Finite Group Databasebeta

← #7732389

Subgroups — #7732389

Order 512.

7060 conjugacy classes of subgroups.

The subgroup lattice has 1293 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3558C211yesmaximal, characteristic
3#51073C214yesmaximal, complemented
4#50696C214yesmaximal, complemented
5#47724C218yesmaximal, complemented
6#44044C218yesmaximal, complemented
7#39746C212yesmaximal, complemented
8#39164C212yesmaximal, complemented
9#38094C212yesmaximal, complemented
10#38084C212yesmaximal, complemented
11#37746C214yesmaximal, complemented
12#37707C214yesmaximal, complemented
13#37676C212yesmaximal, complemented
14#37675C212yesmaximal, complemented
15#37537C211yesmaximal, characteristic, complemented
16#37424C212yesmaximal, complemented
17#37389C212yesmaximal, complemented
18#36376C212yesmaximal, complemented
19D4×#124C212yesmaximal, complemented
20#35677C212yesmaximal, complemented
21#35669C212yesmaximal, complemented
22#35249C211yesmaximal, characteristic, complemented
23#35180C211yesmaximal, characteristic, complemented
24C2×#2545C211yesmaximal, characteristic, complemented
25#34083C211yesmaximal, characteristic, complemented
26#3558—216no—
27C2×#562C2212yes—
28C2×H(3,𝔽4)C2212yes—
29#3523—216no—
30C2×#559C2212yes—
31C2×#557C2212yescomplemented
32C2×#557C2211yescharacteristic, complemented
33C2×#557C2211yescharacteristic, complemented
34C2×#556C2212yescomplemented
35C2×#556C2211yescharacteristic, complemented
36C2×#552C2214yescomplemented
37C2×#552C2212yescomplemented
38C2×D4×Q8C2212yescomplemented
39C2×D4×Q8C2211yescharacteristic, complemented
40C2×#548C2212yes—
41C2×#546C2214yes—
42C2×#546C2212yes—
43C2×D42C2212yes—
44C2×#542C2212yes—
45C2×#541C2212yescomplemented
46C2×#541C2214yescomplemented
47C2×#538C2212yes—
48C2×#538C2214yes—
49C2×#536C2212yescomplemented
50C2×#535C2212yes—
51C2×#534C2212yes—
52C2×#533C2212yescomplemented
53C2×#533C2211yescharacteristic, complemented
54C2×#532C2211yescharacteristic
55C22×C4⋊Q8C2211yescharacteristic, complemented
56C2×#529C2212yes—
57C2×#529C2211yescharacteristic
58C22×#124C2211yescharacteristic
59C22×#124C2211yescharacteristic
60C22×#124C2212yescomplemented
61C2×#519C2212yescomplemented
62C22×C4×Q8C2211yescharacteristic, complemented
63#2861C2212yescomplemented
64#2858C2212yes—
65#2857C2212yescomplemented
66#2854C2214yescomplemented
67#2850C2212yes—
68#2850C2212yescomplemented
69#2850C2212yescomplemented
70#2820C2214yescomplemented
71#2731C2218yescomplemented
72#2725C2218yescomplemented
73#2715C2218yescomplemented
74#2711C2218yescomplemented
75#2711C2218yescomplemented
76#2711C2218yescomplemented
77#2707C2218yescomplemented
78#2704C2218yescomplemented
79#2695C2218yescomplemented
80#2694C2218yescomplemented
81#2694C2218yescomplemented
82#2691C2218yescomplemented
83#2685C2218yescomplemented
84#2685C2218yescomplemented
85#2685C2218yescomplemented
86#2684C2218yescomplemented
87#2677C2218yescomplemented
88#2674C2218yescomplemented
89#2674C2218yescomplemented
90#2672C2218yescomplemented
91#2658C2212yescomplemented
92#2658C2212yescomplemented
93#2641C2212yes—
94#2640C2212yescomplemented
95#2639C2214yescomplemented
96#2632C2214yescomplemented
97#2632C2214yescomplemented
98#2626C2214yescomplemented
99#2621C2212yescomplemented
100#2620C2212yes—
101#2592C2214yescomplemented
102#2580C2214yescomplemented
103#2568C2212yescomplemented
104#2567C2211yescharacteristic, complemented
105#2567C2211yescharacteristic, complemented
