Finite Group Databasebeta

← #7715684

Subgroups — #7715684

Order 512.

6100 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3555C212yesmaximal, complemented
2#48819C218yesmaximal, complemented
3#48816C218yesmaximal, complemented
4#47822C218yesmaximal, complemented
5#47787C218yesmaximal, complemented
6#39744C212yesmaximal, complemented
7#39740C212yesmaximal, complemented
8#39619C212yesmaximal, complemented
9#39613C212yesmaximal, complemented
10#39172C212yesmaximal, complemented
11#39170C212yesmaximal, complemented
12#39163C212yesmaximal, complemented
13#39162C212yesmaximal, complemented
14#37641C211yesmaximal, characteristic, complemented
15#37542C211yesmaximal, characteristic
16#37421C211yesmaximal, characteristic
17#37389C212yesmaximal, complemented
18#37387C211yesmaximal, characteristic, complemented
19#35331C211yesmaximal, characteristic
20#35326C212yesmaximal, complemented
21#35319C211yesmaximal, characteristic, complemented
22#35318C212yesmaximal, complemented
23#34074C211yesmaximal, characteristic, complemented
24#3555—232no—
25C2×#563C2214yes—
26C2×#563C2214yes—
27C2×Q82C2212yes—
28C2×#557C2212yes—
29C2×#557C2212yes—
30C2×#557C2212yes—
31C2×#556C2212yes—
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#556C2214yes—
35C2×#554C2212yes—
36C2×#552C2214yes—
37C2×#544C2214yes—
38C2×#542C2212yes—
39C2×#542C2212yes—
40C2×#541C2212yes—
41C2×#541C2212yes—
42C2×#541C2214yes—
43C2×#541C2214yes—
44C2×#541C2214yes—
45C2×#533C2212yes—
46C2×#533C2211yescharacteristic
47C2×#529C2212yes—
48#2868C2211yescharacteristic
49#2862C2212yes—
50#2862C2211yescharacteristic
51#2861C2212yes—
52#2859C2211yescharacteristic
53#2858C2211yescharacteristic
54#2857C2212yes—
55#2857C2212yes—
56#2850C2212yes—
57#2850C2212yes—
58#2823C2214yes—
59#2822C2214yes—
60#2732C2218yes—
61#2729C2218yes—
62#2729C2218yes—
63#2728C2218yes—
64#2727C2218yes—
65#2726C2218yes—
66#2725C2218yes—
67#2725C2218yes—
68#2722C2214yes—
69#2722C2214yes—
70#2721C2218yes—
71#2721C2218yes—
72#2719C2218yes—
73#2719C2218yes—
74#2716C2218yes—
75#2716C2218yes—
76#2715C2218yes—
77#2713C2218yes—
78#2713C2218yes—
79#2712C2214yes—
80#2704C2218yes—
81#2704C2218yes—
82#2702C2218yes—
83#2702C2218yes—
84#2695C2218yes—
85#2693C2214yes—
86#2660C2212yes—
87#2660C2212yes—
88#2658C2212yes—
89#2658C2212yes—
90#2642C2212yes—
91#2642C2212yes—
92#2640C2212yes—
93#2640C2212yes—
94#2630C2218yes—
95#2625C2218yes—
96#2621C2211yescharacteristic
97#2621C2212yes—
98#2621C2211yescharacteristic
99#2621C2211yescharacteristic
100#2620C2212yes—
101#2619C2211yescharacteristic
102#2611C2218yes—
103#2609C2214yes—
104#2604C2218yes—
105#2582C2214yes—
106#2568C2212yes—
107#2568C2212yes—
108#2568C2212yes—
109#2568C2212yes—
110#2567C2212yes—
111#2566C2212yes—
112#2566C2212yes—
113#2565C2212yes—
114#2565C2212yes—
115#2565C2212yes—
116#2565C2212yes—
117#2564C2218yes—
118#2563C2212yes—
119#2560C2218yes—
120#2557C2218yes—
121#2556C2218yes—
122#2553C2218yes—
123#2547C2212yes—
124#2546C2212yes—
125#2546C2212yes—
126#2546C2212yes—
127#2546C2212yes—
128#2546C2212yes—
129#2545C2212yes—
130#2545C2212yes—
131#2545C2212yes—
132#2545C2212yes—
133#2544C2212yes—
134#2544C2212yes—
135#2521C2218yes—
136#2519C2218yes—
137#2506C2218yes—
138#2498C2218yes—
139#2496C2218yes—
140#2481C2218yes—
141#2479C2218yes—
142#2479C2218yes—
