Finite Group Databasebeta

← #7630893

Subgroups — #7630893

Order 512.

5102 conjugacy classes of subgroups.

The subgroup lattice has 1083 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35974C214yesmaximal, complemented
2#35970C214yesmaximal, complemented
3#35942C218yesmaximal, complemented
4#35869C214yesmaximal, complemented
5#35860C214yesmaximal, complemented
6#35848C218yesmaximal, complemented
7#35327C211yesmaximal, characteristic
8#35313C211yesmaximal, characteristic, complemented
9#35307C211yesmaximal, characteristic, complemented
10#35299C214yesmaximal, complemented
11#35290C214yesmaximal, complemented
12#35279C211yesmaximal, characteristic, complemented
13#35270C214yesmaximal, complemented
14#35266C211yesmaximal, characteristic, complemented
15#35254C211yesmaximal, characteristic
16#34638C211yesmaximal, characteristic, complemented
17#34619C214yesmaximal, complemented
18C2×#2640C211yesmaximal, characteristic, complemented
19#34269C211yesmaximal, characteristic
20#34268C211yesmaximal, characteristic, complemented
21#34255C211yesmaximal, characteristic, complemented
22#34254C211yesmaximal, characteristic, complemented
23#34216C211yesmaximal, characteristic, complemented
24#34211C211yesmaximal, characteristic, complemented
25#33999C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#535C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C2×#518C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2863C2214yescomplemented
36#2860C2214yes—
37#2857C2214yescomplemented
38#2855C2214yescomplemented
39#2854C2214yes—
40#2850C2214yes—
41#2654C2218yescomplemented
42#2653C2218yescomplemented
43#2650C2218yescomplemented
44#2649C2218yescomplemented
45#2647C2212yescomplemented
46#2647C2212yescomplemented
47#2647C2212yescomplemented
48#2647C2212yescomplemented
49#2646C2214yes—
50#2646C2214yes—
51#2645C2214yescomplemented
52#2644C2214yes—
53#2640C2214yes—
54#2640C2214yes—
55#2640C2212yes—
56#2640C2212yes—
57#2640C2212yes—
58#2640C2212yes—
59#2628C2214yescomplemented
60#2625C2214yescomplemented
61#2624C2214yes—
62#2620C2214yes—
63#2596C2218yescomplemented
64#2589C2218yescomplemented
65#2578C2218yescomplemented
66#2574C2218yescomplemented
67#2573C2218yescomplemented
68#2572C2218yescomplemented
69#2568C2212yescomplemented
70#2567C2212yescomplemented
71#2563C2212yescomplemented
72#2560C2218yescomplemented
73#2553C2218yescomplemented
74#2545C2212yes—
75#2545C2212yes—
76#2544C2212yes—
77#2544C2212yes—
78#2542C2212yescomplemented
79#2534C2214yes—
80#2534C2214yes—
81#2532C2218yescomplemented
82#2532C2218yescomplemented
83#2531C2218yescomplemented
84#2530C2218yescomplemented
85#2529C2218yescomplemented
86#2527C2218yescomplemented
87#2525C2218yescomplemented
88#2516C2218yescomplemented
89#2514C2214yescomplemented
90#2513C2214yes—
91#2512C2214yes—
92#2511C2214yescomplemented
93#2510C2218yescomplemented
94#2493C2218yes—
95#2488C2218yescomplemented
96#2487C2214yes—
97#2480C2218yes—
98#2478C2218yescomplemented
99#2477C2218yescomplemented
100#2469C2218yescomplemented
101#2458C2218yescomplemented
102#2450C2218yescomplemented
103#2448C2214yes—
104#2447C2214yescomplemented
105#2446C2214yescomplemented
106#2445C2214yes—
107#2419C2218yes—
108#2419C2218yescomplemented
109#2418C2218yes—
110#2409C2214yes—
111#2402C2214yescomplemented
112#2402C2214yescomplemented
113#2401C2218yescomplemented
114#2398C2218yescomplemented
115#2396C2218yescomplemented
116#2395C2218yescomplemented
117C2×#397C2214yes—
118C2×#393C2214yes—
119#2369C2214yescomplemented
120#2367C2214yes—
121#2367C2214yes—
122#2367C2214yes—
123#2367C2214yescomplemented
124#2366C2214yes—
125#2365C2214yescomplemented
126#2365C2214yescomplemented
127#2359C2218yes—
128#2358C2218yes—
129#2357C2214yes—
130#2356C2214yescomplemented
131#2355C2214yescomplemented
132#2354C2214yes—
133#2345C2214yes—
134#2343C2218yes—
135#2342C2214yes—
136#2342C2218yes—
137#2342C2214yes—
138Q8×C22⋊C4C2214yes—
139#2331C2214yescomplemented
140#2326C2214yes—
141#2324C2214yes—
142#2323C2214yescomplemented
143#2320C2214yescomplemented
144#2319C2214yes—