106#2566C2212yescomplemented
107#2565C2212yescomplemented
108#2563C2212yescomplemented
109#2562C2214yescomplemented
110#2556C2218yescomplemented
111#2548C2212yes—
112#2548C2212yes—
113#2548C2211yescharacteristic, complemented
114#2548C2212yescomplemented
115#2548C2211yescharacteristic, complemented
116#2547C2212yescomplemented
117#2547C2212yescomplemented
118#2546C2212yescomplemented
119#2545C2214yescomplemented
120#2545C2212yescomplemented
121#2545C2212yescomplemented
122#2545C2212yescomplemented
123#2545C2212yescomplemented
124#2545C2212yescomplemented
125#2545C2212yescomplemented
126#2545C2212yescomplemented
127#2545C2212yescomplemented
128#2545C2214yescomplemented
129#2521C2218yescomplemented
130#2501C2212yescomplemented
131#2500C2212yes—
132#2499C2212yescomplemented
133#2491C2218yescomplemented
134#2482C2214yescomplemented
135#2480C2218yescomplemented
136#2474C2218yescomplemented
137#2472C2218yescomplemented
138#2472C2218yescomplemented
139#2470C2218yescomplemented
140#2469C2218yescomplemented
141#2465C2218yescomplemented
142#2460C2218yescomplemented
143#2458C2218yescomplemented
144#2458C2218yescomplemented
145#2454C2218yescomplemented
146#2449C2218yescomplemented
147#2448C2218yescomplemented
148#2443C2218yescomplemented
149#2437C2218yescomplemented
150#2436C2212yes—
151#2436C2212yescomplemented
152#2435C2212yes—
153#2435C2212yescomplemented
154#2435C2212yescomplemented
155#2434C2212yescomplemented
156#2434C2212yescomplemented
157#2432C2212yescomplemented
158#2432C2212yescomplemented
159#2426C2218yescomplemented
160#2426C2218yescomplemented
161#2425C2218yescomplemented
162#2418C2218yescomplemented
163#2411C2218yescomplemented
164#2411C2218yescomplemented
165#2411C2218yescomplemented
166#2406C2214yescomplemented
167#2405C2218yescomplemented
168C2×#396C2214yescomplemented
169#2359C2218yescomplemented
170D4×C22⋊C4C2218yescomplemented
171#2337C2212yescomplemented
172#2336C2212yescomplemented
173#2334C2214yescomplemented
174#2329C2212yescomplemented
175#2327C2212yescomplemented
176#2326C2212yescomplemented
177#2326C2212yescomplemented
178#2326C2212yescomplemented
179#2325C2212yes—
180#2322C2214yescomplemented
181#2311C2214yescomplemented
182#2309C2212yescomplemented
183C4×C4⋊Q8C2212yescomplemented
184C4×#124C2212yescomplemented
185#2298C2212yescomplemented
186#2297C2212yescomplemented
187#2296C2212yescomplemented
188#2295C2212yescomplemented
189C2×#391C2211yescharacteristic, complemented
190C2×#390C2211yescharacteristic
191#2290C2212yescomplemented
192#2290C2212yescomplemented
193C2×#388C2214yescomplemented
194#2283C2211yescharacteristic, complemented
195C42×D4C2212yescomplemented
196C2×C4×C4⋊C4C2211yescharacteristic, complemented
197C22×#41C2312yes—
198C22×#41C2312yes—
199C23×Q8C2311yescharacteristic
200C23×Q8C2312yes—
201C23×Q8C2311yescharacteristic
202C23×D4C2312yes—
203C23×D4C2314yes—
204C23×D4C2311yescharacteristic
205#562—216no—
206H(3,𝔽4)—216no—
207#559—216no—
208#557—216no—
209#557—28no—
210#557—28no—
211#556—216no—
212#556—28no—
213#552—232no—
214#552—216no—
215D4×Q8—216no—
216D4×Q8—28no—
217#548—216no—
218#546—232no—
219#546—216no—
220D42—216no—
221#542—216no—
222#541—232no—
223#541—216no—
224#538—232no—
225#538—216no—
226#536—48no—
227#535—216no—
228#534—216no—
229#533—216no—
230#533—28no—
231#532—28no—
232C2×C4⋊Q8—44no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2314yes—
245C2×#127C2312yes—
246C2×#127C2311yescharacteristic
