Finite Group Databasebeta

← #7674376

Subgroups — #7674376

Order 512.

7018 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C22×#542C211yesmaximal, characteristic, complemented
3#45227C214yesmaximal, complemented
4#45207C214yesmaximal, complemented
5#45077C214yesmaximal, complemented
6#45051C214yesmaximal, complemented
7#39377C214yesmaximal, complemented
8#39374C214yesmaximal, complemented
9#38046C214yesmaximal, complemented
10#38044C214yesmaximal, complemented
11#38039C214yesmaximal, complemented
12#38037C214yesmaximal, complemented
13#37767C214yesmaximal, complemented
14#37766C214yesmaximal, complemented
15#35672C211yesmaximal, characteristic, complemented
16#35661C211yesmaximal, characteristic, complemented
17#35540C211yesmaximal, characteristic, complemented
18#35514C211yesmaximal, characteristic
19#35281C211yesmaximal, characteristic, complemented
20#35279C211yesmaximal, characteristic, complemented
21#35182C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic, complemented
23#34634C211yesmaximal, characteristic, complemented
24#34249C211yesmaximal, characteristic, complemented
25#34248C211yesmaximal, characteristic, complemented
26#34211C211yesmaximal, characteristic, complemented
27#34065C211yesmaximal, characteristic, complemented
28#3510—216no—
29C2×#559C2212yescomplemented
30C2×#559C2212yescomplemented
31C2×#556C2212yescomplemented
32C2×#556C2212yescomplemented
33C2×#551C2214yes—
34C2×#551C2214yes—
35C2×#542—216no—
36C2×#542C2214yes—
37C2×#542C2214yes—
38C2×#542C2214yes—
39C2×#542C2214yes—
40C2×#542C2212yescomplemented
41C2×#542C2212yescomplemented
42C2×#536C2211yescharacteristic
43C2×#535C2211yescharacteristic
44C2×#533C2211yescharacteristic
45C22×C4⋊Q8C2211yescharacteristic
46C2×#529C2212yescomplemented
47C2×#529C2212yescomplemented
48C22×#126C2212yes—
49C22×#124C2212yes—
50C22×#124C2211yescharacteristic
51C2×#525C2211yescharacteristic
52C22×#123C2212yes—
53C22×C22⋊Q8C2211yescharacteristic
54C22×C22⋊Q8C2212yes—
55C22×#121C2211yescharacteristic
56C2×#519C2211yescharacteristic
57C2×#519C2211yescharacteristic
58C2×#518C2211yescharacteristic
59C2×#518C2211yescharacteristic
60C2×C4×#41C2211yescharacteristic
61C22×C4×Q8C2211yescharacteristic
62C22×C4×D4C2211yescharacteristic
63C22×#117C2211yescharacteristic
64#2868C2212yescomplemented
65#2862C2212yescomplemented
66#2857C2214yescomplemented
67#2853C2214yes—
68#2849C2214yes—
69#2722C2218yescomplemented
70#2718C2218yescomplemented
71#2718C2218yescomplemented
72#2718C2218yescomplemented
73#2715C2218yescomplemented
74#2710C2218yescomplemented
75#2710C2218yescomplemented
76#2706C2218yescomplemented
77#2698C2218yescomplemented
78#2695C2218yescomplemented
79#2689C2218yescomplemented
80#2689C2218yescomplemented
81#2680C2218yescomplemented
82#2674C2218yescomplemented
83#2674C2218yescomplemented
84#2672C2218yescomplemented
85#2660C2212yescomplemented
86#2660C2212yescomplemented
87#2629C2212yescomplemented
88#2629C2212yescomplemented
89#2628C2212yescomplemented
90#2628C2212yescomplemented
91#2628C2214yescomplemented
92#2627C2212yes—
93#2627C2212yes—
94#2626C2212yes—
95#2626C2212yes—
96#2623C2214yes—
97#2622C2214yes—
98#2568C2212yescomplemented
99#2567C2212yescomplemented
100#2567C2214yescomplemented
101#2563C2212yescomplemented
