Finite Group Databasebeta

← #7646529

Subgroups — #7646529

Order 512.

4622 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42976C214yesmaximal, complemented
2#42959C214yesmaximal, complemented
3#42165C214yesmaximal, complemented
4#42163C214yesmaximal, complemented
5#39515C212yesmaximal, complemented
6#39514C212yesmaximal, complemented
7#39202C212yesmaximal, complemented
8#39201C212yesmaximal, complemented
9#37858C214yesmaximal, complemented
10#37857C214yesmaximal, complemented
11#37573C214yesmaximal, complemented
12#36822C214yesmaximal, complemented
13#36816C214yesmaximal, complemented
14#35605C214yesmaximal, complemented
15#35298C211yesmaximal, characteristic, complemented
16#35237C211yesmaximal, characteristic
17#35219C214yesmaximal, complemented
18#35218C214yesmaximal, complemented
19#34946C211yesmaximal, characteristic, complemented
20#34912C211yesmaximal, characteristic, complemented
21#34231C211yesmaximal, characteristic, complemented
22#34155C211yesmaximal, characteristic, complemented
23#34058C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#532C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27#2868C2211yescharacteristic, complemented
28#2862C2211yescharacteristic, complemented
29#2858C2211yescharacteristic, complemented
30#2858C2211yescharacteristic, complemented
31#2853C2218yescomplemented
32#2852C2218yescomplemented
33#2847C2212yes—
34#2847C2212yes—
35#2838C2218yescomplemented
36#2829C2218yes—
37#2798C2218yescomplemented
38#2797C2218yescomplemented
39#2759C2218yescomplemented
40#2752C2218yescomplemented
41#2746C2218yes—
42#2743C2218yes—
43#2740C2218yes—
44#2737C2218yes—
45#2716C2218yescomplemented
46#2716C2218yescomplemented
47#2712C2218yescomplemented
48#2710C2218yescomplemented
49#2697C2218yes—
50#2685C2218yes—
51#2685C2218yes—
52#2684C2218yes—
53#2662C2218yes—
54#2654C2218yescomplemented
55#2653C2218yescomplemented
56#2652C2218yescomplemented
57#2649C2218yescomplemented
58#2648C2218yes—
59#2631C2214yes—
60#2629C2214yescomplemented
61#2628C2214yescomplemented
62#2624C2214yescomplemented
63#2624C2214yescomplemented
64#2620C2214yes—
65#2608C2212yes—
66#2607C2212yes—
67#2606C2212yescomplemented
68#2605C2212yescomplemented
69#2597C2218yescomplemented
70#2595C2218yescomplemented
71#2592C2214yes—
72#2581C2214yescomplemented
73#2580C2214yescomplemented
74#2578C2218yescomplemented
75#2576C2218yescomplemented
76#2573C2218yescomplemented
77#2572C2218yescomplemented
78#2570C2214yescomplemented
79#2570C2214yescomplemented
80#2570C2212yescomplemented
81#2566C2214yescomplemented
82#2563C2212yes—
83#2563C2212yes—
84#2562C2212yes—
85#2562C2212yes—
86#2561C2214yes—
87#2554C2218yes—
88#2553C2218yescomplemented
89#2550C2212yescomplemented
90#2548C2214yes—
91#2548C2214yes—
92#2547C2212yes—
93#2545C2212yescomplemented
94#2545C2212yescomplemented
95#2544C2214yes—
96#2541C2212yes—
97#2535C2214yes—
98#2531C2218yescomplemented
99#2526C2218yescomplemented
100#2521C2218yescomplemented
101#2516C2218yescomplemented
102#2514C2214yescomplemented
103#2513C2214yescomplemented
104#2512C2214yes—
105#2512C2214yes—
106#2504C2212yes—
107#2503C2212yes—
108#2500C2214yes—
109#2496C2214yescomplemented
110#2496C2214yescomplemented
111#2495C2214yescomplemented
112#2494C2214yescomplemented
113#2491C2214yescomplemented
114#2490C2214yescomplemented
115#2479C2218yescomplemented
116#2474C2218yescomplemented
117#2448C2214yes—
118#2448C2214yescomplemented
119#2447C2214yescomplemented
120#2445C2214yes—
121#2441C2212yes—
122#2439C2212yes—
123#2435C2212yes—
124#2433C2212yes—
125#2432C2212yes—
126#2432C2212yes—
127#2422C2214yescomplemented
128#2420C2214yescomplemented
129#2404C2214yes—
130#2398C2214yes—
131#2396C2214yes—
132#2372C2214yescomplemented
133#2369C2212yescomplemented
134#2369C2212yescomplemented
135#2366C2212yescomplemented
136#2365C2212yescomplemented
137#2363C2214yes—
138#2363C2214yes—
139#2362C2214yes—
140#2356C2214yescomplemented
141#2347C2212yes—
142#2346C2212yes—
143#2332C2214yes—
144#2328C2214yes—
145#2326C2214yescomplemented