247#529—216no—
248#529D4116yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2311yescharacteristic
264C2×#124—28no—
265C2×#124—44no—
266C2×#124—48no—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2314yes—
277C2×#124C2314yes—
278C2×#124C2314yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2318yes—
287C2×#124C2311yescharacteristic
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2318yes—
294C2×#123C2318yes—
295C2×#123C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2318yes—
307C2×C22⋊Q8C2311yescharacteristic
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2311yescharacteristic
317C2×#120C2314yes—
318C2×#120C2314yes—
319C2×#120C2314yes—
320C2×#120C2314yes—
321C2×#120C2314yes—
322#519—216no—
323C2×C4×Q8—28no—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2314yes—
336C2×C4×Q8C2314yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2311yescharacteristic
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2314yes—
354C2×#117C2314yes—
355C2×#117C2314yes—
356C2×#117C2312yes—
357C2×#117C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2311yescharacteristic
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2314yes—
362C22×C22⋊C4C2312yes—
363C22×C22⋊C4C2312yes—
364C22×C22⋊C4C2314yes—
365C22×C22⋊C4C2314yes—
366C22×C22⋊C4C2318yes—
367C22×C22⋊C4C2314yes—
368C22×C42C2312yes—
369C22×C42C2312yes—
370C22×C42C2311yescharacteristic
371C22×C42C2311yescharacteristic
372C22×C42C2311yescharacteristic
373#400C2318yes—
374#399C2318yes—
375#399C2318yes—
376#399C2318yes—
377#399C2318yes—
378#399C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#397C2318yes—
383#397C2318yes—
384#397C2318yes—
385#397C2318yes—
386#397C2318yes—
387#396C2318yes—
388#396C2318yes—
389#396C2318yes—
390#396C2318yes—
391#396C2318yes—
392#396C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#395C2318yes—
398#395C2314yes—
399#395C2314yes—
400#395C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2314yes—
405#394C2314yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#394C2318yes—
412#394C2318yes—
413#394C2318yes—
414#394C2318yes—
415#393C2318yes—
416#393C2318yes—
417#393C2318yes—
418#393C2318yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2318yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2318yes—
436#390C2312yes—
437#390C2318yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2318yes—
442#390C2318yes—
443#390C2318yes—
444#390C2312yes—
445#390C2318yes—
446#390C2314yes—
447#389C2318yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2318yes—
454#389C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2314yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#387C2318yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2318yes—
482#387C2318yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2318yes—
487#386C2318yes—
488#386C2318yes—
489#386C2314yes—
490#386C2314yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#385C2318yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2318yes—
500#385C2318yes—
501#385C2314yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#384C2312yes—
508#384C2312yes—
509#383C2312yes—
510#382C2312yes—
511#382C2312yes—
512#382C2312yes—
513#381C2312yes—
514#380C2318yes—
515#380C2318yes—
516#380C2312yes—
517#380C2318yes—
518#380C2318yes—
519#379C2318yes—
520#379C2318yes—
521#379C2318yes—
522#379C2318yes—
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2318yes—
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2312yes—
