57#2626C2214yes—
58#2625C2212yes—
59#2625C2212yes—
60#2624C2212yes—
61#2624C2212yes—
62#2601C2218yescomplemented
63#2596C2218yescomplemented
64#2596C2218yescomplemented
65#2592C2214yescomplemented
66#2591C2214yes—
67#2589C2218yescomplemented
68#2581C2214yescomplemented
69#2576C2218yescomplemented
70#2575C2218yes—
71#2575C2218yescomplemented
72#2573C2218yes—
73#2571C2214yescomplemented
74#2570C2214yescomplemented
75#2570C2214yescomplemented
76#2561C2214yes—
77#2561C2218yes—
78#2538C2214yescomplemented
79#2533C2218yescomplemented
80#2532C2218yescomplemented
81#2531C2218yescomplemented
82#2530C2218yescomplemented
83#2529C2218yescomplemented
84#2528C2218yescomplemented
85#2527C2218yescomplemented
86#2526C2218yescomplemented
87#2516C2218yescomplemented
88#2514C2214yescomplemented
89#2513C2214yescomplemented
90#2512C2214yescomplemented
91#2511C2214yescomplemented
92#2504C2212yes—
93#2504C2212yes—
94#2503C2212yes—
95#2503C2212yescomplemented
96#2502C2212yescomplemented
97#2501C2212yes—
98#2500C2214yes—
99#2499C2214yes—
100#2488C2218yescomplemented
101#2484C2214yescomplemented
102#2483C2214yes—
103#2482C2214yes—
104#2481C2218yescomplemented
105#2480C2218yes—
106#2477C2218yescomplemented
107#2449C2218yescomplemented
108#2448C2214yescomplemented
109#2447C2214yescomplemented
110#2436C2212yes—
111#2435C2212yes—
112#2419C2218yescomplemented
113#2405C2214yes—
114#2396C2214yes—
115#2396C2214yescomplemented
116#2378C2214yes—
117#2377C2214yes—
118#2367C2214yescomplemented
119#2361C2214yes—
120#2360C2214yescomplemented
121#2357C2214yescomplemented
122#2355C2214yescomplemented
123#2355C2214yescomplemented
124#2346C2214yes—
125#2346C2214yes—
126#2346C2214yescomplemented
127#2346C2214yescomplemented
128#2345C2212yes—
129#2344C2212yescomplemented
130#2342C2214yes—
131Q8×C22⋊C4C2212yescomplemented
132D4×C22⋊C4C2214yes—
133D4×C22⋊C4C2212yes—
134#2329C2214yescomplemented
135#2325C2214yes—
136#2324C2214yes—
137#2323C2214yes—
138#2318C2218yescomplemented
139#2317C2212yes—
140#2317C2212yescomplemented
141#2316C2212yescomplemented
142#2315C2212yes—
143#2313C2212yescomplemented
144#2312C2212yes—
145#2310C2212yescomplemented
146#2309C2212yes—
147#2308C2214yes—
148C4×C22⋊Q8C2214yescomplemented
149C4×#123C2218yescomplemented
150C2×#389C2212yescomplemented
151C2×#388C2214yes—
152C2×#382C2212yescomplemented
153#2280C2211yescharacteristic
154#2280C2211yescharacteristic
155C2×#380C2211yescharacteristic
156C2×C4×C4⋊C4C2212yescomplemented
157C2×C4×C22⋊C4C2211yescharacteristic
158C2×#376C2212yescomplemented
159C23×Q8C2311yescharacteristic
160C23×D4C2312yes—
161C23×D4C2311yescharacteristic
162C24×C4C2311yescharacteristic
163C2×#126C2318yes—
164C2×#124C2314yes—
165C2×#123C2318yes—
166C2×C22⋊Q8—28no—
167C2×C22⋊Q8C2312yes—
168C2×C22⋊Q8C2312yes—
169C2×C22⋊Q8C2312yes—
170C2×C22⋊Q8C2312yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2318yes—
173C2×#121—28no—
174C2×#121C2312yes—
175C2×#121C2312yes—
176C2×#121C2312yes—
177C2×#121C2312yes—
178C2×C4×Q8C2314yes—
179C2×C4×Q8C2314yes—
180C2×C4×D4C2318yes—
181C2×C4×D4C2314yes—
182C2×#117—28no—
183C2×#117C2312yes—
184C2×#117C2312yes—
185C2×#117C2312yes—
186C2×#117C2312yes—
187C2×#117C2312yes—
188C2×#117C2312yes—
189C2×#117C2314yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2314yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2314yes—
202C22×C22⋊C4C2312yes—
203C22×C42C2312yes—
204C22×C42C2312yes—
205C22×C42C2314yes—
206#401C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2314yes—
214#400C2318yes—
215#400C2314yes—
216#400C2314yes—
217#400C2314yes—
