Finite Group Databasebeta

← #7644214

Subgroups — #7644214

Order 512.

5232 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42903C214yesmaximal, complemented
2#42900C214yesmaximal, complemented
3#42858C214yesmaximal, complemented
4#42857C214yesmaximal, complemented
5#42853C214yesmaximal, complemented
6#42851C214yesmaximal, complemented
7#42847C214yesmaximal, complemented
8#42844C214yesmaximal, complemented
9#37497C218yesmaximal, complemented
10#36997C218yesmaximal, complemented
11#35667C211yesmaximal, characteristic, complemented
12#35666C211yesmaximal, characteristic, complemented
13#35662C211yesmaximal, characteristic, complemented
14#35660C211yesmaximal, characteristic
15#35629C211yesmaximal, characteristic, complemented
16#35628C211yesmaximal, characteristic, complemented
17#35621C211yesmaximal, characteristic, complemented
18#35618C211yesmaximal, characteristic, complemented
19#35182C211yesmaximal, characteristic, complemented
20#35153C211yesmaximal, characteristic, complemented
21#34639C211yesmaximal, characteristic, complemented
22#34637C211yesmaximal, characteristic, complemented
23#34266C211yesmaximal, characteristic, complemented
24#34257C211yesmaximal, characteristic, complemented
25C2×#2327C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2854C2214yes—
40#2853C2214yes—
41#2833C2218yes—
42#2831C2218yes—
43#2830C2218yes—
44#2829C2218yes—
45#2808C2218yes—
46#2805C2218yes—
47#2803C2218yes—
48#2800C2218yes—
49#2797C2218yes—
50#2788C2218yes—
51#2787C2218yes—
52#2787C2218yes—
53#2786C2218yes—
54#2784C2218yes—
55#2781C2218yes—
56#2774C2218yes—
57#2770C2218yes—
58#2759C2218yes—
59#2750C2218yes—
60#2745C2218yes—
61#2666C2218yes—
62#2665C2218yes—
63#2653C2218yes—
64#2652C2218yes—
65#2652C2218yes—
66#2651C2218yes—
67#2649C2218yes—
68#2648C2218yes—
69#2645C2212yes—
70#2645C2212yes—
71#2644C2212yes—
72#2644C2212yes—
73#2643C2214yes—
74#2643C2214yes—
75#2642C2212yes—
76#2641C2212yes—
77#2640C2212yes—
78#2640C2212yes—
79#2639C2214yes—
80#2639C2214yes—
81#2623C2214yes—
82#2618C2214yes—
83#2592C2214yes—
84#2589C2218yes—
85#2587C2218yes—
86#2582C2214yes—
87#2581C2214yes—
88#2578C2218yes—
89#2576C2218yes—
90#2568C2214yes—
91#2547C2212yes—
92#2546C2212yes—
93#2546C2214yes—
94#2545C2212yes—
95#2545C2214yes—
96#2544C2212yes—
97#2514C2214yes—
98#2513C2214yes—
99#2510C2218yes—
100#2504C2212yes—
101#2503C2212yes—
102#2500C2212yes—
103#2499C2212yes—
104#2495C2214yes—
105#2494C2214yes—
106#2492C2214yes—
107#2489C2214yes—
108#2488C2218yes—
109#2453C2214yes—
110#2451C2214yes—
111#2448C2214yes—
112#2446C2214yes—
113#2444C2218yes—
114#2438C2218yes—
115#2436C2212yes—
116#2434C2212yes—
117#2434C2212yes—
118#2434C2214yes—
119#2434C2212yes—
120#2432C2212yes—
121#2432C2214yes—
122#2432C2212yes—
123#2432C2212yes—
124#2431C2212yes—
125#2430C2218yes—
126#2429C2214yes—
127#2429C2214yes—
128#2429C2214yes—
129#2429C2214yes—
130#2426C2214yes—
131#2426C2214yes—
132#2425C2218yes—
133#2423C2214yes—
134#2421C2214yes—
135#2421C2214yes—
136#2420C2214yes—
137#2417C2214yes—
138#2415C2214yes—
139#2413C2218yes—
140#2409C2214yes—
141#2407C2214yes—
142#2406C2218yes—
143#2401C2214yes—
144#2401C2214yes—
145#2398C2214yes—
146#2398C2214yes—
147#2367C2214yes—
148#2365C2214yes—
149#2362C2214yes—
150#2360C2214yes—
151#2341C2214yes—
152#2341C2214yes—
153Q8×C22⋊C4C2214yes—
154Q8×C22⋊C4C2214yes—
155#2327C2214yes—
156#2327C2214yes—
157#2327C2214yes—
158#2327C2214yes—
159#2322C2214yes—
160#2317C2211yescharacteristic
161#2316C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2211yescharacteristic
164#2311C2211yescharacteristic
165#2311C2214yes—
166#2310C2211yescharacteristic
167#2310C2211yescharacteristic
168C4×#123C2214yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2214yes—
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#387C2214yes—
183C2×#387C2214yes—
184C2×#382C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2314yes—
194C22×#41C2312yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200#537—44no—
201#536—28no—
202#536—44no—
203#536—44no—
204#536—44no—
205#533—44no—
206#532—44no—
207C2×C4⋊Q8—28no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×#127C2311yescharacteristic
218C2×#125C2312yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241#520—44no—