527C4×C4⋊C4C2312yes—
528C4×C4⋊C4C2311yescharacteristic
529C4×C4⋊C4C2311yescharacteristic
530C4×C4⋊C4C2312yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2312yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2314yes—
535C4×C22⋊C4C2318yes—
536C4×C22⋊C4C2318yes—
537C4×C22⋊C4C2312yes—
538C4×C22⋊C4C2312yes—
539C4×C22⋊C4C2312yes—
540#376C2312yes—
541#376C2312yes—
542C2×#95C2312yes—
543C2×#95C2314yes—
544C43C2312yes—
545C25C2412yes—
546C25C2414yes—
547C2×#41—28no—
548C2×#41—28no—
549C2×#41—48no—
550C2×#41—44no—
551C2×#41—44no—
552C22×Q8—24no—
553C22×Q8—28no—
554C22×Q8—24no—
555C22×Q8—28no—
556C22×Q8—24no—
557C22×Q8—42no—
558C22×Q8—44no—
559C22×Q8—42no—
560C22×Q8—42no—
561C22×Q8C2412yes—
562C22×Q8C2411yescharacteristic
563C22×Q8C2412yes—
564C22×Q8C2414yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2412yes—
570C22×Q8C2411yescharacteristic
571C22×D4—216no—
572C22×D4—24no—
573C22×D4—28no—
574C22×D4—42no—
575C22×D4—44no—
576C22×D4—42no—
577C22×D4—44no—
578C22×D4—416no—
579C22×D4C2414yes—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2412yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2414yes—
586C22×D4C2414yes—
587C22×D4C2412yes—
588C22×D4C2412yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2411yescharacteristic
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2414yes—
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2411yescharacteristic
606C4⋊Q8—28no—
607C4⋊Q8—28no—
608C4⋊Q8—28no—
609C4⋊Q8—216no—
610C4⋊Q8—24no—
611C4⋊Q8—24no—
612C4⋊Q8—24no—
613C4⋊Q8—28no—
614C4⋊Q8—44no—
615C4⋊Q8—44no—
616C4⋊Q8—44no—
617C4⋊Q8—48no—
618#127—24no—
619#127—28no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—216no—
624#126—216no—
625#126C2×D4116yes—
626#125—28no—
627#125—216no—
628#125—216no—
629#125—216no—
630#125—216no—
631#125—216no—
632#125—28no—
633#125—28no—
634#125C2×D418yes—
635#124—216no—
636#124—28no—
637#124—28no—
638#124—28no—
639#124—216no—
640#124—216no—
641#124—28no—
642#124—28no—
643#124—28no—
644#124—28no—
645#124—28no—
646#124—28no—
647#124—44no—
648#124—44no—
649#124—44no—
650#124—44no—
651#124—44no—
652#124—44no—
653#124—48no—
654#124—416no—
655#124C2×D418yes—
656#123—216no—
657#123—216no—
658#123—216no—
659#123—216no—
660#123—216no—
661#123—416no—
662#123—416no—
663#123C2×D4116yes—
664C22⋊Q8—28no—
665C22⋊Q8—28no—
666C22⋊Q8—28no—
667C22⋊Q8—28no—
668C22⋊Q8—28no—
669C22⋊Q8—216no—
670C22⋊Q8—216no—
671C22⋊Q8—216no—
672C22⋊Q8—216no—
673C22⋊Q8—216no—
674C22⋊Q8—416no—
675C22⋊Q8C2×D418yes—
676#121—216no—
677#121—28no—
678#121—28no—
679#121—28no—
680#121—216no—
681#121—216no—
682#121—216no—
683#121—216no—
684#121C2×D418yes—
685#120—216no—
686#120—216no—
687#120—216no—
688#120—216no—
689#120—216no—
690C4×Q8—28no—
691C4×Q8—216no—
692C4×Q8—216no—
693C4×Q8—28no—
694C4×Q8—28no—
695C4×Q8—24no—
696C4×Q8—28no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—28no—
700C4×Q8—24no—
701C4×Q8—28no—
702C4×Q8—28no—
703C4×Q8—28no—
704C4×Q8—28no—
705C4×Q8—28no—
706C4×Q8C2×D418yes—
707C4×D4—216no—
708C4×D4—28no—
709C4×D4—216no—
710C4×D4—216no—
711C4×D4—28no—
712C4×D4—28no—
713C4×D4—28no—
714C4×D4—48no—
715C4×D4C2×D4116yes—
716C4×D4C2×D418yes—
717#117—28no—
718#117—28no—
719#117—216no—
720#117—216no—
721#117—216no—
722#117—44no—
723#117C2×D4116yes—
724C2×C4⋊C4—24no—
725C2×C4⋊C4—28no—
726C2×C4⋊C4—48no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C22⋊C4—28no—
773C2×C22⋊C4—28no—
774C2×C22⋊C4—216no—
775C2×C22⋊C4—48no—
