Finite Group Databasebeta

← #7646832

Subgroups — #7646832

Order 512.

4690 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42638C214yesmaximal, complemented
2#42626C214yesmaximal, complemented
3#42582C214yesmaximal, complemented
4#42569C214yesmaximal, complemented
5#40167C214yesmaximal, complemented
6#40059C214yesmaximal, complemented
7#39399C214yesmaximal, complemented
8#39027C214yesmaximal, complemented
9#37460C214yesmaximal, complemented
10#36760C214yesmaximal, complemented
11#36728C214yesmaximal, complemented
12#35558C212yesmaximal
13#35555C212yesmaximal, complemented
14#35310C214yesmaximal, complemented
15#35266C212yesmaximal
16#35174C211yesmaximal, characteristic
17#35174C211yesmaximal, characteristic
18#35167C211yesmaximal, characteristic, complemented
19#35159C211yesmaximal, characteristic, complemented
20#34815C212yesmaximal, complemented
21#34271C211yesmaximal, characteristic, complemented
22C2×#2354C211yesmaximal, characteristic
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C2×#541C2214yescomplemented
27C22×C4×D4C2211yescharacteristic
28C22×#117C2212yes—
29#2860C2214yes—
30#2860C2214yes—
31#2857C2214yes—
32#2851C2214yes—
33#2848C2214yes—
34#2848C2214yes—
35#2836C2218yescomplemented
36#2831C2218yescomplemented
37#2798C2218yescomplemented
38#2783C2218yescomplemented
39#2772C2218yescomplemented
40#2754C2218yescomplemented
41#2747C2218yescomplemented
42#2747C2218yescomplemented
43#2725C2218yescomplemented
44#2725C2218yescomplemented
45#2722C2218yescomplemented
46#2722C2218yescomplemented
47#2721C2218yescomplemented
48#2716C2218yescomplemented
49#2704C2218yescomplemented
50#2704C2218yescomplemented
51#2690C2218yescomplemented
52#2690C2218yescomplemented
53#2664C2218yescomplemented
54#2659C2214yes—
55#2654C2218yescomplemented
56#2650C2218yescomplemented
57#2646C2214yes—
58#2644C2214yes—
59#2644C2214yes—
60#2637C2218yescomplemented
61#2629C2214yescomplemented
62#2626C2214yes—
63#2626C2214yes—
64#2625C2214yescomplemented
65#2625C2214yescomplemented
66#2621C2214yescomplemented
67#2570C2214yescomplemented
68#2570C2214yescomplemented
69#2552C2214yescomplemented
70#2552C2214yescomplemented
71#2552C2214yescomplemented
72#2551C2214yescomplemented
73#2550C2214yescomplemented
74#2550C2214yescomplemented
75#2519C2218yescomplemented
76#2513C2214yes—
77#2513C2214yes—
78#2513C2214yes—
79#2513C2214yes—
80#2513C2214yes—
81#2513C2214yes—
82#2512C2214yes—
83#2512C2214yes—
84#2512C2214yes—
85#2512C2214yes—
86#2512C2214yes—
87#2512C2214yes—
88#2509C2214yescomplemented
89#2509C2212yescomplemented
90#2509C2212yescomplemented
91#2508C2212yescomplemented
92#2508C2214yescomplemented
93#2508C2212yescomplemented
94#2507C2214yescomplemented
95#2507C2214yescomplemented
96#2507C2212yescomplemented
97#2507C2214yescomplemented
98#2507C2212yescomplemented
99#2506C2214yescomplemented
100#2506C2212yescomplemented
101#2506C2214yescomplemented
102#2506C2214yescomplemented
103#2506C2212yescomplemented
104#2505C2214yes—
105#2505C2214yes—
106#2480C2218yes—
107#2480C2218yes—
108#2480C2218yes—
109#2480C2218yes—
110#2478C2218yescomplemented
111#2478C2218yescomplemented
112#2475C2218yescomplemented
113#2475C2218yescomplemented
114#2473C2218yes—
115#2473C2214yes—
116#2473C2218yes—
117#2473C2214yes—
118#2469C2218yescomplemented
119#2454C2214yes—
120#2454C2214yes—
121#2454C2214yes—
122#2454C2214yes—
123#2452C2214yes—
124#2452C2214yes—
125#2452C2214yes—
126#2452C2214yes—
127#2402C2214yescomplemented
128#2402C2214yescomplemented
129#2370C2214yescomplemented
130#2370C2214yescomplemented
131#2369C2214yescomplemented
