Finite Group Databasebeta

← #7673809

Subgroups — #7673809

Order 512.

5600 conjugacy classes of subgroups.

The subgroup lattice has 1175 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45368C214yesmaximal, complemented
2#45366C214yesmaximal, complemented
3#45150C214yesmaximal, complemented
4#44995C214yesmaximal, complemented
5#39044C214yesmaximal, complemented
6#39040C214yesmaximal, complemented
7#38204C214yesmaximal, complemented
8#38200C214yesmaximal, complemented
9#37964C218yesmaximal, complemented
10#37849C218yesmaximal, complemented
11#35630C211yesmaximal, characteristic, complemented
12#35628C211yesmaximal, characteristic, complemented
13#35541C211yesmaximal, characteristic, complemented
14#35515C211yesmaximal, characteristic, complemented
15#35313C211yesmaximal, characteristic, complemented
16#35307C211yesmaximal, characteristic, complemented
17#35227C211yesmaximal, characteristic, complemented
18#35149C211yesmaximal, characteristic
19#34634C211yesmaximal, characteristic, complemented
20#34269C211yesmaximal, characteristic, complemented
21#34255C211yesmaximal, characteristic, complemented
22#34178C211yesmaximal, characteristic, complemented
23#34172C211yesmaximal, characteristic, complemented
24#34065C211yesmaximal, characteristic, complemented
25C2×#2311C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C2×#518C2211yescharacteristic
32C2×#518C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2863C2214yescomplemented
37#2855C2214yescomplemented
38#2849C2214yes—
39#2849C2214yes—
40#2760C2218yescomplemented
41#2750C2218yescomplemented
42#2749C2218yescomplemented
43#2746C2218yescomplemented
44#2746C2218yescomplemented
45#2745C2218yescomplemented
46#2744C2218yescomplemented
47#2743C2218yescomplemented
48#2743C2218yescomplemented
49#2743C2218yescomplemented
50#2740C2218yescomplemented
51#2739C2218yescomplemented
52#2738C2218yescomplemented
53#2737C2218yescomplemented
54#2696C2218yescomplemented
55#2693C2218yescomplemented
56#2645C2214yescomplemented
57#2629C2212yescomplemented
58#2629C2212yescomplemented
59#2628C2212yescomplemented
60#2628C2212yescomplemented
61#2627C2214yes—
62#2626C2214yes—
63#2625C2214yescomplemented
64#2623C2214yes—
65#2613C2214yes—
66#2609C2218yescomplemented
67#2598C2218yescomplemented
68#2592C2214yescomplemented
69#2580C2214yescomplemented
70#2576C2218yescomplemented
71#2572C2218yescomplemented
72#2569C2218yescomplemented
73#2568C2214yescomplemented
74#2564C2218yescomplemented
75#2538C2214yescomplemented
76#2514C2214yescomplemented
77#2514C2214yescomplemented
78#2514C2214yescomplemented
79#2511C2214yescomplemented
80#2511C2214yescomplemented
81#2511C2214yescomplemented
82#2510C2218yescomplemented
83#2505C2218yescomplemented
84#2504C2212yescomplemented
85#2503C2212yescomplemented
86#2502C2212yescomplemented
87#2501C2212yescomplemented
88#2498C2218yescomplemented
89#2493C2218yes—
90#2493C2218yes—
91#2493C2218yescomplemented
92#2492C2214yescomplemented
93#2489C2214yescomplemented
94#2488C2218yes—
95#2487C2214yescomplemented
96#2486C2214yescomplemented
97#2477C2218yescomplemented
98#2471C2218yescomplemented
99#2471C2218yescomplemented
100#2457C2218yescomplemented
101#2454C2214yescomplemented
102#2452C2214yescomplemented
103#2447C2214yescomplemented
104#2447C2214yescomplemented
105#2446C2214yescomplemented
106#2445C2214yescomplemented
107#2438C2218yescomplemented
108#2437C2218yes—
109#2432C2212yes—
110#2432C2212yes—
111#2431C2212yes—
112#2431C2212yes—
113#2422C2214yescomplemented
114#2420C2214yescomplemented
115#2419C2218yes—
116#2419C2218yescomplemented
117#2412C2218yes—
118#2407C2214yes—
119#2407C2214yes—
120#2396C2214yescomplemented
121#2396C2214yescomplemented
122#2367C2214yescomplemented
123#2366C2214yescomplemented
124#2358C2218yes—
125#2357C2214yescomplemented
126#2354C2214yescomplemented
127#2345C2214yescomplemented
128#2345C2214yescomplemented
129#2344C2214yescomplemented
130#2344C2214yescomplemented
131#2342C2218yes—
132#2339C2214yes—
133#2339C2214yes—
134#2339C2214yes—
135#2339C2214yes—
136#2324C2212yescomplemented
137#2324C2212yescomplemented
138#2324C2214yescomplemented
139#2323C2212yescomplemented
140#2323C2212yescomplemented
141#2322C2214yes—
142#2321C2214yes—
143#2319C2214yescomplemented
144#2317C2211yescharacteristic
145#2317C2211yescharacteristic
146#2316C2211yescharacteristic
147#2316C2211yescharacteristic
