Finite Group Databasebeta

← #7657482

Subgroups — #7657482

Order 512.

4646 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42639C214yesmaximal, complemented
2#42634C214yesmaximal
3#40907C218yesmaximal, complemented
4#40901C218yesmaximal, complemented
5#39609C212yesmaximal, complemented
6#39513C211yesmaximal, characteristic, complemented
7#39379C211yesmaximal, characteristic, complemented
8#37889C212yesmaximal, complemented
9#37859C214yesmaximal, complemented
10#37709C212yesmaximal, complemented
11#37631C212yesmaximal, complemented
12#37509C214yesmaximal, complemented
13#36188C211yesmaximal, characteristic, complemented
14#36161C212yesmaximal
15#36132C211yesmaximal, characteristic, complemented
16#35919C214yesmaximal, complemented
17#35869C214yesmaximal, complemented
18#35310C212yesmaximal, complemented
19#35284C211yesmaximal, characteristic, complemented
20#34634C212yesmaximal, complemented
21#34629C211yesmaximal, characteristic, complemented
22#34324C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic
24C2×#556C2212yes—
25C2×#541C2212yescomplemented
26C2×#533C2212yescomplemented
27C22×C4×D4C2211yescharacteristic
28C22×#117C2212yes—
29#2868C2211yescharacteristic, complemented
30#2859C2211yescharacteristic, complemented
31#2857C2212yes—
32#2857C2212yescomplemented
33#2851C2212yescomplemented
34#2848C2214yes—
35#2838C2218yescomplemented
36#2835C2218yescomplemented
37#2827C2218yes—
38#2793C2218yescomplemented
39#2787C2218yescomplemented
40#2779C2218yes—
41#2774C2218yescomplemented
42#2745C2218yescomplemented
43#2742C2218yes—
44#2739C2218yescomplemented
45#2736C2218yes—
46#2735C2218yes—
47#2725C2218yescomplemented
48#2702C2218yes—
49#2690C2218yescomplemented
50#2655C2214yescomplemented
51#2655C2218yescomplemented
52#2653C2218yes—
53#2652C2214yes—
54#2652C2218yescomplemented
55#2650C2218yescomplemented
56#2650C2218yescomplemented
57#2647C2211yescharacteristic, complemented
58#2647C2212yescomplemented
59#2645C2212yescomplemented
60#2645C2214yescomplemented
61#2642C2211yescharacteristic, complemented
62#2640C2214yes—
63#2629C2211yescharacteristic
64#2629C2212yes—
65#2629C2212yescomplemented
66#2629C2212yescomplemented
67#2628C2214yes—
68#2628C2214yescomplemented
69#2627C2218yescomplemented
70#2626C2218yes—
71#2625C2212yes—
72#2625C2214yescomplemented
73#2621C2211yescharacteristic
74#2596C2218yescomplemented
75#2588C2218yescomplemented
76#2575C2218yes—
77#2574C2218yescomplemented
78#2568C2212yescomplemented
79#2567C2214yescomplemented
80#2551C2212yescomplemented
81#2547C2212yes—
82#2547C2214yes—
83#2545C2214yes—
84#2538C2212yes—
85#2530C2218yescomplemented
86#2529C2218yescomplemented
87#2528C2218yescomplemented
88#2527C2218yes—
89#2512C2214yes—
90#2511C2214yescomplemented
91#2509C2214yescomplemented
92#2507C2214yescomplemented
93#2506C2214yescomplemented
94#2499C2214yescomplemented
95#2497C2214yes—
96#2497C2214yescomplemented
97#2496C2218yescomplemented
98#2494C2214yescomplemented
99#2492C2214yes—
100#2492C2214yescomplemented
101#2485C2214yes—
102#2480C2218yes—
103#2480C2218yes—
104#2478C2218yescomplemented
105#2475C2218yes—
106#2473C2218yescomplemented
107#2469C2218yescomplemented
108#2466C2218yes—
109#2465C2218yescomplemented
110#2453C2218yescomplemented
111#2452C2214yes—
112#2451C2214yescomplemented
113#2451C2214yescomplemented
114#2448C2214yes—
115#2447C2214yes—
116#2446C2214yescomplemented
117#2446C2214yescomplemented
118#2439C2214yescomplemented
119#2435C2214yes—
120#2429C2214yes—
