Finite Group Databasebeta

← #7641999

Subgroups — #7641999

Order 512.

4338 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37582C214yesmaximal, complemented
2#37580C214yesmaximal, complemented
3#37526C212yesmaximal, complemented
4#37522C212yesmaximal, complemented
5#37519C212yesmaximal
6#37514C212yesmaximal
7#37510C214yesmaximal, complemented
8#37509C214yesmaximal, complemented
9#35322C211yesmaximal, characteristic, complemented
10#35297C212yesmaximal
11#35294C211yesmaximal, characteristic, complemented
12#35291C212yesmaximal, complemented
13#35291C212yesmaximal, complemented
14#35284C212yesmaximal, complemented
15#35283C212yesmaximal, complemented
16#35221C214yesmaximal, complemented
17#35217C214yesmaximal, complemented
18#35204C214yesmaximal, complemented
19#35183C214yesmaximal, complemented
20#35163C214yesmaximal, complemented
21#35162C214yesmaximal, complemented
22C4×#533C212yesmaximal, complemented
23#34026C211yesmaximal, characteristic
24C2×#533C2212yes—
25C2×C4×#41C2211yescharacteristic
26#2868C2211yescharacteristic
27#2868C2211yescharacteristic
28#2866C2218yes—
29#2865C2218yes—
30#2864C2218yes—
31#2863C2218yes—
32#2862C2212yes—
33#2862C2211yescharacteristic
34#2859C2212yes—
35#2859C2211yescharacteristic
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2839C2218yes—
41#2835C2214yes—
42#2834C2214yes—
43#2833C2214yes—
44#2830C2214yes—
45#2827C2218yes—
46#2666C2218yes—
47#2666C2218yes—
48#2655C2218yes—
49#2655C2218yes—
50#2655C2218yes—
51#2654C2218yes—
52#2653C2218yes—
53#2652C2218yes—
54#2652C2218yes—
55#2651C2218yes—
56#2650C2218yes—
57#2649C2218yes—
58#2647C2214yes—
59#2647C2214yes—
60#2645C2214yes—
61#2645C2214yes—
62#2629C2214yes—
63#2629C2212yes—
64#2628C2214yes—
65#2628C2212yes—
66#2625C2214yes—
67#2625C2214yes—
68#2625C2214yes—
69#2621C2212yes—
70#2621C2212yes—
71#2616C2214yes—
72#2596C2218yes—
73#2594C2218yes—
74#2593C2214yes—
75#2590C2218yes—
76#2588C2218yes—
77#2586C2214yes—
78#2585C2218yes—
79#2584C2214yes—
80#2581C2214yes—
81#2570C2214yes—
82#2565C2214yes—
83#2565C2214yes—
84#2562C2214yes—
85#2550C2214yes—
86#2536C2214yes—
87#2533C2218yes—
88#2532C2218yes—
89#2529C2218yes—
90#2528C2218yes—
91#2523C2214yes—
92#2518C2218yes—
93#2517C2214yes—
94#2514C2214yes—
95#2514C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2509C2214yes—
99#2509C2214yes—
100#2508C2214yes—
101#2508C2214yes—
102#2507C2214yes—
103#2507C2214yes—
104#2499C2214yes—
105#2499C2214yes—
106#2497C2214yes—
107#2497C2214yes—
108#2495C2214yes—
109#2495C2214yes—
110#2494C2214yes—
111#2494C2214yes—
112#2492C2214yes—
113#2492C2214yes—
114#2489C2214yes—
115#2489C2214yes—
116#2485C2214yes—
117#2485C2214yes—
118#2453C2214yes—
119#2453C2214yes—
120#2451C2214yes—
121#2451C2214yes—
122#2446C2214yes—
123#2446C2214yes—
124#2441C2214yes—
125#2439C2214yes—
126#2429C2214yes—
127#2429C2214yes—
128#2423C2214yes—
129#2423C2214yes—
130#2421C2214yes—
131#2421C2214yes—
132#2415C2214yes—
133#2415C2214yes—
134#2331C2214yes—
135#2331C2212yes—
136#2330C2214yes—
137#2330C2212yes—
138#2327C2212yes—
139#2327C2212yes—
140#2323C2214yes—
141#2323C2214yes—
142#2323C2214yes—
143#2323C2214yes—
144#2320C2214yes—
145#2320C2214yes—
146#2314C2214yes—
147#2314C2214yes—
148C4×C4⋊Q8C2212yes—
149C4×C4⋊Q8C2212yes—
150C4×C4⋊Q8C2212yes—
151C4×C4⋊Q8C2212yes—
152C4×#125C2214yes—
153C4×#125C2214yes—
154C4×C22⋊Q8C2214yes—
