Finite Group Databasebeta

← #7665638

Subgroups — #7665638

Order 512.

7357 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#39962C216yesmaximal, complemented
4#39959C216yesmaximal, complemented
5#39857C216yesmaximal, complemented
6#39856C216yesmaximal, complemented
7#39468C213yesmaximal, complemented
8#39340C213yesmaximal, complemented
9#38923C213yesmaximal, complemented
10#38908C213yesmaximal, complemented
11#36577C211yesmaximal, characteristic, complemented
12Q8×#121C211yesmaximal, characteristic, complemented
13#36445C211yesmaximal, characteristic, complemented
14#36444C212yesmaximal, complemented
15#36444C211yesmaximal, characteristic, complemented
16#36435C212yesmaximal, complemented
17#36434C212yesmaximal, complemented
18#36430C212yesmaximal, complemented
19#35297C213yesmaximal, complemented
20#35241C213yesmaximal, complemented
21#35189C213yesmaximal, complemented
22C4⋊C4×#41C211yesmaximal, characteristic, complemented
23C4×#537C213yesmaximal, complemented
24#3482—216no—
25#3480—216no—
26C2×#559C2213yes—
27C2×#557C2211yescharacteristic
28C2×#557C2211yescharacteristic
29C2×#556C2213yes—
30C2×#556C2213yes—
31C2×#553C2213yes—
32C2×#553C2213yes—
33C2×#552C2216yes—
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2212yes—
37C2×#548C2212yes—
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2212yes—
41C2×#547C2213yes—
42C2×#537C2213yes—
43C2×#533C2213yes—
44C2×#532C2213yes—
45C2×#529C2213yes—
46C2×#529C2213yes—
47C2×#529C2216yes—
48C2×C4×#41C2213yes—
49C2×C4×#41C2213yes—
50C2×C4×#41C2211yescharacteristic
51C2×C4×#41C2212yes—
52C2×C4×#41C2211yescharacteristic
53C22×C4×Q8C2212yes—
54C22×C4×Q8C2211yescharacteristic
55#2857C2213yes—
56#2857C2216yes—
57#2857C2213yes—
58#2857C2213yes—
59#2857C2213yes—
60#2851C2216yes—
61#2850C2216yes—
62#2850C2216yes—
63#2722C22112yes—
64#2715C22112yes—
65#2695C22112yes—
66#2695C22112yes—
67#2693C22112yes—
68#2691C22112yes—
69#2672C22112yes—
70#2671C22112yes—
71#2664C22112yes—
72#2630C22112yes—
73#2625C2216yes—
74#2616C2216yes—
75#2601C22112yes—
76#2584C2216yes—
77#2582C2213yes—
78#2581C2216yes—
79#2568C2213yes—
80#2565C2216yes—
81#2562C2216yes—
82#2547C2216yes—
83#2547C2213yes—
84#2546C2213yes—
85#2545C2216yes—
86#2544C2216yes—
87#2542C2213yes—
88#2538C2213yes—
89#2538C2213yes—
90#2537C2213yes—
91#2537C2216yes—
92#2536C2216yes—
93#2535C2216yes—
94#2498C22112yes—
95#2485C2216yes—
96#2485C2216yes—
97#2485C2216yes—
98#2454C2216yes—
99#2453C2216yes—
100#2453C2216yes—
101#2451C2216yes—
102#2442C2216yes—
103#2442C2216yes—
104#2441C2216yes—
105#2440C2216yes—
106#2429C2216yes—
107#2429C2216yes—
108#2428C2216yes—
109#2427C2216yes—
110#2427C2216yes—
111#2427C2216yes—
112#2427C2216yes—
113#2426C2216yes—
114#2417C2216yes—
115#2417C2216yes—
116#2417C2216yes—
117#2417C2216yes—
118#2416C2216yes—
119#2415C2216yes—
120#2415C2216yes—
121#2415C2216yes—
122#2415C2216yes—
123#2414C2216yes—
124#2407C2216yes—
125#2351C2212yes—
126#2351C2212yes—
127Q8×C4⋊C4C2211yescharacteristic
128Q8×C4⋊C4C2211yescharacteristic
129Q8×C4⋊C4C2212yes—
130#2349C2216yes—
131D4×C4⋊C4C2213yes—
132D4×C4⋊C4C2213yes—
133#2341C2212yes—
134Q8×C22⋊C4C2212yes—
135Q8×C22⋊C4C2212yes—
136Q8×C22⋊C4C2212yes—
137#2325C2216yes—
138#2325C2216yes—