148#2313C2214yes—
149#2311C2211yescharacteristic
150#2311C2214yes—
151#2311C2212yes—
152#2311C2212yes—
153#2311C2214yes—
154#2311C2212yes—
155#2311C2212yes—
156#2311C2211yescharacteristic
157#2310C2211yescharacteristic
158#2310C2211yescharacteristic
159#2310C2211yescharacteristic
160#2309C2211yescharacteristic
161#2308C2214yes—
162C4×#121C2214yescomplemented
163#2297C2211yescharacteristic
164#2296C2211yescharacteristic
165#2296C2211yescharacteristic
166#2296C2211yescharacteristic
167C2×#391C2211yescharacteristic
168C2×#391C2211yescharacteristic
169#2293C2212yescomplemented
170#2293C2212yescomplemented
171#2293C2214yescomplemented
172C2×#390C2211yescharacteristic
173C2×#390C2211yescharacteristic
174#2290C2212yescomplemented
175#2290C2212yescomplemented
176C2×#386C2214yes—
177#2285C2211yescharacteristic
178#2280C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2214yes—
182C2×#381C2214yes—
183C2×#380C2214yes—
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41—28no—
188C22×#41—28no—
189C22×#41—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2312yes—
192C22×#41C2312yes—
193C22×#41C2312yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×D4C2312yes—
197C23×D4C2311yescharacteristic
198C24×C4C2312yes—
199C24×C4C2311yescharacteristic
200C24×C4C2312yes—
201#536—44no—
202#535—28no—
203#533—44no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×#127C2312yes—
207C2×#125C2312yes—
208C2×#124C2312yes—
209C2×#124C2312yes—
210#525—28no—
211C2×#123C2312yes—
212C2×#123C2314yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2314yes—
223C2×#120C2312yes—
224C2×#120C2314yes—
225#518—28no—
226#518—44no—
227C4×#41—44no—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2318yes—
239C2×#117—44no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2318yes—
255C2×#117C2318yes—
256C22×C4⋊C4—28no—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C22⋊C4C2314yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2314yes—
269C22×C22⋊C4C2314yes—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273#401C2318yes—
274#401C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2314yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#399C2318yes—
288#399C2318yes—
289#399C2314yes—
290#399C2314yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#396C2314yes—
304#396C2314yes—
305#396C2318yes—
306#396C2314yes—
307#396C2314yes—
308#396C2318yes—
309#395C2314yes—
310#395C2314yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#393C2318yes—
316#393C2314yes—
317#393C2318yes—
318#393C2314yes—
319#392C2318yes—
320#392C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2318yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2314yes—
350#390C2314yes—
351#390C2312yes—
352#390C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#388C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#385C2314yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#385C2314yes—
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#383C2318yes—
433#383C2318yes—
434#382C2318yes—
435#382C2312yes—
436#382C2312yes—
437#382C2312yes—
438#381C2314yes—
439#381C2314yes—
440#381C2314yes—
441#381C2312yes—
442#381C2312yes—
443#381C2318yes—
444#381C2318yes—
445#381C2318yes—
446#381C2318yes—
447#381C2318yes—
448#381C2318yes—
449#381C2318yes—
450#381C2312yes—
451#380C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2318yes—
455#380C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2318yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2318yes—
468#380C2314yes—
469#379C2312yes—
470#379C2312yes—
471#379C2314yes—
472#379C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498#376C2312yes—
499C2×#95C2318yes—
500C2×#95C2318yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2412yes—
505C25C2411yescharacteristic
506C2×#41—28no—
507C2×#41—28no—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—28no—
514C2×#41—28no—
515C2×#41—28no—
516C2×#41—24no—
517C2×#41—44no—
518C2×#41—44no—
519C2×#41—44no—
520C2×#41—44no—
521C2×#41—464no—
522C22×Q8—24no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×D4—28no—
530C22×D4—28no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—44no—
534C22×D4#4118yes—
535C22×D4C2412yes—
536C22×D4C2411yescharacteristic
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2418yes—
543C22×D4C2412yes—
544C23×C4—24no—
545C23×C4—24no—
546C23×C4—28no—
547C23×C4—28no—