146#2324C2214yescomplemented
147#2324C2214yescomplemented
148#2320C2212yescomplemented
149#2319C2212yes—
150#2319C2212yes—
151#2319C2212yes—
152#2319C2212yes—
153#2316C2212yes—
154#2314C2214yescomplemented
155#2314C2214yescomplemented
156#2312C2212yes—
157#2312C2212yes—
158#2309C2212yes—
159C4×C4⋊Q8C2212yescomplemented
160C4×#125C2212yescomplemented
161C4×#125C2214yescomplemented
162C4×#124C2214yes—
163#2297C2214yes—
164#2295C2214yescomplemented
165#2293C2212yes—
166#2293C2212yes—
167#2293C2214yes—
168#2293C2212yescomplemented
169#2293C2212yescomplemented
170#2283C2211yescharacteristic
171#2280C2214yes—
172#2280C2214yes—
173#2276C2212yescomplemented
174C42×D4C2212yescomplemented
175C42×D4C2212yescomplemented
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2211yescharacteristic
179C22×#41C2312yes—
180C23×D4C2311yescharacteristic
181C24×C4C2312yes—
182#533—28no—
183#532—28no—
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×#127C2311yescharacteristic
191C2×#127C2314yes—
192C2×#126C2318yes—
193C2×#126C2318yes—
194C2×#125C2312yes—
195C2×#125C2312yes—
196C2×#124C2312yes—
197C2×#124C2314yes—
198C2×#124C2314yes—
199C2×#124C2312yes—
200C2×#124C2312yes—
201C2×#124C2318yes—
202C2×#123C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×#121C2312yes—
206C2×#121C2312yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#120C2314yes—
210C2×#120C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2314yes—
215C2×C4×D4—28no—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2314yes—
228C2×#117C2314yes—
229C2×#117C2312yes—
230C2×#117C2314yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C42C2314yes—
234C22×C42C2311yescharacteristic
235#401C2318yes—
236#400C2314yes—
237#400C2314yes—
238#400C2318yes—
239#400C2314yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#399C2318yes—
244#399C2318yes—
245#399C2318yes—
246#399C2314yes—
247#398C2318yes—
248#398C2314yes—
249#398C2318yes—
250#398C2314yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2314yes—
267#396C2314yes—
268#395C2318yes—
269#395C2314yes—
270#394C2314yes—
271#394C2314yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#393C2318yes—
283#393C2318yes—
284#393C2318yes—
285#393C2318yes—
286#393C2314yes—
287#392C2318yes—
288#392C2318yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2318yes—
295#391C2312yes—
296#391C2312yes—
297#391C2314yes—
298#391C2318yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2312yes—
303#390C2314yes—
304#390C2312yes—
305#390C2312yes—
306#390C2312yes—
307#390C2314yes—
308#390C2314yes—
309#390C2318yes—
310#390C2318yes—
311#390C2314yes—
312#390C2314yes—
313#390C2312yes—
314#390C2312yes—
315#390C2318yes—
316#390C2314yes—
317#390C2314yes—
318#390C2318yes—
319#389C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2312yes—
323#389C2312yes—
324#389C2314yes—
325#389C2312yes—
326#389C2312yes—
327#389C2312yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#388C2318yes—
338#388C2318yes—
339#388C2314yes—
340#388C2314yes—
341#388C2314yes—
342#388C2314yes—
343#388C2314yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2314yes—
366#387C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2314yes—
373#387C2314yes—
374#387C2318yes—
375#387C2314yes—
376#387C2314yes—
377#387C2318yes—
378#387C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2314yes—
387#386C2314yes—
388#386C2318yes—
389#386C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#384C2312yes—
396#384C2314yes—
397#384C2314yes—
398#383C2314yes—
399#383C2318yes—
400#383C2312yes—
401#382C2312yes—
402#382C2312yes—
403#382C2314yes—
404#382C2314yes—
405#382C2314yes—
406#382C2314yes—
407#381C2318yes—
408#381C2314yes—
409#381C2318yes—
410#381C2314yes—
411#381C2312yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#379C2318yes—
425#379C2314yes—
426#379C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2312yes—
464#376C2312yes—
465#376C2312yes—
466#376C2312yes—
467#376C2314yes—
468#376C2312yes—
469C43C2311yescharacteristic
470C43C2312yes—
471C43C2311yescharacteristic