139#2324C2216yes—
140#2324C2211yescharacteristic
141#2324C2213yes—
142#2323C2216yes—
143#2323C2213yes—
144#2323C2213yes—
145#2323C2216yes—
146#2316C2213yes—
147#2311C2213yes—
148#2311C2213yes—
149C4×C22⋊Q8C2213yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2216yes—
152C4×#121C2216yes—
153C4×#121C2216yes—
154C4×#121C2216yes—
155C4×#121C2213yes—
156C4×#121C2213yes—
157#2296C2216yes—
158#2285C2213yes—
159C2×C4×C4⋊C4C2213yes—
160C22×#41C2311yescharacteristic
161C22×#41C2313yes—
162C22×#41C2313yes—
163C22×#41C2311yescharacteristic
164C23×Q8C2311yescharacteristic
165C23×Q8C2312yes—
166#559—224no—
167#557—28no—
168#557—28no—
169#556—224no—
170#556—224no—
171#553—224no—
172#553—224no—
173#552—248no—
174#550—28no—
175D4×Q8—28no—
176D4×Q8—48no—
177#548—28no—
178#548—216no—
179#548—28no—
180#548—48no—
181#547—224no—
182#537—224no—
183#533—224no—
184#532—224no—
185C2×C4⋊Q8C2313yes—
186C2×C4⋊Q8C2313yes—
187C2×C4⋊Q8C2313yes—
188C2×C4⋊Q8C2316yes—
189C2×#127C2313yes—
190#529—224no—
191#529—248no—
192#529—224no—
193C2×#126C2316yes—
194C2×#126C23112yes—
195C2×#126C2316yes—
196C2×#125C2316yes—
197C2×#125C2313yes—
198C2×#125C2316yes—
199C2×#125C2313yes—
200C2×#124C2313yes—
201C2×#124C2316yes—
202C2×#124C2313yes—
203C2×#124C2316yes—
204C2×#124C2316yes—
205C2×#123C2316yes—
206C2×#123C23112yes—
207C2×#123C2316yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2313yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2313yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2316yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C2316yes—
220C2×#121C2313yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C2313yes—
225C2×#121C2316yes—
226C2×#121C2313yes—
227C2×#121C2316yes—
228C2×#121C2313yes—
229C2×#121C2313yes—
230C2×#121C2316yes—
231C2×#121C2311yescharacteristic
232C4×#41—28no—
233C4×#41—224no—
234C4×#41—224no—
235C4×#41—48no—
236C4×#41D4116yescomplemented
237C2×C4×Q8—28no—
238C2×C4×Q8—216no—
239C2×C4×Q8C2316yes—
240C2×C4×Q8C2313yes—
241C2×C4×Q8C2313yes—
242C2×C4×Q8C2313yes—
243C2×C4×Q8C2313yes—
244C2×C4×Q8C2313yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2316yes—
251C2×C4×Q8C2313yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4C2313yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2316yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2313yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2313yes—
272C2×C4×D4C2313yes—
273C2×#117C2313yes—
274C2×#117C2313yes—
275C2×#117C2311yescharacteristic
276C2×#117C2313yes—
277C2×#117C2316yes—
278C2×#117C2313yes—
279C2×#117C2316yes—
280C2×#117C2316yes—
281C2×#117C2313yes—
282C22×C4⋊C4C2313yes—
283C22×C4⋊C4C2316yes—
284C22×C4⋊C4C2313yes—
285C22×C4⋊C4C2313yes—
286C22×C42C2316yes—
287C22×C42C2313yes—
288C22×C42C2313yes—
289C22×C42C2316yes—
290C22×C42C2313yes—
291#400C23112yes—
292#400C23112yes—
293#399C23112yes—
294#398C23112yes—
295#398C23112yes—
296#398C23112yes—
297#398C23112yes—
298#398C23112yes—
299#397C23112yes—
300#397C23112yes—
301#397C23112yes—
302#397C23112yes—
303#396C23112yes—
304#396C23112yes—
305#396C23112yes—
306#396C23112yes—
307#395C23112yes—
308#394C23112yes—
309#394C23112yes—
310#394C23112yes—
311#394C23112yes—
312#394C23112yes—
313#394C23112yes—
314#392C23112yes—
315#391C2316yes—
