Finite Group Databasebeta

← #7681221

Subgroups — #7681221

Order 512.

4575 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59751C214yesmaximal, complemented
2#59713C214yesmaximal
3#59669C214yesmaximal, complemented
4#59505C214yesmaximal, complemented
5#44425C218yesmaximal, complemented
6#44323C218yesmaximal, complemented
7#39514C211yesmaximal, characteristic, complemented
8#39513C212yesmaximal, complemented
9#39379C211yesmaximal, characteristic, complemented
10#39373C212yesmaximal, complemented
11#39125C212yesmaximal
12#38273C214yesmaximal, complemented
13#36600C211yesmaximal, characteristic, complemented
14Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
15#36287C212yesmaximal, complemented
16#35604C214yesmaximal, complemented
17#35294C212yesmaximal, complemented
18#35284C211yesmaximal, characteristic, complemented
19#34941C212yesmaximal, complemented
20#34335C212yesmaximal, complemented
21#34281C212yesmaximal, complemented
22#34151C211yesmaximal, characteristic
23C4×#541C211yesmaximal, characteristic, complemented
24C2×Q82C2212yes—
25C2×#541C2211yescharacteristic
26C2×#541C2212yes—
27C2×#529C2211yescharacteristic
28#2868C2212yes—
29#2868C2211yescharacteristic
30#2859C2214yes—
31#2859C2212yes—
32#2859C2211yescharacteristic
33#2857C2212yes—
34#2793C2218yes—
35#2793C2218yes—
36#2775C2218yes—
37#2774C2218yes—
38#2773C2218yes—
39#2767C2218yes—
40#2727C2218yes—
41#2726C2218yes—
42#2725C2218yes—
43#2716C2218yes—
44#2716C2218yes—
45#2674C2218yes—
46#2647C2212yes—
47#2629C2212yes—
48#2629C2212yes—
49#2629C2212yes—
50#2628C2214yes—
51#2612C2218yes—
52#2604C2218yes—
53#2596C2218yes—
54#2588C2218yes—
55#2585C2218yes—
56#2574C2218yes—
57#2570C2214yes—
58#2570C2214yes—
59#2570C2218yes—
60#2567C2214yes—
61#2567C2212yes—
62#2563C2212yes—
63#2556C2218yes—
64#2552C2212yes—
65#2551C2214yes—
66#2551C2218yes—
67#2550C2214yes—
68#2550C2218yes—
69#2547C2214yes—
70#2545C2218yes—
71#2538C2212yes—
72#2536C2214yes—
73#2533C2218yes—
74#2530C2218yes—
75#2529C2218yes—
76#2521C2218yes—
77#2520C2218yes—
78#2519C2218yes—
79#2519C2218yes—
80#2519C2218yes—
81#2512C2214yes—
82#2512C2214yes—
83#2508C2214yes—
84#2507C2214yes—
85#2506C2214yes—
86#2506C2214yes—
87#2497C2214yes—
88#2497C2214yes—
89#2497C2214yes—
90#2496C2214yes—
91#2491C2214yes—
92#2478C2218yes—
93#2474C2218yes—
94#2462C2218yes—
95#2454C2214yes—
96#2453C2214yes—
97#2448C2214yes—
98#2446C2218yes—
99#2446C2214yes—
100#2441C2218yes—
101#2441C2214yes—
102#2439C2218yes—
103#2429C2214yes—
104#2423C2214yes—
105#2423C2214yes—
106#2421C2214yes—
107#2421C2214yes—
108#2396C2218yes—
109#2374C2214yes—
110#2373C2218yes—
111#2373C2218yes—
112#2373C2214yes—
113#2371C2218yes—
114#2370C2212yes—
115#2370C2218yes—
116#2370C2214yes—
117#2370C2214yes—
118#2369C2214yes—
119#2369C2212yes—
120#2367C2212yes—
121#2365C2218yes—
122#2365C2214yes—
123#2363C2212yes—
124#2362C2212yes—
125#2355C2214yes—
126#2355C2212yes—
127#2351C2214yes—
128Q8×C4⋊C4C2212yes—
129Q8×C4⋊C4C2214yes—
130#2346C2214yes—
131#2336C2214yes—
132#2334C2214yes—
133#2331C2214yes—
134#2331C2218yes—
135#2330C2211yescharacteristic
136#2330C2212yes—
137#2327C2211yescharacteristic
138#2323C2212yes—
139#2323C2214yes—
140#2320C2212yes—
141#2314C2212yes—
142#2314C2211yescharacteristic
143#2314C2212yes—
144C4×C4⋊Q8C2214yes—
145C4×C4⋊Q8C2212yes—
146C4×C4⋊Q8C2211yescharacteristic
147C4×C4⋊Q8C2212yes—
148C4×#125C2214yes—
149C4×#125C2214yes—
150C4×#125C2211yescharacteristic
151C4×#125C2212yes—
152C4×#126C2214yes—
