Finite Group Databasebeta

← #7658922

Subgroups — #7658922

Order 512.

6484 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3515C211yesmaximal, characteristic, complemented
3#42967C212yesmaximal, complemented
4#42917C212yesmaximal, complemented
5#42802C214yesmaximal, complemented
6#42683C212yesmaximal, complemented
7#42678C212yesmaximal, complemented
8#42309C214yesmaximal, complemented
9#42173C214yesmaximal, complemented
10#41985C214yesmaximal, complemented
11#41947C214yesmaximal, complemented
12#40532C218yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37607C212yesmaximal, complemented
15#37549C212yesmaximal, complemented
16#37546C211yesmaximal, characteristic, complemented
17#37541C212yesmaximal, complemented
18#37537C211yesmaximal, characteristic, complemented
19#36699C211yesmaximal, characteristic, complemented
20#36684C212yesmaximal, complemented
21#35997C212yesmaximal, complemented
22#35982C212yesmaximal, complemented
23#35938C212yesmaximal, complemented
24#35909C212yesmaximal, complemented
25#35778C214yesmaximal, complemented
26#34193C211yesmaximal, characteristic, complemented
27#3515—216no—
28#3510—216no—
29C2×#559C2212yes—
30C2×#559C2212yes—
31C2×#557C2211yescharacteristic, complemented
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#554C2211yescharacteristic, complemented
35C2×#554C2211yescharacteristic, complemented
36C2×#553C2212yes—
37C2×#552C2212yes—
38C2×#552C2212yes—
39C2×#552C2214yescomplemented
40C2×#551C2214yes—
41C2×#551C2214yes—
42C2×#547C2212yes—
43C2×#547C2211yescharacteristic, complemented
44C2×#542C2212yes—
45C2×#542C2212yes—
46C2×#541C2212yescomplemented
47C2×#539C2214yes—
48C2×#536C2211yescharacteristic
49C2×#535C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#533C2211yescharacteristic
52C2×#529C2211yescharacteristic
53C2×#529C2212yes—
54C2×#529C2212yes—
55C2×#529C2212yescomplemented
56C22×#125C2212yescomplemented
57C22×#124C2211yescharacteristic
58C2×#520C2212yescomplemented
59C2×#519C2211yescharacteristic
60C2×#518C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62#2823C2218yescomplemented
63#2822C2212yescomplemented
64#2822C2212yescomplemented
65#2822C2211yescharacteristic, complemented
66#2822C2211yescharacteristic, complemented
67#2821C2212yescomplemented
68#2821C2212yescomplemented
69#2820C2212yes—
70#2820C2212yes—
71#2820C2212yes—
72#2820C2211yescharacteristic, complemented
73#2820C2211yescharacteristic, complemented
74#2819C2212yes—
75#2817C2212yes—
76#2816C2212yes—
77#2814C2214yes—
78#2814C2214yescomplemented
79#2814C2214yescomplemented
80#2813C2214yes—
81#2813C2214yescomplemented
82#2727C2218yescomplemented
83#2725C2218yescomplemented
84#2724C2218yes—
85#2710C2218yescomplemented
86#2706C2218yescomplemented
87#2704C2218yescomplemented
88#2702C2218yescomplemented
89#2701C2218yes—
90#2697C2218yes—
91#2687C2218yescomplemented
92#2678C2218yes—
93#2674C2218yescomplemented
94#2664C2214yescomplemented
95#2664C2218yescomplemented
96#2664C2214yescomplemented
97#2663C2214yescomplemented
98#2662C2214yes—
99#2661C2214yes—
100#2658C2212yes—
101#2640C2212yes—
102#2638C2214yescomplemented
103#2635C2214yescomplemented
104#2634C2214yescomplemented
105#2633C2214yes—
106#2632C2214yes—
107#2630C2218yescomplemented
108#2629C2218yescomplemented
109#2627C2214yescomplemented
110#2626C2214yes—
111#2626C2212yes—
112#2625C2214yes—
113#2625C2212yes—
114#2625C2212yes—
115#2623C2214yescomplemented
116#2623C2214yescomplemented