316#391C2316yes—
317#391C2313yes—
318#391C2313yes—
319#391C2316yes—
320#391C2316yes—
321#391C2316yes—
322#391C2316yes—
323#391C2316yes—
324#391C2316yes—
325#390C2311yescharacteristic
326#390C2313yes—
327#390C2316yes—
328#390C2312yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#389C2311yescharacteristic
333#389C2313yes—
334#389C2313yes—
335#389C2316yes—
336#389C2313yes—
337#389C2316yes—
338#389C2316yes—
339#389C2316yes—
340#389C23112yes—
341#389C2316yes—
342#389C2316yes—
343#389C2316yes—
344#389C2316yes—
345#389C2316yes—
346#389C2316yes—
347#389C2316yes—
348#389C2316yes—
349#389C2316yes—
350#389C2316yes—
351#389C2316yes—
352#389C2316yes—
353#389C2316yes—
354#388C2316yes—
355#388C23112yes—
356#388C2312yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#388C23112yes—
364#388C23112yes—
365#387C2316yes—
366#387C23112yes—
367#387C2316yes—
368#387C2316yes—
369#387C2316yes—
370#387C23112yes—
371#386C2316yes—
372#386C2316yes—
373#386C2316yes—
374#386C2316yes—
375#386C2312yes—
376#386C2316yes—
377#386C2316yes—
378#386C2316yes—
379#386C23112yes—
380#386C23112yes—
381#386C23112yes—
382#385C2312yes—
383#385C2316yes—
384#385C2316yes—
385#385C2316yes—
386#385C23112yes—
387#385C23112yes—
388#385C23112yes—
389#384C2316yes—
390#384C2313yes—
391#384C2313yes—
392#382C2316yes—
393#382C2316yes—
394#380C2316yes—
395#380C2316yes—
396#380C2316yes—
397#380C2316yes—
398#380C2311yescharacteristic
399#380C2313yes—
400#380C2316yes—
401#380C2313yes—
402#380C2316yes—
403#380C2313yes—
404#380C2316yes—
405#380C2316yes—
406#380C2316yes—
407#380C2316yes—
408#380C2316yes—
409#380C2316yes—
410#380C2316yes—
411#380C23112yes—
412#380C23112yes—
413#380C2316yes—
414#380C2316yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2316yes—
417C4×C4⋊C4C2313yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2313yes—
420C4×C4⋊C4C2316yes—
421C4×C4⋊C4C2313yes—
422C4×C4⋊C4C2316yes—
423C4×C4⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C2×#95C2316yes—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—24no—
433C2×#41—24no—
434C2×#41—212no—
435C2×#41—212no—
436C2×#41—212no—
437C2×#41—212no—
438C2×#41—46no—
439C2×#41—46no—
440C2×#41C2×D418yes—
441C22×Q8—24no—
442C22×Q8—28no—
443C22×Q8—28no—
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8—28no—
447C22×Q8C2413yes—
448C22×Q8C2413yes—
449C22×Q8C2416yes—
450C22×Q8C2413yes—
451C22×Q8C2411yescharacteristic
452C22×D4C2413yes—
453C22×D4C2413yes—
454C22×D4C2413yes—
455C22×D4C2416yes—
456C22×D4C2413yes—
457C22×D4C2413yes—
458C22×D4C2411yescharacteristic
459C22×D4C2416yes—
460C22×D4C2416yes—
461C22×D4C2412yes—
462C23×C4C2413yes—
463C23×C4C2416yes—
464C23×C4C2413yes—
465C23×C4C2413yes—
466C23×C4C2416yes—
467C23×C4C2413yes—
468C23×C4C2413yes—
469C23×C4C2411yescharacteristic
470C23×C4C2413yes—
471C23×C4C2416yes—
472C23×C4C2413yes—
473C23×C4C2412yes—
474C23×C4C2416yes—
475C23×C4C2413yes—
476C4⋊Q8—212no—
477C4⋊Q8—212no—
478C4⋊Q8—212no—
479C4⋊Q8—412no—
480#127—212no—
481#126—248no—
482#126—224no—
483#126—224no—
484#125—224no—
485#125—212no—
486#125—212no—
487#125—224no—
488#124—224no—
489#124—212no—
490#124—224no—
491#124—212no—
492#124—412no—
493#123—224no—
494#123—248no—
495#123—224no—
496C22⋊Q8—212no—
497C22⋊Q8—224no—