153C4×C22⋊Q8C2214yes—
154C4×C22⋊Q8C2212yes—
155#2298C2212yes—
156#2295C2211yescharacteristic
157#2295C2214yes—
158#2295C2214yes—
159#2293C2214yes—
160#2293C2212yes—
161#2293C2211yescharacteristic
162#2290C2212yes—
163#2285C2214yes—
164#2276C2214yes—
165C42×Q8C2212yes—
166C42×Q8C2211yescharacteristic
167C42×D4C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C4×#117C2211yescharacteristic
170C4×#117C2212yes—
171Q82—216no—
172#541—28no—
173#541—216no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2318yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2318yes—
180C2×C4⋊Q8C2311yescharacteristic
181#529—28no—
182C2×#126C2314yes—
183C2×#126C2312yes—
184C2×#126C2318yes—
185C2×#126C2318yes—
186C2×#125C2311yescharacteristic
187C2×#125C2312yes—
188C2×#125C2314yes—
189C2×#125C2314yes—
190C2×#125C2311yescharacteristic
191C2×#125C2318yes—
192C2×#125C2318yes—
193C2×#124C2311yescharacteristic
194C2×#124C2318yes—
195C2×#123C2312yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2311yescharacteristic
199C2×C22⋊Q8C2314yes—
200C2×#121C2311yescharacteristic
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2314yes—
208C2×C4×Q8C2318yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2311yescharacteristic
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2312yes—
213C2×C4×D4C2312yes—
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2318yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#399C2318yes—
230#399C2318yes—
231#399C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#395C2318yes—
252#395C2318yes—
253#395C2318yes—
254#395C2318yes—
255#394C2318yes—
256#393C2318yes—
257#393C2318yes—
258#391C2312yes—
259#391C2314yes—
260#391C2314yes—
261#391C2318yes—
262#391C2312yes—
263#391C2318yes—
264#391C2318yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2312yes—
269#391C2314yes—
270#390C2314yes—
271#390C2312yes—
272#390C2314yes—
273#390C2314yes—
274#389C2314yes—
275#389C2312yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2312yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2318yes—
285#389C2318yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#389C2312yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2312yes—
294#389C2314yes—
295#389C2318yes—
296#389C2314yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2318yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2314yes—
307#389C2314yes—
308#388C2314yes—
309#388C2314yes—
310#388C2314yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2314yes—
322#388C2318yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2318yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2318yes—
333#387C2318yes—
334#387C2314yes—
335#387C2314yes—
336#387C2314yes—
337#387C2314yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2314yes—
351#387C2318yes—
352#387C2314yes—
353#387C2318yes—
354#387C2318yes—
355#387C2314yes—
356#387C2318yes—
357#387C2318yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#387C2314yes—
362#386C2314yes—
363#385C2318yes—
364#385C2314yes—
365#385C2314yes—
366#384C2311yescharacteristic
367#384C2312yes—
368#384C2312yes—
369#384C2314yes—
370#384C2312yes—
371#384C2314yes—
372#384C2314yes—
373#384C2318yes—
374#384C2314yes—
375#383C2314yes—
376#382C2311yescharacteristic
377#382C2314yes—
378#382C2314yes—
379#382C2312yes—
380#382C2318yes—
381#382C2314yes—
382#382C2318yes—
383#382C2318yes—
384#380C2314yes—
385#380C2314yes—
386#380C2312yes—
387#380C2314yes—
388#380C2318yes—
389#380C2314yes—
