Finite Group Databasebeta

← #7644213

Subgroups — #7644213

Order 512.

4444 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42902C214yesmaximal, complemented
2#42901C214yesmaximal, complemented
3#42864C214yesmaximal, complemented
4#42863C214yesmaximal, complemented
5#42854C214yesmaximal, complemented
6#42850C214yesmaximal, complemented
7#42848C214yesmaximal, complemented
8#42845C214yesmaximal, complemented
9#37507C218yesmaximal, complemented
10#36998C218yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35673C211yesmaximal, characteristic
13#35668C211yesmaximal, characteristic, complemented
14#35667C211yesmaximal, characteristic
15#35630C211yesmaximal, characteristic, complemented
16#35627C211yesmaximal, characteristic, complemented
17#35620C211yesmaximal, characteristic
18#35619C211yesmaximal, characteristic
19#35182C211yesmaximal, characteristic
20#35154C211yesmaximal, characteristic, complemented
21#34639C211yesmaximal, characteristic
22#34638C211yesmaximal, characteristic, complemented
23#34266C211yesmaximal, characteristic
24#34249C211yesmaximal, characteristic, complemented
25C2×#2327C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2855C2214yes—
36#2853C2214yes—
37#2839C2218yes—
38#2839C2218yes—
39#2838C2218yes—
40#2836C2218yes—
41#2810C2218yes—
42#2809C2218yes—
43#2802C2218yes—
44#2798C2218yes—
45#2794C2218yes—
46#2793C2218yes—
47#2791C2218yes—
48#2790C2218yes—
49#2789C2218yes—
50#2787C2218yes—
51#2783C2218yes—
52#2776C2218yes—
53#2775C2218yes—
54#2771C2218yes—
55#2767C2218yes—
56#2744C2218yes—
57#2667C2218yes—
58#2666C2218yes—
59#2655C2218yes—
60#2655C2218yes—
61#2655C2218yes—
62#2654C2218yes—
63#2652C2218yes—
64#2650C2218yes—
65#2647C2212yes—
66#2647C2212yes—
67#2647C2212yes—
68#2647C2212yes—
69#2646C2214yes—
70#2646C2214yes—
71#2645C2212yes—
72#2645C2212yes—
73#2644C2212yes—
74#2644C2212yes—
75#2643C2214yes—
76#2643C2214yes—
77#2627C2214yes—
78#2623C2214yes—
79#2590C2218yes—
80#2588C2218yes—
81#2577C2218yes—
82#2575C2218yes—
83#2571C2214yes—
84#2570C2214yes—
85#2568C2212yes—
86#2568C2212yes—
87#2567C2212yes—
88#2566C2212yes—
89#2565C2212yes—
90#2565C2212yes—
91#2565C2212yes—
92#2563C2212yes—
93#2546C2212yes—
94#2546C2212yes—
95#2545C2212yes—
96#2545C2212yes—
97#2514C2214yes—
98#2514C2214yes—
99#2511C2214yes—
100#2511C2214yes—
101#2509C2214yes—
102#2508C2214yes—
103#2505C2218yes—
104#2503C2212yes—
105#2502C2212yes—
106#2499C2212yes—
107#2499C2212yes—
108#2498C2218yes—
109#2493C2218yes—
110#2484C2218yes—
111#2453C2214yes—
112#2453C2214yes—
113#2453C2214yes—
114#2451C2214yes—
115#2451C2214yes—
116#2451C2214yes—
117#2450C2218yes—
118#2448C2214yes—
119#2448C2214yes—
120#2447C2214yes—
121#2446C2214yes—
122#2446C2214yes—
123#2446C2214yes—
124#2446C2214yes—
125#2446C2214yes—
126#2446C2214yes—
127#2446C2214yes—
128#2442C2214yes—
129#2439C2214yes—
130#2438C2218yes—
131#2429C2214yes—
132#2429C2214yes—
133#2423C2214yes—
134#2423C2214yes—
135#2421C2214yes—
136#2421C2214yes—
137#2419C2218yes—
138#2413C2218yes—
139#2402C2214yes—
140#2402C2214yes—
141#2401C2214yes—
142#2401C2214yes—
143#2367C2214yes—
144#2365C2214yes—
145#2362C2214yes—
146#2360C2214yes—
147#2351C2214yes—
148#2351C2214yes—
149Q8×C4⋊C4C2214yes—
150Q8×C4⋊C4C2214yes—
151#2327C2214yes—
152#2327C2214yes—
153#2327C2214yes—
154#2327C2214yes—
155#2322C2214yes—
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2317C2214yes—
160#2316C2211yescharacteristic
161#2311C2211yescharacteristic
162#2310C2211yescharacteristic
163#2310C2211yescharacteristic
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166C4×#123C2214yes—
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2214yes—
