Finite Group Databasebeta

← #7644386

Subgroups — #7644386

Order 512.

5414 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42953C214yesmaximal, complemented
2#42931C214yesmaximal, complemented
3#42816C214yesmaximal, complemented
4#42486C214yesmaximal, complemented
5#41998C218yesmaximal, complemented
6#40609C218yesmaximal, complemented
7#37481C212yesmaximal, complemented
8#37477C212yesmaximal, complemented
9#37476C214yesmaximal, complemented
10#37425C212yesmaximal, complemented
11#37310C214yesmaximal, complemented
12#37307C212yesmaximal, complemented
13#35639C212yesmaximal, complemented
14#35575C212yesmaximal, complemented
15#35532C212yesmaximal, complemented
16#35519C212yesmaximal, complemented
17#35253C212yesmaximal, complemented
18#34634C211yesmaximal, characteristic, complemented
19C2×#2629C211yesmaximal, characteristic, complemented
20#34175C212yesmaximal
21#34044C211yesmaximal, characteristic
22C23×#41C2211yescharacteristic
23C2×#544C2212yescomplemented
24C2×#533C2211yescharacteristic, complemented
25C22×#125C2211yescharacteristic, complemented
26C2×#520C2212yes—
27C2×#520C2212yes—
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2857C2214yescomplemented
31#2851C2214yescomplemented
32#2842C2218yes—
33#2841C2218yes—
34#2841C2218yescomplemented
35#2841C2218yescomplemented
36#2809C2218yescomplemented
37#2806C2218yescomplemented
38#2806C2218yescomplemented
39#2799C2218yescomplemented
40#2784C2218yescomplemented
41#2780C2218yescomplemented
42#2780C2218yescomplemented
43#2780C2218yescomplemented
44#2780C2218yescomplemented
45#2748C2218yescomplemented
46#2748C2218yescomplemented
47#2732C2218yescomplemented
48#2732C2218yescomplemented
49#2692C2218yescomplemented
50#2692C2218yescomplemented
51#2683C2218yescomplemented
52#2667C2218yes—
53#2667C2218yescomplemented
54#2667C2218yescomplemented
55#2665C2218yes—
56#2659C2218yescomplemented
57#2646C2218yescomplemented
58#2629C2214yes—
59#2629C2212yes—
60#2629C2212yes—
61#2629C2211yescharacteristic
62#2629C2211yescharacteristic
63#2629C2214yes—
64#2629C2211yescharacteristic, complemented
65#2629C2212yescomplemented
66#2629C2214yescomplemented
67#2629C2212yescomplemented
68#2629C2211yescharacteristic, complemented
69#2628C2212yes—
70#2628C2214yes—
71#2628C2212yescomplemented
72#2627C2214yescomplemented
73#2626C2214yes—
74#2626C2218yes—
75#2626C2218yes—
76#2608C2218yes—
77#2582C2214yescomplemented
78#2581C2214yescomplemented
79#2580C2214yescomplemented
80#2579C2218yescomplemented
81#2569C2218yescomplemented
82#2567C2214yescomplemented
83#2566C2214yescomplemented
84#2565C2214yescomplemented
85#2564C2218yescomplemented
86#2549C2218yescomplemented
87#2542C2214yescomplemented
88#2538C2214yescomplemented
89#2487C2218yescomplemented
90#2454C2214yescomplemented
91#2454C2214yescomplemented
92#2454C2214yescomplemented
93#2453C2214yescomplemented
94#2453C2214yescomplemented
95#2453C2214yescomplemented
96#2452C2214yescomplemented
97#2451C2214yescomplemented
98#2450C2218yescomplemented
99#2449C2218yescomplemented
100#2449C2218yescomplemented
101#2449C2218yescomplemented
102#2442C2214yescomplemented
103#2442C2214yescomplemented
104#2442C2214yescomplemented
105#2442C2214yescomplemented
106#2442C2214yescomplemented
107#2441C2214yes—
108#2441C2214yescomplemented
109#2441C2214yescomplemented
110#2441C2214yescomplemented
111#2441C2214yescomplemented
112#2441C2214yescomplemented
113#2441C2214yescomplemented
114#2440C2214yescomplemented
