Finite Group Databasebeta

← #7652081

Subgroups — #7652081

Order 512.

5306 conjugacy classes of subgroups.

The subgroup lattice has 1131 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42941C214yesmaximal, complemented
2#42853C214yesmaximal, complemented
3#42715C214yesmaximal, complemented
4#42696C214yesmaximal, complemented
5#41532C218yesmaximal, complemented
6#40073C214yesmaximal, complemented
7#40031C214yesmaximal, complemented
8#39663C214yesmaximal, complemented
9#39640C214yesmaximal, complemented
10#38605C218yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35666C211yesmaximal, characteristic
14#35666C211yesmaximal, characteristic
15#35630C211yesmaximal, characteristic, complemented
16#35628C211yesmaximal, characteristic, complemented
17#35320C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35182C211yesmaximal, characteristic, complemented
20C2×#2546C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34276C211yesmaximal, characteristic, complemented
24#34266C211yesmaximal, characteristic, complemented
25#34259C211yesmaximal, characteristic
26C22×2−1+4C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2862C2214yes—
40#2857C2214yes—
41#2853C2214yes—
42#2833C2218yes—
43#2827C2218yes—
44#2806C2218yes—
45#2805C2218yes—
46#2788C2218yes—
47#2787C2218yes—
48#2781C2218yes—
49#2779C2218yes—
50#2774C2218yes—
51#2774C2218yes—
52#2771C2218yes—
53#2770C2218yes—
54#2768C2218yes—
55#2765C2218yes—
56#2765C2218yes—
57#2764C2218yes—
58#2741C2218yes—
59#2702C2218yes—
60#2666C2218yes—
61#2666C2218yes—
62#2653C2218yes—
63#2652C2218yes—
64#2649C2218yes—
65#2646C2218yes—
66#2642C2214yes—
67#2623C2214yes—
68#2621C2214yes—
69#2592C2214yes—
70#2589C2218yes—
71#2587C2218yes—
72#2586C2218yes—
73#2568C2214yes—
74#2568C2214yes—
75#2568C2214yes—
76#2547C2214yes—
77#2546C2212yes—
78#2546C2212yes—
79#2546C2214yes—
80#2546C2214yes—
81#2546C2214yes—
82#2546C2214yes—
83#2546C2214yes—
84#2545C2212yes—
85#2545C2212yes—
86#2518C2218yes—
87#2514C2212yes—
88#2514C2214yes—
89#2514C2214yes—
90#2513C2212yes—
91#2512C2212yes—
92#2511C2212yes—
93#2511C2214yes—
94#2511C2214yes—
95#2510C2214yes—
96#2505C2218yes—
97#2505C2218yes—
98#2503C2218yes—
99#2493C2218yes—
100#2492C2214yes—
101#2489C2214yes—
102#2488C2218yes—
103#2486C2218yes—
104#2484C2214yes—
105#2484C2214yes—
106#2481C2214yes—
107#2454C2212yes—
108#2453C2212yes—
109#2452C2212yes—
110#2451C2212yes—
111#2450C2214yes—
112#2449C2214yes—
113#2448C2214yes—
114#2446C2214yes—
115#2446C2214yes—
116#2446C2214yes—
117#2446C2214yes—
118#2446C2214yes—
119#2434C2212yes—
120#2434C2214yes—
121#2434C2214yes—
122#2434C2214yes—
123#2434C2212yes—
124#2432C2214yes—
125#2432C2214yes—
126#2432C2212yes—
127#2432C2214yes—
128#2432C2212yes—
129#2429C2214yes—
130#2429C2214yes—
131#2423C2214yes—
132#2421C2214yes—
133#2413C2218yes—
134#2406C2214yes—
135#2406C2218yes—
136#2406C2214yes—
137#2401C2214yes—
138#2396C2214yes—
139C2×#398C2214yes—
140#2367C2214yes—
141#2365C2214yes—
142#2362C2214yes—
143#2362C2214yes—
144#2360C2214yes—
145#2360C2214yes—
146#2359C2218yes—
147Q8×C22⋊C4C2214yes—
148#2339C2218yes—
149#2339C2214yes—
150#2334C2218yes—
151#2329C2218yes—
152#2327C2212yes—
153#2326C2212yes—
154#2322C2214yes—
155#2317C2211yescharacteristic
156#2311C2211yescharacteristic
157#2311C2212yes—
158#2310C2211yescharacteristic
159#2310C2211yescharacteristic
160#2310C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2211yescharacteristic
163#2310C2211yescharacteristic
164#2310C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×#126C2214yes—
167C4×#124C2212yes—
168C4×C22⋊Q8C2214yes—
169C4×#123C2214yes—
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2212yes—
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#391C2212yes—
182C2×#389C2214yes—
183#2285C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2312yes—
193C22×#41C2314yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200#536—28no—
201#536—28no—
202#536—44no—
203#536—44no—
204#533—44no—
205C2×C4⋊Q8—44no—
206C2×C4⋊Q8—44no—
207C2×C4⋊Q8—44no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2312yes—
221C2×#126C2314yes—
222C2×#125C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238#520—44no—
239#519—44no—
240C4×#41—44no—
241C2×C4×Q8—44no—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2312yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276C22×C42C2312yes—