498C22⋊Q8—224no—
499C22⋊Q8—212no—
500C22⋊Q8—212no—
501C22⋊Q8—224no—
502C22⋊Q8—212no—
503C22⋊Q8—224no—
504C22⋊Q8—412no—
505C22⋊Q8—412no—
506C22⋊Q8—412no—
507C22⋊Q8—412no—
508#121—224no—
509#121—212no—
510#121—212no—
511#121—212no—
512#121—224no—
513#121—224no—
514#121—212no—
515#121—212no—
516#121—224no—
517#121—224no—
518#121—412no—
519#121#4118yescomplemented
520C4×Q8—28no—
521C4×Q8—24no—
522C4×Q8—24no—
523C4×Q8—28no—
524C4×Q8—28no—
525C4×Q8—224no—
526C4×Q8—212no—
527C4×Q8—212no—
528C4×Q8—224no—
529C4×Q8—212no—
530C4×Q8—212no—
531C4×Q8—212no—
532C4×Q8—212no—
533C4×Q8C2×D418yes—
534C4×Q8C2×D418yes—
535C4×D4—224no—
536C4×D4—224no—
537C4×D4—212no—
538C4×D4—212no—
539C4×D4—212no—
540C4×D4—212no—
541C4×D4—224no—
542C4×D4—212no—
543C4×D4—24no—
544C4×D4—212no—
545C4×D4—212no—
546C4×D4—212no—
547C4×D4—212no—
548C4×D4—412no—
549C4×D4—412no—
550C4×D4—412no—
551C4×D4—412no—
552C4×D4C2×D4124yes—
553C4×D4C2×D4124yes—
554#117—212no—
555#117—212no—
556#117—224no—
557#117—212no—
558#117—24no—
559#117—212no—
560#117—224no—
561#117—412no—
562#117C2×D4124yes—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—212no—
565C2×C4⋊C4—212no—
566C2×C4⋊C4—46no—
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C24112yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C24112yes—
597C2×C4⋊C4C24112yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2413yes—
603C2×C4⋊C4C2413yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2411yescharacteristic
607C2×C22⋊C4C2411yescharacteristic
608C2×C22⋊C4C2413yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2413yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C24112yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C24112yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2412yes—
634C2×C42—224no—
635C2×C42—212no—
636C2×C42—212no—
637C2×C42—412no—
638C2×C42C2×D4124yes—
639C2×C42C2411yescharacteristic
640C2×C42C2413yes—
641C2×C42C2416yes—
642C2×C42C2413yes—
643C2×C42C2416yes—
644C2×C42C2413yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C2413yes—
648C2×C42C2416yes—
649C2×C42C2413yes—
650C2×C42C2416yes—
651C2×C42C2412yes—
652C2×C42C2411yescharacteristic
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656#95C2412yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2412yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2412yes—
669#95C2416yes—
670#95C2416yes—
671#95C24112yes—
672#95C2416yes—
673#95C24112yes—
674#95C24112yes—
675#95C24112yes—
676#95C24112yes—
677C24C2513yes—
678C24C2513yes—
679C24C2512yes—
680C24C2511yescharacteristic
681#41—232no—
682#41—448no—
683#41—448no—
684#41—416no—
685C2×Q8—26no—
686C2×Q8—212no—
687C2×Q8—26no—
688C2×Q8—26no—
689C2×Q8—26no—
690C2×Q8—26no—
691C2×Q8—212no—
692C2×Q8—26no—
693C2×Q8—26no—
694C2×Q8—212no—
695C2×Q8—26no—
696C2×Q8—43no—
697C2×Q8—416no—
698C2×Q8—432no—
699C2×Q8C22×D414yes—
700C2×Q8H(5,𝔽2)14yes—
701C2×Q82−1+414yes—
702C2×D4—26no—
703C2×D4—212no—
704C2×D4—26no—
705C2×D4—26no—
706C2×D4—26no—
707C2×D4—212no—
708C2×D4—212no—
709C2×D4—212no—
710C2×D4—22no—
711C2×D4—26no—
712C2×D4—26no—
713C2×D4—26no—
714C2×D4—26no—
715C2×D4—26no—
716C2×D4—26no—
717C2×D4—26no—
718C2×D4—22no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—43no—
722C2×D4—43no—
723C2×D4—46no—