472C43C2312yes—
473C25C2412yes—
474C2×#41—28no—
475C2×#41—82no—
476C2×#41—82no—
477C22×Q8C2412yes—
478C22×Q8C2412yes—
479C22×Q8C2412yes—
480C22×Q8C2414yes—
481C22×D4—24no—
482C22×D4—44no—
483C22×D4C2412yes—
484C22×D4C2412yes—
485C22×D4C2412yes—
486C22×D4C2412yes—
487C22×D4C2414yes—
488C22×D4C2412yes—
489C22×D4C2418yes—
490C22×D4C2418yes—
491C23×C4—28no—
492C23×C4—48no—
493C23×C4C2414yes—
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2418yes—
500C23×C4C2411yescharacteristic
501C4⋊Q8—24no—
502C4⋊Q8—24no—
503C4⋊Q8—24no—
504C4⋊Q8—44no—
505C4⋊Q8—82no—
506C4⋊Q8—82no—
507#127—24no—
508#127—48no—
509#126—88no—
510#126—88no—
511#125—28no—
512#125—44no—
513#124—28no—
514#124—48no—
515#124—48no—
516#124—82no—
517#124—82no—
518#124—88no—
519#123—88no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522#121—28no—
523#121—28no—
524#121—48no—
525#121—48no—
526#120—84no—
527#120—84no—
528C4×Q8—28no—
529C4×Q8—28no—
530C4×Q8—48no—
531C4×Q8—48no—
532C4×D4—28no—
533C4×D4—28no—
534C4×D4—28no—
535C4×D4—28no—
536C4×D4—28no—
537C4×D4—28no—
538C4×D4—48no—
539C4×D4—48no—
540#117—28no—
541#117—48no—
542#117—48no—
543#117—44no—
544#117—44no—
545#117—44no—
546#117—84no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C22⋊C4—28no—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C42—84no—
620C2×C42#4118yes—
621C2×C42C2414yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2414yes—
626C2×C42C2412yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2418yes—
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2418yes—
637C2×C42C2418yes—
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#95C2412yes—
647#95C2412yes—
648#95C2412yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2414yes—
655#95C2414yes—
656#95C2412yes—
657#95C2412yes—
658#95C2414yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2414yes—
672#95C2418yes—
673#95C2414yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685C24—24no—
686C24—44no—
687C24—42no—
688C24—42no—
689C24—44no—
690C24C2514yes—
691C24C2514yes—
692C24C2511yescharacteristic
693#41—816no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—28no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—42no—
701C2×Q8—42no—
702C2×Q8—44no—
703C2×Q8—42no—
704C2×Q8—42no—
705C2×D4—28no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—44no—
716C2×D4—416no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—48no—
740C22×C4—48no—
741C22×C4—48no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—816no—
746C22×C4C2×#4114yes—
747C22×C4C2×#4114yes—
748C22×C4C2×#4114yes—
749C22×C4C2514yes—
750C22×C4C2514yes—
751C22×C4C2514yes—
752C22×C4C2514yes—
753C22×C4C2514yes—
754C22×C4C2512yes—
755C22×C4C2514yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2514yes—
759C22×C4C2512yes—
760C22×C4C2512yes—
761C22×C4C2512yes—
762C22×C4C2514yes—
763C22×C4C2511yescharacteristic
764C22×C4C2511yescharacteristic
765C22×C4C2511yescharacteristic
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—24no—
774C4⋊C4—24no—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—48no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—48no—
796C4⋊C4—44no—
797C4⋊C4—48no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—42no—
811C22⋊C4—42no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—44no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C42—28no—
840C42—28no—
841C42—24no—
842C42—24no—
843C42—24no—
844C42—24no—
845C42—28no—
846C42—28no—
847C42—42no—
848C42—42no—
849C42—48no—
850C42—44no—
851C42—44no—
852C42—42no—
853C42—42no—
854C42—48no—
855C42—41no—
856C42—41no—
857C42—48no—
858C42—41no—
859C42—41no—
860C42C2×#4114yes—
861C42C2×#4114yes—
862C42C2×#4114yes—
863C42C2×#4114yes—
864C23—22no—
865C23—22no—
866C23—21no—
867C23—21no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—28no—
872C23—28no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—48no—
881C23—84no—
882C23—84no—
883C23—88no—
884C23—88no—
885C23C22×#4112yes—
886C23C2611yescharacteristic
887Q8—48no—
888Q8—84no—
889Q8—84no—
