Finite Group Databasebeta

← #7679709

Subgroups — #7679709

Order 512.

6918 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
1C2×#3512C212yesmaximal, complemented
2#59826C214yesmaximal, complemented
3#59392C214yesmaximal, complemented
4#59290C214yesmaximal, complemented
5#59213C214yesmaximal, complemented
6#43542C218yesmaximal, complemented
7#43534C218yesmaximal, complemented
8#39385C211yesmaximal, characteristic, complemented
9#39378C211yesmaximal, characteristic, complemented
10#39340C212yesmaximal, complemented
11#37784C214yesmaximal, complemented
12#37705C212yesmaximal, complemented
13#37700C212yesmaximal, complemented
14#36127C211yesmaximal, characteristic, complemented
15#36116C212yesmaximal, complemented
16D4×#125C211yesmaximal, characteristic, complemented
17#35654C214yesmaximal, complemented
18#35319C211yesmaximal, characteristic, complemented
19#35309C212yesmaximal, complemented
20#34932C212yesmaximal, complemented
21#34308C212yesmaximal, complemented
22#34141C211yesmaximal, characteristic, complemented
23C4×#540C211yesmaximal, characteristic, complemented
24#3512—232no—
25C2×#553C2218yes—
26C2×#553C2218yes—
27C2×#553C2218yes—
28C2×#552C2218yes—
29C2×#547C2212yes—
30C2×#541C2212yes—
31C2×#541C2212yes—
32C2×#540C2212yes—
33C2×#540C2211yescharacteristic
34C2×#537C2214yes—
35C2×#532C2212yes—
36C2×#532C2211yescharacteristic
37C2×#529C2214yes—
38C2×#529C2214yes—
39C22×#125C2212yes—
40C2×#520C2214yes—
41C2×C4×#41C2212yes—
42#2868C2211yescharacteristic
43#2859C2211yescharacteristic
44#2857C2212yes—
45#2857C2212yes—
46#2855C2214yes—
47#2851C2212yes—
48#2725C2218yes—
49#2721C2218yes—
50#2719C2218yes—
51#2708C2218yes—
52#2708C2218yes—
53#2701C2218yes—
54#2701C2218yes—
55#2698C2218yes—
56#2691C2218yes—
57#2688C2218yes—
58#2672C2218yes—
59#2671C2218yes—
60#2642C2212yes—
61#2629C2212yes—
62#2621C2212yes—
63#2621C2212yes—
64#2616C2214yes—
65#2600C2218yes—
66#2579C2218yes—
67#2553C2218yes—
68#2552C2212yes—
69#2552C2214yes—
70#2547C2212yes—
71#2542C2212yes—
72#2537C2214yes—
73#2537C2214yes—
74#2537C2212yes—
75#2512C2214yes—
76#2506C2214yes—
77#2506C2214yes—
78#2506C2214yes—
79#2496C2214yes—
80#2496C2214yes—
81#2496C2214yes—
82#2496C2214yes—
83#2489C2214yes—
84#2486C2214yes—
85#2486C2214yes—
86#2485C2218yes—
87#2484C2218yes—
88#2481C2218yes—
89#2478C2218yes—
90#2478C2218yes—
91#2476C2218yes—
92#2473C2218yes—
93#2470C2218yes—
94#2468C2218yes—
95#2468C2218yes—
96#2466C2218yes—
97#2462C2218yes—
98#2460C2218yes—
99#2457C2218yes—
100#2453C2214yes—
101#2447C2214yes—
102#2444C2218yes—
103#2444C2218yes—
104#2442C2214yes—
105#2442C2218yes—
106#2440C2214yes—
107#2438C2218yes—
108#2432C2214yes—
109#2429C2214yes—
110#2428C2214yes—
111#2427C2214yes—
112#2422C2214yes—
113#2422C2218yes—
114#2420C2218yes—
115#2420C2214yes—
116#2419C2218yes—
117#2419C2218yes—
118#2417C2214yes—
119#2416C2214yes—
120#2416C2214yes—
121#2407C2214yes—
122#2395C2218yes—
123#2367C2214yes—
124#2366C2212yes—
125#2365C2212yes—
126#2365C2212yes—
127#2364C2214yes—
128#2361C2214yes—
129#2361C2212yes—
130#2361C2212yes—
131#2360C2214yes—
132#2359C2218yes—
133D4×C4⋊C4C2214yes—
134D4×C4⋊C4C2212yes—
135D4×C4⋊C4C2212yes—
136D4×C4⋊C4C2214yes—
137D4×C4⋊C4C2214yes—
138#2344C2214yes—
139#2344C2214yes—
140#2339C2214yes—
141#2335C2214yes—
142#2333C2214yes—
143#2330C2211yescharacteristic
144#2328C2211yescharacteristic
145#2327C2212yes—
146#2324C2212yes—
147#2323C2214yes—
148#2322C2218yes—
149#2319C2212yes—
150#2314C2211yescharacteristic
151C4×C4⋊Q8C2212yes—
152C4×#127C2211yescharacteristic
153C4×#125C2211yescharacteristic
154C4×C22⋊Q8C2214yes—
155C4×#123C2214yes—
156C4×#121C2214yes—
157C4×#121C2214yes—
158C4×#121C2212yes—
159C4×#121C2214yes—
160#2297C2212yes—
161#2293C2211yescharacteristic
162#2293C2211yescharacteristic
163C2×#389C2214yes—
164#2290C2212yes—
165#2290C2212yes—
166#2285C2214yes—
167C42×D4C2212yes—
