Finite Group Databasebeta

← #7626922

Subgroups — #7626922

Order 512.

7524 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic
2#34494C213yesmaximal, complemented
3#34483C216yesmaximal, complemented
4#34480C213yesmaximal, complemented
5#34461C216yesmaximal, complemented
6#34431C216yesmaximal, complemented
7#34418C216yesmaximal, complemented
8#34393C213yesmaximal, complemented
9#34384C213yesmaximal, complemented
10#34337C211yesmaximal, characteristic, complemented
11#34313C212yesmaximal, complemented
12#34313C213yesmaximal, complemented
13#34313C211yesmaximal, characteristic, complemented
14#34308C213yesmaximal, complemented
15#34295C212yesmaximal, complemented
16#34263C212yesmaximal, complemented
17#34250C212yesmaximal, complemented
18#34207C213yesmaximal, complemented
19#34183C211yesmaximal, characteristic, complemented
20C4×#557C211yesmaximal, characteristic, complemented
21C4×#550C211yesmaximal, characteristic, complemented
22#34125C211yesmaximal, characteristic, complemented
23#34084C213yesmaximal, complemented
24#3517C4132yescomplemented
25C2×#557C2211yescharacteristic
26C2×#553C2216yes—
27C2×#550C2211yescharacteristic
28C2×#550C2213yes—
29C2×#550C2212yes—
30C2×#547C2213yes—
31C2×#540C2216yes—
32C2×#532C2213yes—
33C2×#529C2213yes—
34C2×#520C2216yes—
35C2×#520C2212yes—
36C2×#520C2212yes—
37C2×#520C2212yes—
38C2×C4×#41C2212yes—
39C2×C4×#41C2211yescharacteristic
40#2383C22112yes—
41#2377C22112yes—
42#2377C22112yes—
43#2376C22112yes—
44#2370C2216yes—
45#2370C2216yes—
46#2366C2213yes—
47#2366C2216yes—
48#2366C2216yes—
49#2366C2213yes—
50#2365C2213yes—
51#2365C2213yes—
52#2363C2216yes—
53#2363C2216yes—
54#2361C2216yes—
55#2361C2216yes—
56#2361C22112yes—
57#2361C2216yes—
58#2361C2216yes—
59#2361C2216yes—
60#2361C2216yes—
61#2361C2216yes—
62#2360C2216yes—
63#2359C22112yes—
64#2357C2213yes—
65#2357C2213yes—
66#2357C2216yes—
67#2355C2213yes—
68#2354C2213yes—
69#2354C2216yes—
70#2354C2216yes—
71#2352C2216yes—
72#2351C2211yescharacteristic
73#2351C2211yescharacteristic
74#2351C2212yes—
75Q8×C4⋊C4C2213yes—
76Q8×C4⋊C4C2212yes—
77Q8×C4⋊C4C2211yescharacteristic
78Q8×C4⋊C4C2211yescharacteristic
79Q8×C4⋊C4C2212yes—
80#2349C2216yes—
81#2349C2216yes—
82D4×C4⋊C4C2213yes—
83D4×C4⋊C4C2213yes—
84D4×C4⋊C4C2216yes—
85D4×C4⋊C4C2213yes—
86D4×C4⋊C4C2216yes—
87D4×C4⋊C4C2216yes—
88D4×C4⋊C4C2216yes—
89D4×C4⋊C4C2216yes—
90#2347C2213yes—
91#2347C2213yes—
92#2345C2216yes—
93#2344C2216yes—
94#2341C2211yescharacteristic
95#2341C2216yes—
96#2341C2212yes—
97#2341C2212yes—
98#2341C2211yescharacteristic
99#2339C2216yes—
100#2335C2216yes—
101#2335C2216yes—
102#2335C22112yes—
103#2334C2216yes—
104#2334C2216yes—
105#2330C2216yes—
106#2330C2211yescharacteristic
107#2330C2213yes—
108#2328C2216yes—
109#2326C2213yes—
110#2326C2213yes—
111#2326C2216yes—
112#2325C22112yes—
113#2324C2213yes—
114#2324C2216yes—
115#2324C2216yes—
116#2324C2216yes—
117#2324C22112yes—
118#2324C2213yes—
119#2324C2216yes—
120#2323C2213yes—
121#2323C2213yes—
122#2322C22112yes—
123#2322C22112yes—
124#2319C2216yes—
125#2318C22112yes—
126#2317C2216yes—
127#2317C2216yes—
128#2316C2216yes—
129#2314C2216yes—
130#2311C2216yes—
131C4×C4⋊Q8C2213yes—