155C4×C22⋊Q8C2214yes—
156C4×C22⋊Q8C2214yes—
157C4×C22⋊Q8C2214yes—
158#2298C2212yes—
159#2298C2212yes—
160#2297C2211yescharacteristic
161#2297C2211yescharacteristic
162#2296C2214yes—
163#2296C2211yescharacteristic
164#2296C2211yescharacteristic
165#2295C2214yes—
166#2295C2212yes—
167#2295C2212yes—
168#2295C2214yes—
169#2293C2212yes—
170#2293C2212yes—
171#2290C2212yes—
172#2290C2212yes—
173#2290C2212yes—
174#2290C2212yes—
175#2285C2212yes—
176C42×Q8C2214yes—
177C42×Q8C2214yes—
178C4×#117C2214yes—
179C4×#117C2212yes—
180C4×#117C2212yes—
181C4×#117C2211yescharacteristic
182C2×C43C2211yescharacteristic
183C22×#41C2311yescharacteristic
184#533—216no—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2314yes—
190C2×C4⋊Q8C2312yes—
191C2×#125C2314yes—
192C2×#125C2314yes—
193C2×#125C2312yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C4×#41—28no—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2312yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2311yescharacteristic
215C2×#117C2314yes—
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2314yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#401C2318yes—
228#401C2318yes—
229#400C2318yes—
230#400C2314yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#399C2318yes—
245#399C2314yes—
246#398C2314yes—
247#398C2314yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2314yes—
265#397C2318yes—
266#397C2314yes—
267#397C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#395C2314yes—
272#395C2318yes—
273#395C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#393C2318yes—
278#393C2314yes—
279#391C2314yes—
280#391C2314yes—
281#391C2314yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2311yescharacteristic
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2311yescharacteristic
295#391C2318yes—
296#391C2318yes—
297#391C2318yes—
298#391C2312yes—
299#390C2311yescharacteristic
300#390C2311yescharacteristic
301#390C2312yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2318yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2312yes—
325#389C2314yes—
326#389C2314yes—
327#389C2312yes—
328#389C2318yes—
329#389C2318yes—
330#389C2314yes—
331#389C2318yes—
332#389C2314yes—
333#389C2312yes—
334#389C2312yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2312yes—
348#388C2312yes—
349#388C2312yes—
350#388C2312yes—
351#388C2312yes—
352#388C2312yes—
353#388C2312yes—
354#388C2312yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2312yes—
382#387C2312yes—
383#387C2312yes—
384#387C2312yes—
385#387C2312yes—
386#387C2312yes—
387#387C2312yes—
388#387C2312yes—
389#386C2312yes—
390#386C2312yes—
391#386C2312yes—
392#386C2312yes—
393#385C2318yes—
394#385C2311yescharacteristic
395#385C2311yescharacteristic
396#385C2318yes—
397#385C2312yes—
398#385C2312yes—
399#385C2311yescharacteristic
400#385C2311yescharacteristic
401#384C2312yes—
402#384C2312yes—
403#384C2314yes—
404#384C2314yes—
405#384C2314yes—
406#384C2312yes—
407#383C2318yes—
408#383C2318yes—
409#382C2314yes—
410#382C2314yes—
411#382C2314yes—
412#382C2314yes—
413#382C2318yes—
414#382C2318yes—
415#382C2312yes—
416#382C2312yes—
417#382C2312yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2318yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2318yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2318yes—
466#376C2312yes—
467#376C2312yes—