102#2546C2214yescomplemented
103#2542C2212yescomplemented
104#2538C2214yescomplemented
105#2537C2214yes—
106#2536C2214yescomplemented
107#2535C2214yes—
108#2521C2218yescomplemented
109#2521C2218yescomplemented
110#2502C2214yes—
111#2501C2218yescomplemented
112#2496C2218yescomplemented
113#2491C2218yescomplemented
114#2488C2218yescomplemented
115#2488C2218yescomplemented
116#2487C2214yes—
117#2484C2214yes—
118#2483C2214yes—
119#2482C2214yes—
120#2478C2218yescomplemented
121#2474C2218yescomplemented
122#2468C2218yescomplemented
123#2461C2218yescomplemented
124#2449C2218yescomplemented
125#2448C2214yescomplemented
126#2447C2214yescomplemented
127#2446C2214yescomplemented
128#2445C2214yescomplemented
129#2440C2218yescomplemented
130#2438C2218yescomplemented
131#2434C2214yes—
132#2429C2214yescomplemented
133#2428C2214yes—
134#2427C2214yes—
135#2426C2214yescomplemented
136#2425C2218yescomplemented
137#2423C2214yescomplemented
138#2423C2214yescomplemented
139#2423C2214yescomplemented
140#2422C2214yes—
141#2422C2214yes—
142#2422C2214yescomplemented
143#2421C2214yescomplemented
144#2421C2214yescomplemented
145#2421C2214yescomplemented
146#2420C2214yes—
147#2420C2214yes—
148#2420C2214yescomplemented
149#2413C2214yes—
150#2413C2218yescomplemented
151#2412C2214yes—
152#2411C2214yes—
153#2410C2214yes—
154#2409C2214yes—
155#2405C2214yes—
156#2396C2214yescomplemented
157#2396C2214yescomplemented
158#2367C2214yescomplemented
159#2367C2214yescomplemented
160#2351C2214yescomplemented
161#2351C2214yescomplemented
162Q8×C4⋊C4C2214yescomplemented
163Q8×C4⋊C4C2214yescomplemented
164#2349C2214yescomplemented
165#2349C2214yescomplemented
166D4×C4⋊C4C2214yescomplemented
167D4×C4⋊C4C2214yescomplemented
168#2342C2214yes—
169#2342C2214yes—
170#2326C2214yescomplemented
171#2324C2212yescomplemented
172#2324C2212yescomplemented
173#2323C2212yescomplemented
174#2323C2212yescomplemented
175#2322C2212yes—
176#2322C2212yes—
177#2321C2212yes—
178#2321C2212yes—
179#2317C2211yescharacteristic
180#2317C2211yescharacteristic
181#2317C2211yescharacteristic
182#2317C2211yescharacteristic
183#2317C2214yes—
184#2317C2211yescharacteristic
185#2317C2211yescharacteristic
186#2315C2214yes—
187#2311C2211yescharacteristic
188#2311C2211yescharacteristic
189#2310C2211yescharacteristic
190#2309C2211yescharacteristic
191C4×#124C2214yescomplemented
192#2297C2211yescharacteristic
193#2296C2211yescharacteristic
194#2296C2211yescharacteristic
195#2296C2211yescharacteristic
196#2296C2214yes—
197#2293C2214yescomplemented
198#2290C2214yescomplemented
199C2×#385C2214yes—
200#2285C2211yescharacteristic
201#2280C2211yescharacteristic
202#2280C2211yescharacteristic
203#2280C2211yescharacteristic
204C4×#117C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C23×Q8C2312yes—
208C23×D4C2311yescharacteristic
209C23×D4C2312yes—
210C24×C4C2311yescharacteristic
211C24×C4C2312yes—
212#559—216no—
213#559—216no—
214#556—216no—
215#556—216no—
216#551—232no—
217#551—232no—
218#542—232no—
219#542—232no—
220#542—232no—
221#542—232no—
222#542—216no—
223#542—216no—
224#536—28no—
225#535—28no—
226#533—28no—
227C2×C4⋊Q8—28no—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2318yes—
236C2×#127C2312yes—
237#529—216no—
238#529—216no—
239C2×#126—216no—