277#401C2314yes—
278#401C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2314yes—
291#400C2318yes—
292#400C2318yes—
293#400C2314yes—
294#400C2314yes—
295#399C2318yes—
296#399C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#398C2314yes—
309#398C2314yes—
310#397C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2314yes—
316#397C2314yes—
317#396C2314yes—
318#396C2318yes—
319#396C2314yes—
320#396C2318yes—
321#396C2314yes—
322#395C2318yes—
323#395C2318yes—
324#395C2314yes—
325#395C2318yes—
326#395C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#393C2318yes—
332#393C2314yes—
333#391C2311yescharacteristic
334#391C2312yes—
335#391C2312yes—
336#391C2311yescharacteristic
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2312yes—
342#391C2312yes—
343#391C2314yes—
344#391C2314yes—
345#391C2318yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2312yes—
351#391C2314yes—
352#391C2312yes—
353#391C2314yes—
354#391C2312yes—
355#391C2318yes—
356#391C2318yes—
357#391C2318yes—
358#391C2314yes—
359#391C2312yes—
360#391C2311yescharacteristic
361#391C2314yes—
362#391C2314yes—
363#391C2318yes—
364#391C2312yes—
365#391C2312yes—
366#391C2311yescharacteristic
367#391C2312yes—
368#390C2312yes—
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#389C2318yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#389C2312yes—
388#389C2312yes—
389#389C2318yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#387C2318yes—
425#386C2318yes—
426#386C2314yes—
427#386C2312yes—
428#386C2314yes—
429#386C2318yes—
430#386C2312yes—
431#386C2314yes—
432#386C2312yes—
433#386C2312yes—
434#386C2314yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2312yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2312yes—
446#385C2312yes—
447#385C2318yes—
448#385C2318yes—
449#385C2314yes—
450#385C2314yes—
451#385C2314yes—
452#385C2312yes—
453#384C2312yes—
454#384C2312yes—
455#383C2314yes—
456#383C2318yes—
457#382C2318yes—
458#382C2318yes—
459#382C2318yes—
460#382C2312yes—
461#382C2312yes—
462#381C2314yes—
463#381C2314yes—
464#381C2318yes—
465#381C2314yes—
466#381C2314yes—
467#381C2314yes—
468#381C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2318yes—
472#380C2318yes—
473#380C2314yes—
474#380C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2318yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501#376C2312yes—
502C2×#95C2318yes—
503C2×#95C2314yes—
504C2×#95C2314yes—
505C2×#95C2312yes—
506C43C2312yes—
5072−1+4—464no—
508C2×#41—216no—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—48no—
517C2×#41—48no—
518C2×#41—44no—
519C2×#41—44no—
520C2×#41—44no—
521C2×#41—44no—
522C2×#41#4118yes—
523C22×Q8—28no—
524C22×Q8—24no—
525C22×Q8—24no—
526C22×Q8—28no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—24no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2411yescharacteristic
545C22×Q8C2411yescharacteristic
546C22×Q8C2414yes—
547C22×Q8C2414yes—
548C22×D4C2412yes—
549C22×D4C2411yescharacteristic
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2414yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2411yescharacteristic
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2412yes—
563C23×C4C2414yes—
564C23×C4C2414yes—
565C23×C4C2414yes—
566C23×C4C2414yes—
567C23×C4C2411yescharacteristic
568C4⋊Q8—28no—
569C4⋊Q8—28no—
570C4⋊Q8—44no—
571C4⋊Q8—44no—
572C4⋊Q8—44no—
573C4⋊Q8—48no—
574C4⋊Q8—48no—
575C4⋊Q8—48no—
576C4⋊Q8—48no—
577C4⋊Q8—44no—
578C4⋊Q8—44no—
579C4⋊Q8—44no—
580C4⋊Q8—44no—
581#126—216no—
582#125—44no—
583#124—28no—
584#124—28no—
585#124—44no—
586#124—44no—
587#123—216no—
588#123—216no—
589#123—48no—
590#123—48no—
591C22⋊Q8—216no—
592C22⋊Q8—216no—
593C22⋊Q8—216no—
594C22⋊Q8—48no—
595C22⋊Q8—44no—
596C22⋊Q8—44no—
597C22⋊Q8—48no—
598C4×Q8—48no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×Q8—44no—
602C4×Q8—44no—
603C4×Q8—44no—
604C4×Q8—44no—
605C4×Q8—44no—
606C4×Q8—44no—
607C4×D4—44no—
608C4×D4—44no—
609C4×D4—48no—
610C4×D4—48no—
611#117—24no—
612#117—24no—
613#117—24no—
614#117—24no—
615#117—24no—
616#117—24no—
617#117—44no—
618#117—48no—
619#117—44no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—28no—
622C2×C4⋊C4—44no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—48no—
627C2×C4⋊C4—48no—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—24no—