145#2317C2211yescharacteristic
146#2317C2211yescharacteristic
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2311C2211yescharacteristic
150#2311C2211yescharacteristic
151#2310C2211yescharacteristic
152#2310C2211yescharacteristic
153#2309C2211yescharacteristic
154#2309C2211yescharacteristic
155C4×C4⋊Q8C2214yescomplemented
156C4×#124C2214yes—
157C4×C22⋊Q8C2214yescomplemented
158C4×#121C2214yes—
159#2296C2211yescharacteristic
160#2296C2211yescharacteristic
161#2296C2211yescharacteristic
162#2296C2211yescharacteristic
163#2295C2214yescomplemented
164C2×#391C2211yescharacteristic
165C2×#391C2211yescharacteristic
166#2293C2214yes—
167C2×#390C2211yescharacteristic
168C2×#390C2211yescharacteristic
169#2285C2211yescharacteristic
170#2285C2211yescharacteristic
171#2276C2212yescomplemented
172#2276C2212yescomplemented
173#2275C2214yes—
174#2275C2214yes—
175#2275C2212yescomplemented
176#2275C2212yescomplemented
177#2274C2211yescharacteristic
178#2274C2211yescharacteristic
179C4×#117C2211yescharacteristic
180C4×#117C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C4×#117C2212yescomplemented
183C4×#117C2212yescomplemented
184C4×#117C2212yescomplemented
185C2×#376C2211yescharacteristic
186C2×#376C2212yescomplemented
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2312yes—
190C23×D4C2311yescharacteristic
191#536—28no—
192#535—28no—
193C2×C4⋊Q8—28no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×#127C2312yes—
200C2×#126C2318yes—
201C2×#124—28no—
202C2×#124C2312yes—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#123C2314yes—
209C2×#123C2318yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2318yes—
212C2×#121C2314yes—
213C2×#120C2314yes—
214#519—28no—
215#518—28no—
216C4×#41—28no—
217C4×#41—28no—
218C4×#41—28no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2318yes—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2318yes—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2318yes—
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C22⋊C4C2314yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2314yes—
256C22×C22⋊C4C2314yes—
257C22×C42C2312yes—
258C22×C42C2312yes—
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2312yes—
262C22×C42C2311yescharacteristic
263#401C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#399C2318yes—
278#399C2318yes—
279#398C2314yes—
280#398C2314yes—
281#398C2318yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#395C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#393C2318yes—
311#391C2318yes—
312#391C2318yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2318yes—
321#391C2312yes—
322#391C2312yes—
323#391C2318yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#390C2318yes—
329#390C2312yes—
330#390C2312yes—
331#390C2314yes—
332#390C2314yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2318yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2314yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#385C2314yes—
399#385C2314yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2314yes—
404#385C2314yes—
405#385C2318yes—
406#385C2314yes—
407#385C2314yes—
408#385C2318yes—
409#384C2312yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#383C2318yes—
414#383C2318yes—
415#382C2312yes—
416#382C2312yes—
417#382C2318yes—
418#382C2312yes—
419#382C2312yes—
420#381C2314yes—
421#381C2314yes—
422#381C2318yes—
423#381C2318yes—
424#380C2318yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2318yes—
430#380C2312yes—
431#380C2312yes—
432#380C2312yes—
433#380C2312yes—
434#379C2314yes—
435#379C2314yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480#376C2312yes—
481#376C2312yes—
482#376C2318yes—
483#376C2311yescharacteristic
484#376C2311yescharacteristic
485#376C2311yescharacteristic
486#376C2311yescharacteristic
487#376C2312yes—
488#376C2312yes—
489#376C2312yes—
490#376C2314yes—
491#376C2314yes—
492C2×#95C2314yes—
493C2×#95C2314yes—
494C2×#95C2312yes—
495C2×#95C2312yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C43C2312yes—
499C43C2312yes—
500C43C2312yes—