240C2×#126C2318yes—
241C2×#126C2318yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2311yescharacteristic
247C2×#125C2311yescharacteristic
248C2×#124—216no—
249C2×#124D4116yescomplemented
250C2×#124C2318yes—
251C2×#124C2318yes—
252C2×#124C2314yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260#525—28no—
261C2×#123—216no—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2318yes—
265C2×#123C2318yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2318yes—
271C2×#123C2318yes—
272C2×C22⋊Q8—28no—
273C2×C22⋊Q8—216no—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2318yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2318yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2318yes—
286C2×#121—28no—
287C2×#121C2312yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2318yes—
293C2×#120C2312yes—
294C2×#120C2314yes—
295#519—28no—
296#519—28no—
297#518—28no—
298#518—28no—
299C4×#41—28no—
300C2×C4×Q8—28no—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4—28no—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×#117—28no—
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2311yescharacteristic
336C2×#117C2314yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2311yescharacteristic
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2318yes—
354C22×C22⋊C4C2312yes—
355C22×C22⋊C4C2314yes—
356C22×C22⋊C4C2314yes—
357C22×C22⋊C4C2311yescharacteristic
358C22×C22⋊C4C2311yescharacteristic
359C22×C22⋊C4C2312yes—
360C22×C22⋊C4C2312yes—
361C22×C22⋊C4C2312yes—
362C22×C22⋊C4C2312yes—
363C22×C42C2312yes—
364C22×C42C2312yes—
365C22×C42C2311yescharacteristic
366C22×C42C2311yescharacteristic
367#400C2318yes—
368#400C2318yes—
369#400C2314yes—
370#400C2314yes—
371#400C2318yes—
372#399C2318yes—
373#399C2314yes—
374#399C2314yes—
375#399C2318yes—
376#399C2318yes—
377#398C2318yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2318yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2318yes—
390#397C2318yes—
391#397C2318yes—
392#397C2318yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2318yes—
398#396C2318yes—
399#395C2318yes—
400#395C2318yes—
401#395C2318yes—
402#395C2314yes—
403#395C2314yes—
404#394C2318yes—
405#394C2318yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#393C2318yes—
412#393C2314yes—
413#393C2314yes—
414#392C2318yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2318yes—
420#391C2318yes—
421#391C2312yes—
422#391C2318yes—
423#390C2312yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#390C2312yes—
430#390C2318yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2318yes—
436#389C2314yes—
437#389C2314yes—
438#389C2318yes—
439#389C2318yes—
440#389C2314yes—
441#389C2314yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2318yes—
448#389C2312yes—
449#389C2318yes—
450#389C2318yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2318yes—
458#388C2318yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#387C2314yes—
468#387C2314yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2318yes—
473#386C2314yes—
474#386C2314yes—
475#386C2312yes—
476#386C2312yes—
477#386C2314yes—
478#386C2314yes—
479#386C2318yes—
480#386C2318yes—
481#386C2318yes—
482#386C2318yes—
483#385C2312yes—
484#385C2312yes—
485#385C2314yes—
486#385C2314yes—
487#385C2318yes—
