Finite Group Databasebeta

← #7646833

Subgroups — #7646833

Order 512.

5174 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42635C214yesmaximal, complemented
2#42624C214yesmaximal, complemented
3#42588C214yesmaximal, complemented
4#42574C214yesmaximal, complemented
5#40179C214yesmaximal, complemented
6#40050C214yesmaximal, complemented
7#39406C214yesmaximal, complemented
8#39033C214yesmaximal, complemented
9#37462C214yesmaximal, complemented
10#36766C214yesmaximal, complemented
11#36729C214yesmaximal, complemented
12#35532C212yesmaximal, complemented
13#35531C212yesmaximal, complemented
14#35264C212yesmaximal, complemented
15#35260C214yesmaximal, complemented
16#35174C211yesmaximal, characteristic, complemented
17#35168C211yesmaximal, characteristic
18#35167C211yesmaximal, characteristic, complemented
19#35158C211yesmaximal, characteristic, complemented
20#34816C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2354C211yesmaximal, characteristic, complemented
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2212yes—
26C2×#542C2214yescomplemented
27C2×#537C2211yescharacteristic
28C2×#535C2212yes—
29C2×#520C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×#117C2212yes—
32#2861C2214yes—
33#2858C2214yes—
34#2857C2214yes—
35#2850C2214yes—
36#2848C2214yes—
37#2847C2214yes—
38#2838C2218yescomplemented
39#2829C2218yescomplemented
40#2801C2218yescomplemented
41#2795C2218yescomplemented
42#2773C2218yescomplemented
43#2759C2218yescomplemented
44#2757C2218yescomplemented
45#2747C2218yescomplemented
46#2742C2218yescomplemented
47#2741C2218yescomplemented
48#2730C2218yescomplemented
49#2717C2218yescomplemented
50#2710C2218yescomplemented
51#2702C2218yescomplemented
52#2692C2218yescomplemented
53#2691C2218yescomplemented
54#2674C2218yescomplemented
55#2672C2218yescomplemented
56#2663C2218yescomplemented
57#2659C2214yes—
58#2653C2218yescomplemented
59#2651C2218yescomplemented
60#2641C2214yes—
61#2640C2214yes—
62#2639C2214yes—
63#2632C2218yescomplemented
64#2628C2214yescomplemented
65#2626C2214yes—
66#2625C2214yescomplemented
67#2624C2214yescomplemented
68#2620C2214yescomplemented
69#2617C2214yes—
70#2567C2214yescomplemented
71#2566C2214yescomplemented
72#2565C2214yescomplemented
73#2552C2214yescomplemented
74#2551C2214yescomplemented
75#2550C2214yescomplemented
76#2550C2214yescomplemented
77#2542C2214yescomplemented
78#2525C2218yescomplemented
79#2514C2212yescomplemented
80#2514C2212yescomplemented
81#2513C2212yescomplemented
82#2513C2212yescomplemented
83#2512C2212yescomplemented
84#2512C2212yescomplemented
85#2511C2212yescomplemented
86#2511C2212yescomplemented
87#2510C2214yes—
88#2510C2214yes—
89#2504C2214yes—
90#2501C2214yes—
91#2500C2214yes—
92#2500C2214yes—
93#2492C2214yescomplemented
94#2491C2214yes—
95#2491C2214yes—
96#2491C2214yescomplemented
97#2490C2214yes—
98#2490C2214yes—
99#2490C2214yescomplemented
100#2489C2214yescomplemented
101#2481C2214yes—
102#2481C2214yes—
103#2479C2218yescomplemented
104#2477C2218yescomplemented
105#2474C2218yescomplemented
106#2472C2218yes—
107#2472C2218yes—
108#2470C2218yescomplemented
109#2461C2218yescomplemented
110#2454C2214yes—
111#2454C2214yes—
112#2452C2214yes—
113#2452C2214yes—
114#2449C2218yes—
115#2449C2218yes—
116#2448C2214yes—
117#2448C2214yes—
118#2445C2214yes—
119#2445C2214yes—
120#2441C2214yescomplemented
121#2441C2214yescomplemented
122#2440C2214yescomplemented
123#2440C2214yescomplemented
124#2428C2214yes—
125#2428C2214yes—
126#2427C2214yes—
127#2427C2214yes—
128#2418C2218yes—
129#2418C2218yes—
130#2401C2214yescomplemented
131#2401C2214yescomplemented
132#2363C2214yescomplemented
133#2362C2214yescomplemented
134#2361C2214yescomplemented
135#2360C2214yescomplemented
136#2354C2214yes—
137#2354C2214yes—
138#2354C2214yes—
139#2354C2214yes—
140#2331C2214yescomplemented