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C22×#41C2314yes—
173C22×#41C2312yes—
174#553—264no—
175#553—264no—
176#553—264no—
177#552—264no—
178#547—216no—
179#541—216no—
180#541—216no—
181#540—216no—
182#540D4116yescomplemented
183#537—232no—
184#532—216no—
185#532—28no—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2312yes—
190C2×#127C2311yescharacteristic
191C2×#127C2311yescharacteristic
192#529—232no—
193#529—232no—
194C2×#126C2318yes—
195C2×#126C2318yes—
196C2×#126C2318yes—
197C2×#126C2318yes—
198C2×#125—216no—
199C2×#125C2312yes—
200C2×#125C2314yes—
201C2×#125C2318yes—
202C2×#125C2318yes—
203C2×#125C2318yes—
204C2×#125C2311yescharacteristic
205C2×#124C2312yes—
206C2×#124C2314yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×#123C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2314yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×#121C2318yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#121C2314yes—
228C2×#121C2312yes—
229C2×#121C2314yes—
230#520—232no—
231C4×#41—216no—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2318yes—
257C2×#117C2318yes—
258C2×#117C2312yes—
259C2×#117C2318yes—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2318yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2318yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C42C2312yes—
269C22×C42C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2312yes—
272C22×C42C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#399C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#395C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#392C2318yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#390C2312yes—
315#390C2314yes—
316#390C2312yes—
317#390C2314yes—
318#390C2312yes—
319#390C2312yes—
320#390C2314yes—
321#390C2314yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2312yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2312yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2318yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2318yes—
340#389C2312yes—
341#389C2314yes—
342#389C2318yes—
343#388C2314yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2318yes—
348#388C2318yes—
349#388C2314yes—
350#388C2314yes—
351#388C2318yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2318yes—
356#387C2314yes—
357#387C2314yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2314yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2314yes—
369#387C2314yes—
370#387C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2318yes—
379#386C2314yes—
380#386C2318yes—
381#386C2314yes—
382#386C2314yes—
383#386C2314yes—
384#386C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2314yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2314yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2314yes—
398#385C2318yes—
399#384C2311yescharacteristic
400#384C2312yes—
401#384C2314yes—
402#384C2314yes—
403#384C2314yes—
404#384C2314yes—
405#382C2311yescharacteristic
406#382C2312yes—
407#382C2318yes—
408#381C2314yes—
409#381C2318yes—
410#381C2318yes—
411#381C2318yes—
412#381C2318yes—
413#380C2312yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2318yes—
421#380C2314yes—
422#380C2318yes—
423#380C2314yes—
424#380C2318yes—
425#380C2318yes—
426#380C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2318yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2312yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2312yes—
458#376C2311yescharacteristic
459#376C2311yescharacteristic
460C2×#95C2318yes—
461C2×#95C2312yes—
462C43C2311yescharacteristic
463C43C2311yescharacteristic
464C2×#41—216no—
465C2×#41—28no—
466C2×#41—28no—
467C2×#41—216no—
468C2×#41—44no—
469C2×#41—48no—
470C22×Q8C2414yes—
471C22×Q8C2412yes—
472C22×D4C2411yescharacteristic
473C22×D4C2412yes—
474C22×D4C2412yes—
475C22×D4C2418yes—
476C22×D4C2412yes—
477C22×D4C2412yes—
478C22×D4C2411yescharacteristic