776C2×C22⋊C4—416no—
777C2×C22⋊C4—48no—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C42—28no—
819C2×C42—42no—
820C2×C42—44no—
821C2×C42—42no—
822C2×C42C2×D418yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2411yescharacteristic
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846#95C2418yes—
847#95C2414yes—
848#95C2414yes—
849#95C2418yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2414yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2412yes—
863#95C2412yes—
864#95C2414yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24—24no—
870C24—28no—
871C24—28no—
872C24—42no—
873C24—44no—
874C24—42no—
875C24—44no—
876C24—48no—
877C24—48no—
878C24—44no—
879C24C2514yes—
880C24C2514yes—
881C24C2512yes—
882C24C2511yescharacteristic
883#41—816no—
884#41—816no—
885C2×Q8—22no—
886C2×Q8—24no—
887C2×Q8—28no—
888C2×Q8—24no—
889C2×Q8—22no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—24no—
893C2×Q8—24no—
894C2×Q8—28no—
895C2×Q8—24no—
896C2×Q8—24no—
897C2×Q8—22no—
898C2×Q8—24no—
899C2×Q8—22no—
900C2×Q8—22no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—44no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—44no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—44no—
910C2×Q8—416no—
911C2×Q8—432no—
912C2×Q8—88no—
913C2×Q8C22×D414yes—
914C2×Q8H(5,𝔽2)14yes—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—216no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—28no—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—24no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—24no—
931C2×D4—24no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—48no—
937C2×D4—44no—
938C2×D4—42no—
939C2×D4—48no—
940C2×D4—48no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—88no—
945C2×D4—816no—
946C2×D4—832no—
947C2×D4C22×D418yes—
948C2×D4C22×D414yes—
949C22×C4—24no—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—22no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—24no—
958C22×C4—28no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—28no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—28no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—48no—
979C22×C4—42no—
980C22×C4—48no—
981C22×C4—44no—
982C22×C4C22×D414yes—
983C22×C4C22×D414yes—
984C22×C4C22×D418yes—
985C22×C4C22×D414yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2512yes—
1006C22×C4C2511yescharacteristic
1007C4⋊C4—24no—
1008C4⋊C4—22no—
1009C4⋊C4—24no—
1010C4⋊C4—22no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—28no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—216no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—48no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—48no—
1042C4⋊C4—48no—
1043C4⋊C4—48no—
1044C4⋊C4—48no—
1045C4⋊C4C22×D418yes—
1046C4⋊C4C22×D418yes—
1047C4⋊C4C22×D418yes—
1048C4⋊C4C22×D414yes—
1049C4⋊C4C22×D418yes—
1050C4⋊C4C22×D414yes—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—216no—
1068C22⋊C4—216no—
1069C22⋊C4—48no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C22⋊C4—48no—
1073C22⋊C4—48no—
1074C22⋊C4—48no—
1075C22⋊C4—44no—
1076C22⋊C4—48no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—48no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4C22×D418yes—
1087C22⋊C4C22×D418yes—
1088C22⋊C4C22×D418yes—
1089C22⋊C4C22×D418yes—
1090C22⋊C4C22×D418yes—
1091C42—24no—
1092C42—24no—
1093C42—24no—
1094C42—24no—
1095C42—28no—
1096C42—28no—
1097C42—28no—
1098C42—28no—
1099C42—28no—