488#385C2318yes—
489#385C2312yes—
490#385C2312yes—
491#385C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2312yes—
503#385C2312yes—
504#385C2318yes—
505#384C2312yes—
506#384C2312yes—
507#384C2318yes—
508#384C2312yes—
509#384C2312yes—
510#384C2318yes—
511#384C2312yes—
512#384C2312yes—
513#384C2312yes—
514#382C2312yes—
515#382C2312yes—
516#382C2312yes—
517#382C2312yes—
518#382C2312yes—
519#382C2312yes—
520#382C2318yes—
521#382C2312yes—
522#381C2314yes—
523#381C2312yes—
524#381C2318yes—
525#381C2312yes—
526#381C2312yes—
527#381C2318yes—
528#380C2318yes—
529#380C2314yes—
530#380C2314yes—
531#380C2318yes—
532#380C2318yes—
533#380C2312yes—
534#380C2312yes—
535#380C2312yes—
536#380C2312yes—
537#380C2312yes—
538#380C2312yes—
539#380C2312yes—
540#380C2312yes—
541#380C2318yes—
542#379C2314yes—
543#379C2312yes—
544#379C2312yes—
545#379C2312yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2312yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2318yes—
554C4×C4⋊C4C2318yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2318yes—
558C4×C22⋊C4C2318yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563#376C2312yes—
564C2×#95C2318yes—
565C43C2312yes—
566C25C2411yescharacteristic
567C25C2412yes—
568C2×#41—24no—
569C2×#41—24no—
570C2×#41—24no—
571C22×Q8—28no—
572C22×Q8—24no—
573C22×Q8—24no—
574C22×Q8—84no—
575C22×Q8C2×D418yes—
576C22×Q8C2411yescharacteristic
577C22×Q8C2412yes—
578C22×Q8C2412yes—
579C22×Q8C2412yes—
580C22×Q8C2412yes—
581C22×Q8C2414yes—
582C22×Q8C2414yes—
583C22×D4—28no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—84no—
587C22×D4C2×D418yes—
588C22×D4C2412yes—
589C22×D4C2411yescharacteristic
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2414yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C22×D4C2418yes—
596C23×C4—28no—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—84no—
601C23×C4C2411yescharacteristic
602C23×C4C2412yes—
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2411yescharacteristic
607C23×C4C2412yes—
608C23×C4C2411yescharacteristic
609C23×C4C2412yes—
610C23×C4C2414yes—
611C23×C4C2418yes—
612C23×C4C2414yes—
613C23×C4C2418yes—
614C23×C4C2412yes—
615C23×C4C2412yes—
616C23×C4C2411yescharacteristic
617C23×C4C2411yescharacteristic
618C23×C4C2411yescharacteristic
619C4⋊Q8—28no—
620C4⋊Q8—28no—
621C4⋊Q8—28no—
622C4⋊Q8—28no—
623C4⋊Q8—28no—
624C4⋊Q8—24no—
625C4⋊Q8—24no—
626C4⋊Q8—88no—
627#127—28no—
628#126—232no—
629#126—232no—
630#126—216no—
631#126—216no—
632#126—216no—
633#126—216no—
634#125—24no—
635#125—24no—
636#124—28no—
637#124—28no—
638#124—232no—
639#124—232no—
640#124—216no—
641#124—216no—
642#124C2×D4116yes—
643#124C2×D4116yes—
644#124C2×D4116yes—
645#124C2×D4116yes—
646#123—216no—
647#123—232no—
648#123—232no—
649#123—216no—
650#123—216no—
651#123—216no—
652#123—216no—
653#123—28no—
654#123—88no—
655#123—88no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—28no—
662C22⋊Q8—28no—
663C22⋊Q8—232no—
664C22⋊Q8—232no—
665C22⋊Q8—216no—
666C22⋊Q8—216no—
667C22⋊Q8—88no—
668#121—216no—
669#121—216no—
670#121—28no—
671#121—28no—
672#121—28no—
673#121—88no—
674#120—216no—
675#120—28no—
676C4×Q8—216no—
677C4×Q8—216no—
678C4×Q8—28no—
679C4×Q8—28no—
680C4×Q8—28no—
681C4×Q8—28no—
682C4×Q8—216no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—28no—