121#2423C2214yes—
122#2421C2214yescomplemented
123#2415C2214yes—
124#2402C2214yescomplemented
125#2401C2214yes—
126#2396C2218yes—
127#2396C2218yescomplemented
128#2373C2218yescomplemented
129#2367C2214yes—
130#2367C2214yes—
131#2365C2212yescomplemented
132#2365C2214yescomplemented
133#2365C2214yescomplemented
134#2362C2214yescomplemented
135#2360C2214yes—
136#2355C2214yescomplemented
137#2354C2212yes—
138#2354C2212yes—
139#2352C2214yes—
140Q8×C4⋊C4C2212yescomplemented
141D4×C4⋊C4C2212yes—
142#2346C2214yescomplemented
143#2344C2212yes—
144#2342C2214yes—
145D4×C22⋊C4C2212yes—
146#2334C2218yescomplemented
147#2330C2212yescomplemented
148#2326C2214yes—
149#2323C2214yes—
150#2314C2212yes—
151#2314C2212yescomplemented
152C4×C4⋊Q8C2212yescomplemented
153C4×C4⋊Q8C2211yescharacteristic, complemented
154C4×#125C2211yescharacteristic, complemented
155C4×C22⋊Q8C2212yes—
156C4×C22⋊Q8C2214yescomplemented
157#2296C2214yescomplemented
158#2295C2212yescomplemented
159#2293C2211yescharacteristic
160#2293C2211yescharacteristic
161#2290C2212yes—
162#2290C2212yes—
163#2285C2211yescharacteristic
164#2285C2212yescomplemented
165#2280C2214yes—
166#2280C2212yes—
167#2276C2214yescomplemented
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C23×D4C2311yescharacteristic
172C24×C4C2312yes—
173#556—216no—
174#541—48no—
175#533—48no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2311yescharacteristic
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×#126C2318yes—
182C2×#126C2318yes—
183C2×#125C2311yescharacteristic
184C2×#125C2312yes—
185C2×#125C2318yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×C22⋊Q8C2312yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2318yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2318yes—
199C2×C4×D4—28no—
200C2×C4×D4C2311yescharacteristic
201C2×C4×D4C2312yes—
202C2×C4×D4C2311yescharacteristic
203C2×C4×D4C2312yes—
204C2×C4×D4C2311yescharacteristic
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×#117—48no—
209C2×#117C2311yescharacteristic
210C2×#117C2312yes—
211C2×#117C2314yes—
212C2×#117C2311yescharacteristic
213C2×#117C2312yes—
214C2×#117C2314yes—
215C2×#117C2314yes—
216C2×#117C2314yes—
217C2×#117C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2314yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2314yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225#401C2318yes—
226#401C2314yes—
227#400C2318yes—
228#400C2314yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2314yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2314yes—
238#400C2318yes—
239#400C2318yes—
240#400C2314yes—
241#400C2314yes—
242#400C2314yes—
243#400C2314yes—
244#399C2318yes—
245#399C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2314yes—
249#398C2318yes—
250#398C2314yes—
251#398C2314yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2314yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2314yes—
267#397C2314yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2314yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#395C2318yes—
279#394C2318yes—
280#394C2318yes—
281#393C2318yes—
282#393C2318yes—
283#393C2318yes—
284#393C2318yes—
285#391C2314yes—
286#391C2312yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#391C2318yes—
292#391C2314yes—
293#391C2318yes—
294#391C2314yes—
295#391C2312yes—
296#391C2312yes—
297#391C2312yes—
298#391C2318yes—
299#390C2314yes—
300#390C2312yes—
301#390C2312yes—
302#390C2314yes—
303#389C2312yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2318yes—