115#2440C2214yescomplemented
116#2440C2214yescomplemented
117#2440C2214yescomplemented
118#2440C2214yescomplemented
119#2439C2214yes—
120#2439C2214yescomplemented
121#2439C2214yescomplemented
122#2438C2218yescomplemented
123#2437C2218yes—
124#2437C2218yes—
125#2417C2218yescomplemented
126#2396C2214yes—
127#2396C2214yescomplemented
128C2×#398C2214yescomplemented
129C2×#396C2214yes—
130#2341C2214yes—
131Q8×C22⋊C4C2214yes—
132#2339C2218yes—
133#2339C2214yes—
134D4×C22⋊C4C2218yes—
135D4×C22⋊C4C2214yes—
136#2317C2212yescomplemented
137#2317C2212yescomplemented
138#2316C2212yescomplemented
139#2311C2214yes—
140#2311C2214yes—
141#2311C2212yes—
142#2311C2214yes—
143#2311C2212yes—
144#2311C2212yes—
145#2311C2212yes—
146#2310C2212yes—
147#2309C2212yes—
148#2308C2214yes—
149#2297C2212yes—
150#2297C2212yes—
151#2297C2212yes—
152#2297C2212yes—
153#2296C2212yescomplemented
154C2×#389C2212yescomplemented
155#2285C2211yescharacteristic, complemented
156C2×#384C2211yescharacteristic, complemented
157#2280C2212yes—
158#2280C2212yes—
159#2280C2214yes—
160#2280C2212yes—
161C2×#380C2212yes—
162C2×#380C2214yes—
163C22×#41—44no—
164C22×#41—44no—
165C22×#41Q8116yescomplemented
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C22×#41C2312yes—
170C23×Q8C2311yescharacteristic
171C23×D4C2312yes—
172C23×D4C2311yescharacteristic
173C24×C4C2311yescharacteristic
174C24×C4C2312yes—
175#544—48no—
176#533—44no—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2312yes—
180C2×#125—44no—
181C2×#125C2314yes—
182C2×#125C2314yes—
183C2×#125C2312yes—
184C2×#125C2312yes—
185C2×#125C2314yes—
186C2×#125C2311yescharacteristic
187C2×#125C2311yescharacteristic
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2318yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2318yes—
195#520—48no—
196#520—48no—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×D4C2318yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2314yes—
204C2×#117—44no—
205C2×#117—44no—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2311yescharacteristic
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2314yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2314yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2318yes—
233C22×C22⋊C4C2314yes—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237#400C2318yes—
238#400C2314yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2314yes—
244#399C2318yes—
245#399C2318yes—
246#399C2318yes—
247#399C2318yes—
248#399C2318yes—
249#399C2318yes—
250#399C2318yes—
251#399C2314yes—
252#399C2314yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#398C2314yes—
266#398C2314yes—
267#398C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2314yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2314yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2314yes—
286#396C2314yes—
287#396C2318yes—
288#396C2318yes—
289#395C2318yes—
290#395C2318yes—
291#395C2318yes—
292#395C2318yes—
293#395C2314yes—
294#395C2318yes—
295#395C2314yes—
296#393C2318yes—
297#393C2318yes—
298#393C2318yes—
299#393C2314yes—
300#393C2314yes—
301#391C2312yes—
302#391C2314yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2318yes—
310#391C2318yes—
311#391C2318yes—
312#391C2318yes—
313#391C2318yes—
314#390C2312yes—
315#390C2312yes—
316#390C2314yes—
317#390C2312yes—
318#390C2312yes—
319#390C2314yes—
320#390C2314yes—
321#390C2318yes—
322#390C2314yes—
323#390C2318yes—
324#389C2318yes—