117#2621C2214yes—
118#2620C2214yes—
119#2618C2214yes—
120#2617C2212yes—
121#2611C2214yescomplemented
122#2611C2214yescomplemented
123#2604C2214yescomplemented
124#2603C2214yescomplemented
125#2601C2218yescomplemented
126#2599C2214yescomplemented
127#2598C2214yes—
128#2592C2212yes—
129#2591C2214yes—
130#2584C2214yescomplemented
131#2583C2214yescomplemented
132#2582C2214yescomplemented
133#2579C2218yescomplemented
134#2568C2212yescomplemented
135#2568C2212yescomplemented
136#2562C2214yes—
137#2560C2218yescomplemented
138#2556C2218yescomplemented
139#2546C2212yescomplemented
140#2546C2212yescomplemented
141#2546C2214yescomplemented
142#2545C2214yes—
143#2545C2214yes—
144#2540C2212yes—
145#2519C2218yescomplemented
146#2487C2214yescomplemented
147#2486C2214yescomplemented
148#2482C2214yes—
149#2480C2218yes—
150#2478C2218yes—
151#2474C2218yescomplemented
152#2470C2218yes—
153#2470C2218yescomplemented
154#2459C2218yescomplemented
155#2455C2218yescomplemented
156#2454C2214yes—
157#2453C2214yescomplemented
158#2452C2218yescomplemented
159#2447C2214yescomplemented
160#2445C2214yes—
161#2435C2212yes—
162#2434C2212yes—
163#2432C2214yescomplemented
164#2431C2214yes—
165#2429C2214yescomplemented
166#2429C2214yescomplemented
167#2427C2214yes—
168#2426C2214yes—
169#2418C2218yes—
170#2413C2218yescomplemented
171#2411C2214yes—
172#2409C2212yes—
173#2408C2212yes—
174#2399C2212yescomplemented
175#2398C2212yescomplemented
176#2396C2214yescomplemented
177#2396C2214yescomplemented
178#2396C2214yescomplemented
179#2395C2212yes—
180#2395C2212yes—
181#2392C2214yes—
182#2392C2214yescomplemented
183#2392C2218yescomplemented
184#2367C2214yes—
185#2365C2214yescomplemented
186#2361C2214yes—
187#2360C2214yescomplemented
188#2354C2214yes—
189#2354C2212yescomplemented
190Q8×C4⋊C4C2212yescomplemented
191#2347C2212yes—
192#2347C2214yescomplemented
193#2341C2212yes—
194#2319C2214yes—
195#2319C2212yescomplemented
196#2285C2211yescharacteristic
197#2285C2212yescomplemented
198#2283C2211yescharacteristic
199#2283C2212yescomplemented
200#2276C2212yescomplemented
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205#559—216no—
206#559—216no—
207#557—28no—
208#556—216no—
209#556—216no—
210#554—28no—
211#554—28no—
212#553—216no—
213#552—216no—
214#552—216no—
215#552—232no—
216#551—232no—
217#551—232no—
218#547—216no—
219#547—28no—
220#542—216no—
221#542—216no—
222#541—216no—
223#539—232no—
224#536—28no—
225#535—28no—
226#533—28no—
227#533—28no—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2314yes—
236C2×#127C2312yes—
237#529—216no—
238#529—216no—
239#529—28no—
240#529—216no—
241C2×#126C2314yes—
242C2×#126C2312yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125—216no—
250C2×#125C2314yes—
251C2×#125C2311yescharacteristic
252C2×#125C2312yes—
253C2×#125C2311yescharacteristic
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#124—28no—
262C2×#124C2311yescharacteristic
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2314yes—
271C2×#124C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2312yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2318yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#120C2314yes—
305C2×#120C2314yes—
306#520—216no—
307#519—28no—
308#518—28no—
309C4×#41D4116yescomplemented
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2318yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×#117C2314yes—
342C2×#117C2314yes—
343C2×#117C2314yes—