242#519—44no—
243C2×C4×Q8—44no—
244C2×C4×Q8—44no—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2314yes—
262C2×#117C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273C22×C42C2312yes—
274#401C2314yes—
275#401C2318yes—
276#401C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#400C2318yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#399C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#396C2314yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2314yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#394C2314yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2314yes—
337#394C2314yes—
338#394C2314yes—
339#393C2314yes—
340#393C2318yes—
341#393C2318yes—
342#393C2314yes—
343#393C2314yes—
344#393C2314yes—
345#392C2318yes—
346#391C2314yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2314yes—
351#391C2312yes—
352#391C2318yes—
353#391C2312yes—
354#391C2312yes—
355#391C2312yes—
356#391C2314yes—
357#391C2318yes—
358#391C2318yes—
359#391C2314yes—
360#391C2318yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#391C2312yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#390C2312yes—
373#390C2312yes—
374#390C2318yes—
375#390C2312yes—
376#390C2318yes—
377#390C2312yes—
378#390C2312yes—
379#390C2312yes—
380#390C2318yes—
381#390C2312yes—
382#390C2312yes—
383#390C2312yes—
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2312yes—
391#389C2312yes—
392#389C2318yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#386C2312yes—
432#386C2312yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2318yes—
437#386C2318yes—
438#386C2312yes—
439#386C2318yes—
440#386C2318yes—
441#386C2312yes—
442#386C2312yes—
443#386C2312yes—
444#386C2314yes—
445#386C2314yes—
446#386C2314yes—
447#386C2314yes—
448#385C2314yes—
449#385C2318yes—
450#385C2312yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2312yes—
458#385C2314yes—
459#385C2314yes—
460#384C2312yes—
461#383C2318yes—
462#382C2318yes—
463#382C2312yes—
464#382C2314yes—
465#382C2312yes—
466#382C2312yes—
467#381C2314yes—
468#381C2314yes—
469#381C2318yes—
470#380C2314yes—
471#380C2314yes—
472#380C2318yes—
473#380C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2318yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498#376C2312yes—
499#376C2312yes—
500#376C2312yes—
501#376C2312yes—
502C2×#95C2312yes—
503C2×#95C2312yes—
504C2×#95C2314yes—
505C2×#95C2314yes—
506C2×#95C2314yes—
5072−1+4—464no—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—24no—
511C2×#41—216no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—48no—
521C2×#41—48no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41—44no—
525C2×#41—44no—
526C22×Q8—28no—
527C22×Q8—28no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8#4118yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2411yescharacteristic
542C22×Q8C2411yescharacteristic
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C22×Q8C2414yes—
546C22×Q8C2414yes—
547C22×D4C2412yes—
548C22×D4C2411yescharacteristic
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2414yes—
554C22×D4C2414yes—
555C22×D4C2414yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2412yes—
567C23×C4C2414yes—
568C23×C4C2414yes—
569C23×C4C2414yes—
570C23×C4C2411yescharacteristic
571C4⋊Q8—28no—
572C4⋊Q8—28no—
573C4⋊Q8—216no—
574C4⋊Q8—28no—
575C4⋊Q8—44no—
576C4⋊Q8—42no—
577C4⋊Q8—44no—
578C4⋊Q8—44no—
579C4⋊Q8—44no—
580#127—42no—
581#125—44no—
582#124—28no—
583#124—42no—
584#124—42no—
585#124—44no—
586#124—44no—
587#124—44no—
588#123—216no—
589#123—48no—
590#123—48no—
591#123—48no—
592C22⋊Q8—216no—
593C22⋊Q8—48no—
594C22⋊Q8—44no—
595C22⋊Q8—44no—
596C22⋊Q8—48no—
597C22⋊Q8—48no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600#121—44no—
601#121—44no—
602#121—48no—
603#121—48no—
604C4×Q8—48no—
605C4×Q8—48no—
606C4×Q8—48no—
607C4×Q8—48no—
608C4×Q8—48no—
609C4×Q8—48no—
610C4×Q8—48no—
611C4×Q8—44no—
612C4×D4—44no—
613C4×D4—48no—
614C4×D4—48no—
615#117—24no—
616#117—24no—
617#117—24no—
618#117—24no—
619#117—24no—
620#117—48no—
621#117—44no—
622C2×C4⋊C4—216no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
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×C42—24no—
695C2×C42—24no—
696C2×C42—24no—