548C23×C4—28no—
549C23×C4—44no—
550C23×C4—84no—
551C23×C4#4118yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2414yes—
555C23×C4C2414yes—
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2418yes—
566C23×C4C2414yes—
567C23×C4C2414yes—
568C23×C4C2418yes—
569C23×C4C2414yes—
570C23×C4C2411yescharacteristic
571C4⋊Q8—44no—
572C4⋊Q8—44no—
573#127—28no—
574#125—44no—
575#124—28no—
576#124—44no—
577#123—28no—
578#123—48no—
579#123—88no—
580#123—88no—
581C22⋊Q8—24no—
582C22⋊Q8—24no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—88no—
586#121—216no—
587#121—24no—
588#121—24no—
589#120—28no—
590#120—216no—
591C4×Q8—48no—
592C4×Q8—44no—
593C4×D4—216no—
594C4×D4—216no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—44no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—48no—
601C4×D4—88no—
602#117—24no—
603#117—24no—
604#117—24no—
605#117—24no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—42no—
610#117—42no—
611#117—42no—
612#117—42no—
613#117—44no—
614#117—44no—
615#117—44no—
616#117—88no—
617#117—88no—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—28no—
620C2×C4⋊C4—28no—
621C2×C4⋊C4—28no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C22⋊C4—216no—
664C2×C22⋊C4—48no—
665C2×C22⋊C4—44no—
666C2×C22⋊C4—84no—
667C2×C22⋊C4—84no—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C42—24no—
705C2×C42—24no—
706C2×C42—44no—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2418yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24—22no—
762C24—22no—
763C24—24no—
764C24—24no—
765C24—42no—
766C24—42no—
767C24—44no—
768C24—44no—
769C24C2×#4118yes—
770C24C2×#4114yes—
771C24C2512yes—
772C24C2511yescharacteristic
773C24C2511yescharacteristic
774C24C2514yes—
775C24C2511yescharacteristic
776#41—432no—
777#41—432no—
778#41—432no—
779#41—432no—
780#41—416no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—416no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—216no—
804C2×D4—232no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—22no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—48no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—48no—
818C2×D4—432no—
819C2×D4C2×#4118yes—
820C2×D4C2×#4118yes—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—232no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—24no—
838C22×C4—216no—
839C22×C4—28no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—24no—
849C22×C4—48no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—48no—
860C22×C4—42no—
861C22×C4—48no—
862C22×C4—42no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—432no—
868C22×C4—816no—
869C22×C4C2×#4114yes—
870C22×C4C2×#4114yes—
871C22×C4C2×#4114yes—
872C22×C4C2×#4114yes—
873C22×C4C2×#4114yes—
874C22×C4C2×#4114yes—
875C22×C4C2×#4114yes—
876C22×C4H(5,𝔽2)14yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2514yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2514yes—
883C22×C4C2512yes—
884C22×C4C2514yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2512yes—
890C22×C4C2514yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—216no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—216no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—48no—
969C22⋊C4—44no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—22no—
975C42—22no—
976C42—24no—
977C42—24no—
978C42—22no—
979C42—22no—
980C42—24no—
981C42—24no—
982C42—24no—
983C42—44no—
984C42—44no—
985C42—44no—
986C42—48no—
987C42—48no—
988C23—22no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—24no—
993C23—21no—
994C23—21no—
995C23—24no—
996C23—28no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—28no—
1002C23—28no—
1003C23—216no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—44no—
1010C23—44no—
1011C23—416no—
1012C23—48no—
1013C23—48no—
1014C23—84no—
1015C23—84no—
1016C23—88no—
1017C23C22×#4118yes—
1018C23C22×#4112yes—
1019C23C22×#4112yes—
1020C23C22×#4112yes—
1021C23C22×#4112yes—
1022C23C2×H(5,𝔽2)12yes—
1023C23C2611yescharacteristic
1024Q8—48no—
1025Q8—48no—
1026Q8—44no—
1027Q8—88no—
1028D4—216no—
1029D4—216no—
1030D4—416no—
1031D4—416no—
1032D4—48no—
1033D4—44no—
1034D4—816no—
1035D4—84no—
1036D4—84no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—28no—
1042C2×C4—28no—
1043C2×C4—28no—
1044C2×C4—28no—
1045C2×C4—28no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—28no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—28no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—416no—