325#389C2318yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#386C2314yes—
358#386C2314yes—
359#386C2314yes—
360#386C2314yes—
361#386C2314yes—
362#386C2314yes—
363#386C2314yes—
364#386C2314yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2314yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#384C2314yes—
386#384C2314yes—
387#384C2314yes—
388#384C2311yescharacteristic
389#384C2312yes—
390#384C2312yes—
391#384C2311yescharacteristic
392#382C2314yes—
393#382C2314yes—
394#382C2312yes—
395#381C2314yes—
396#381C2314yes—
397#381C2318yes—
398#381C2314yes—
399#380C2314yes—
400#380C2318yes—
401#380C2314yes—
402#380C2314yes—
403#380C2312yes—
404#380C2314yes—
405#380C2312yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2318yes—
413#380C2318yes—
414#380C2318yes—
415#380C2318yes—
416#380C2314yes—
417#380C2314yes—
418#380C2318yes—
419#380C2312yes—
420#380C2314yes—
421#380C2312yes—
422#380C2318yes—
423#380C2318yes—
424#379C2314yes—
425#379C2314yes—
426#379C2318yes—
427#379C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C2×#95C2314yes—
440C2×#95C2318yes—
441C2×#95C2314yes—
442C25C2411yescharacteristic
443C25C2412yes—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—44no—
447C2×#41—44no—
448C2×#41—44no—
449C2×#41—44no—
450C2×#41—44no—
451C2×#41—44no—
452C2×#41—464no—
453C2×#41C2×Q8116yes—
454C2×#41C2×Q8116yes—
455C2×#41C2×Q8116yes—
456C2×#41C2×Q8116yes—
457C22×Q8—42no—
458C22×Q8—42no—
459C22×Q8C2×Q818yes—
460C22×Q8C2412yes—
461C22×Q8C2414yes—
462C22×Q8C2418yes—
463C22×Q8C2412yes—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4—44no—
467C22×D4—44no—
468C22×D4C2×Q818yes—
469C22×D4C2×Q8116yes—
470C22×D4C2414yes—
471C22×D4C2412yes—
472C22×D4C2414yes—
473C22×D4C2412yes—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—44no—
477C23×C4—44no—
478C23×C4C2×Q818yes—
479C23×C4C2×Q8116yes—
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C23×C4C2414yes—
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2412yes—
487C23×C4C2414yes—
488C23×C4C2414yes—
489C23×C4C2412yes—
490C23×C4C2418yes—
491C23×C4C2418yes—
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2414yes—
496C23×C4C2411yescharacteristic
497C4⋊Q8—44no—
498C4⋊Q8—48no—
499C4⋊Q8—48no—
500#125—44no—
501#125—44no—
502#125—48no—
503#125—42no—
504#125—42no—
505#125—48no—
506#125—48no—
507C22⋊Q8—48no—
508C22⋊Q8—416no—
509C22⋊Q8—88no—
510C22⋊Q8—88no—
511C22⋊Q8—88no—
512C22⋊Q8—88no—
513C22⋊Q8—88no—
514C4×Q8—48no—
515C4×Q8—48no—
516C4×Q8—48no—
517C4×D4—48no—
518C4×D4—48no—
519C4×D4—416no—
520C4×D4—416no—
521#117—28no—
522#117—28no—
523#117—28no—
524#117—44no—
525#117—44no—
526#117—42no—
527#117—42no—
528#117—42no—
529#117—42no—
530#117—44no—
531#117—44no—
532#117—44no—
533#117—48no—
534#117—48no—
535C2×C4⋊C4—28no—
536C2×C4⋊C4—28no—
537C2×C4⋊C4—42no—
538C2×C4⋊C4—42no—
539C2×C4⋊C4—48no—
540C2×C4⋊C4—48no—
541C2×C4⋊C4—44no—
542C2×C4⋊C4—48no—
543C2×C4⋊C4—84no—
544C2×C4⋊C4—84no—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C22⋊C4—44no—
588C2×C22⋊C4—44no—
589C2×C22⋊C4—84no—
590C2×C22⋊C4—88no—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C42—24no—
620C2×C42—24no—
621C2×C42—44no—
622C2×C42C2412yes—
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2412yes—
627C2×C42C2414yes—
628C2×C42C2411yescharacteristic
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2418yes—
633C2×C42C2418yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666C24—22no—
667C24—22no—
668C24—42no—
669C24—44no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—44no—