468#376C2311yescharacteristic
469#376C2311yescharacteristic
470#376C2312yes—
471#376C2312yes—
472#376C2318yes—
473C43C2312yes—
474C43C2312yes—
475C43C2312yes—
476C43C2311yescharacteristic
477C43C2311yescharacteristic
478C43C2318yes—
479C43C2312yes—
480C2×#41—24no—
481C2×#41—42no—
482C2×#41—42no—
483C22×Q8C2414yes—
484C22×Q8C2414yes—
485C22×Q8C2411yescharacteristic
486C22×Q8C2414yes—
487C22×D4C2412yes—
488C22×D4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2411yescharacteristic
493C23×C4C2412yes—
494C23×C4C2411yescharacteristic
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C4⋊Q8—28no—
498C4⋊Q8—28no—
499C4⋊Q8—48no—
500C4⋊Q8—44no—
501C4⋊Q8—44no—
502C4⋊Q8—44no—
503#125—216no—
504#125—48no—
505#125—44no—
506C22⋊Q8—216no—
507C22⋊Q8—216no—
508C22⋊Q8—48no—
509C22⋊Q8—48no—
510C22⋊Q8—48no—
511C22⋊Q8—48no—
512C4×Q8—28no—
513C4×Q8—216no—
514C4×Q8—216no—
515C4×Q8—216no—
516C4×Q8—48no—
517C4×Q8—48no—
518C4×Q8—48no—
519C4×D4—28no—
520C4×D4—28no—
521C4×D4—28no—
522#117—24no—
523#117—216no—
524#117—28no—
525#117—28no—
526#117—28no—
527#117—44no—
528#117—44no—
529#117—42no—
530#117—42no—
531#117—48no—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2414yes—
574C2×C22⋊C4C2411yescharacteristic
575C2×C22⋊C4C2411yescharacteristic
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2411yescharacteristic
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2411yescharacteristic
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C42—28no—
596C2×C42—28no—
597C2×C42—44no—
598C2×C42—42no—
599C2×C42—42no—
600C2×C42#4118yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2418yes—
604C2×C42C2412yes—
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2412yes—
609C2×C42C2411yescharacteristic
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2418yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2412yes—
621C2×C42C2418yes—
622C2×C42C2418yes—
623C2×C42C2418yes—
624C2×C42C2418yes—
625C2×C42C2412yes—
626C2×C42C2411yescharacteristic
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2412yes—
632C2×C42C2411yescharacteristic
633C2×C42C2412yes—
634#95C2412yes—
635#95C2412yes—
636#95C2418yes—
637#95C2418yes—
638#95C2412yes—
639#95C2412yes—
640#95C2412yes—
641#95C2412yes—
642#95C2412yes—
643#95C2412yes—
644#95C2412yes—
645#95C2412yes—
646#95C2412yes—
647#95C2412yes—
648#95C2412yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2412yes—
655#95C2412yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2414yes—
673#95C2418yes—
674#95C2414yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2418yes—
681#95C2414yes—
682#95C2418yes—
683C24C2512yes—
684C24C2511yescharacteristic
685#41—416no—
686C2×Q8—22no—
687C2×Q8—28no—
688C2×Q8—28no—
689C2×Q8—28no—
690C2×Q8—28no—
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—41no—
694C2×Q8—41no—
695C2×Q8—48no—
696C2×Q8—44no—
697C2×D4—24no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—41no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—41no—
723C22×C4C2×#4118yes—
724C22×C4C2×#4114yes—
725C22×C4C2511yescharacteristic
726C22×C4C2511yescharacteristic
727C22×C4C2511yescharacteristic
728C22×C4C2512yes—
729C22×C4C2518yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2512yes—
733C22×C4C2512yes—
734C22×C4C2512yes—
735C22×C4C2518yes—
736C22×C4C2512yes—
737C22×C4C2518yes—
738C22×C4C2518yes—
739C22×C4C2511yescharacteristic