344C2×#117C2312yes—
345C2×#117C2311yescharacteristic
346C2×#117C2311yescharacteristic
347C2×#117C2312yes—
348C2×#117C2314yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2314yes—
352C2×#117C2311yescharacteristic
353C2×#117C2312yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C22⋊C4C2312yes—
360C22×C22⋊C4C2312yes—
361C22×C22⋊C4C2314yes—
362C22×C42C2311yescharacteristic
363C22×C42C2312yes—
364#400C2314yes—
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2318yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2312yes—
379#399C2312yes—
380#399C2318yes—
381#399C2318yes—
382#398C2318yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2318yes—
389#398C2314yes—
390#398C2318yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2318yes—
397#398C2318yes—
398#398C2318yes—
399#398C2318yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2312yes—
408#397C2318yes—
409#397C2318yes—
410#397C2318yes—
411#397C2318yes—
412#397C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2314yes—
417#396C2314yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#396C2318yes—
422#396C2318yes—
423#396C2318yes—
424#396C2318yes—
425#395C2312yes—
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#394C2318yes—
433#394C2312yes—
434#394C2312yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2318yes—
440#394C2314yes—
441#394C2318yes—
442#394C2318yes—
443#394C2318yes—
444#394C2318yes—
445#394C2318yes—
446#394C2318yes—
447#393C2318yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2318yes—
455#392C2318yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2318yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#390C2318yes—
464#390C2318yes—
465#390C2314yes—
466#390C2314yes—
467#390C2318yes—
468#390C2314yes—
469#389C2318yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2318yes—
474#389C2318yes—
475#389C2318yes—
476#389C2318yes—
477#389C2318yes—
478#389C2318yes—
479#389C2318yes—
480#389C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#388C2318yes—
491#388C2318yes—
492#388C2318yes—
493#388C2318yes—
494#388C2318yes—
495#387C2318yes—
496#387C2318yes—
497#387C2318yes—
498#387C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2314yes—
504#386C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2314yes—
512#385C2318yes—
513#385C2318yes—
514#384C2314yes—
515#384C2312yes—
516#383C2312yes—
517#383C2314yes—
518#382C2312yes—
519#382C2311yescharacteristic
520#382C2311yescharacteristic
521#382C2314yes—
522#381C2312yes—
523#381C2314yes—
524#381C2318yes—
525#380C2318yes—
526#380C2318yes—
527#380C2312yes—
528#380C2314yes—
529#380C2314yes—
530#380C2312yes—
531#380C2314yes—
532#380C2312yes—
533#379C2314yes—
534#379C2318yes—
535C4×C4⋊C4C2318yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2312yes—
543C4×C4⋊C4C2318yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2314yes—
553#376C2312yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—44no—
557C2×#41—48no—
558C2×#41C2×D418yes—
559C22×Q8—24no—
560C22×Q8—44no—
561C22×Q8C2412yes—
562C22×Q8C2412yes—
563C22×Q8C2411yescharacteristic
564C22×Q8C2411yescharacteristic
565C22×Q8C2412yes—
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×D4—24no—
570C22×D4—44no—
571C22×D4C2412yes—
572C22×D4C2411yescharacteristic
573C22×D4C2411yescharacteristic
574C22×D4C2414yes—
575C22×D4C2412yes—
576C22×D4C2412yes—
577C22×D4C2414yes—
578C22×D4C2414yes—
579C22×D4C2418yes—
580C22×D4C2412yes—
581C23×C4C2412yes—
582C23×C4C2411yescharacteristic