1100C42—24no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—42no—
1105C42—44no—
1106C42—42no—
1107C42—44no—
1108C42—44no—
1109C42C22×D414yes—
1110C42C22×D414yes—
1111C42C22×D414yes—
1112C42C22×D414yes—
1113C42C22×D418yes—
1114C23—21no—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—24no—
1119C23—22no—
1120C23—24no—
1121C23—24no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—24no—
1126C23—28no—
1127C23—28no—
1128C23—24no—
1129C23—28no—
1130C23—28no—
1131C23—48no—
1132C23—84no—
1133C23—88no—
1134C23—88no—
1135C23—84no—
1136C23—88no—
1137C23—88no—
1138C23—88no—
1139C23—816no—
1140C23—168no—
1141C23C23×D414yes—
1142C23C23×D412yes—
1143C23#58514yes—
1144C23C2611yescharacteristic
1145Q8—28no—
1146Q8—44no—
1147Q8—416no—
1148Q8—48no—
1149Q8—48no—
1150Q8—48no—
1151Q8—44no—
1152Q8—48no—
1153Q8—84no—
1154Q8—84no—
1155D4—216no—
1156D4—44no—
1157D4—416no—
1158D4—48no—
1159D4—48no—
1160D4—84no—
1161D4—88no—
1162D4—88no—
1163D4—84no—
1164D4—88no—
1165D4—84no—
1166D4—88no—
1167D4—88no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—28no—
1181C2×C4—28no—
1182C2×C4—216no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—28no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—28no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—44no—
1213C2×C4—48no—
1214C2×C4—416no—
1215C2×C4—48no—
1216C2×C4—48no—
1217C2×C4—88no—
1218C2×C4—88no—
1219C2×C4—88no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—88no—
1223C2×C4C23×D412yes—
1224C2×C4C23×D412yes—
1225C2×C4C23×D412yes—
1226C2×C4C23×D414yes—
1227C2×C4C23×D414yes—
1228C2×C4C23×D414yes—
1229C2×C4C23×D412yes—
1230C2×C4C23×D412yes—
1231C2×C4C23×D412yes—
1232C2×C4C2×H(5,𝔽2)14yes—
1233C2×C4C2×H(5,𝔽2)12yes—
1234C2×C4#58512yes—
1235C22—22no—
1236C22—22no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—24no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—48no—
1251C22—48no—
1252C22—48no—
1253C22—48no—
1254C22—168no—
1255C22—1616no—
1256C22#350014yes—
1257C22C24×D411yescharacteristic
1258C22C22×H(5,𝔽2)11yescharacteristic
1259C22C2×#58511yescharacteristic
1260C22C2×#58512yes—
1261C222−1+612yes—
1262C4—24no—
1263C4—22no—
1264C4—24no—
1265C4—22no—
1266C4—22no—
1267C4—24no—
1268C4—22no—
1269C4—22no—
1270C4—24no—
1271C4—44no—
1272C4—42no—
1273C4—44no—
1274C4—42no—
1275C4—42no—
1276C4—44no—
1277C4—44no—
1278C4—44no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4#348814yes—
1283C2—24no—
1284C2—44no—
1285C2—84no—
1286C2—84no—
1287C2C2×#348811yescharacteristic
1288C2C2×#350011yescharacteristic
1289C2#6285911yescharacteristic
1290C2#6289712yes—
1291C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3558C2
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×#3523C2semidirect
3. #51073C2semidirect
4. #50696C2semidirect
5. #47724C2semidirect
6. #44044C2semidirect
7. #39746C2semidirect
8. #39164C2semidirect
9. #38094C2semidirect
10. #38084C2semidirect
11. #37746C2semidirect
12. #37707C2semidirect
13. #37676C2semidirect
14. #37675C2semidirect
15. #37537C2semidirect
16. #37424C2semidirect
17. #37389C2semidirect
18. #36376C2semidirect
19. D4×#124C2semidirect
20. #35677C2semidirect
21. #35669C2semidirect
22. #35249C2semidirect
23. #35180C2semidirect
24. C2×#2545C2semidirect
25. #34083C2semidirect
31. C2×#557C22semidirect
32. C2×#557C22semidirect
33. C2×#557C22semidirect
34. C2×#556C22semidirect
35. C2×#556C22semidirect
36. C2×#552C22semidirect
37. C2×#552C22semidirect
38. C2×D4×Q8C22semidirect