890Q8—88no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—84no—
896D4—88no—
897D4—168no—
898D4—168no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—28no—
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—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—44no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—88no—
952C2×C4—84no—
953C2×C4—816no—
954C2×C4C22×#4112yes—
955C2×C4C22×#4112yes—
956C2×C4C22×#4112yes—
957C2×C4C22×#4112yes—
958C2×C4C22×#4112yes—
959C2×C4C22×#4112yes—
960C2×C4#58514yes—
961C2×C4#58514yes—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—42no—
966C22—42no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—48no—
973C22—44no—
974C22—48no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—816no—
980C22C23×#4111yescharacteristic
981C22C2×#58512yes—
982C22C2×#58512yes—
983C22H(7,𝔽2)11yescharacteristic
984C22H(7,𝔽2)11yescharacteristic
985C4—22no—
986C4—22no—
987C4—22no—
988C4—22no—
989C4—44no—
990C4—44no—
991C4—44no—
992C4—42no—
993C4—44no—
994C4—44no—
995C4—44no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—44no—
1003C4#345514yes—
1004C4#351014yes—
1005C2—42no—
1006C2—84no—
1007C2—84no—
1008C2C2×#345511yescharacteristic
1009C2C2×#351011yescharacteristic
1010C2#6285511yescharacteristic
1011C2#6293712yes—
1012C2#6293812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35237C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42976C2semidirect
2. #42959C2semidirect
3. #42165C2semidirect
4. #42163C2semidirect
5. #39515C2semidirect
6. #39514C2semidirect
7. #39202C2semidirect
8. #39201C2semidirect
9. #37858C2semidirect
10. #37857C2semidirect
11. #37573C2semidirect
12. #36822C2semidirect
13. #36816C2semidirect
14. #35605C2semidirect
15. #35298C2semidirect
17. #35219C2semidirect
18. #35218C2semidirect
19. #34946C2semidirect
20. #34912C2semidirect
21. #34231C2semidirect
22. #34155C2semidirect
23. #34058C2semidirect
27. #2868C22semidirect
28. #2862C22semidirect
29. #2858C22semidirect
30. #2858C22semidirect
31. #2853C22semidirect
32. #2852C22semidirect
35. #2838C22semidirect
37. #2798C22semidirect
38. #2797C22semidirect
39. #2759C22semidirect
40. #2752C22semidirect
45. #2716C22semidirect
46. #2716C22semidirect
47. #2712C22semidirect
48. #2710C22semidirect
54. #2654C22semidirect
55. #2653C22semidirect
56. #2652C22semidirect
57. #2649C22semidirect
60. #2629C22semidirect
61. #2628C22semidirect
62. #2624C22semidirect
63. #2624C22semidirect
67. #2606C22semidirect
68. #2605C22semidirect
69. #2597C22semidirect
70. #2595C22semidirect
72. #2581C22semidirect
73. #2580C22semidirect
74. #2578C22semidirect
75. #2576C22semidirect
76. #2573C22semidirect
77. #2572C22semidirect
78. #2570C22semidirect
79. #2570C22semidirect
80. #2570C22semidirect
81. #2566C22semidirect
88. #2553C22semidirect
89. #2550C22semidirect
93. #2545C22semidirect
94. #2545C22semidirect
98. #2531C22semidirect
99. #2526C22semidirect
100. #2521C22semidirect
101. #2516C22semidirect
102. #2514C22semidirect
103. #2513C22semidirect
109. #2496C22semidirect
110. #2496C22semidirect
111. #2495C22semidirect
112. #2494C22semidirect
113. #2491C22semidirect
114. #2490C22semidirect
115. #2479C22semidirect
116. #2474C22semidirect
118. #2448C22semidirect
119. #2447C22semidirect
127. #2422C22semidirect
128. #2420C22semidirect
132. #2372C22semidirect
133. #2369C22semidirect
134. #2369C22semidirect
135. #2366C22semidirect
136. #2365C22semidirect
140. #2356C22semidirect
145. #2326C22semidirect
146. #2324C22semidirect
147. #2324C22semidirect
148. #2320C22semidirect
154. #2314C22semidirect
155. #2314C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×#125C22semidirect
161. C4×#125C22semidirect
164. #2295C22semidirect
168. #2293C22semidirect
169. #2293C22semidirect
173. #2276C22semidirect
174. C42×D4C22semidirect
175. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#429762
#429592
#421652
#421632
#395152
#395142
#392022
#392012
#378582
#378572
#375732
#368222
#368162
#356052
#352982
#352372
#352192
#352182
#349462
#349122
#342312
#341552
#340582