218#400C2314yes—
219#400C2314yes—
220#400C2318yes—
221#399C2314yes—
222#399C2314yes—
223#399C2314yes—
224#399C2314yes—
225#399C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2314yes—
229#398C2314yes—
230#398C2314yes—
231#398C2314yes—
232#398C2314yes—
233#398C2314yes—
234#397C2318yes—
235#397C2314yes—
236#397C2314yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2314yes—
243#397C2314yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#396C2314yes—
248#396C2314yes—
249#396C2314yes—
250#396C2318yes—
251#396C2314yes—
252#396C2318yes—
253#396C2318yes—
254#395C2318yes—
255#395C2314yes—
256#395C2314yes—
257#394C2318yes—
258#394C2314yes—
259#394C2314yes—
260#394C2318yes—
261#393C2314yes—
262#393C2318yes—
263#393C2314yes—
264#393C2314yes—
265#393C2314yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2318yes—
273#391C2314yes—
274#391C2318yes—
275#390C2314yes—
276#390C2314yes—
277#390C2314yes—
278#390C2314yes—
279#390C2314yes—
280#390C2318yes—
281#390C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2318yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
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#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2314yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2314yes—
337#387C2318yes—
338#387C2318yes—
339#386C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2314yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2314yes—
357#384C2314yes—
358#384C2314yes—
359#383C2318yes—
360#382C2314yes—
361#382C2314yes—
362#382C2314yes—
363#382C2318yes—
364#382C2318yes—
365#382C2318yes—
366#382C2318yes—
367#381C2318yes—
368#381C2318yes—
369#381C2318yes—
370#381C2318yes—
371#381C2314yes—
372#381C2318yes—
373#381C2312yes—
374#381C2312yes—
375#380C2311yescharacteristic
376#380C2312yes—
377#380C2311yescharacteristic
378#380C2312yes—
379#380C2311yescharacteristic
380#380C2314yes—
381#380C2311yescharacteristic
382#380C2314yes—
383#380C2318yes—
384#380C2312yes—
385#380C2312yes—
386#380C2312yes—
387#380C2312yes—
388#380C2314yes—
389#379C2318yes—
390#379C2318yes—
391#379C2314yes—
392#379C2312yes—
393#379C2312yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C22⋊C4C2312yes—
405C4×C22⋊C4C2318yes—
406C4×C22⋊C4C2314yes—
407C4×C22⋊C4C2314yes—
408C4×C22⋊C4C2318yes—
409C4×C22⋊C4C2318yes—
410C4×C22⋊C4C2312yes—
411C4×C22⋊C4C2312yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2312yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2312yes—
417#376C2318yes—
418#376C2318yes—
419C2×#95C2314yes—
420C2×#95C2312yes—
421C2×#95C2311yescharacteristic
422C2×#95C2311yescharacteristic
423C2×#95C2314yes—
424C25C2411yescharacteristic
425C25C2412yes—
426C22×Q8—24no—
427C22×Q8—44no—
428C22×Q8C2412yes—
429C22×Q8C2412yes—
430C22×Q8C2414yes—
431C22×D4—28no—
432C22×D4—24no—
433C22×D4—44no—
434C22×D4—48no—
435C22×D4C2414yes—
436C22×D4C2412yes—
437C22×D4C2414yes—
438C22×D4C2412yes—
439C23×C4—44no—
440C23×C4#4118yes—
441C23×C4C2412yes—
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2414yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2412yes—
452C23×C4C2418yes—
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456#126—88no—
457#124—48no—
458#123—416no—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—48no—
464C22⋊Q8—88no—
465#121—28no—
466#121—28no—
467#121—28no—
468#121—28no—
469C4×Q8—48no—
470C4×Q8—48no—
471C4×D4—48no—
472C4×D4—416no—
473#117—28no—
474#117—28no—
475#117—28no—
476#117—28no—
477#117—44no—
478#117—44no—
479#117—84no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—44no—
486C2×C4⋊C4—84no—