143#2477C2218yes—
144#2475C2218yes—
145#2473C2218yes—
146#2469C2218yes—
147#2465C2218yes—
148#2453C2218yes—
149#2451C2218yes—
150#2446C2218yes—
151#2446C2218yes—
152#2441C2218yes—
153#2439C2218yes—
154#2423C2218yes—
155#2421C2218yes—
156#2331C2214yes—
157#2330C2214yes—
158#2329C2214yes—
159#2329C2214yes—
160#2328C2211yescharacteristic
161#2327C2211yescharacteristic
162#2327C2212yes—
163#2327C2211yescharacteristic
164#2327C2212yes—
165#2327C2212yes—
166#2327C2211yescharacteristic
167#2326C2212yes—
168#2326C2212yes—
169#2326C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×#124C2212yes—
173C4×#124C2212yes—
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2295C2212yes—
177#2295C2212yes—
178#2295C2212yes—
179#2295C2212yes—
180#2285C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C4×#117C2211yescharacteristic
183C2×#376C2211yescharacteristic
184#563—232no—
185#563—232no—
186Q82—216no—
187#557—216no—
188#557—216no—
189#557—216no—
190#556—232no—
191#556—216no—
192#556—216no—
193#556—216no—
194#554—216no—
195#552—232no—
196#544—232no—
197#542—216no—
198#542—216no—
199#541—232no—
200#541—232no—
201#541—232no—
202#541—216no—
203#541—216no—
204#533—216no—
205#533D4116yescomplemented
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2312yes—
224C2×#127C2311yescharacteristic
225#529—216no—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#125C2312yes—
240C2×#125C2312yes—
241C2×#125C2312yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#125C2314yes—
246C2×#125C2314yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#125C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×#121C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×#117C2314yes—
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2314yes—
305C2×#117C2314yes—
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C22×C4⋊C4C2314yes—
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314#400C2318yes—
315#400C2318yes—
316#400C2318yes—
317#400C2318yes—
318#400C2318yes—
319#400C2318yes—
320#400C2318yes—
321#400C2318yes—
322#399C2318yes—
323#399C2318yes—
324#399C2318yes—
325#399C2318yes—
326#398C2314yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2314yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2314yes—
336#398C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2318yes—
341#397C2318yes—
342#397C2318yes—
343#397C2314yes—
344#397C2318yes—
345#397C2314yes—
346#397C2314yes—
347#397C2318yes—
348#396C2318yes—
349#396C2318yes—
350#396C2318yes—
351#396C2318yes—
352#396C2318yes—
353#396C2318yes—
354#396C2318yes—
355#395C2318yes—
356#395C2318yes—
357#395C2318yes—
358#394C2314yes—
359#394C2318yes—
360#394C2318yes—
361#394C2318yes—
362#393C2318yes—
363#393C2318yes—
364#393C2318yes—
365#392C2314yes—
366#391C2318yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#391C2312yes—
371#391C2312yes—
372#391C2312yes—
373#391C2312yes—
374#391C2312yes—
375#391C2312yes—
376#391C2312yes—
377#391C2312yes—
378#391C2318yes—
379#391C2318yes—
380#391C2318yes—
381#391C2318yes—
382#391C2312yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2318yes—
388#390C2318yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2318yes—
405#389C2318yes—
406#389C2318yes—
407#389C2318yes—
408#389C2318yes—
409#389C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2312yes—
455#385C2314yes—