740C22×C4C2512yes—
741C22×C4C2511yescharacteristic
742C22×C4C2512yes—
743C22×C4C2512yes—
744C22×C4C2512yes—
745C22×C4C2511yescharacteristic
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—24no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—216no—
752C4⋊C4—216no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—216no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—42no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4—42no—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—42no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—48no—
787C4⋊C4—44no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—216no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—24no—
796C22⋊C4—24no—
797C22⋊C4—42no—
798C22⋊C4—42no—
799C22⋊C4—42no—
800C22⋊C4—42no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C42—24no—
810C42—24no—
811C42—24no—
812C42—216no—
813C42—24no—
814C42—24no—
815C42—24no—
816C42—24no—
817C42—24no—
818C42—216no—
819C42—24no—
820C42—24no—
821C42—24no—
822C42—24no—
823C42—22no—
824C42—24no—
825C42—22no—
826C42—22no—
827C42—22no—
828C42—24no—
829C42—41no—
830C42—42no—
831C42—42no—
832C42—42no—
833C42—41no—
834C42—48no—
835C42—48no—
836C42—48no—
837C42—48no—
838C42C2×#4114yes—
839C42C2×#4114yes—
840C42C2×#4118yes—
841C422−1+418yes—
842C23—22no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23C22×#4112yes—
854C23C2611yescharacteristic
855Q8—44no—
856Q8—416no—
857Q8—416no—
858Q8—164no—
859D4—44no—
860D4—48no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—28no—
870C2×C4—216no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—28no—
882C2×C4—28no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—22no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—44no—
913C2×C4—48no—
914C2×C4—44no—
915C2×C4—48no—
916C2×C4—48no—
917C2×C4—48no—
918C2×C4C22×#4114yes—
919C2×C4C22×#4112yes—
920C2×C4C22×#4112yes—
921C2×C4C22×#4114yes—
922C2×C4C2×2−1+414yes—
923C2×C4C2×2−1+414yes—
924C2×C4C2×2−1+414yes—
925C2×C4#58512yes—
926C2×C4#58512yes—
927C2×C4#58514yes—
928C22—24no—
929C22—22no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C23×#4111yescharacteristic
941C22C22×2−1+412yes—
942C22C2×#58511yescharacteristic
943C22C2×#58511yescharacteristic
944C22C2×#58512yes—
945C4—24no—
946C4—24no—
947C4—24no—
948C4—22no—
949C4—41no—
950C4—41no—
951C4—42no—
952C4—42no—
953C4—48no—
954C4—42no—
955C4—41no—
956C4—42no—
957C4—48no—
958C4—41no—
959C4—42no—
960C4—42no—
961C4—48no—
962C4—42no—
963C4—48no—
964C4#345514yes—
965C4#346118yes—
966C2—42no—
967C2—82no—
968C2C2×#346112yes—
969C2C2×#345511yescharacteristic
970C2#6283711yescharacteristic
971C2#6283812yes—
972C2#6283911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37582C2semidirect
2. #37580C2semidirect
3. #37526C2semidirect
4. #37522C2semidirect
7. #37510C2semidirect
8. #37509C2semidirect
9. #35322C2semidirect
11. #35294C2semidirect
12. #35291C2semidirect
13. #35291C2semidirect
14. #35284C2semidirect
15. #35283C2semidirect
16. #35221C2semidirect
17. #35217C2semidirect
18. #35204C2semidirect
19. #35183C2semidirect
20. #35163C2semidirect
21. #35162C2semidirect
22. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#375822
#375802
#375262
#375222
#375192
#375142
#375102
#375092
#353222
#352972
#352942
#352912
#352842
#352832
#352212
#352172
#352042
#351832
#351632
#351622
C4×#5332
#340262