141#2330C2214yescomplemented
142#2329C2214yes—
143#2325C2214yes—
144#2324C2214yescomplemented
145#2323C2214yescomplemented
146#2317C2212yes—
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2314C2214yescomplemented
150#2311C2212yes—
151#2309C2212yes—
152C4×C4⋊Q8C2214yescomplemented
153C4×#125C2214yescomplemented
154C4×#126C2214yescomplemented
155C4×#126C2214yescomplemented
156C4×C22⋊Q8C2214yes—
157C4×#121C2214yes—
158#2297C2212yes—
159#2297C2212yes—
160#2297C2212yes—
161#2296C2212yes—
162C2×#390C2211yescharacteristic
163C2×#390C2211yescharacteristic
164C2×#388C2212yes—
165C2×#388C2212yes—
166#2285C2212yes—
167C2×#384C2211yescharacteristic
168C2×#380C2212yes—
169C4×#117C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C4⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C23×D4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#544—48no—
178#542—416no—
179#537—28no—
180#535—48no—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×#127C2314yes—
186C2×#126C2314yes—
187C2×#126C2314yes—
188C2×#125C2314yes—
189C2×#125C2314yes—
190C2×#125C2314yes—
191C2×#124C2314yes—
192C2×#124C2318yes—
193C2×#124C2314yes—
194C2×#124C2318yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2318yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#120C2318yes—
211#520—48no—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2314yes—
214C2×C4×D4—28no—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2318yes—
220C2×#117—48no—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2314yes—
224C2×#117C2312yes—
225C2×#117C2314yes—
226C2×#117C2314yes—
227C2×#117C2314yes—
228C2×#117C2314yes—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2314yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246C22×C42C2312yes—
247#401C2314yes—
248#401C2314yes—
249#400C2314yes—
250#400C2318yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#399C2318yes—
257#399C2318yes—
258#399C2318yes—
259#399C2318yes—
260#399C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#397C2314yes—
266#397C2314yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2314yes—
276#397C2314yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2314yes—
282#396C2314yes—
283#395C2318yes—
284#395C2318yes—
285#395C2318yes—
286#395C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#393C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2318yes—
302#392C2318yes—
303#391C2318yes—
304#391C2312yes—
305#391C2314yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2312yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2318yes—
323#390C2312yes—
324#390C2314yes—
325#390C2318yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2312yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2314yes—
388#386C2318yes—
389#386C2314yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2314yes—
394#386C2314yes—
395#386C2318yes—
396#386C2314yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2314yes—
402#385C2318yes—
403#385C2318yes—
404#385C2314yes—
405#384C2314yes—
406#384C2314yes—
407#384C2314yes—
408#384C2314yes—
409#384C2312yes—
410#384C2312yes—
411#383C2314yes—
412#383C2314yes—
413#382C2314yes—
414#382C2314yes—
415#382C2312yes—
416#382C2312yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2318yes—
427#380C2318yes—
428#380C2314yes—
429#379C2318yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458#376C2314yes—
459C2×#95C2312yes—
460C2×#95C2312yes—
461C2×#95C2311yescharacteristic
462C2×#95C2311yescharacteristic
463C43C2314yes—
464C25C2412yes—
465C2×#41—28no—
466C2×#41—28no—
467C2×#41—28no—
468C22×Q8C2412yes—
469C22×Q8C2414yes—
470C22×Q8C2418yes—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2412yes—
477C22×D4C2414yes—
478C22×D4C2418yes—
479C22×D4C2418yes—
480C23×C4—28no—
481C23×C4—44no—
482C23×C4—44no—
483C23×C4C2411yescharacteristic
484C23×C4C2414yes—