390#380C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2312yes—
439#376C2311yescharacteristic
440#376C2311yescharacteristic
441#376C2312yes—
442#376C2318yes—
443#376C2318yes—
444#376C2312yes—
445C43C2314yes—
446C43C2311yescharacteristic
447C43C2312yes—
448C43C2311yescharacteristic
449C43C2312yes—
450C22×Q8C2412yes—
451C22×Q8C2411yescharacteristic
452C22×Q8C2414yes—
453C22×Q8C2418yes—
454C22×D4C2411yescharacteristic
455C22×D4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2412yes—
458C23×C4C2411yescharacteristic
459C23×C4C2414yes—
460C23×C4C2411yescharacteristic
461C4⋊Q8—216no—
462C4⋊Q8—232no—
463C4⋊Q8—28no—
464C4⋊Q8—216no—
465C4⋊Q8—88no—
466C4⋊Q8—84no—
467C4⋊Q8#4118yes—
468#126—28no—
469#126—216no—
470#126—232no—
471#126—88no—
472#125—24no—
473#125—216no—
474#125—232no—
475#125—216no—
476#125—24no—
477#125—28no—
478#125—88no—
479#124—24no—
480#124—88no—
481#123—28no—
482C22⋊Q8—24no—
483C22⋊Q8—216no—
484C22⋊Q8—28no—
485C22⋊Q8—84no—
486#121—24no—
487C4×Q8—28no—
488C4×Q8—216no—
489C4×Q8—216no—
490C4×Q8—28no—
491C4×Q8—28no—
492C4×Q8—216no—
493C4×Q8—28no—
494C4×Q8—84no—
495C4×Q8—88no—
496C4×Q8#4118yes—
497C4×D4—28no—
498C4×D4—24no—
499C4×D4—28no—
500#117—28no—
501#117—28no—
502#117—24no—
503#117—28no—
504#117—24no—
505#117—88no—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2411yescharacteristic
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2412yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C42—24no—
571C2×C42—28no—
572C2×C42C2411yescharacteristic
573C2×C42C2411yescharacteristic
574C2×C42C2412yes—
575C2×C42C2414yes—
576C2×C42C2411yescharacteristic
577C2×C42C2412yes—
578C2×C42C2414yes—
579C2×C42C2418yes—
580C2×C42C2414yes—
581C2×C42C2418yes—
582C2×C42C2414yes—
583C2×C42C2412yes—
584C2×C42C2414yes—
585C2×C42C2411yescharacteristic
586C2×C42C2414yes—
587C2×C42C2411yescharacteristic
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2418yes—
592C2×C42C2412yes—
593C2×C42C2414yes—
594C2×C42C2418yes—
595C2×C42C2418yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2412yes—
599C2×C42C2411yescharacteristic
600C2×C42C2412yes—
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603#95C2414yes—
604#95C2414yes—
605#95C2412yes—
606#95C2412yes—
607#95C2412yes—
608#95C2414yes—
609#95C2412yes—
610#95C2412yes—
611#95C2414yes—
612#95C2418yes—
613#95C2412yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2418yes—
644C24C2512yes—
645C24C2511yescharacteristic
646C2×Q8—24no—
647C2×Q8—28no—
648C2×Q8—216no—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—48no—
652C2×Q8—44no—
653C2×Q8—44no—
654C2×Q8—48no—
655C2×Q8C2×#4114yes—
656C2×Q8C2×#4118yes—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—44no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—24no—
666C22×C4—28no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—22no—
670C22×C4—28no—
671C22×C4—22no—
672C22×C4—44no—
673C22×C4—42no—
674C22×C4C2511yescharacteristic
675C22×C4C2514yes—
676C22×C4C2512yes—
677C22×C4C2511yescharacteristic
678C22×C4C2512yes—
679C22×C4C2512yes—
680C22×C4C2514yes—
681C22×C4C2514yes—
682C22×C4C2518yes—
683C22×C4C2518yes—
684C22×C4C2514yes—
685C22×C4C2511yescharacteristic
686C22×C4C2512yes—
687C22×C4C2514yes—
688C22×C4C2512yes—
689C22×C4C2511yescharacteristic
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2514yes—
693C22×C4C2511yescharacteristic
694C22×C4C2511yescharacteristic
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—28no—
699C4⋊C4—22no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—216no—