479C22×D4C2418yes—
480C22×D4C2412yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C23×C4C2411yescharacteristic
484C23×C4C2414yes—
485C23×C4C2412yes—
486C23×C4C2418yes—
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2418yes—
490C23×C4C2418yes—
491C23×C4C2414yes—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2411yescharacteristic
495C23×C4C2414yes—
496C23×C4C2414yes—
497C4⋊Q8—24no—
498C4⋊Q8—28no—
499C4⋊Q8—28no—
500C4⋊Q8—44no—
501#127—24no—
502#127C2×D418yes—
503#126—232no—
504#126—232no—
505#126—232no—
506#126—232no—
507#125—216no—
508#125—232no—
509#125—232no—
510#125—232no—
511#125—28no—
512#125C2×D418yes—
513#124—216no—
514#124—28no—
515#123—232no—
516#123—232no—
517#123—232no—
518#123—232no—
519#123C2×D4132yes—
520C22⋊Q8—216no—
521C22⋊Q8—216no—
522C22⋊Q8—216no—
523C22⋊Q8—232no—
524C22⋊Q8—48no—
525#121—216no—
526#121—232no—
527#121—232no—
528#121—232no—
529#121—232no—
530#121—24no—
531#121—216no—
532#121—24no—
533#121—232no—
534#121—28no—
535#121—48no—
536#121C2×D4116yes—
537#121C2×D4132yes—
538C4×Q8—216no—
539C4×Q8—216no—
540C4×Q8—216no—
541C4×D4—216no—
542C4×D4—232no—
543C4×D4—232no—
544C4×D4—232no—
545C4×D4—232no—
546C4×D4—28no—
547C4×D4—216no—
548C4×D4—216no—
549C4×D4—216no—
550C4×D4—232no—
551C4×D4—24no—
552C4×D4—28no—
553C4×D4—44no—
554C4×D4—48no—
555C4×D4—44no—
556C4×D4—44no—
557C4×D4—48no—
558C4×D4—48no—
559C4×D4C2×D4116yes—
560C4×D4#4118yes—
561#117—232no—
562#117—232no—
563#117—232no—
564#117—28no—
565#117—28no—
566#117—42no—
567#117C2×D418yes—
568C2×C4⋊C4—232no—
569C2×C4⋊C4—216no—
570C2×C4⋊C4—232no—
571C2×C4⋊C4—216no—
572C2×C4⋊C4—44no—
573C2×C4⋊C4—48no—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C42—28no—
642C2×C42—28no—
643C2×C42—28no—
644C2×C42—24no—
645C2×C42—48no—
646C2×C42C2412yes—
647C2×C42C2418yes—
648C2×C42C2418yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668#95C2414yes—
669#95C2412yes—
670#95C2418yes—
671#95C2414yes—
672#95C2412yes—
673#95C2418yes—
674#95C2418yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2412yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699C24C2512yes—
700C24C2514yes—
701C24C2511yescharacteristic
702C24C2512yes—
703#41—432no—
704#41—464no—
705C2×Q8—24no—
706C2×Q8—28no—
707C2×Q8—28no—
708C2×Q8—24no—
709C2×Q8—28no—
710C2×Q8—42no—
711C2×D4—24no—
712C2×D4—216no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—216no—
716C2×D4—24no—
717C2×D4—216no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—22no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—48no—
733C2×D4—42no—
734C2×D4—48no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4C22×D418yes—
738C2×D4C22×D4116yes—
739C2×D4C22×D4116yes—
740C2×D4C2×#4114yes—
741C22×C4—24no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—24no—
745C22×C4—216no—
746C22×C4—28no—
747C22×C4—216no—
748C22×C4—24no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—216no—
752C22×C4—24no—
753C22×C4—28no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—216no—
760C22×C4—22no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—48no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—48no—
767C22×C4—44no—
768C22×C4—48no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—42no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4C22×D414yes—
779C22×C4C22×D4116yes—
780C22×C4C2×#4118yes—
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2511yescharacteristic
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2518yes—
790C22×C4C2512yes—
791C22×C4C2518yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C4⋊C4—28no—
801C4⋊C4—216no—
802C4⋊C4—216no—
803C4⋊C4—216no—
804C4⋊C4—28no—
805C4⋊C4—216no—
806C4⋊C4—216no—
807C4⋊C4—216no—
808C4⋊C4—28no—
809C4⋊C4—216no—
810C4⋊C4—216no—
811C4⋊C4—216no—
812C4⋊C4—28no—
813C4⋊C4—216no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—48no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—48no—