724C2×D4—43no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—46no—
729C2×D4C22×D4112yes—
730C2×D4C2×#4114yes—
731C2×D4C2×#4118yes—
732C22×C4—22no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—22no—
738C22×C4—212no—
739C22×C4—24no—
740C22×C4—212no—
741C22×C4—26no—
742C22×C4—212no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—212no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—26no—
750C22×C4—212no—
751C22×C4—26no—
752C22×C4—26no—
753C22×C4—26no—
754C22×C4—26no—
755C22×C4—212no—
756C22×C4—43no—
757C22×C4—43no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—46no—
761C22×C4—46no—
762C22×C4—46no—
763C22×C4—46no—
764C22×C4—43no—
765C22×C4—43no—
766C22×C4—43no—
767C22×C4—43no—
768C22×C4—46no—
769C22×C4—46no—
770C22×C4C22×D4112yes—
771C22×C4C22×D4112yes—
772C22×C4C22×D4112yes—
773C22×C4C2×#4114yes—
774C22×C4C2512yes—
775C22×C4C2511yescharacteristic
776C22×C4C2516yes—
777C22×C4C2513yes—
778C22×C4C2516yes—
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C22×C4C2513yes—
782C22×C4C2516yes—
783C22×C4C2513yes—
784C22×C4C2516yes—
785C22×C4C2511yescharacteristic
786C22×C4C2513yes—
787C22×C4C2513yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2512yes—
791C22×C4C2511yescharacteristic
792C22×C4C2513yes—
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—224no—
796C4⋊C4—212no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—26no—
801C4⋊C4—212no—
802C4⋊C4—26no—
803C4⋊C4—26no—
804C4⋊C4—26no—
805C4⋊C4—26no—
806C4⋊C4—26no—
807C4⋊C4—212no—
808C4⋊C4—212no—
809C4⋊C4—212no—
810C4⋊C4—212no—
811C4⋊C4—212no—
812C4⋊C4—26no—
813C4⋊C4—212no—
814C4⋊C4—212no—
815C4⋊C4—212no—
816C4⋊C4—212no—
817C4⋊C4—22no—
818C4⋊C4—26no—
819C4⋊C4—46no—
820C4⋊C4—46no—
821C4⋊C4—46no—
822C4⋊C4—42no—
823C4⋊C4—46no—
824C4⋊C4—46no—
825C4⋊C4—46no—
826C4⋊C4—412no—
827C4⋊C4—412no—
828C4⋊C4C22×D4112yes—
829C4⋊C4C22×D4112yes—
830C4⋊C4C2×#4114yes—
831C22⋊C4—26no—
832C22⋊C4—26no—
833C22⋊C4—212no—
834C22⋊C4—224no—
835C22⋊C4—212no—
836C22⋊C4—212no—
837C22⋊C4—212no—
838C22⋊C4—24no—
839C22⋊C4—22no—
840C22⋊C4—22no—
841C22⋊C4—26no—
842C22⋊C4—212no—
843C22⋊C4—212no—
844C22⋊C4—26no—
845C22⋊C4—212no—
846C22⋊C4—212no—
847C22⋊C4—46no—
848C22⋊C4—42no—
849C22⋊C4—46no—
850C22⋊C4—42no—
851C22⋊C4—412no—
852C22⋊C4—42no—
853C22⋊C4—46no—
854C22⋊C4—46no—
855C22⋊C4—46no—
856C22⋊C4—412no—
857C22⋊C4—412no—
858C22⋊C4C22×D4124yes—
859C22⋊C4C2×#4118yes—
860C42—22no—
861C42—26no—
862C42—212no—
863C42—26no—
864C42—212no—
865C42—26no—
866C42—26no—
867C42—212no—
868C42—26no—
869C42—212no—
870C42—212no—
871C42—42no—
872C42—46no—
873C42C22×D4112yes—
874C42C22×D4112yes—
875C42C22×D414yes—
876C42C22×D4112yes—
877C23—22no—
878C23—21no—
879C23—23no—
880C23—21no—
881C23—22no—
882C23—23no—
883C23—22no—
884C23—21no—
885C23—23no—
886C23—23no—
887C23—21no—
888C23—22no—
889C23—22no—
890C23—21no—
891C23—21no—
892C23—23no—
893C23—23no—
894C23—22no—
895C23—23no—
896C23—23no—
897C23—23no—
898C23—23no—
899C23—23no—
900C23—23no—
901C23—23no—
902C23C23×D416yes—
903C23C22×#4112yes—
904C23C22×#4114yes—
905C23C2611yescharacteristic
906Q8—412no—
907Q8—412no—
908Q8—424no—
909Q8—412no—
910Q8#537116yescomplemented
911D4—224no—
912D4—28no—
913D4—48no—
914D4—412no—
915D4—412no—
916D4—412no—
917D4—424no—