178C2×#391C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#387C2214yes—
181C2×#387C2214yes—
182#2285C2211yescharacteristic
183#2285C2211yescharacteristic
184C2×#382C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190#544—44no—
191#536—28no—
192#536—44no—
193C2×C4⋊Q8—28no—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#123C2314yes—
206C2×#123C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211#520—44no—
212#519—28no—
213#519—44no—
214C2×C4×Q8—44no—
215C2×C4×Q8—44no—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2314yes—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2314yes—
237C2×#117C2314yes—
238C2×#117C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249C22×C42C2312yes—
250#401C2318yes—
251#401C2314yes—
252#401C2314yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2314yes—
259#400C2318yes—
260#400C2314yes—
261#400C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#399C2318yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2314yes—
318#396C2314yes—
319#395C2318yes—
320#395C2318yes—
321#393C2318yes—
322#391C2312yes—
323#391C2311yescharacteristic
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2311yescharacteristic
338#391C2318yes—
339#391C2318yes—
340#391C2314yes—
341#391C2314yes—
342#391C2312yes—
343#391C2312yes—
344#391C2318yes—
345#391C2312yes—
346#391C2312yes—
347#390C2311yescharacteristic
348#390C2312yes—
349#390C2311yescharacteristic
350#390C2312yes—
351#390C2312yes—
352#389C2318yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#386C2314yes—
420#386C2312yes—
421#386C2312yes—
422#386C2314yes—
423#386C2314yes—
424#385C2318yes—
425#385C2312yes—
426#385C2312yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2318yes—
431#385C2312yes—
432#385C2318yes—
433#385C2312yes—
434#385C2312yes—
435#385C2312yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2312yes—
443#384C2311yescharacteristic
444#384C2312yes—
445#384C2318yes—
446#384C2312yes—
447#383C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2311yescharacteristic
451#382C2312yes—
452#382C2312yes—
453#382C2311yescharacteristic
454#382C2314yes—
455#382C2312yes—
456#382C2318yes—
457#382C2318yes—
458#382C2312yes—
459#381C2314yes—
460#381C2314yes—
461#381C2314yes—
462#381C2314yes—
463#381C2318yes—
464#380C2318yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2314yes—
492#376C2312yes—
493#376C2312yes—
494#376C2312yes—
495#376C2312yes—
496C2×#95C2312yes—
497C2×#95C2312yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C22×Q8—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8—24no—
509C22×Q8#4118yes—
510C22×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2412yes—
514C22×Q8C2412yes—
515C22×Q8C2414yes—
516C22×D4C2412yes—
517C22×D4C2411yescharacteristic
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2412yes—
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C4⋊Q8—216no—
530C4⋊Q8—28no—
531C4⋊Q8—28no—
532C4⋊Q8—28no—
533C4⋊Q8—44no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536#125—44no—
537#125—44no—
538#124—28no—
539#124—44no—
540#123—216no—
541#123—48no—
542C22⋊Q8—216no—
543C22⋊Q8—48no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C4×Q8—216no—
547C4×Q8—216no—
548C4×Q8—48no—
549C4×Q8—48no—
550C4×Q8—48no—
551C4×Q8—48no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×D4—44no—
558C4×D4—48no—
559#117—216no—
560#117—24no—
561#117—24no—
562#117—24no—
563#117—24no—
564#117—24no—
565#117—24no—
566#117—24no—
567#117—48no—
568#117—44no—
569C2×C4⋊C4—216no—
570C2×C4⋊C4—24no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—44no—
573C2×C4⋊C4—44no—
574C2×C4⋊C4—44no—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C42—24no—