827C4⋊C4—42no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4C22×D418yes—
833C4⋊C4C22×D4116yes—
834C4⋊C4C22×D418yes—
835C4⋊C4C2×#4114yes—
836C22⋊C4—216no—
837C22⋊C4—216no—
838C22⋊C4—216no—
839C22⋊C4—216no—
840C22⋊C4—216no—
841C22⋊C4—24no—
842C22⋊C4—216no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—216no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—28no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—42no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4C22×D4116yes—
864C22⋊C4C22×D4116yes—
865C22⋊C4C22×D418yes—
866C22⋊C4C2×#4118yes—
867C42—24no—
868C42—24no—
869C42—28no—
870C42—28no—
871C42—28no—
872C42—216no—
873C42—216no—
874C42—22no—
875C42—22no—
876C42—22no—
877C42—24no—
878C42—28no—
879C42—22no—
880C42—22no—
881C42—24no—
882C42—44no—
883C42—44no—
884C42—42no—
885C42—42no—
886C42C22×D414yes—
887C42C22×D414yes—
888C42C2×#4114yes—
889C23—22no—
890C23—24no—
891C23—21no—
892C23—24no—
893C23—22no—
894C23—24no—
895C23—21no—
896C23—24no—
897C23—24no—
898C23—22no—
899C23—24no—
900C23—24no—
901C23—22no—
902C23—24no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—24no—
907C23—24no—
908C23C23×D418yes—
909C23C23×D412yes—
910C23C22×#4114yes—
911C23C2611yescharacteristic
912Q8—48no—
913Q8—416no—
914D4—216no—
915D4—28no—
916D4—416no—
917D4—416no—
918D4—48no—
919D4—48no—
920D4—48no—
921D4—432no—
922D4—44no—
923D4—816no—
924D4—84no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—216no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—28no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—22no—
959C2×C4—28no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—416no—
970C2×C4—432no—
971C2×C4—48no—
972C2×C4—44no—
973C2×C4—416no—
974C2×C4—88no—
975C2×C4—816no—
976C2×C4—88no—
977C2×C4—82no—
978C2×C4—88no—
979C2×C4—816no—
980C2×C4—88no—
981C2×C4C23×D414yes—
982C2×C4C23×D412yes—
983C2×C4C23×D414yes—
984C2×C4C23×D418yes—
985C2×C4C23×D412yes—
986C2×C4C22×#4112yes—
987C2×C4C22×#4114yes—
988C2×C4C22×#4112yes—
989C2×C4C22×#4112yes—
990C2×C4#58512yes—
991C2×C4#58514yes—
992C22—28no—
993C22—24no—
994C22—28no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—22no—
999C22—28no—
1000C22—44no—
1001C22—44no—
1002C22—41no—
1003C22—41no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—42no—
1008C22—44no—
1009C22—44no—
1010C22—42no—
1011C22—42no—
1012C22—44no—
1013C22—42no—
1014C22C24×D411yescharacteristic
1015C22C23×#4111yescharacteristic
1016C22C2×#58512yes—
1017C22C2×#58511yescharacteristic
1018C222−1+612yes—
1019C4—24no—
1020C4—28no—
1021C4—24no—
1022C4—22no—
1023C4—24no—
1024C4—22no—
1025C4—44no—
1026C4—44no—
1027C4—48no—
1028C4—41no—
1029C4—44no—
1030C4—41no—
1031C4—42no—
1032C4—44no—
1033C4—42no—
1034C4—42no—
1035C4—48no—
1036C4D4×#4114yes—
1037C4#351214yescomplemented
1038C2—48no—
1039C2—42no—
1040C2—44no—
1041C2—82no—
1042C2C2×D4×#4111yescharacteristic
1043C2C2×#351211yescharacteristic
1044C2#6286111yescharacteristic
1045C2#6293912yes—
1046C2#6298812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3512C2semidirect
2. #59826C2semidirect
3. #59392C2semidirect
4. #59290C2semidirect
5. #59213C2semidirect
6. #43542C2semidirect
7. #43534C2semidirect
8. #39385C2semidirect
9. #39378C2semidirect
10. #39340C2semidirect
11. #37784C2semidirect
12. #37705C2semidirect
13. #37700C2semidirect
14. #36127C2semidirect
15. #36116C2semidirect
16. D4×#125C2semidirect
17. #35654C2semidirect
18. #35319C2semidirect
19. #35309C2semidirect
20. #34932C2semidirect
21. #34308C2semidirect
22. #34141C2semidirect
23. C4×#540C2semidirect
182. #540D4semidirect
1037. C4#3512semidirect

Maximal subgroups

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

subgroupindex
C2×#35122
#598262
#593922
#592902
#592132
#435422
#435342
#393852
#393782
#393402
#377842
#377052
#377002
#361272
#361162
D4×#1252
#356542
#353192
#353092
#349322
#343082
#341412
C4×#5402