132#2365C2214yescomplemented
133#2354C2214yes—
134#2354C2214yes—
135#2354C2214yes—
136#2354C2214yes—
137#2331C2214yescomplemented
138#2330C2214yescomplemented
139#2329C2214yes—
140#2329C2214yes—
141#2323C2214yescomplemented
142#2323C2214yescomplemented
143#2317C2212yes—
144#2317C2212yes—
145#2316C2211yescharacteristic
146#2316C2211yescharacteristic
147#2316C2212yes—
148#2314C2214yescomplemented
149#2309C2212yes—
150#2309C2212yes—
151C4×C4⋊Q8C2214yescomplemented
152C4×#125C2214yescomplemented
153C4×#125C2214yescomplemented
154C4×#125C2214yescomplemented
155C4×C22⋊Q8C2214yes—
156C4×C22⋊Q8C2214yes—
157#2296C2212yes—
158#2296C2212yes—
159#2296C2212yes—
160#2296C2212yes—
161C2×#390C2211yescharacteristic
162C2×#390C2211yescharacteristic
163C2×#388C2212yes—
164C2×#388C2212yes—
165#2285C2212yes—
166C2×#384C2211yescharacteristic
167C2×#380C2212yes—
168#2274C2212yes—
169C4×#117C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C4⋊C4C2211yescharacteristic
173C23×D4C2311yescharacteristic
174C24×C4C2312yes—
175#544—28no—
176#544—28no—
177#541—416no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×#126C2318yes—
182C2×#126C2318yes—
183C2×#126C2318yes—
184C2×#126C2318yes—
185C2×#125C2314yes—
186C2×#125C2314yes—
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×#125C2314yes—
190C2×#125C2318yes—
191C2×#125C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×D4—28no—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×#117—48no—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2314yes—
210C2×#117C2314yes—
211C2×#117C2314yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228C22×C42C2312yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2314yes—
233#400C2314yes—
234#400C2318yes—
235#400C2314yes—
236#400C2318yes—
237#400C2314yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#399C2318yes—
242#399C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2314yes—
248#398C2318yes—
249#398C2318yes—
250#398C2314yes—
251#398C2314yes—
252#398C2318yes—
253#398C2314yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2314yes—
258#398C2314yes—
259#398C2314yes—
260#398C2314yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#395C2318yes—
282#395C2318yes—
283#393C2318yes—
284#393C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2318yes—
290#391C2314yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2312yes—
313#389C2312yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2318yes—
327#389C2314yes—
328#389C2318yes—
329#389C2318yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2318yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#387C2314yes—
362#387C2314yes—
363#387C2318yes—
364#387C2318yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2314yes—
391#385C2314yes—
392#385C2314yes—
393#385C2314yes—
394#385C2314yes—
395#384C2314yes—
396#384C2314yes—
397#384C2314yes—
398#384C2314yes—
399#384C2314yes—
400#384C2312yes—
401#384C2312yes—
402#382C2314yes—
403#382C2314yes—
404#382C2314yes—
405#382C2314yes—
406#382C2314yes—
407#382C2312yes—
408#382C2312yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2318yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2318yes—
418#380C2318yes—
419#380C2314yes—
420#379C2318yes—
421#379C2318yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2314yes—
455#376C2314yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C2×#95C2311yescharacteristic
459C2×#95C2311yescharacteristic
460C43C2314yes—
461C25C2412yes—
462C22×Q8C2414yes—
463C22×Q8C2414yes—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4C2414yes—
468C23×C4—28no—
469C23×C4—44no—
470C23×C4—44no—