308#389C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2312yes—
315#389C2312yes—
316#389C2314yes—
317#389C2318yes—
318#389C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2312yes—
326#389C2312yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2314yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2314yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2314yes—
344#388C2314yes—
345#388C2318yes—
346#387C2314yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2314yes—
356#387C2318yes—
357#387C2314yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2314yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2314yes—
367#387C2318yes—
368#387C2314yes—
369#386C2314yes—
370#386C2314yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2314yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2314yes—
380#385C2314yes—
381#384C2312yes—
382#384C2311yescharacteristic
383#384C2312yes—
384#384C2314yes—
385#384C2312yes—
386#384C2312yes—
387#384C2314yes—
388#382C2311yescharacteristic
389#382C2314yes—
390#382C2312yes—
391#382C2318yes—
392#382C2312yes—
393#381C2314yes—
394#381C2318yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2312yes—
400#380C2312yes—
401#380C2314yes—
402#380C2318yes—
403#380C2314yes—
404#380C2312yes—
405#380C2318yes—
406#380C2314yes—
407#380C2314yes—
408#379C2318yes—
409#379C2314yes—
410#379C2318yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2312yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2312yes—
445#376C2314yes—
446#376C2311yescharacteristic
447#376C2318yes—
448#376C2311yescharacteristic
449C43C2311yescharacteristic
450C43C2311yescharacteristic
451C25C2412yes—
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×Q8C2418yes—
455C22×D4—24no—
456C22×D4—44no—
457C22×D4C2411yescharacteristic
458C22×D4C2411yescharacteristic
459C22×D4C2412yes—
460C23×C4—28no—
461C23×C4—28no—
462C23×C4—44no—
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2414yes—
472C23×C4C2414yes—
473C4⋊Q8—28no—
474C4⋊Q8—24no—
475C4⋊Q8—48no—
476C4⋊Q8—48no—
477C4⋊Q8—48no—
478#126—232no—
479#126—416no—
480#125—24no—
481#125—28no—
482#125—416no—
483#124—216no—
484#124—48no—
485C22⋊Q8—216no—
486C22⋊Q8—28no—
487C22⋊Q8—416no—
488C22⋊Q8—48no—
489C22⋊Q8—48no—
490C4×Q8—216no—
491C4×Q8—28no—
492C4×Q8—416no—
493C4×Q8—48no—
494C4×Q8—48no—
495C4×Q8—48no—
496C4×D4—24no—
497C4×D4—28no—
498C4×D4—24no—
499C4×D4—28no—
500C4×D4—24no—
501C4×D4—44no—
502C4×D4—44no—
503C4×D4#4118yes—
504#117—216no—
505#117—24no—
506#117—24no—
507#117—28no—
508#117—44no—
509#117—44no—
510#117—48no—
511#117—48no—
512#117—48no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—48no—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2411yescharacteristic
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2411yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—48no—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2412yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2412yes—
581C2×C42—24no—
582C2×C42—28no—
583C2×C42—44no—
584C2×C42C2411yescharacteristic
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2412yes—
588C2×C42C2418yes—
589C2×C42C2411yescharacteristic
590C2×C42C2411yescharacteristic
591C2×C42C2411yescharacteristic
592C2×C42C2411yescharacteristic
593C2×C42C2411yescharacteristic
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2418yes—
600C2×C42C2418yes—
601C2×C42C2418yes—
602C2×C42C2418yes—
603C2×C42C2412yes—
604C2×C42C2412yes—
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607#95C2414yes—