697C2×C42—44no—
698C2×C42—44no—
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2411yescharacteristic
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721#95C2414yes—
722#95C2418yes—
723#95C2418yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764C24C2512yes—
765C24C2512yes—
766C24C2511yescharacteristic
767#41—232no—
768#41—432no—
769#41—464no—
770#41—432no—
771#41—416no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—28no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—28no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—432no—
802C2×Q8—432no—
803C2×Q8—416no—
804C2×Q8—416no—
805C2×Q8—416no—
806C2×Q8C2×#4114yes—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—28no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4C2×#4118yes—
821C2×D4C2×#4114yes—
822C22×C4—22no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—28no—
829C22×C4—24no—
830C22×C4—22no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—28no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—48no—
859C22×C4C2×#4118yes—
860C22×C4C2×#4114yes—
861C22×C4H(5,𝔽2)14yes—
862C22×C4H(5,𝔽2)14yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2514yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2514yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2512yes—
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—216no—
888C4⋊C4—216no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—48no—
926C4⋊C42−1+418yescomplemented
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—216no—
930C22⋊C4—216no—
931C22⋊C4—24no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C42—24no—
952C42—24no—
953C42—22no—
954C42—22no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—22no—
960C42—22no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—28no—
966C42—44no—
967C42—48no—
968C42—44no—
969C42—48no—
970C42—44no—
971C42—44no—
972C42—44no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23C22×#4114yes—
985C23C22×#4112yes—
986C23C2×H(5,𝔽2)12yes—
987C23C2×H(5,𝔽2)12yes—
988C23C2611yescharacteristic
989Q8—28no—
990Q8—416no—
991Q8—48no—
992Q8—48no—
993Q8—48no—
994Q8—48no—
995Q8—48no—
996Q8—44no—
997Q8—48no—
998Q8—88no—
999D4—216no—
1000D4—28no—
1001D4—416no—
1002D4—48no—
1003D4—44no—
1004C2×C4—28no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—216no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—416no—
1060C2×C4—44no—
1061C2×C4—416no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—48no—
1066C2×C4—88no—
1067C2×C4—84no—
1068C2×C4—164no—
1069C2×C4#538116yes—
1070C2×C4C22×#4114yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×2−1+414yes—
1078C2×C4C2×2−1+414yes—
1079C2×C4C2×2−1+414yes—
1080C22—24no—
1081C22—22no—
1082C22—22no—
1083C22—24no—
1084C22—28no—
1085C22—24no—
1086C22—42no—
1087C22—42no—
1088C22—44no—
1089C22—44no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—44no—
1094C22C2×#53814yes—
1095C22C23×#4111yescharacteristic
1096C22C22×H(5,𝔽2)11yescharacteristic
1097C22C22×H(5,𝔽2)11yescharacteristic
1098C22C22×2−1+412yes—
1099C222−1+612yes—
1100C4—24no—
1101C4—24no—
1102C4—24no—
1103C4—24no—
1104C4—44no—
1105C4—44no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—44no—
1115C4—44no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—44no—
1120C4C2×#53814yes—
1121C4C2×#53814yes—
1122C2—24no—
1123C2—44no—
1124C2—82no—
1125C2C22×#53811yescharacteristic
1126C2#6283311yescharacteristic
1127C2#6288711yescharacteristic
1128C2#6294212yes—
1129C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×2−1+4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42941C2semidirect
2. #42853C2semidirect
3. #42715C2semidirect
4. #42696C2semidirect
5. #41532C2semidirect
6. #40073C2semidirect
7. #40031C2semidirect
8. #39663C2semidirect
9. #39640C2semidirect
10. #38605C2semidirect
11. #35674C2semidirect
12. #35667C2semidirect
15. #35630C2semidirect
16. #35628C2semidirect
17. #35320C2semidirect
18. #35316C2semidirect
19. #35182C2semidirect
20. C2×#2546C2semidirect
21. #34816C2semidirect
22. #34745C2semidirect
23. #34276C2semidirect
24. #34266C2semidirect
926. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#429412
#428532
#427152
#426962
#415322
#400732
#400312
#396632
#396402
#386052
#356742
#356672
#356662
#356302
#356282
#353202
#353162
#351822
C2×#25462
#348162
#347452
#342762
#342662
#342592