697C2×C42—44no—
698C2×C42—44no—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24C2512yes—
762C24C2512yes—
763C24C2512yes—
764C24C2511yescharacteristic
765#41—464no—
766#41—432no—
767#41—432no—
768#41—416no—
769#41—416no—
770#41—416no—
771C2×Q8—232no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—28no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—22no—
791C2×Q8—22no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×Q8—432no—
798C2×Q8—432no—
799C2×Q8—416no—
800C2×Q8C2×#4118yes—
801C2×Q8C2×#4118yes—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—22no—
812C2×D4—28no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—48no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—28no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4C2×#4118yes—
865C22×C4C2×#4114yes—
866C22×C4H(5,𝔽2)14yes—
867C22×C4H(5,𝔽2)14yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2512yes—
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2512yes—
886C22×C4C2514yes—
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C4⋊C4—216no—
890C4⋊C4—216no—
891C4⋊C4—24no—
892C4⋊C4—216no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—216no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C42—24no—
956C42—22no—
957C42—22no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—22no—
963C42—22no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—48no—
969C42—48no—
970C42—48no—
971C42—44no—
972C42—48no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23C22×#4112yes—
991C23C2×H(5,𝔽2)12yes—
992C23C2×H(5,𝔽2)12yes—
993C23C2611yescharacteristic
994Q8—216no—
995Q8—216no—
996Q8—416no—
997Q8—48no—
998Q8—48no—
999Q8—44no—
1000Q8—44no—
1001Q8—44no—
1002Q8—88no—
1003D4—416no—
1004D4—48no—
1005D4—48no—
1006D4—48no—
1007D4—44no—
1008D4—44no—
1009D4—44no—
1010D4—88no—
1011D4—164no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—216no—
1015C2×C4—22no—
1016C2×C4—22no—
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—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—28no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—28no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—416no—
1066C2×C4—416no—
1067C2×C4—48no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—48no—
1071C2×C4—48no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—84no—
1075C2×C4—84no—
1076C2×C4—84no—
1077C2×C4—164no—
1078C2×C4#538116yes—
1079C2×C4C22×#4118yes—
1080C2×C4C22×#4112yes—
1081C2×C4C22×#4112yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C22—24no—
1087C22—22no—
1088C22—22no—
1089C22—24no—
1090C22—44no—
1091C22—44no—
1092C22—44no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22C2×#53814yes—
1106C22C23×#4111yescharacteristic
1107C22C22×H(5,𝔽2)11yescharacteristic
1108C22C22×H(5,𝔽2)11yescharacteristic
1109C222−1+612yes—
1110C222−1+612yes—
1111C4—28no—
1112C4—44no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—44no—
1120C4—42no—
1121C4—44no—
1122C4—42no—
1123C4—42no—
1124C4—44no—
1125C4—44no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—44no—
1130C4C2×#53814yes—
1131C4C2×#53814yes—
1132C2—24no—
1133C2—82no—
1134C2—82no—
1135C2—82no—
1136C2C22×#53811yescharacteristic
1137C2#6285012yes—
1138C2#6288711yescharacteristic
1139C2#6288711yescharacteristic
1140C2#6288812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35660C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42903C2semidirect
2. #42900C2semidirect
3. #42858C2semidirect
4. #42857C2semidirect
5. #42853C2semidirect
6. #42851C2semidirect
7. #42847C2semidirect
8. #42844C2semidirect
9. #37497C2semidirect
10. #36997C2semidirect
11. #35667C2semidirect
12. #35666C2semidirect
13. #35662C2semidirect
15. #35629C2semidirect
16. #35628C2semidirect
17. #35621C2semidirect
18. #35618C2semidirect
19. #35182C2semidirect
20. #35153C2semidirect
21. #34639C2semidirect
22. #34637C2semidirect
23. #34266C2semidirect
24. #34257C2semidirect
25. C2×#2327C2semidirect

Maximal subgroups

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

subgroupindex
#429032
#429002
#428582
#428572
#428532
#428512
#428472
#428442
#374972
#369972
#356672
#356662
#356622
#356602
#356292
#356282
#356212
#356182
#351822
#351532
#346392
#346372
#342662
#342572
C2×#23272