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2414yes—
488C23×C4C2414yes—
489C23×C4C2412yes—
490C23×C4C2412yes—
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C23×C4C2411yescharacteristic
494C23×C4C2418yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C4⋊Q8—216no—
498C4⋊Q8—48no—
499C4⋊Q8—48no—
500C4⋊Q8—48no—
501#127—48no—
502#126—216no—
503#126—48no—
504#125—216no—
505#125—48no—
506#125—48no—
507#124—48no—
508#124—416no—
509#124—48no—
510#124—88no—
511#123—416no—
512#123—88no—
513C22⋊Q8—216no—
514C22⋊Q8—216no—
515C22⋊Q8—416no—
516C22⋊Q8—416no—
517C22⋊Q8—48no—
518C22⋊Q8—48no—
519C22⋊Q8—88no—
520#121—216no—
521#121—216no—
522#121—48no—
523#121—48no—
524#121—48no—
525#121—48no—
526#120—416no—
527C4×Q8—48no—
528C4×Q8—48no—
529C4×D4—216no—
530C4×D4—216no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—416no—
534#117—28no—
535#117—28no—
536#117—28no—
537#117—216no—
538#117—48no—
539#117—48no—
540#117—48no—
541#117—48no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C4⋊C4—44no—
547C2×C4⋊C4—48no—
548C2×C4⋊C4—82no—
549C2×C4⋊C4#4118yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C22⋊C4—28no—
590C2×C22⋊C4—44no—
591C2×C22⋊C4—44no—
592C2×C22⋊C4—82no—
593C2×C22⋊C4—82no—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C42—24no—
627C2×C42—24no—
628C2×C42—24no—
629C2×C42—44no—
630C2×C42—44no—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2414yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2418yes—
646C2×C42C2414yes—
647C2×C42C2414yes—
648C2×C42C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2412yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2418yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685C24—24no—
686C24—24no—
687C24—24no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24C2514yes—
693C24C2514yes—
694C24C2511yescharacteristic
695#41—432no—
696C2×Q8—24no—
697C2×Q8—28no—
698C2×Q8—24no—
699C2×Q8—24no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—48no—
703C2×Q8—48no—
704C2×Q8—48no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—24no—
710C2×D4—28no—
711C2×D4—24no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—24no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—416no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—42no—
744C22×C4—41no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—42no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—432no—
763C22×C4C2×#4118yes—
764C22×C4C2×#4114yes—
765C22×C4H(5,𝔽2)14yes—
766C22×C42−1+414yes—
767C22×C4C2514yes—
768C22×C4C2511yescharacteristic
769C22×C4C2511yescharacteristic
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2512yes—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—216no—
792C4⋊C4—28no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—24no—
805C4⋊C4—28no—
806C4⋊C4—42no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—48no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4C2×#41116yes—
825C4⋊C4H(5,𝔽2)14yes—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—216no—
830C22⋊C4—216no—
831C22⋊C4—28no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C42—24no—
859C42—24no—
860C42—28no—
861C42—28no—
862C42—28no—
863C42—28no—
864C42—28no—
865C42—28no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—44no—
871C42—44no—
872C42—44no—
873C42—48no—
874C42—44no—
875C42—44no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—48no—
895C23—48no—
896C23—48no—
897C23—84no—
898C23—84no—
899C23—84no—
900C23—84no—
901C23C22×#4112yes—
902C23C2×H(5,𝔽2)12yes—
903C23C2×2−1+412yes—
904C23C2611yescharacteristic
905Q8—48no—
906Q8—88no—
907Q8—168no—
908D4—416no—
909D4—416no—
910D4—48no—
911D4—88no—
912D4—168no—
913D4—168no—
914C2×C4—28no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—24no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—24no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—48no—