686C4×Q8—28no—
687C4×Q8—216no—
688C4×D4—216no—
689C4×D4—216no—
690C4×D4—28no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4—28no—
695C4×D4—28no—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—24no—
700C4×D4—24no—
701C4×D4—216no—
702C4×D4—216no—
703#117—24no—
704#117—24no—
705#117—24no—
706#117—216no—
707#117—24no—
708#117—24no—
709#117—24no—
710#117—216no—
711#117—216no—
712#117—216no—
713#117—28no—
714#117—28no—
715#117—28no—
716#117—28no—
717#117—28no—
718#117#4118yes—
719C2×C4⋊C4—24no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—24no—
722C2×C4⋊C4—24no—
723C2×C4⋊C4—28no—
724C2×C4⋊C4—28no—
725C2×C4⋊C4—28no—
726C2×C4⋊C4—88no—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2418yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C22⋊C4—28no—
778C2×C22⋊C4—216no—
779C2×C22⋊C4—28no—
780C2×C22⋊C4—24no—
781C2×C22⋊C4—24no—
782C2×C22⋊C4—28no—
783C2×C22⋊C4—216no—
784C2×C22⋊C4C2×D4116yes—
785C2×C22⋊C4C2×D4116yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2418yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C42—24no—
828C2×C42—28no—
829C2×C42—28no—
830C2×C42C2×D418yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2418yes—
843C2×C42C2412yes—
844C2×C42C2418yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2412yes—
852#95C2414yes—
853#95C2414yes—
854#95C2418yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2418yes—
868#95C2418yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2418yes—
874#95C2414yes—
875#95C2418yes—
876#95C2418yes—
877#95C2418yes—
878#95C2418yes—
879#95C2418yes—
880C24—24no—
881C24—24no—
882C24—22no—
883C24—22no—
884C24—22no—
885C24—44no—
886C24—42no—
887C24—44no—
888C24—42no—
889C24C22×D418yes—
890C24C2512yes—
891C24C2512yes—
892C24C2514yes—
893C24C2511yescharacteristic
894#41—416no—
895C2×Q8—232no—
896C2×Q8—22no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—28no—
900C2×Q8—28no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—22no—
904C2×Q8—24no—
905C2×Q8—24no—
906C2×Q8—22no—
907C2×Q8—48no—
908C2×Q8—44no—
909C2×Q8—48no—
910C2×Q8—44no—
911C2×Q8—816no—
912C2×Q8C22×D418yes—
913C2×Q8C22×D418yes—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—216no—
920C2×D4—232no—
921C2×D4—22no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—22no—
925C2×D4—28no—
926C2×D4—24no—
927C2×D4—24no—
928C2×D4—22no—
929C2×D4—44no—
930C2×D4—48no—
931C2×D4—48no—
932C2×D4—48no—
933C2×D4—44no—
934C2×D4—48no—
935C2×D4—816no—
936C2×D4C22×D418yes—
937C2×D4C22×D418yes—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—24no—
943C22×C4—22no—
944C22×C4—24no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—28no—
948C22×C4—28no—
949C22×C4—216no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—216no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—44no—
967C22×C4—42no—
968C22×C4—48no—
969C22×C4—48no—
970C22×C4—48no—
971C22×C4—44no—
972C22×C4—48no—
973C22×C4—48no—
974C22×C4—44no—
975C22×C4—48no—
976C22×C4—416no—
977C22×C4—816no—
978C22×C4C22×D418yes—
979C22×C4C22×D414yes—
980C22×C4C22×D414yes—
981C22×C4C22×D414yes—
982C22×C4C2×#4114yes—
983C22×C42−1+414yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2514yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2514yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—216no—