918D4—412no—
919D4—812no—
920D4—812no—
921C2×C4—21no—
922C2×C4—23no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—23no—
927C2×C4—21no—
928C2×C4—23no—
929C2×C4—23no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—224no—
934C2×C4—224no—
935C2×C4—28no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—23no—
940C2×C4—23no—
941C2×C4—26no—
942C2×C4—23no—
943C2×C4—26no—
944C2×C4—26no—
945C2×C4—23no—
946C2×C4—26no—
947C2×C4—22no—
948C2×C4—26no—
949C2×C4—26no—
950C2×C4—26no—
951C2×C4—21no—
952C2×C4—23no—
953C2×C4—21no—
954C2×C4—23no—
955C2×C4—26no—
956C2×C4—26no—
957C2×C4—26no—
958C2×C4—22no—
959C2×C4—23no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—23no—
965C2×C4—22no—
966C2×C4—26no—
967C2×C4—21no—
968C2×C4—23no—
969C2×C4—412no—
970C2×C4—424no—
971C2×C4—48no—
972C2×C4—412no—
973C2×C4—424no—
974C2×C4—412no—
975C2×C4—412no—
976C2×C4—812no—
977C2×C4—86no—
978C2×C4—86no—
979C2×C4—812no—
980C2×C4C23×D412yes—
981C2×C4C23×D416yes—
982C2×C4C23×D416yes—
983C2×C4C23×D412yes—
984C2×C4C23×D416yes—
985C2×C4C23×D412yes—
986C2×C4C22×#4114yes—
987C2×C4C22×#4112yes—
988C2×C4C22×#4112yes—
989C2×C4C2×H(5,𝔽2)16yes—
990C2×C4C2×2−1+416yes—
991C2×C4#58512yes—
992C22—22no—
993C22—24no—
994C22—24no—
995C22—22no—
996C22—26no—
997C22—26no—
998C22—22no—
999C22—26no—
1000C22—24no—
1001C22—43no—
1002C22—43no—
1003C22—42no—
1004C22—41no—
1005C22—43no—
1006C22—41no—
1007C22—42no—
1008C22—42no—
1009C22—41no—
1010C22—41no—
1011C22—42no—
1012C22—43no—
1013C22—43no—
1014C22—43no—
1015C22—43no—
1016C22—43no—
1017C22—43no—
1018C22—43no—
1019C22—43no—
1020C22C24×D411yescharacteristic
1021C22C23×#4111yescharacteristic
1022C22C22×H(5,𝔽2)11yescharacteristic
1023C22C22×2−1+411yescharacteristic
1024C22C2×#58511yescharacteristic
1025C222−1+611yescharacteristic
1026C222−1+611yescharacteristic
1027C4—24no—
1028C4—22no—
1029C4—26no—
1030C4—22no—
1031C4—26no—
1032C4—22no—
1033C4—46no—
1034C4—42no—
1035C4—41no—
1036C4—43no—
1037C4—46no—
1038C4—42no—
1039C4—41no—
1040C4—43no—
1041C4—46no—
1042C4—43no—
1043C4—46no—
1044C4C2×#537112yes—
1045C4D4×#4114yes—
1046C2—42no—
1047C2—44no—
1048C2—46no—
1049C2—83no—
1050C2C22×#53711yescharacteristic
1051C2C2×D4×#4111yescharacteristic
1052C2#6285911yescharacteristic
1053C2#6292211yescharacteristic
1054C2#6295311yescharacteristic
1055C2#6298411yescharacteristic
1056C2#6300111yescharacteristic
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×#3482C2semidirect
2. C2×#3480C2semidirect
3. #39962C2semidirect
4. #39959C2semidirect
5. #39857C2semidirect
6. #39856C2semidirect
7. #39468C2semidirect
8. #39340C2semidirect
9. #38923C2semidirect
10. #38908C2semidirect
11. #36577C2semidirect
12. Q8×#121C2semidirect
13. #36445C2semidirect
14. #36444C2semidirect
15. #36444C2semidirect
16. #36435C2semidirect
17. #36434C2semidirect
18. #36430C2semidirect
19. #35297C2semidirect
20. #35241C2semidirect
21. #35189C2semidirect
22. C4⋊C4×#41C2semidirect
23. C4×#537C2semidirect
236. C4×#41D4semidirect
519. #121#41semidirect
910. Q8#537semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
C2×#34802
#399622
#399592
#398572
#398562
#394682
#393402
#389232
#389082
#365772
Q8×#1212
#364452
#364442
#364352
#364342
#364302
#352972
#352412
#351892
C4⋊C4×#412
C4×#5372