583C23×C4C2412yes—
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C4⋊Q8—28no—
595C4⋊Q8—28no—
596C4⋊Q8—24no—
597C4⋊Q8—24no—
598C4⋊Q8—24no—
599C4⋊Q8—24no—
600C4⋊Q8—48no—
601C4⋊Q8—84no—
602#127—28no—
603#126—216no—
604#126—216no—
605#126—216no—
606#126—216no—
607#126—216no—
608#126—216no—
609#126—216no—
610#126—28no—
611#125—216no—
612#125—216no—
613#125—28no—
614#125—24no—
615#125—28no—
616#125—216no—
617#125—216no—
618#125—28no—
619#125—28no—
620#125—24no—
621#125—24no—
622#124—28no—
623#124—28no—
624#124—216no—
625#124—216no—
626#124—28no—
627#124—28no—
628#124—28no—
629#124—28no—
630#124—24no—
631#124—48no—
632#123—216no—
633#123—216no—
634#123—28no—
635#123—216no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—88no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—24no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—216no—
653C22⋊Q8—28no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—48no—
658#121—216no—
659#121—28no—
660#121—28no—
661#121—28no—
662#121—24no—
663#121—48no—
664#120—216no—
665#120—84no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—24no—
674C4×Q8—28no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—48no—
678C4×Q8C2×D418yes—
679C4×Q8C2×D418yes—
680C4×D4—28no—
681C4×D4—216no—
682C4×D4—28no—
683C4×D4—216no—
684C4×D4—216no—
685C4×D4—28no—
686C4×D4—28no—
687C4×D4—216no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4—24no—
691C4×D4—28no—
692C4×D4—88no—
693C4×D4C2×D418yes—
694C4×D4C2×D4116yes—
695C4×D4C2×D418yes—
696C4×D4C2×D4116yes—
697#117—24no—
698#117—24no—
699#117—28no—
700#117—216no—
701#117—216no—
702#117—28no—
703#117—216no—
704#117—216no—
705#117—216no—
706#117—84no—
707#117—82no—
708#117C2×D418yes—
709#117C2×D4116yes—
710C2×C4⋊C4—216no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—216no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2418yes—
753C2×C4⋊C4C2418yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C22⋊C4—28no—
770C2×C22⋊C4—28no—
771C2×C22⋊C4—216no—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C42C2×D418yes—
813C2×C42C2×D4116yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2418yes—
823C2×C42C2414yes—
824C2×C42C2418yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832#95C2412yes—
833#95C2414yes—
834#95C2412yes—
835#95C2418yes—
836#95C2414yes—
837#95C2412yes—
838#95C2414yes—
839#95C2414yes—
840#95C2412yes—
841#95C2414yes—
842#95C2418yes—
843#95C2414yes—
844#95C2418yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2414yes—
849#95C2418yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853#95C2414yes—
854#95C2414yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860C24—24no—
861C24—44no—
862C24—42no—
863C24—44no—
864C24—42no—
865C24C2514yes—
866C24C2512yes—
867C24C2511yescharacteristic
868C24C2512yes—
869#41—416no—
870#41—432no—
871C2×Q8—22no—
872C2×Q8—24no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—28no—
880C2×Q8—28no—
881C2×Q8—44no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—44no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—416no—
889C2×Q8C22×D414yes—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—24no—
894C2×D4—22no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—28no—
899C2×D4—44no—
900C2×D4—42no—
901C2×D4—44no—
902C2×D4—48no—
903C2×D4—416no—
904C2×D4—48no—
905C2×D4—42no—
906C2×D4—48no—
907C2×D4—44no—
908C2×D4—48no—
909C2×D4—44no—
910C2×D4—48no—
911C2×D4—42no—
912C2×D4C22×D414yes—