608#95C2414yes—
609#95C2412yes—
610#95C2412yes—
611#95C2412yes—
612#95C2412yes—
613#95C2418yes—
614#95C2414yes—
615#95C2414yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2412yes—
621#95C2412yes—
622#95C2414yes—
623#95C2418yes—
624#95C2418yes—
625#95C2414yes—
626#95C2414yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650C24—24no—
651C24—24no—
652C24—42no—
653C24—44no—
654C24—44no—
655C24C2512yes—
656C24C2512yes—
657C24C2511yescharacteristic
658C2×Q8—24no—
659C2×Q8—28no—
660C2×Q8—24no—
661C2×Q8—24no—
662C2×Q8—28no—
663C2×Q8—28no—
664C2×Q8—48no—
665C2×Q8—48no—
666C2×Q8—48no—
667C2×D4—24no—
668C2×D4—22no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—44no—
672C2×D4—416no—
673C2×D4C2×#4114yes—
674C22×C4—22no—
675C22×C4—24no—
676C22×C4—22no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—22no—
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—22no—
690C22×C4—28no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—432no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—42no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4C2×#4118yes—
702C22×C42−1+414yes—
703C22×C4C2512yes—
704C22×C4C2512yes—
705C22×C4C2514yes—
706C22×C4C2511yescharacteristic
707C22×C4C2511yescharacteristic
708C22×C4C2512yes—
709C22×C4C2514yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2514yes—
713C22×C4C2518yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2518yes—
717C22×C4C2512yes—
718C22×C4C2511yescharacteristic
719C22×C4C2512yes—
720C22×C4C2511yescharacteristic
721C22×C4C2511yescharacteristic
722C22×C4C2511yescharacteristic
723C4⋊C4—24no—
724C4⋊C4—22no—
725C4⋊C4—24no—
726C4⋊C4—28no—
727C4⋊C4—216no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—24no—
731C4⋊C4—28no—
732C4⋊C4—24no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—216no—
736C4⋊C4—28no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—28no—
740C4⋊C4—24no—
741C4⋊C4—24no—
742C4⋊C4—28no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4C2×#4114yes—
763C22⋊C4—24no—
764C22⋊C4—216no—
765C22⋊C4—216no—
766C22⋊C4—24no—
767C22⋊C4—28no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—28no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—44no—
779C22⋊C4—48no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4C2×#4118yes—
787C42—22no—
788C42—22no—
789C42—22no—
790C42—216no—
791C42—28no—
792C42—28no—
793C42—24no—
794C42—22no—
795C42—24no—
796C42—22no—
797C42—22no—
798C42—24no—
799C42—24no—
800C42—28no—
801C42—44no—
802C42—42no—
803C42—42no—
804C42—48no—
805C42—48no—
806C42—48no—
807C42—48no—
808C42C2×#4114yes—
809C42H(5,𝔽2)14yes—
810C23—21no—
811C23—21no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—24no—
816C23—24no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—24no—
822C23—24no—
823C23—48no—
824C23—48no—
825C23—84no—
826C23—88no—
827C23—88no—
828C23C22×#4114yes—
829C23C2×2−1+412yes—
830C23C2611yescharacteristic
831Q8—416no—
832Q8—48no—
833Q8—816no—
834D4—28no—
835D4—48no—
836D4—44no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—216no—
846C2×C4—24no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—24no—
850C2×C4—28no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—28no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—28no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—48no—
887C2×C4—48no—
888C2×C4—48no—
889C2×C4—44no—
890C2×C4—48no—
891C2×C4—82no—
892C2×C4—88no—
893C2×C4—88no—
894C2×C4C22×#4114yes—
895C2×C4C22×#4112yes—
896C2×C4C22×#4112yes—