674C24C22×Q814yes—
675C24C22×Q818yes—
676C24C2511yescharacteristic
677C24C2511yescharacteristic
678C24C2514yes—
679C24C2511yescharacteristic
680#41—264no—
681#41—432no—
682#41—432no—
683#41—432no—
684C2×Q8—24no—
685C2×Q8—24no—
686C2×Q8—42no—
687C2×Q8—42no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—48no—
692C2×Q8—48no—
693C2×Q8—48no—
694C2×Q8—416no—
695C2×Q8C22×Q818yes—
696C2×Q8C22×Q818yes—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—416no—
702C2×D4—42no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—42no—
706C2×D4—432no—
707C2×D4C22×Q8116yes—
708C2×D4C22×Q818yes—
709C2×D4C22×Q818yes—
710C2×D4C22×Q8116yes—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—232no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—432no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—42no—
744C22×C4—44no—
745C22×C4—48no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4C22×Q814yes—
752C22×C4C22×Q814yes—
753C22×C4C22×Q814yes—
754C22×C4C22×Q814yes—
755C22×C4C22×Q814yes—
756C22×C4C22×Q8116yes—
757C22×C4C22×Q818yes—
758C22×C4C22×Q8116yes—
759C22×C4C22×Q814yes—
760C22×C4H(5,𝔽2)14yes—
761C22×C4H(5,𝔽2)14yes—
762C22×C4C2514yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2518yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2518yes—
774C22×C4C2511yescharacteristic
775C22×C4C2514yes—
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—42no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—42no—
794C4⋊C4—42no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—48no—
806C4⋊C4—44no—
807C4⋊C4—48no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—48no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—44no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—42no—
825C22⋊C4—42no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—44no—
829C22⋊C4—48no—
830C22⋊C4—44no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C42—24no—
850C42—24no—
851C42—22no—
852C42—22no—
853C42—22no—
854C42—22no—
855C42—28no—
856C42—28no—
857C42—28no—
858C42—44no—
859C42—48no—
860C42—48no—
861C23—22no—
862C23—22no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—24no—
867C23—24no—
868C23—21no—
869C23—22no—
870C23—24no—
871C23—22no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—22no—
876C23—22no—
877C23—28no—
878C23—48no—
879C23—48no—
880C23—416no—
881C23—84no—
882C23—82no—
883C23—82no—
884C23—88no—
885C23—84no—
886C23—84no—
887C23C23×Q812yes—
888C23C23×Q812yes—
889C23C23×Q818yes—
890C23C23×Q812yes—
891C23C2×H(5,𝔽2)12yes—
892C23C2×H(5,𝔽2)12yes—
893C23C2611yescharacteristic
894Q8—216no—
895Q8—48no—
896Q8—88no—
897Q8—168no—
898D4—232no—
899D4—216no—
900D4—48no—
901D4—416no—
902C2×C4—21no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—232no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—28no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—48no—
951C2×C4—416no—
952C2×C4—48no—
953C2×C4—84no—
954C2×C4—88no—
955C2×C4—88no—
956C2×C4—84no—
957C2×C4—84no—
958C2×C4—168no—
959C2×C4—168no—
960C2×C4#543116yes—
961C2×C4C23×Q812yes—
962C2×C4C23×Q812yes—
963C2×C4C23×Q818yes—
964C2×C4C23×Q812yes—
965C2×C4C23×Q812yes—
966C2×C4C2×H(5,𝔽2)12yes—
967C2×C4C2×H(5,𝔽2)12yes—
968C2×C4C2×H(5,𝔽2)12yes—
969C2×C4C2×H(5,𝔽2)12yes—
970C22—24no—
971C22—24no—
972C22—22no—
973C22—22no—
974C22—24no—
975C22—24no—
976C22—28no—
977C22—28no—
978C22—22no—
979C22—22no—
980C22—28no—
981C22—44no—
982C22—42no—
983C22—44no—
984C22—42no—
985C22—41no—
986C22—44no—