501C25C2412yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41#4118yes—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8—28no—
509C22×Q8—84no—
510C22×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2414yes—
514C22×Q8C2414yes—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2412yes—
521C22×D4C2411yescharacteristic
522C22×D4C2418yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2418yes—
530C23×C4C2414yes—
531C23×C4C2412yes—
532C23×C4C2414yes—
533C23×C4C2412yes—
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C4⋊Q8—28no—
538C4⋊Q8—28no—
539C4⋊Q8—28no—
540C4⋊Q8—28no—
541C4⋊Q8—28no—
542#127—28no—
543#126—88no—
544#124—28no—
545#124—28no—
546#124—28no—
547#124—28no—
548#124—28no—
549#124—28no—
550#123—216no—
551#123—88no—
552C22⋊Q8—216no—
553C22⋊Q8—88no—
554#121—216no—
555#120—216no—
556C4×Q8—28no—
557C4×Q8—28no—
558C4×Q8—216no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—216no—
562C4×Q8—88no—
563C4×D4—216no—
564C4×D4—28no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—216no—
569C4×D4—216no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—216no—
573C4×D4—88no—
574#117—28no—
575#117—24no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—216no—
582#117—28no—
583#117—28no—
584#117—88no—
585#117#4118yes—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C22⋊C4—28no—
626C2×C22⋊C4—28no—
627C2×C22⋊C4—216no—
628C2×C22⋊C4—84no—
629C2×C22⋊C4—84no—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2412yes—
658C2×C42—28no—
659C2×C42—24no—
660C2×C42—24no—
661C2×C42—28no—
662C2×C42—28no—
663C2×C42#4118yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2412yes—
669C2×C42C2418yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2418yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2412yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#95C2412yes—
695#95C2412yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2412yes—
701#95C2412yes—
702#95C2412yes—
703#95C2414yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736C24—24no—
737C24—24no—
738C24—24no—
739C24—44no—
740C24—44no—
741C24C2514yes—
742C24C2512yes—
743C24C2511yescharacteristic
744#41—232no—
745C2×Q8—22no—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—28no—
754C2×Q8—28no—
755C2×Q8—48no—
756C2×Q8—48no—
757C2×Q8—416no—
758C2×Q8—816no—
759C2×Q8C2×#4114yes—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—216no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—416no—
774C2×D4C2×#4118yes—
775C2×D4C2×#4114yes—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—28no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—28no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—216no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—48no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—48no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4C2×#4118yes—
807C22×C4C2×#4114yes—
808C22×C4C2×#4114yes—
809C22×C4C2×#4114yes—
810C22×C4C2×#4114yes—
811C22×C4C2×#4114yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2514yes—
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—216no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—216no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4C2×#4118yes—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—28no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—216no—
878C22⋊C4—216no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—216no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4C2×#4118yes—
898C42—22no—
899C42—22no—
900C42—24no—
901C42—22no—
902C42—22no—
903C42—24no—
904C42—28no—
905C42—24no—
906C42—24no—
907C42—28no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—24no—
912C42—216no—
913C42—24no—
914C42—24no—
915C42—44no—
916C42—44no—
917C42—44no—
918C42—44no—
919C42—48no—
920C42—48no—
921C42—44no—
922C42—44no—
923C42C2×#4114yes—
924C42C2×#4118yes—
925C42C2×#4114yes—
926C42C2×#4114yes—
927C42C2×#4114yes—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—28no—
938C23—28no—
939C23—48no—
940C23—84no—
941C23—88no—
942C23—88no—
943C23—84no—
944C23C22×#4114yes—
945C23C22×#4112yes—
946C23C22×#4112yes—
947C23C22×#4112yes—