39. C2×D4×Q8C22semidirect
45. C2×#541C22semidirect
46. C2×#541C22semidirect
49. C2×#536C22semidirect
52. C2×#533C22semidirect
53. C2×#533C22semidirect
55. C22×C4⋊Q8C22semidirect
60. C22×#124C22semidirect
61. C2×#519C22semidirect
62. C22×C4×Q8C22semidirect
63. #2861C22semidirect
65. #2857C22semidirect
66. #2854C22semidirect
68. #2850C22semidirect
69. #2850C22semidirect
70. #2820C22semidirect
71. #2731C22semidirect
72. #2725C22semidirect
73. #2715C22semidirect
74. #2711C22semidirect
75. #2711C22semidirect
76. #2711C22semidirect
77. #2707C22semidirect
78. #2704C22semidirect
79. #2695C22semidirect
80. #2694C22semidirect
81. #2694C22semidirect
82. #2691C22semidirect
83. #2685C22semidirect
84. #2685C22semidirect
85. #2685C22semidirect
86. #2684C22semidirect
87. #2677C22semidirect
88. #2674C22semidirect
89. #2674C22semidirect
90. #2672C22semidirect
91. #2658C22semidirect
92. #2658C22semidirect
94. #2640C22semidirect
95. #2639C22semidirect
96. #2632C22semidirect
97. #2632C22semidirect
98. #2626C22semidirect
99. #2621C22semidirect
101. #2592C22semidirect
102. #2580C22semidirect
103. #2568C22semidirect
104. #2567C22semidirect
105. #2567C22semidirect
106. #2566C22semidirect
107. #2565C22semidirect
108. #2563C22semidirect
109. #2562C22semidirect
110. #2556C22semidirect
113. #2548C22semidirect
114. #2548C22semidirect
115. #2548C22semidirect
116. #2547C22semidirect
117. #2547C22semidirect
118. #2546C22semidirect
119. #2545C22semidirect
120. #2545C22semidirect
121. #2545C22semidirect
122. #2545C22semidirect
123. #2545C22semidirect
124. #2545C22semidirect
125. #2545C22semidirect
126. #2545C22semidirect
127. #2545C22semidirect
128. #2545C22semidirect
129. #2521C22semidirect
130. #2501C22semidirect
132. #2499C22semidirect
133. #2491C22semidirect
134. #2482C22semidirect
135. #2480C22semidirect
136. #2474C22semidirect
137. #2472C22semidirect
138. #2472C22semidirect
139. #2470C22semidirect
140. #2469C22semidirect
141. #2465C22semidirect
142. #2460C22semidirect
143. #2458C22semidirect
144. #2458C22semidirect
145. #2454C22semidirect
146. #2449C22semidirect
147. #2448C22semidirect
148. #2443C22semidirect
149. #2437C22semidirect
151. #2436C22semidirect
153. #2435C22semidirect
154. #2435C22semidirect
155. #2434C22semidirect
156. #2434C22semidirect
157. #2432C22semidirect
158. #2432C22semidirect
159. #2426C22semidirect
160. #2426C22semidirect
161. #2425C22semidirect
162. #2418C22semidirect
163. #2411C22semidirect
164. #2411C22semidirect
165. #2411C22semidirect
166. #2406C22semidirect
167. #2405C22semidirect
168. C2×#396C22semidirect
169. #2359C22semidirect
170. D4×C22⋊C4C22semidirect
171. #2337C22semidirect
172. #2336C22semidirect
173. #2334C22semidirect
174. #2329C22semidirect
175. #2327C22semidirect
176. #2326C22semidirect
177. #2326C22semidirect
178. #2326C22semidirect
180. #2322C22semidirect
181. #2311C22semidirect
182. #2309C22semidirect
183. C4×C4⋊Q8C22semidirect
184. C4×#124C22semidirect
185. #2298C22semidirect
186. #2297C22semidirect
187. #2296C22semidirect
188. #2295C22semidirect
189. C2×#391C22semidirect
191. #2290C22semidirect
192. #2290C22semidirect
193. C2×#388C22semidirect
194. #2283C22semidirect
195. C42×D4C22semidirect
196. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C2×#35582
#510732
#506962
#477242
#440442
#397462
#391642
#380942
#380842
#377462
#377072
#376762
#376752
#375372
#374242
#373892
#363762
D4×#1242
#356772
#356692
#352492
#351802
C2×#25452
#340832