487C2×C4⋊C4C2412yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2418yes—
521C2×C22⋊C4—28no—
522C2×C22⋊C4—28no—
523C2×C22⋊C4—28no—
524C2×C22⋊C4—44no—
525C2×C22⋊C4—82no—
526C2×C22⋊C4—84no—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2412yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C42—28no—
557C2×C42—44no—
558C2×C42—48no—
559C2×C42C2414yes—
560C2×C42C2414yes—
561C2×C42C2414yes—
562C2×C42C2414yes—
563C2×C42C2414yes—
564C2×C42C2418yes—
565C2×C42C2418yes—
566C2×C42C2418yes—
567C2×C42C2418yes—
568C2×C42C2418yes—
569C2×C42C2414yes—
570#95C2412yes—
571#95C2412yes—
572#95C2414yes—
573#95C2414yes—
574#95C2418yes—
575#95C2418yes—
576#95C2412yes—
577#95C2412yes—
578#95C2418yes—
579#95C2418yes—
580#95C2414yes—
581#95C2414yes—
582#95C2418yes—
583#95C2418yes—
584#95C2412yes—
585#95C2414yes—
586#95C2412yes—
587#95C2412yes—
588#95C2414yes—
589#95C2412yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2414yes—
595#95C2418yes—
596#95C2414yes—
597#95C2418yes—
598#95C2414yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2414yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610C24—24no—
611C24—24no—
612C24—41no—
613C24—42no—
614C24—41no—
615C24—42no—
616C24—42no—
617C24—44no—
618C24—44no—
619C24C2×#4114yes—
620C24C2514yes—
621C24C2511yescharacteristic
622C24C2511yescharacteristic
623C24C2511yescharacteristic
624C2×Q8—24no—
625C2×Q8—24no—
626C2×Q8—28no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—88no—
632C2×D4—28no—
633C2×D4—216no—
634C2×D4—28no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—28no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—88no—
641C2×D4—816no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—28no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—28no—
653C22×C4—24no—
654C22×C4—416no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—42no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—48no—
671C22×C4—48no—
672C22×C4—48no—
673C22×C4C2×#4114yes—
674C22×C4C2×#4114yes—
675C22×C4C2×#4114yes—
676C22×C4C2×#4114yes—
677C22×C4C2×#4114yes—
678C22×C4C2×#4114yes—
679C22×C4C2514yes—
680C22×C4C2514yes—
681C22×C4C2514yes—
682C22×C4C2514yes—
683C22×C4C2514yes—
684C22×C4C2518yes—
685C22×C4C2514yes—
686C22×C4C2514yes—
687C22×C4C2514yes—
688C22×C4C2514yes—
689C22×C4C2514yes—
690C22×C4C2514yes—
691C22×C4C2511yescharacteristic
692C22×C4C2511yescharacteristic
693C22×C4C2511yescharacteristic
694C22×C4C2511yescharacteristic
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—28no—
706C4⋊C4—44no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—48no—
712C4⋊C4—42no—
713C4⋊C4—42no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—48no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—44no—
725C4⋊C4—48no—
726C4⋊C4—48no—
727C4⋊C4—48no—
728C4⋊C4—44no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—42no—
741C22⋊C4—44no—
742C22⋊C4—48no—
743C22⋊C4—42no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—42no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C22⋊C4—48no—
757C22⋊C4—48no—
758C42—28no—
759C42—28no—
760C42—28no—
761C42—28no—
762C42—28no—
763C42—44no—
764C42—48no—
765C42—48no—
766C42—48no—
767C42—48no—
768C42—48no—
769C23—22no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—28no—
781C23—24no—
782C23—28no—
783C23—28no—
784C23—24no—
785C23—24no—
786C23—44no—
787C23—44no—
788C23—48no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23—84no—
793C23—164no—
794C23—164no—
795C23C22×#4112yes—
796C23C22×#4112yes—
797C23C22×#4112yes—
798C23#58514yes—
799C23C2611yescharacteristic
800Q8—48no—
801Q8—84no—