948C23C2611yescharacteristic
949Q8—28no—
950Q8—416no—
951Q8—48no—
952Q8—48no—
953Q8—88no—
954D4—216no—
955D4—28no—
956D4—48no—
957D4—48no—
958D4—816no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—216no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—48no—
1009C2×C4—84no—
1010C2×C4—816no—
1011C2×C4—88no—
1012C2×C4—84no—
1013C2×C4—84no—
1014C2×C4—84no—
1015C2×C4—88no—
1016C2×C4—84no—
1017C2×C4—84no—
1018C2×C4#529116yes—
1019C2×C4C22×#4118yes—
1020C2×C4C22×#4112yes—
1021C2×C4C22×#4112yes—
1022C2×C4C22×#4114yes—
1023C2×C4C22×#4112yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C22×#4112yes—
1027C2×C4C22×#4112yes—
1028C2×C4C22×#4112yes—
1029C2×C4C22×#4112yes—
1030C2×C4C22×#4112yes—
1031C22—22no—
1032C22—24no—
1033C22—24no—
1034C22—22no—
1035C22—28no—
1036C22—24no—
1037C22—42no—
1038C22—44no—
1039C22—42no—
1040C22—44no—
1041C22—48no—
1042C22—48no—
1043C22—44no—
1044C22—44no—
1045C22—168no—
1046C22C2×#52914yes—
1047C22C23×#4111yescharacteristic
1048C22C23×#4111yescharacteristic
1049C22C23×#4111yescharacteristic
1050C22H(7,𝔽2)12yes—
1051C222−1+612yes—
1052C4—22no—
1053C4—22no—
1054C4—28no—
1055C4—22no—
1056C4—22no—
1057C4—24no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—44no—
1062C4—44no—
1063C4—42no—
1064C4—42no—
1065C4—44no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—44no—
1070C4—42no—
1071C4—44no—
1072C4C2×#52914yes—
1073C4C2×#52914yes—
1074C2—24no—
1075C2—44no—
1076C2—84no—
1077C2C22×#52911yescharacteristic
1078C2#6285511yescharacteristic
1079C2#6285712yes—
1080C2#6285712yes—
1081C2#6286011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35974C2semidirect
2. #35970C2semidirect
3. #35942C2semidirect
4. #35869C2semidirect
5. #35860C2semidirect
6. #35848C2semidirect
8. #35313C2semidirect
9. #35307C2semidirect
10. #35299C2semidirect
11. #35290C2semidirect
12. #35279C2semidirect
13. #35270C2semidirect
14. #35266C2semidirect
16. #34638C2semidirect
17. #34619C2semidirect
18. C2×#2640C2semidirect
20. #34268C2semidirect
21. #34255C2semidirect
22. #34254C2semidirect
23. #34216C2semidirect
24. #34211C2semidirect
25. #33999C2semidirect
35. #2863C22semidirect
37. #2857C22semidirect
38. #2855C22semidirect
41. #2654C22semidirect
42. #2653C22semidirect
43. #2650C22semidirect
44. #2649C22semidirect
45. #2647C22semidirect
46. #2647C22semidirect
47. #2647C22semidirect
48. #2647C22semidirect
51. #2645C22semidirect
59. #2628C22semidirect
60. #2625C22semidirect
63. #2596C22semidirect
64. #2589C22semidirect
65. #2578C22semidirect
66. #2574C22semidirect
67. #2573C22semidirect
68. #2572C22semidirect
69. #2568C22semidirect
70. #2567C22semidirect
71. #2563C22semidirect
72. #2560C22semidirect
73. #2553C22semidirect
78. #2542C22semidirect
81. #2532C22semidirect
82. #2532C22semidirect
83. #2531C22semidirect
84. #2530C22semidirect
85. #2529C22semidirect
86. #2527C22semidirect
87. #2525C22semidirect
88. #2516C22semidirect
89. #2514C22semidirect
92. #2511C22semidirect
93. #2510C22semidirect
95. #2488C22semidirect
98. #2478C22semidirect
99. #2477C22semidirect
100. #2469C22semidirect
101. #2458C22semidirect
102. #2450C22semidirect
104. #2447C22semidirect
105. #2446C22semidirect
108. #2419C22semidirect
111. #2402C22semidirect
112. #2402C22semidirect
113. #2401C22semidirect
114. #2398C22semidirect
115. #2396C22semidirect
116. #2395C22semidirect
119. #2369C22semidirect
123. #2367C22semidirect
125. #2365C22semidirect
126. #2365C22semidirect
130. #2356C22semidirect
131. #2355C22semidirect
139. #2331C22semidirect
142. #2323C22semidirect
143. #2320C22semidirect
155. C4×C4⋊Q8C22semidirect
157. C4×C22⋊Q8C22semidirect
163. #2295C22semidirect
171. #2276C22semidirect
172. #2276C22semidirect
175. #2275C22semidirect
176. #2275C22semidirect
182. C4×#117C22semidirect
183. C4×#117C22semidirect
184. C4×#117C22semidirect
186. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#359742
#359702
#359422
#358692
#358602
#358482
#353272
#353132
#353072
#352992
#352902
#352792
#352702
#352662
#352542
#346382
#346192
C2×#26402
#342692
#342682
#342552
#342542
#342162
#342112
#339992