456#385C2312yes—
457#384C2312yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2318yes—
462#382C2311yescharacteristic
463#382C2312yes—
464#382C2311yescharacteristic
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#382C2312yes—
468#382C2312yes—
469#382C2312yes—
470#382C2318yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2314yes—
475#380C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2318yes—
491#376C2312yes—
492#376C2312yes—
493#376C2312yes—
494#376C2311yescharacteristic
495#376C2311yescharacteristic
496#376C2312yes—
497#376C2312yes—
498C2×#95C2314yes—
499C43C2311yescharacteristic
500C43C2312yes—
501C43C2311yescharacteristic
502C22×Q8C2412yes—
503C22×Q8C2412yes—
504C22×Q8C2412yes—
505C22×Q8C2414yes—
506C22×Q8C2414yes—
507C22×Q8C2414yes—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×D4C2412yes—
511C22×D4C2414yes—
512C22×D4C2414yes—
513C23×C4C2411yescharacteristic
514C23×C4C2414yes—
515C23×C4C2414yes—
516C23×C4C2414yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C4⋊Q8—216no—
521C4⋊Q8—216no—
522C4⋊Q8—216no—
523C4⋊Q8—216no—
524C4⋊Q8—216no—
525C4⋊Q8—28no—
526C4⋊Q8—28no—
527C4⋊Q8—28no—
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531C4⋊Q8—28no—
532C4⋊Q8—44no—
533C4⋊Q8—44no—
534C4⋊Q8—42no—
535C4⋊Q8—42no—
536C4⋊Q8—42no—
537C4⋊Q8C2×D4116yes—
538#127—42no—
539#126—216no—
540#126—216no—
541#126—216no—
542#126—216no—
543#126—216no—
544#126—216no—
545#126—216no—
546#126—216no—
547#126—216no—
548#126—216no—
549#126—216no—
550#126—216no—
551#126—216no—
552#125—216no—
553#125—216no—
554#125—216no—
555#125—216no—
556#125—216no—
557#125—216no—
558#125—216no—
559#125—216no—
560#125—216no—
561#125—216no—
562#125—216no—
563#125—28no—
564#125—216no—
565#125—28no—
566#125—28no—
567#125C2×D4116yes—
568#124—216no—
569#124—216no—
570#124—28no—
571#124—28no—
572#124—28no—
573#124—28no—
574#124—44no—
575#124—44no—
576#123—216no—
577#123—216no—
578#123—216no—
579C22⋊Q8—216no—
580C22⋊Q8—216no—
581C22⋊Q8—216no—
582C22⋊Q8—216no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—28no—
586C22⋊Q8—216no—
587C22⋊Q8—216no—
588C22⋊Q8—216no—
589C22⋊Q8—216no—
590C22⋊Q8—216no—
591C22⋊Q8C2×D4116yes—
592C22⋊Q8C2×D4116yes—
593#121—28no—
594C4×Q8—216no—
595C4×Q8—216no—
596C4×Q8—216no—
597C4×Q8—216no—
598C4×Q8—28no—
599C4×Q8—216no—
600C4×Q8—28no—
601C4×Q8—28no—
602C4×Q8—28no—
603C4×Q8—28no—
604C4×Q8—28no—
605C4×Q8—28no—
606C4×Q8—28no—
607C4×Q8—28no—
608C4×Q8C2×D4116yes—
609C4×Q8C2×D4116yes—
610C4×D4—216no—
611C4×D4—28no—
612C4×D4—28no—
613C4×D4—28no—
614#117—216no—
615#117—216no—
616#117—216no—
617#117—216no—
618#117—216no—
619#117—42no—
620#117—42no—
621#117C2×D418yes—
622#117C2×D418yes—
623C2×C4⋊C4—216no—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2411yescharacteristic
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2411yescharacteristic
705C2×C42—24no—
706C2×C42—42no—
707C2×C42C2×D418yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2412yes—
731C2×C42C2411yescharacteristic
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768C24C2514yes—
769C24C2511yescharacteristic
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—48no—
785C2×Q8—48no—
786C2×Q8—48no—
787C2×Q8C22×D418yes—
788C2×Q8C22×D418yes—
789C2×D4—28no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—48no—
794C2×D4—44no—