1091C2×C4—416no—
1092C2×C4—416no—
1093C2×C4—48no—
1094C2×C4—48no—
1095C2×C4—816no—
1096C2×C4—84no—
1097C2×C4—84no—
1098C2×C4—84no—
1099C2×C4—84no—
1100C2×C4—88no—
1101C2×C4—88no—
1102C2×C4—168no—
1103C2×C4#551116yes—
1104C2×C4C22×#4112yes—
1105C2×C4C22×#4112yes—
1106C2×C4C22×#4112yes—
1107C2×C4C22×#4112yes—
1108C2×C4C22×#4112yes—
1109C2×C4C22×#4112yes—
1110C2×C4C2×H(5,𝔽2)12yes—
1111C2×C4C2×H(5,𝔽2)12yes—
1112C22—24no—
1113C22—22no—
1114C22—22no—
1115C22—24no—
1116C22—216no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—28no—
1124C22—416no—
1125C22—42no—
1126C22—42no—
1127C22—44no—
1128C22—44no—
1129C22—48no—
1130C22—42no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—44no—
1136C22—42no—
1137C22—816no—
1138C22C2×#55114yes—
1139C22C23×#4111yescharacteristic
1140C22C23×#4111yescharacteristic
1141C22C22×H(5,𝔽2)11yescharacteristic
1142C22H(7,𝔽2)12yes—
1143C222−1+612yes—
1144C4—22no—
1145C4—22no—
1146C4—44no—
1147C4—44no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—44no—
1157C4—42no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—42no—
1162C4C2×#55114yes—
1163C4C2×#55114yes—
1164C2—24no—
1165C2—42no—
1166C2—42no—
1167C2—48no—
1168C2—82no—
1169C2C22×#55111yescharacteristic
1170C2#6284712yes—
1171C2#6285511yescharacteristic
1172C2#6286011yescharacteristic
1173C2#6287512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35149C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45368C2semidirect
2. #45366C2semidirect
3. #45150C2semidirect
4. #44995C2semidirect
5. #39044C2semidirect
6. #39040C2semidirect
7. #38204C2semidirect
8. #38200C2semidirect
9. #37964C2semidirect
10. #37849C2semidirect
11. #35630C2semidirect
12. #35628C2semidirect
13. #35541C2semidirect
14. #35515C2semidirect
15. #35313C2semidirect
16. #35307C2semidirect
17. #35227C2semidirect
19. #34634C2semidirect
20. #34269C2semidirect
21. #34255C2semidirect
22. #34178C2semidirect
23. #34172C2semidirect
24. #34065C2semidirect
25. C2×#2311C2semidirect
36. #2863C22semidirect
37. #2855C22semidirect
40. #2760C22semidirect
41. #2750C22semidirect
42. #2749C22semidirect
43. #2746C22semidirect
44. #2746C22semidirect
45. #2745C22semidirect
46. #2744C22semidirect
47. #2743C22semidirect
48. #2743C22semidirect
49. #2743C22semidirect
50. #2740C22semidirect
51. #2739C22semidirect
52. #2738C22semidirect
53. #2737C22semidirect
54. #2696C22semidirect
55. #2693C22semidirect
56. #2645C22semidirect
57. #2629C22semidirect
58. #2629C22semidirect
59. #2628C22semidirect
60. #2628C22semidirect
63. #2625C22semidirect
66. #2609C22semidirect
67. #2598C22semidirect
68. #2592C22semidirect
69. #2580C22semidirect
70. #2576C22semidirect
71. #2572C22semidirect
72. #2569C22semidirect
73. #2568C22semidirect
74. #2564C22semidirect
75. #2538C22semidirect
76. #2514C22semidirect
77. #2514C22semidirect
78. #2514C22semidirect
79. #2511C22semidirect
80. #2511C22semidirect
81. #2511C22semidirect
82. #2510C22semidirect
83. #2505C22semidirect
84. #2504C22semidirect
85. #2503C22semidirect
86. #2502C22semidirect
87. #2501C22semidirect
88. #2498C22semidirect
91. #2493C22semidirect
92. #2492C22semidirect
93. #2489C22semidirect
95. #2487C22semidirect
96. #2486C22semidirect
97. #2477C22semidirect
98. #2471C22semidirect
99. #2471C22semidirect
100. #2457C22semidirect
101. #2454C22semidirect
102. #2452C22semidirect
103. #2447C22semidirect
104. #2447C22semidirect
105. #2446C22semidirect
106. #2445C22semidirect
107. #2438C22semidirect
113. #2422C22semidirect
114. #2420C22semidirect
116. #2419C22semidirect
120. #2396C22semidirect
121. #2396C22semidirect
122. #2367C22semidirect
123. #2366C22semidirect
125. #2357C22semidirect
126. #2354C22semidirect
127. #2345C22semidirect
128. #2345C22semidirect
129. #2344C22semidirect
130. #2344C22semidirect
136. #2324C22semidirect
137. #2324C22semidirect
138. #2324C22semidirect
139. #2323C22semidirect
140. #2323C22semidirect
143. #2319C22semidirect
162. C4×#121C22semidirect
169. #2293C22semidirect
170. #2293C22semidirect
171. #2293C22semidirect
174. #2290C22semidirect
175. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#453682
#453662
#451502
#449952
#390442
#390402
#382042
#382002
#379642
#378492
#356302
#356282
#355412
#355152
#353132
#353072
#352272
#351492
#346342
#342692
#342552
#341782
#341722
#340652
C2×#23112