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2414yes—
475C23×C4C2414yes—
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C4⋊Q8—216no—
484C4⋊Q8—216no—
485C4⋊Q8—48no—
486#126—416no—
487#126—416no—
488#126—88no—
489#126—88no—
490#125—216no—
491#125—216no—
492#125—216no—
493#125—48no—
494#125—48no—
495#125—416no—
496#125—88no—
497C22⋊Q8—216no—
498C22⋊Q8—216no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501C22⋊Q8—48no—
502C22⋊Q8—48no—
503C4×Q8—48no—
504C4×Q8—48no—
505C4×D4—216no—
506C4×D4—216no—
507#117—28no—
508#117—28no—
509#117—28no—
510#117—28no—
511#117—216no—
512#117—48no—
513#117—48no—
514#117—48no—
515C2×C4⋊C4—24no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—42no—
519C2×C4⋊C4—44no—
520C2×C4⋊C4—82no—
521C2×C4⋊C4#4118yes—
522C2×C4⋊C4C2411yescharacteristic
523C2×C4⋊C4C2411yescharacteristic
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C22⋊C4—28no—
577C2×C22⋊C4—44no—
578C2×C22⋊C4—44no—
579C2×C22⋊C4—82no—
580C2×C22⋊C4—82no—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C42—24no—
601C2×C42—24no—
602C2×C42—24no—
603C2×C42—44no—
604C2×C42—44no—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2414yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2418yes—
621C2×C42C2418yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2412yes—
628#95C2412yes—
629#95C2412yes—
630#95C2412yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665C24—24no—
666C24—24no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24C2514yes—
673C24C2511yescharacteristic
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—416no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—42no—
701C22×C4—41no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—42no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—432no—
717C22×C4C2×#4118yes—
718C22×C4C2×#4114yes—
719C22×C42−1+414yes—
720C22×C42−1+414yes—
721C22×C4C2514yes—
722C22×C4C2511yescharacteristic
723C22×C4C2511yescharacteristic
724C22×C4C2512yes—
725C22×C4C2512yes—
726C22×C4C2514yes—
727C22×C4C2514yes—
728C22×C4C2512yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2511yescharacteristic
738C22×C4C2511yescharacteristic
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C22×C4C2512yes—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C4⋊C4—216no—
749C4⋊C4—216no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—22no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—42no—
769C4⋊C4—44no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—48no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—48no—
789C4⋊C4—48no—
790C4⋊C4—48no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4C2×#41116yes—
795C4⋊C4H(5,𝔽2)14yes—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—216no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C42—24no—
816C42—24no—
817C42—28no—
818C42—28no—
819C42—28no—
820C42—28no—
821C42—28no—
822C42—24no—
823C42—24no—
824C42—24no—
825C42—24no—
826C42—28no—
827C42—28no—
828C42—44no—
829C42—44no—
830C42—44no—
831C42—48no—
832C42—44no—
833C42—48no—
834C42—44no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—48no—
847C23—48no—
848C23—48no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23C22×#4112yes—
854C23C2×2−1+412yes—
855C23C2×2−1+412yes—
856C23C2611yescharacteristic
857Q8—88no—
858Q8—88no—
859D4—416no—
860C2×C4—28no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—24no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—24no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—48no—
917C2×C4—416no—
918C2×C4—416no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—84no—
923C2×C4—84no—
924C2×C4—82no—