1016C4⋊C4—216no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—216no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—48no—
1045C4⋊C4—48no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—48no—
1051C4⋊C4—44no—
1052C4⋊C4—48no—
1053C4⋊C4—44no—
1054C4⋊C4—48no—
1055C4⋊C4—48no—
1056C4⋊C4C2×#4118yes—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—216no—
1062C22⋊C4—216no—
1063C22⋊C4—24no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—216no—
1074C22⋊C4—24no—
1075C22⋊C4—24no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—216no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—48no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C22⋊C4—48no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4C22×D4116yes—
1094C22⋊C4C22×D4116yes—
1095C22⋊C4C22×D4116yes—
1096C22⋊C4C22×D4116yes—
1097C22⋊C4C2×#4118yes—
1098C42—24no—
1099C42—24no—
1100C42—24no—
1101C42—24no—
1102C42—24no—
1103C42—216no—
1104C42—28no—
1105C42—28no—
1106C42—24no—
1107C42—24no—
1108C42—24no—
1109C42—216no—
1110C42—24no—
1111C42—24no—
1112C42—44no—
1113C42—44no—
1114C42C22×D414yes—
1115C42C22×D414yes—
1116C42C22×D414yes—
1117C42C22×D414yes—
1118C42C2×#4118yes—
1119C23—22no—
1120C23—22no—
1121C23—24no—
1122C23—24no—
1123C23—28no—
1124C23—28no—
1125C23—216no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—24no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—24no—
1138C23—48no—
1139C23—48no—
1140C23—44no—
1141C23—44no—
1142C23—44no—
1143C23—88no—
1144C23—84no—
1145C23—88no—
1146C23—84no—
1147C23C23×D418yes—
1148C23C23×D412yes—
1149C23C22×#4112yes—
1150C23C2×2−1+412yes—
1151C23C2611yescharacteristic
1152Q8—216no—
1153Q8—216no—
1154Q8—44no—
1155Q8—84no—
1156Q8—84no—
1157Q8—88no—
1158Q8—88no—
1159D4—216no—
1160D4—216no—
1161D4—48no—
1162D4—44no—
1163D4—88no—
1164D4—88no—
1165D4—88no—
1166D4—816no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—216no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—28no—
1203C2×C4—28no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—48no—
1218C2×C4—48no—
1219C2×C4—44no—
1220C2×C4—48no—
1221C2×C4—48no—
1222C2×C4—48no—
1223C2×C4—84no—
1224C2×C4—816no—
1225C2×C4—84no—
1226C2×C4—88no—
1227C2×C4—88no—
1228C2×C4—816no—
1229C2×C4#547116yes—
1230C2×C4C23×D418yes—
1231C2×C4C23×D412yes—
1232C2×C4C23×D412yes—
1233C2×C4C23×D412yes—
1234C2×C4C23×D412yes—
1235C2×C4C23×D412yes—
1236C2×C4C23×D412yes—
1237C2×C4C22×#4118yes—
1238C2×C4C22×#4112yes—
1239C2×C4C22×#4112yes—
1240C2×C4C2×2−1+412yes—
1241C2×C4C2×2−1+412yes—
1242C22—22no—
1243C22—24no—
1244C22—22no—
1245C22—24no—
1246C22—28no—
1247C22—28no—
1248C22—28no—
1249C22—48no—
1250C22—48no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—44no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—816no—
1264C22—88no—
1265C22C2×#54714yes—
1266C22C24×D411yescharacteristic
1267C22C23×#4111yescharacteristic
1268C22C22×2−1+411yescharacteristic
1269C22H(7,𝔽2)12yes—
1270C222−1+612yes—
1271C4—22no—
1272C4—22no—
1273C4—28no—
1274C4—22no—
1275C4—22no—
1276C4—28no—
1277C4—42no—
1278C4—44no—
1279C4—44no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4C2×#54714yes—
1293C4C2×#54714yes—
1294C2—24no—
1295C2—48no—
1296C2—82no—
1297C2—82no—
1298C2C22×#54711yescharacteristic
1299C2#6285211yescharacteristic