968C2×C4—416no—
969C2×C4—416no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—416no—
974C2×C4—84no—
975C2×C4—84no—
976C2×C4—82no—
977C2×C4—82no—
978C2×C4—168no—
979C2×C4#542116yescomplemented
980C2×C4C22×#4118yes—
981C2×C4C22×#4114yes—
982C2×C4C2×H(5,𝔽2)12yes—
983C2×C4C2×H(5,𝔽2)12yes—
984C2×C4C2×H(5,𝔽2)12yes—
985C2×C4C2×H(5,𝔽2)14yes—
986C2×C4C2×2−1+414yes—
987C2×C4#58512yes—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—816no—
1009C22C2×#54214yes—
1010C22C23×#4111yescharacteristic
1011C22C22×H(5,𝔽2)11yescharacteristic
1012C22C22×H(5,𝔽2)11yescharacteristic
1013C22C22×2−1+411yescharacteristic
1014C22C2×#58511yescharacteristic
1015C22H(7,𝔽2)11yescharacteristic
1016C222−1+611yescharacteristic
1017C4—22no—
1018C4—22no—
1019C4—28no—
1020C4—22no—
1021C4—22no—
1022C4—44no—
1023C4—44no—
1024C4—42no—
1025C4—41no—
1026C4—41no—
1027C4—44no—
1028C4—44no—
1029C4—44no—
1030C4—44no—
1031C4—42no—
1032C4—42no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4C2×#54218yes—
1037C2—24no—
1038C2—84no—
1039C2—84no—
1040C2C22×#54211yescharacteristic
1041C2#6277311yescharacteristic
1042C2#6285111yescharacteristic
1043C2#6291511yescharacteristic
1044C2#6291611yescharacteristic
1045C2#6292911yescharacteristic
1046C2#6293111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35168C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42635C2semidirect
2. #42624C2semidirect
3. #42588C2semidirect
4. #42574C2semidirect
5. #40179C2semidirect
6. #40050C2semidirect
7. #39406C2semidirect
8. #39033C2semidirect
9. #37462C2semidirect
10. #36766C2semidirect
11. #36729C2semidirect
12. #35532C2semidirect
13. #35531C2semidirect
14. #35264C2semidirect
15. #35260C2semidirect
16. #35174C2semidirect
18. #35167C2semidirect
19. #35158C2semidirect
20. #34816C2semidirect
21. #34274C2semidirect
22. C2×#2354C2semidirect
23. C4×#544C2semidirect
26. C2×#542C22semidirect
38. #2838C22semidirect
39. #2829C22semidirect
40. #2801C22semidirect
41. #2795C22semidirect
42. #2773C22semidirect
43. #2759C22semidirect
44. #2757C22semidirect
45. #2747C22semidirect
46. #2742C22semidirect
47. #2741C22semidirect
48. #2730C22semidirect
49. #2717C22semidirect
50. #2710C22semidirect
51. #2702C22semidirect
52. #2692C22semidirect
53. #2691C22semidirect
54. #2674C22semidirect
55. #2672C22semidirect
56. #2663C22semidirect
58. #2653C22semidirect
59. #2651C22semidirect
63. #2632C22semidirect
64. #2628C22semidirect
66. #2625C22semidirect
67. #2624C22semidirect
68. #2620C22semidirect
70. #2567C22semidirect
71. #2566C22semidirect
72. #2565C22semidirect
73. #2552C22semidirect
74. #2551C22semidirect
75. #2550C22semidirect
76. #2550C22semidirect
77. #2542C22semidirect
78. #2525C22semidirect
79. #2514C22semidirect
80. #2514C22semidirect
81. #2513C22semidirect
82. #2513C22semidirect
83. #2512C22semidirect
84. #2512C22semidirect
85. #2511C22semidirect
86. #2511C22semidirect
93. #2492C22semidirect
96. #2491C22semidirect
99. #2490C22semidirect
100. #2489C22semidirect
103. #2479C22semidirect
104. #2477C22semidirect
105. #2474C22semidirect
108. #2470C22semidirect
109. #2461C22semidirect
120. #2441C22semidirect
121. #2441C22semidirect
122. #2440C22semidirect
123. #2440C22semidirect
130. #2401C22semidirect
131. #2401C22semidirect
132. #2363C22semidirect
133. #2362C22semidirect
134. #2361C22semidirect
135. #2360C22semidirect
140. #2331C22semidirect
141. #2330C22semidirect
144. #2324C22semidirect
145. #2323C22semidirect
149. #2314C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×#125C22semidirect
154. C4×#126C22semidirect
155. C4×#126C22semidirect
979. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#426352
#426242
#425882
#425742
#401792
#400502
#394062
#390332
#374622
#367662
#367292
#355322
#355312
#352642
#352602
#351742
#351682
#351672
#351582
#348162
#342742
C2×#23542
C4×#5442