705C4⋊C4—28no—
706C4⋊C4—216no—
707C4⋊C4—216no—
708C4⋊C4—28no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—216no—
713C4⋊C4—28no—
714C4⋊C4—216no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—24no—
720C4⋊C4—216no—
721C4⋊C4—216no—
722C4⋊C4—28no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—44no—
726C4⋊C4—48no—
727C4⋊C4—44no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4—44no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—44no—
734C4⋊C4—48no—
735C4⋊C4—48no—
736C4⋊C4—44no—
737C4⋊C4C2×#4114yes—
738C4⋊C4C2×#4118yes—
739C4⋊C4C2×#41116yes—
740C4⋊C42−1+418yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—28no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—28no—
749C22⋊C4—216no—
750C22⋊C4—24no—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C22⋊C4—44no—
757C22⋊C4—48no—
758C22⋊C4—44no—
759C42—22no—
760C42—22no—
761C42—22no—
762C42—22no—
763C42—24no—
764C42—216no—
765C42—28no—
766C42—28no—
767C42—216no—
768C42—24no—
769C42—28no—
770C42—28no—
771C42—22no—
772C42—24no—
773C42—28no—
774C42—24no—
775C42—28no—
776C42—28no—
777C42—44no—
778C42—48no—
779C42—42no—
780C42—44no—
781C42—48no—
782C42—48no—
783C42—44no—
784C42—44no—
785C42—42no—
786C42C2×#4114yes—
787C42C2×#4114yes—
788C42C2×#4118yes—
789C422−1+414yes—
790C23—21no—
791C23—22no—
792C23—22no—
793C23—21no—
794C23—22no—
795C23—21no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23C2611yescharacteristic
801Q8—216no—
802Q8—28no—
803Q8—88no—
804Q8—816no—
805D4—44no—
806D4—84no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—28no—
840C2×C4—21no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—416no—
853C2×C4—44no—
854C2×C4—48no—
855C2×C4—44no—
856C2×C4—82no—
857C2×C4C22×#4114yes—
858C2×C4C22×#4118yes—
859C2×C4C22×#4112yes—
860C2×C4C22×#4114yes—
861C2×C4C22×#4114yes—
862C2×C4C22×#4112yes—
863C2×C4C22×#4112yes—
864C2×C4C22×#4112yes—
865C2×C4C2×2−1+414yes—
866C2×C4C2×2−1+418yes—
867C2×C4C2×2−1+412yes—
868C2×C4C2×2−1+414yes—
869C22—42no—
870C22—44no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—44no—
876C22—42no—
877C22—42no—
878C22—41no—
879C22C23×#4111yescharacteristic
880C22C23×#4111yescharacteristic
881C22C22×2−1+412yes—
882C22C22×2−1+411yescharacteristic
883C22H(7,𝔽2)12yes—
884C4—24no—
885C4—24no—
886C4—22no—
887C4—24no—
888C4—24no—
889C4—28no—
890C4—28no—
891C4—42no—
892C4—44no—
893C4—44no—
894C4—48no—
895C4—41no—
896C4—41no—
897C4—48no—
898C4—44no—
899C4—42no—
900C4—44no—
901C4—41no—
902C4—42no—
903C4#348214yes—
904C4#350914yes—
905C2—81no—
906C2—82no—
907C2C2×#348211yescharacteristic
908C2C2×#350911yescharacteristic
909C2#6285811yescharacteristic
910C2#6294512yes—
911C2#6299912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59751C2semidirect
3. #59669C2semidirect
4. #59505C2semidirect
5. #44425C2semidirect
6. #44323C2semidirect
7. #39514C2semidirect
8. #39513C2semidirect
9. #39379C2semidirect
10. #39373C2semidirect
12. #38273C2semidirect
13. #36600C2semidirect
14. Q8×C4⋊Q8C2semidirect
15. #36287C2semidirect
16. #35604C2semidirect
17. #35294C2semidirect
18. #35284C2semidirect
19. #34941C2semidirect
20. #34335C2semidirect
21. #34281C2semidirect
23. C4×#541C2semidirect

Maximal subgroups

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

subgroupindex
#597512
#597132
#596692
#595052
#444252
#443232
#395142
#395132
#393792
#393732
#391252
#382732
#366002
Q8×C4⋊Q82
#362872
#356042
#352942
#352842
#349412
#343352
#342812
#341512
C4×#5412