897C2×C4C22×#4112yes—
898C2×C4C2×H(5,𝔽2)14yes—
899C2×C4C2×H(5,𝔽2)12yes—
900C2×C4C2×2−1+412yes—
901C2×C4C2×2−1+412yes—
902C2×C4#58514yes—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—41no—
909C22—41no—
910C22—44no—
911C22—44no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—816no—
919C22C23×#4111yescharacteristic
920C22C22×H(5,𝔽2)11yescharacteristic
921C22C22×2−1+411yescharacteristic
922C22C2×#58512yes—
923C222−1+612yes—
924C4—22no—
925C4—24no—
926C4—22no—
927C4—24no—
928C4—42no—
929C4—44no—
930C4—44no—
931C4—41no—
932C4—41no—
933C4—48no—
934C4—42no—
935C4—42no—
936C4—44no—
937C4—44no—
938C4—42no—
939C4—44no—
940C4—48no—
941C4—44no—
942C4#345514yes—
943C4#352014yes—
944C2—44no—
945C2—42no—
946C2—82no—
947C2C2×#345511yescharacteristic
948C2C2×#352011yescharacteristic
949C2#6286111yescharacteristic
950C2#6295912yes—
951C2#6296012yes—
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. #42639C2semidirect
3. #40907C2semidirect
4. #40901C2semidirect
5. #39609C2semidirect
6. #39513C2semidirect
7. #39379C2semidirect
8. #37889C2semidirect
9. #37859C2semidirect
10. #37709C2semidirect
11. #37631C2semidirect
12. #37509C2semidirect
13. #36188C2semidirect
15. #36132C2semidirect
16. #35919C2semidirect
17. #35869C2semidirect
18. #35310C2semidirect
19. #35284C2semidirect
20. #34634C2semidirect
21. #34629C2semidirect
22. #34324C2semidirect
25. C2×#541C22semidirect
26. C2×#533C22semidirect
29. #2868C22semidirect
30. #2859C22semidirect
32. #2857C22semidirect
33. #2851C22semidirect
35. #2838C22semidirect
36. #2835C22semidirect
38. #2793C22semidirect
39. #2787C22semidirect
41. #2774C22semidirect
42. #2745C22semidirect
44. #2739C22semidirect
47. #2725C22semidirect
49. #2690C22semidirect
50. #2655C22semidirect
51. #2655C22semidirect
54. #2652C22semidirect
55. #2650C22semidirect
56. #2650C22semidirect
57. #2647C22semidirect
58. #2647C22semidirect
59. #2645C22semidirect
60. #2645C22semidirect
61. #2642C22semidirect
65. #2629C22semidirect
66. #2629C22semidirect
68. #2628C22semidirect
69. #2627C22semidirect
72. #2625C22semidirect
74. #2596C22semidirect
75. #2588C22semidirect
77. #2574C22semidirect
78. #2568C22semidirect
79. #2567C22semidirect
80. #2551C22semidirect
85. #2530C22semidirect
86. #2529C22semidirect
87. #2528C22semidirect
90. #2511C22semidirect
91. #2509C22semidirect
92. #2507C22semidirect
93. #2506C22semidirect
94. #2499C22semidirect
96. #2497C22semidirect
97. #2496C22semidirect
98. #2494C22semidirect
100. #2492C22semidirect
104. #2478C22semidirect
106. #2473C22semidirect
107. #2469C22semidirect
109. #2465C22semidirect
110. #2453C22semidirect
112. #2451C22semidirect
113. #2451C22semidirect
116. #2446C22semidirect
117. #2446C22semidirect
118. #2439C22semidirect
122. #2421C22semidirect
124. #2402C22semidirect
127. #2396C22semidirect
128. #2373C22semidirect
131. #2365C22semidirect
132. #2365C22semidirect
133. #2365C22semidirect
134. #2362C22semidirect
136. #2355C22semidirect
140. Q8×C4⋊C4C22semidirect
142. #2346C22semidirect
146. #2334C22semidirect
147. #2330C22semidirect
151. #2314C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#125C22semidirect
156. C4×C22⋊Q8C22semidirect
157. #2296C22semidirect
158. #2295C22semidirect
164. #2285C22semidirect
167. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#426392
#426342
#409072
#409012
#396092
#395132
#393792
#378892
#378592
#377092
#376312
#375092
#361882
#361612
#361322
#359192
#358692
#353102
#352842
#346342
#346292
#343242
D4×#1172