644C2×C42—24no—
645C2×C42—24no—
646C2×C42—44no—
647C2×C42—44no—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2418yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2418yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2418yes—
686#95C2414yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722C24C2512yes—
723C24C2511yescharacteristic
724#41—416no—
725C2×Q8—232no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—22no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—22no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—22no—
739C2×Q8—44no—
740C2×Q8—48no—
741C2×Q8—416no—
742C2×Q8C2×#4118yes—
743C2×Q8C2×#4118yes—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—44no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—48no—
774C22×C4C2×#4118yes—
775C22×C4C2×#4114yes—
776C22×C4H(5,𝔽2)14yes—
777C22×C42−1+414yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2514yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C4⋊C4—216no—
802C4⋊C4—216no—
803C4⋊C4—216no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—216no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—24no—
819C4⋊C4—44no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—216no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C42—22no—
870C42—22no—
871C42—24no—
872C42—216no—
873C42—24no—
874C42—24no—
875C42—24no—
876C42—24no—
877C42—24no—
878C42—24no—
879C42—24no—
880C42—24no—
881C42—22no—
882C42—22no—
883C42—24no—
884C42—24no—
885C42—48no—
886C42—48no—
887C42—48no—
888C42—44no—
889C42—44no—
890C42—44no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23—24no—
898C23C22×#4112yes—
899C23C2×H(5,𝔽2)12yes—
900C23C2×2−1+412yes—
901C23C2611yescharacteristic
902Q8—216no—
903Q8—216no—
904Q8—48no—
905Q8—48no—
906Q8—44no—
907Q8—164no—
908D4—48no—
909D4—44no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—216no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—48no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—48no—
969C2×C4—48no—
970C2×C4—84no—
971C2×C4—84no—
972C2×C4—84no—
973C2×C4—164no—
974C2×C4#539116yes—
975C2×C4C22×#4118yes—
976C2×C4C22×#4112yes—
977C2×C4C22×#4112yes—
978C2×C4C2×H(5,𝔽2)12yes—
979C2×C4C2×H(5,𝔽2)12yes—
980C2×C4C2×2−1+412yes—
981C2×C4C2×2−1+412yes—
982C22—24no—
983C22—22no—
984C22—22no—
985C22—24no—
986C22—44no—
987C22—42no—
988C22—42no—
989C22—44no—
990C22—42no—
991C22C2×#53914yes—
992C22C23×#4111yescharacteristic
993C22C22×H(5,𝔽2)11yescharacteristic
994C22C22×2−1+411yescharacteristic
995C222−1+612yes—
996C222−1+612yes—
997C4—28no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—44no—
1009C4—44no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—44no—
1018C4C2×#53914yes—
1019C4C2×#53914yes—
1020C2—24no—
1021C2—82no—
1022C2C22×#53911yescharacteristic
1023C2#6285012yes—
1024C2#6288711yescharacteristic
1025C2#6288711yescharacteristic
1026C2#6288912yes—
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. #42902C2semidirect
2. #42901C2semidirect
3. #42864C2semidirect
4. #42863C2semidirect
5. #42854C2semidirect
6. #42850C2semidirect
7. #42848C2semidirect
8. #42845C2semidirect
9. #37507C2semidirect
10. #36998C2semidirect
11. #35674C2semidirect
13. #35668C2semidirect
15. #35630C2semidirect
16. #35627C2semidirect
20. #35154C2semidirect
22. #34638C2semidirect
24. #34249C2semidirect
25. C2×#2327C2semidirect

Maximal subgroups

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

subgroupindex
#429022
#429012
#428642
#428632
#428542
#428502
#428482
#428452
#375072
#369982
#356742
#356732
#356682
#356672
#356302
#356272
#356202
#356192
#351822
#351542
#346392
#346382
#342662
#342492
C2×#23272