795C2×D4—48no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—24no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—42no—
805C22×C4—44no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—44no—
809C22×C4C22×D414yes—
810C22×C4C22×D418yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—216no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4C22×D418yes—
881C4⋊C4C22×D418yes—
882C4⋊C4C22×D418yes—
883C4⋊C4C22×D418yes—
884C4⋊C4C22×D418yes—
885C4⋊C4C22×D418yes—
886C4⋊C4C22×D418yes—
887C4⋊C4C22×D418yes—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—216no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4C22×D414yes—
911C22⋊C4C22×D418yes—
912C22⋊C4C22×D414yes—
913C42—28no—
914C42—28no—
915C42—28no—
916C42—28no—
917C42—28no—
918C42—28no—
919C42—28no—
920C42—28no—
921C42—28no—
922C42—24no—
923C42—22no—
924C42—24no—
925C42—24no—
926C42—22no—
927C42—22no—
928C42—42no—
929C42—44no—
930C42—44no—
931C42—44no—
932C42—44no—
933C42C22×D414yes—
934C42C22×D418yes—
935C42C22×D414yes—
936C42C22×D414yes—
937C42C22×D418yes—
938C42C22×D414yes—
939C422−1+414yes—
940C23—21no—
941C23—21no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—28no—
947C23—28no—
948C23C23×D412yes—
949C23C2611yescharacteristic
950Q8—48no—
951Q8—48no—
952Q8—48no—
953Q8—48no—
954Q8—48no—
955Q8—88no—
956Q8—88no—
957Q8—88no—
958D4—48no—
959D4—88no—
960D4—164no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
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—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—24no—
1000C2×C4—48no—
1001C2×C4—416no—
1002C2×C4—88no—
1003C2×C4—88no—
1004C2×C4—84no—
1005C2×C4—84no—
1006C2×C4C23×D414yes—
1007C2×C4C23×D414yes—
1008C2×C4C23×D414yes—
1009C2×C4C23×D414yes—
1010C2×C4C23×D414yes—
1011C2×C4C23×D414yes—
1012C2×C4C23×D412yes—
1013C2×C4C23×D412yes—
1014C2×C4C2×2−1+414yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4#58512yes—
1017C22—22no—
1018C22—24no—
1019C22—42no—
1020C22—42no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—48no—
1025C22—48no—
1026C22C24×D411yescharacteristic
1027C22C22×2−1+411yescharacteristic
1028C22C2×#58511yescharacteristic
1029C222−1+614yes—
1030C4—22no—
1031C4—24no—
1032C4—24no—
1033C4—24no—
1034C4—24no—
1035C4—24no—
1036C4—24no—
1037C4—24no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4—44no—
1043C4—44no—
1044C4—44no—
1045C4—42no—
1046C4—44no—
1047C4—42no—
1048C4—44no—
1049C4—42no—
1050C4#349714yes—
1051C2—42no—
1052C2—84no—
1053C2C2×#349711yescharacteristic
1054C2#6285912yes—
1055C2#6288912yes—
1056C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2619C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3555C2semidirect
2. #48819C2semidirect
3. #48816C2semidirect
4. #47822C2semidirect
5. #47787C2semidirect
6. #39744C2semidirect
7. #39740C2semidirect
8. #39619C2semidirect
9. #39613C2semidirect
10. #39172C2semidirect
11. #39170C2semidirect
12. #39163C2semidirect
13. #39162C2semidirect
14. #37641C2semidirect
17. #37389C2semidirect
18. #37387C2semidirect
20. #35326C2semidirect
21. #35319C2semidirect
22. #35318C2semidirect
23. #34074C2semidirect
205. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35552
#488192
#488162
#478222
#477872
#397442
#397402
#396192
#396132
#391722
#391702
#391632
#391622
#376412
#375422
#374212
#373892
#373872
#353312
#353262
#353192
#353182
#340742