925C2×C4—82no—
926C2×C4#541116yescomplemented
927C2×C4C22×#4118yes—
928C2×C4C22×#4114yes—
929C2×C4C2×H(5,𝔽2)12yes—
930C2×C4C2×H(5,𝔽2)12yes—
931C2×C4C2×H(5,𝔽2)12yes—
932C2×C4C2×2−1+414yes—
933C2×C4C2×2−1+414yes—
934C2×C4#58512yes—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—44no—
942C22—44no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—816no—
949C22C2×#54114yes—
950C22C23×#4111yescharacteristic
951C22C22×H(5,𝔽2)11yescharacteristic
952C22C22×2−1+411yescharacteristic
953C22C22×2−1+411yescharacteristic
954C22C2×#58511yescharacteristic
955C22H(7,𝔽2)11yescharacteristic
956C222−1+611yescharacteristic
957C4—22no—
958C4—22no—
959C4—28no—
960C4—22no—
961C4—22no—
962C4—44no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—42no—
967C4—44no—
968C4—41no—
969C4—41no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4—42no—
975C4—42no—
976C4—44no—
977C4C2×#54118yes—
978C2—24no—
979C2—84no—
980C2C22×#54111yescharacteristic
981C2#6277311yescharacteristic
982C2#6285111yescharacteristic
983C2#6291511yescharacteristic
984C2#6291711yescharacteristic
985C2#6292911yescharacteristic
986C2#6293211yescharacteristic
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. #42638C2semidirect
2. #42626C2semidirect
3. #42582C2semidirect
4. #42569C2semidirect
5. #40167C2semidirect
6. #40059C2semidirect
7. #39399C2semidirect
8. #39027C2semidirect
9. #37460C2semidirect
10. #36760C2semidirect
11. #36728C2semidirect
13. #35555C2semidirect
14. #35310C2semidirect
18. #35167C2semidirect
19. #35159C2semidirect
20. #34815C2semidirect
21. #34271C2semidirect
23. C4×#544C2semidirect
26. C2×#541C22semidirect
35. #2836C22semidirect
36. #2831C22semidirect
37. #2798C22semidirect
38. #2783C22semidirect
39. #2772C22semidirect
40. #2754C22semidirect
41. #2747C22semidirect
42. #2747C22semidirect
43. #2725C22semidirect
44. #2725C22semidirect
45. #2722C22semidirect
46. #2722C22semidirect
47. #2721C22semidirect
48. #2716C22semidirect
49. #2704C22semidirect
50. #2704C22semidirect
51. #2690C22semidirect
52. #2690C22semidirect
53. #2664C22semidirect
55. #2654C22semidirect
56. #2650C22semidirect
60. #2637C22semidirect
61. #2629C22semidirect
64. #2625C22semidirect
65. #2625C22semidirect
66. #2621C22semidirect
67. #2570C22semidirect
68. #2570C22semidirect
69. #2552C22semidirect
70. #2552C22semidirect
71. #2552C22semidirect
72. #2551C22semidirect
73. #2550C22semidirect
74. #2550C22semidirect
75. #2519C22semidirect
88. #2509C22semidirect
89. #2509C22semidirect
90. #2509C22semidirect
91. #2508C22semidirect
92. #2508C22semidirect
93. #2508C22semidirect
94. #2507C22semidirect
95. #2507C22semidirect
96. #2507C22semidirect
97. #2507C22semidirect
98. #2507C22semidirect
99. #2506C22semidirect
100. #2506C22semidirect
101. #2506C22semidirect
102. #2506C22semidirect
103. #2506C22semidirect
110. #2478C22semidirect
111. #2478C22semidirect
112. #2475C22semidirect
113. #2475C22semidirect
118. #2469C22semidirect
127. #2402C22semidirect
128. #2402C22semidirect
129. #2370C22semidirect
130. #2370C22semidirect
131. #2369C22semidirect
132. #2365C22semidirect
137. #2331C22semidirect
138. #2330C22semidirect
141. #2323C22semidirect
142. #2323C22semidirect
148. #2314C22semidirect
151. C4×C4⋊Q8C22semidirect
152. C4×#125C22semidirect
153. C4×#125C22semidirect
154. C4×#125C22semidirect
926. C2×C4#541semidirect

Maximal subgroups

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

subgroupindex
#426382
#426262
#425822
#425692
#401672
#400592
#393992
#390272
#374602
#367602
#367282
#355582
#355552
#353102
#352662
#351742
#351672
#351592
#348152
#342712
C2×#23542
C4×#5442