913C2×D4C22×D418yes—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—28no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—42no—
924C22×C4—41no—
925C22×C4—42no—
926C22×C4—44no—
927C22×C4—41no—
928C22×C4—42no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—48no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—48no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4C22×D414yes—
940C22×C4C22×D414yes—
941C22×C4C22×D414yes—
942C22×C4C22×D418yes—
943C22×C4C22×D418yes—
944C22×C4C22×D418yes—
945C22×C4C2514yes—
946C22×C4C2518yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2512yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C4⋊C4—28no—
968C4⋊C4—24no—
969C4⋊C4—22no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—42no—
1003C4⋊C4—48no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—48no—
1011C4⋊C4—48no—
1012C4⋊C4—48no—
1013C4⋊C4—44no—
1014C4⋊C4—48no—
1015C4⋊C4—48no—
1016C4⋊C4—48no—
1017C4⋊C4C22×D414yes—
1018C4⋊C4C22×D414yes—
1019C4⋊C4C22×D418yes—
1020C4⋊C4C22×D418yes—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—24no—
1042C22⋊C4—44no—
1043C22⋊C4—48no—
1044C22⋊C4—44no—
1045C22⋊C4—48no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—48no—
1049C22⋊C4—44no—
1050C22⋊C4—48no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4C22×D418yes—
1059C22⋊C4C22×D418yes—
1060C22⋊C4C22×D418yes—
1061C42—28no—
1062C42—28no—
1063C42—28no—
1064C42—28no—
1065C42—24no—
1066C42—24no—
1067C42—24no—
1068C42—28no—
1069C42—48no—
1070C42—44no—
1071C42—48no—
1072C42C22×D414yes—
1073C42C22×D418yes—
1074C42C22×D418yes—
1075C42C22×D414yes—
1076C42C22×D418yes—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C23—22no—
1080C23—24no—
1081C23—22no—
1082C23—21no—
1083C23—24no—
1084C23—22no—
1085C23—22no—
1086C23—21no—
1087C23—22no—
1088C23—24no—
1089C23—28no—
1090C23—24no—
1091C23—24no—
1092C23—22no—
1093C23—22no—
1094C23—24no—
1095C23—24no—
1096C23—28no—
1097C23—48no—
1098C23—84no—
1099C23—84no—
1100C23—164no—
1101C23—164no—
1102C23C23×D412yes—
1103C23C23×D414yes—
1104C23C2611yescharacteristic
1105Q8—28no—
1106Q8—44no—
1107Q8—48no—
1108Q8—48no—
1109Q8—48no—
1110Q8—84no—
1111Q8—84no—
1112Q8—84no—
1113D4—28no—
1114D4—48no—
1115D4—44no—
1116D4—48no—
1117D4—416no—
1118D4—48no—
1119D4—84no—
1120D4—88no—
1121D4—88no—
1122D4—816no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—28no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—28no—
1148C2×C4—24no—
1149C2×C4—28no—
1150C2×C4—28no—
1151C2×C4—24no—
1152C2×C4—28no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—28no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—48no—
1169C2×C4—44no—
1170C2×C4—48no—
1171C2×C4—44no—
1172C2×C4—48no—
1173C2×C4—48no—
1174C2×C4—416no—
1175C2×C4—48no—
1176C2×C4—88no—
1177C2×C4—88no—
1178C2×C4—88no—
1179C2×C4—88no—
1180C2×C4C23×D412yes—
1181C2×C4C23×D414yes—
1182C2×C4C23×D414yes—
1183C2×C4C23×D412yes—
1184C2×C4C23×D412yes—
1185C2×C4C23×D412yes—
1186C2×C4C23×D412yes—
1187C2×C4C23×D414yes—
1188C2×C4C23×D412yes—
1189C2×C4#58514yes—
1190C22—24no—
1191C22—22no—
1192C22—24no—
1193C22—22no—
1194C22—22no—
1195C22—24no—
1196C22—44no—
1197C22—42no—
1198C22—44no—
1199C22—42no—
1200C22—44no—
1201C22—48no—
1202C22—44no—
1203C22—48no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—168no—
1211C22C24×D411yescharacteristic
1212C22C2×#58512yes—
1213C22H(7,𝔽2)11yescharacteristic
1214C222−1+612yes—
1215C222−1+611yescharacteristic
1216C4—22no—
1217C4—24no—
1218C4—22no—
1219C4—22no—
1220C4—24no—