987C22—41no—
988C22—41no—
989C22—44no—
990C22—41no—
991C22—88no—
992C22—816no—
993C22C2×#54314yes—
994C22C24×Q811yescharacteristic
995C22C22×H(5,𝔽2)11yescharacteristic
996C22C22×H(5,𝔽2)11yescharacteristic
997C22H(7,𝔽2)12yes—
998C222−1+612yes—
999C4—22no—
1000C4—22no—
1001C4—28no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—48no—
1006C4—42no—
1007C4—44no—
1008C4—44no—
1009C4—48no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4C2×#54314yes—
1015C4C2×#54314yes—
1016C2—24no—
1017C2—42no—
1018C2—48no—
1019C2—42no—
1020C2C22×#54311yescharacteristic
1021C2#6285412yes—
1022C2#6287512yes—
1023C2#6288011yescharacteristic
1024C2#6288811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42953C2semidirect
2. #42931C2semidirect
3. #42816C2semidirect
4. #42486C2semidirect
5. #41998C2semidirect
6. #40609C2semidirect
7. #37481C2semidirect
8. #37477C2semidirect
9. #37476C2semidirect
10. #37425C2semidirect
11. #37310C2semidirect
12. #37307C2semidirect
13. #35639C2semidirect
14. #35575C2semidirect
15. #35532C2semidirect
16. #35519C2semidirect
17. #35253C2semidirect
18. #34634C2semidirect
19. C2×#2629C2semidirect
23. C2×#544C22semidirect
24. C2×#533C22semidirect
25. C22×#125C22semidirect
30. #2857C22semidirect
31. #2851C22semidirect
34. #2841C22semidirect
35. #2841C22semidirect
36. #2809C22semidirect
37. #2806C22semidirect
38. #2806C22semidirect
39. #2799C22semidirect
40. #2784C22semidirect
41. #2780C22semidirect
42. #2780C22semidirect
43. #2780C22semidirect
44. #2780C22semidirect
45. #2748C22semidirect
46. #2748C22semidirect
47. #2732C22semidirect
48. #2732C22semidirect
49. #2692C22semidirect
50. #2692C22semidirect
51. #2683C22semidirect
53. #2667C22semidirect
54. #2667C22semidirect
56. #2659C22semidirect
57. #2646C22semidirect
64. #2629C22semidirect
65. #2629C22semidirect
66. #2629C22semidirect
67. #2629C22semidirect
68. #2629C22semidirect
71. #2628C22semidirect
72. #2627C22semidirect
77. #2582C22semidirect
78. #2581C22semidirect
79. #2580C22semidirect
80. #2579C22semidirect
81. #2569C22semidirect
82. #2567C22semidirect
83. #2566C22semidirect
84. #2565C22semidirect
85. #2564C22semidirect
86. #2549C22semidirect
87. #2542C22semidirect
88. #2538C22semidirect
89. #2487C22semidirect
90. #2454C22semidirect
91. #2454C22semidirect
92. #2454C22semidirect
93. #2453C22semidirect
94. #2453C22semidirect
95. #2453C22semidirect
96. #2452C22semidirect
97. #2451C22semidirect
98. #2450C22semidirect
99. #2449C22semidirect
100. #2449C22semidirect
101. #2449C22semidirect
102. #2442C22semidirect
103. #2442C22semidirect
104. #2442C22semidirect
105. #2442C22semidirect
106. #2442C22semidirect
108. #2441C22semidirect
109. #2441C22semidirect
110. #2441C22semidirect
111. #2441C22semidirect
112. #2441C22semidirect
113. #2441C22semidirect
114. #2440C22semidirect
115. #2440C22semidirect
116. #2440C22semidirect
117. #2440C22semidirect
118. #2440C22semidirect
120. #2439C22semidirect
121. #2439C22semidirect
122. #2438C22semidirect
125. #2417C22semidirect
127. #2396C22semidirect
128. C2×#398C22semidirect
136. #2317C22semidirect
137. #2317C22semidirect
138. #2316C22semidirect
153. #2296C22semidirect
154. C2×#389C22semidirect
155. #2285C22semidirect
156. C2×#384C22semidirect
165. C22×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#429532
#429312
#428162
#424862
#419982
#406092
#374812
#374772
#374762
#374252
#373102
#373072
#356392
#355752
#355322
#355192
#352532
#346342
C2×#26292
#341752
#340442