802Q8—88no—
803D4—416no—
804D4—48no—
805D4—84no—
806D4—88no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—48no—
853C2×C4—48no—
854C2×C4—88no—
855C2×C4—84no—
856C2×C4—84no—
857C2×C4—84no—
858C2×C4—168no—
859C2×C4C22×#4112yes—
860C2×C4C22×#4112yes—
861C2×C4C22×#4112yes—
862C2×C4C22×#4112yes—
863C2×C4#58514yes—
864C22—22no—
865C22—22no—
866C22—24no—
867C22—24no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—48no—
882C22—48no—
883C22—88no—
884C22—168no—
885C22#351014yes—
886C22C23×#4111yescharacteristic
887C22C2×#58512yes—
888C22C2×#58512yes—
889C22H(7,𝔽2)11yescharacteristic
890C222−1+611yescharacteristic
891C4—22no—
892C4—22no—
893C4—22no—
894C4—44no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—44no—
899C4—48no—
900C4—44no—
901C4—44no—
902C4—44no—
903C4—44no—
904C4—44no—
905C4—44no—
906C4#349114yes—
907C2—24no—
908C2—42no—
909C2—42no—
910C2—84no—
911C2C2×#349111yescharacteristic
912C2C2×#351011yescharacteristic
913C2#6284511yescharacteristic
914C2#6291012yes—
915C2#6293412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50189C2semidirect
2. #50185C2semidirect
3. #48801C2semidirect
4. #48797C2semidirect
5. #45392C2semidirect
6. #45119C2semidirect
7. #44961C2semidirect
8. #44958C2semidirect
9. #39038C2semidirect
10. #38982C2semidirect
11. #36975C2semidirect
12. #36487C2semidirect
13. #35311C2semidirect
15. #35099C2semidirect
17. #34578C2semidirect
18. #34380C2semidirect
20. C2×#2346C2semidirect
24. #2855C22semidirect
26. #2853C22semidirect
28. #2787C22semidirect
29. #2783C22semidirect
30. #2777C22semidirect
31. #2774C22semidirect
32. #2772C22semidirect
33. #2767C22semidirect
34. #2763C22semidirect
35. #2761C22semidirect
36. #2761C22semidirect
37. #2754C22semidirect
40. #2743C22semidirect
41. #2743C22semidirect
42. #2737C22semidirect
45. #2723C22semidirect
46. #2698C22semidirect
47. #2689C22semidirect
49. #2667C22semidirect
51. #2665C22semidirect
52. #2659C22semidirect
53. #2646C22semidirect
54. #2643C22semidirect
62. #2601C22semidirect
63. #2596C22semidirect
64. #2596C22semidirect
65. #2592C22semidirect
67. #2589C22semidirect
68. #2581C22semidirect
69. #2576C22semidirect
71. #2575C22semidirect
73. #2571C22semidirect
74. #2570C22semidirect
75. #2570C22semidirect
78. #2538C22semidirect
79. #2533C22semidirect
80. #2532C22semidirect
81. #2531C22semidirect
82. #2530C22semidirect
83. #2529C22semidirect
84. #2528C22semidirect
85. #2527C22semidirect
86. #2526C22semidirect
87. #2516C22semidirect
88. #2514C22semidirect
89. #2513C22semidirect
90. #2512C22semidirect
91. #2511C22semidirect
95. #2503C22semidirect
96. #2502C22semidirect
100. #2488C22semidirect
101. #2484C22semidirect
104. #2481C22semidirect
106. #2477C22semidirect
107. #2449C22semidirect
108. #2448C22semidirect
109. #2447C22semidirect
112. #2419C22semidirect
115. #2396C22semidirect
118. #2367C22semidirect
120. #2360C22semidirect
121. #2357C22semidirect
122. #2355C22semidirect
123. #2355C22semidirect
126. #2346C22semidirect
127. #2346C22semidirect
129. #2344C22semidirect
131. Q8×C22⋊C4C22semidirect
134. #2329C22semidirect
138. #2318C22semidirect
140. #2317C22semidirect
141. #2316C22semidirect
143. #2313C22semidirect
145. #2310C22semidirect
148. C4×C22⋊Q8C22semidirect
149. C4×#123C22semidirect
150. C2×#389C22semidirect
152. C2×#382C22semidirect
156. C2×C4×C4⋊C4C22semidirect
158. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#501892
#501852
#488012
#487972
#453922
#451192
#449612
#449582
#390382
#389822
#369752
#364872
#353112
#352622
#350992
#350192
#345782
#343802
#343792
C2×#23462