1221C4—22no—
1222C4—22no—
1223C4—24no—
1224C4—44no—
1225C4—48no—
1226C4—44no—
1227C4—42no—
1228C4—42no—
1229C4—44no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—42no—
1234C4—42no—
1235C4—44no—
1236C4—44no—
1237C4#344914yes—
1238C2—44no—
1239C2—42no—
1240C2—82no—
1241C2—84no—
1242C2C2×#344911yescharacteristic
1243C2#6285311yescharacteristic
1244C2#6285911yescharacteristic
1245C2#6305612yes—
1246C2#6306212yes—
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×#3510C2semidirect
2. C2×#3515C2semidirect
3. #42967C2semidirect
4. #42917C2semidirect
5. #42802C2semidirect
6. #42683C2semidirect
7. #42678C2semidirect
8. #42309C2semidirect
9. #42173C2semidirect
10. #41985C2semidirect
11. #41947C2semidirect
12. #40532C2semidirect
13. #37641C2semidirect
14. #37607C2semidirect
15. #37549C2semidirect
16. #37546C2semidirect
17. #37541C2semidirect
18. #37537C2semidirect
19. #36699C2semidirect
20. #36684C2semidirect
21. #35997C2semidirect
22. #35982C2semidirect
23. #35938C2semidirect
24. #35909C2semidirect
25. #35778C2semidirect
26. #34193C2semidirect
31. C2×#557C22semidirect
34. C2×#554C22semidirect
35. C2×#554C22semidirect
39. C2×#552C22semidirect
43. C2×#547C22semidirect
46. C2×#541C22semidirect
55. C2×#529C22semidirect
56. C22×#125C22semidirect
58. C2×#520C22semidirect
62. #2823C22semidirect
63. #2822C22semidirect
64. #2822C22semidirect
65. #2822C22semidirect
66. #2822C22semidirect
67. #2821C22semidirect
68. #2821C22semidirect
72. #2820C22semidirect
73. #2820C22semidirect
78. #2814C22semidirect
79. #2814C22semidirect
81. #2813C22semidirect
82. #2727C22semidirect
83. #2725C22semidirect
85. #2710C22semidirect
86. #2706C22semidirect
87. #2704C22semidirect
88. #2702C22semidirect
91. #2687C22semidirect
93. #2674C22semidirect
94. #2664C22semidirect
95. #2664C22semidirect
96. #2664C22semidirect
97. #2663C22semidirect
102. #2638C22semidirect
103. #2635C22semidirect
104. #2634C22semidirect
107. #2630C22semidirect
108. #2629C22semidirect
109. #2627C22semidirect
115. #2623C22semidirect
116. #2623C22semidirect
121. #2611C22semidirect
122. #2611C22semidirect
123. #2604C22semidirect
124. #2603C22semidirect
125. #2601C22semidirect
126. #2599C22semidirect
130. #2584C22semidirect
131. #2583C22semidirect
132. #2582C22semidirect
133. #2579C22semidirect
134. #2568C22semidirect
135. #2568C22semidirect
137. #2560C22semidirect
138. #2556C22semidirect
139. #2546C22semidirect
140. #2546C22semidirect
141. #2546C22semidirect
145. #2519C22semidirect
146. #2487C22semidirect
147. #2486C22semidirect
151. #2474C22semidirect
153. #2470C22semidirect
154. #2459C22semidirect
155. #2455C22semidirect
157. #2453C22semidirect
158. #2452C22semidirect
159. #2447C22semidirect
163. #2432C22semidirect
165. #2429C22semidirect
166. #2429C22semidirect
170. #2413C22semidirect
174. #2399C22semidirect
175. #2398C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
178. #2396C22semidirect
182. #2392C22semidirect
183. #2392C22semidirect
185. #2365C22semidirect
187. #2360C22semidirect
189. #2354C22semidirect
190. Q8×C4⋊C4C22semidirect
192. #2347C22semidirect
195. #2319C22semidirect
197. #2285C22semidirect
199. #2283C22semidirect
200. #2276C22semidirect
309. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35152
#429672
#429172
#428022
#426832
#426782
#423092
#421732
#419852
#419472
#405322
#376412
#376072
#375492
#375462
#375412
#375372
#366992
#366842
#359972
#359822
#359382
#359092
#357782
#341932