1300C2#6285712yes—
1301C2#6285911yescharacteristic
1302C2#6287912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35514C2
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×#3510C2semidirect
2. C22×#542C2semidirect
3. #45227C2semidirect
4. #45207C2semidirect
5. #45077C2semidirect
6. #45051C2semidirect
7. #39377C2semidirect
8. #39374C2semidirect
9. #38046C2semidirect
10. #38044C2semidirect
11. #38039C2semidirect
12. #38037C2semidirect
13. #37767C2semidirect
14. #37766C2semidirect
15. #35672C2semidirect
16. #35661C2semidirect
17. #35540C2semidirect
19. #35281C2semidirect
20. #35279C2semidirect
21. #35182C2semidirect
22. #35152C2semidirect
23. #34634C2semidirect
24. #34249C2semidirect
25. #34248C2semidirect
26. #34211C2semidirect
27. #34065C2semidirect
29. C2×#559C22semidirect
30. C2×#559C22semidirect
31. C2×#556C22semidirect
32. C2×#556C22semidirect
40. C2×#542C22semidirect
41. C2×#542C22semidirect
46. C2×#529C22semidirect
47. C2×#529C22semidirect
64. #2868C22semidirect
65. #2862C22semidirect
66. #2857C22semidirect
69. #2722C22semidirect
70. #2718C22semidirect
71. #2718C22semidirect
72. #2718C22semidirect
73. #2715C22semidirect
74. #2710C22semidirect
75. #2710C22semidirect
76. #2706C22semidirect
77. #2698C22semidirect
78. #2695C22semidirect
79. #2689C22semidirect
80. #2689C22semidirect
81. #2680C22semidirect
82. #2674C22semidirect
83. #2674C22semidirect
84. #2672C22semidirect
85. #2660C22semidirect
86. #2660C22semidirect
87. #2629C22semidirect
88. #2629C22semidirect
89. #2628C22semidirect
90. #2628C22semidirect
91. #2628C22semidirect
98. #2568C22semidirect
99. #2567C22semidirect
100. #2567C22semidirect
101. #2563C22semidirect
102. #2546C22semidirect
103. #2542C22semidirect
104. #2538C22semidirect
106. #2536C22semidirect
108. #2521C22semidirect
109. #2521C22semidirect
111. #2501C22semidirect
112. #2496C22semidirect
113. #2491C22semidirect
114. #2488C22semidirect
115. #2488C22semidirect
120. #2478C22semidirect
121. #2474C22semidirect
122. #2468C22semidirect
123. #2461C22semidirect
124. #2449C22semidirect
125. #2448C22semidirect
126. #2447C22semidirect
127. #2446C22semidirect
128. #2445C22semidirect
129. #2440C22semidirect
130. #2438C22semidirect
132. #2429C22semidirect
135. #2426C22semidirect
136. #2425C22semidirect
137. #2423C22semidirect
138. #2423C22semidirect
139. #2423C22semidirect
142. #2422C22semidirect
143. #2421C22semidirect
144. #2421C22semidirect
145. #2421C22semidirect
148. #2420C22semidirect
150. #2413C22semidirect
156. #2396C22semidirect
157. #2396C22semidirect
158. #2367C22semidirect
159. #2367C22semidirect
160. #2351C22semidirect
161. #2351C22semidirect
162. Q8×C4⋊C4C22semidirect
163. Q8×C4⋊C4C22semidirect
164. #2349C22semidirect
165. #2349C22semidirect
166. D4×C4⋊C4C22semidirect
167. D4×C4⋊C4C22semidirect
170. #2326C22semidirect
171. #2324C22semidirect
172. #2324C22semidirect
173. #2323C22semidirect
174. #2323C22semidirect
191. C4×#124C22semidirect
197. #2293C22semidirect
198. #2290C22semidirect
249. C2×#124D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C22×#5422
#452272
#452072
#450772
#450512
#393772
#393742
#380462
#380442
#380392
#380372
#377672
#377662
#356722
#356612
#355402
#355142
#352812
#352792
#351822
#351522
#346342
#342492
#342482
#342112
#340652