132C4×C4⋊Q8C2213yes—
133C4×#127C2216yes—
134C4×#127C2213yes—
135C4×#127C2213yes—
136C4×#125C2216yes—
137C4×#121C2216yes—
138C4×#121C2216yes—
139#2298C2216yes—
140#2296C2216yes—
141#2295C2213yes—
142#2293C2213yes—
143#2293C2213yes—
144#2293C2216yes—
145#2293C2216yes—
146#2293C2213yes—
147C2×#389C2216yes—
148#2290C2216yes—
149#2285C2213yes—
150C2×#384C2213yes—
151#2283C2213yes—
152#2276C2212yes—
153C42×Q8C2211yescharacteristic
154C42×Q8C2213yes—
155C42×Q8C2212yes—
156C42×Q8C2211yescharacteristic
157C42×D4C2213yes—
158C4×#117C2213yes—
159C22×#41C2312yes—
160C22×#41C2311yescharacteristic
161C22×#41C2316yes—
162#557C2×C4116yescomplemented
163#553C2×C4196yescomplemented
164#550C2×C4148yescomplemented
165#550C2×C4116yescomplemented
166#550C2×C4132yescomplemented
167#547C2×C4148yescomplemented
168#540C2×C4196yescomplemented
169#532C2×C4148yescomplemented
170C2×C4⋊Q8C2313yes—
171C2×#127C2313yes—
172C2×#127C2316yes—
173#529C2×C4148yescomplemented
174C2×#126C2316yes—
175C2×#125C2316yes—
176C2×#125C2311yescharacteristic
177C2×#124C2313yes—
178C2×#123C2316yes—
179C2×#123C23112yes—
180C2×C22⋊Q8C2313yes—
181C2×#121C2313yes—
182C2×#121C2316yes—
183C2×#121C23112yes—
184C2×#121C2316yes—
185C2×#121C2316yes—
186C2×#121C2316yes—
187#520—424no—
188#520—48no—
189#520—48no—
190#520C2×C4132yescomplemented
191C4×#41—48no—
192C4×#41C2×C4116yescomplemented
193C2×C4×Q8C2313yes—
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2311yescharacteristic
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2311yescharacteristic
200C2×C4×Q8C2316yes—
201C2×C4×Q8C2313yes—
202C2×C4×Q8C2311yescharacteristic
203C2×C4×Q8C2311yescharacteristic
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2313yes—
206C2×C4×D4C2313yes—
207C2×C4×D4C2316yes—
208C2×C4×D4C2316yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C23112yes—
211C2×C4×D4C2316yes—
212C2×C4×D4C2316yes—
213C2×C4×D4C23112yes—
214C2×C4×D4C2313yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C23112yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C2316yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2313yes—
224C2×C4×D4C2316yes—
225C2×C4×D4C2316yes—
226C2×C4×D4C2313yes—
227C2×#117C2313yes—
228C2×#117C2313yes—
229C2×#117C2316yes—
230C2×#117C2316yes—
231C2×#117C2316yes—
232C2×#117C23112yes—
233C2×#117C2316yes—
234C2×#117C2313yes—
235C22×C4⋊C4C2316yes—
236C22×C4⋊C4C2316yes—
237C22×C4⋊C4C2316yes—
238C22×C4⋊C4C23112yes—
239C22×C4⋊C4C2316yes—
240C22×C4⋊C4C2316yes—
241C22×C42C2316yes—
242C22×C42C2313yes—
243#391C2313yes—
244#391C2316yes—
245#391C2313yes—
246#390C2313yes—
247#390C2316yes—
248#390C2316yes—
249#390C2313yes—
250#390C2316yes—
251#390C2316yes—
252#390C23112yes—
253#390C2316yes—
254#390C2316yes—
255#390C2316yes—
256#390C23112yes—
257#390C2316yes—
258#390C2313yes—
259#390C2313yes—
260#390C2316yes—
261#390C2313yes—
262#390C2313yes—
263#389C2316yes—
264#389C2316yes—
265#389C2316yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2316yes—
270#389C2313yes—
271#389C2316yes—
272#389C23112yes—
273#389C2316yes—
274#389C2316yes—
275#389C2316yes—
276#389C2313yes—
277#389C2316yes—
278#389C23112yes—
279#389C2311yescharacteristic
280#389C2313yes—
281#389C2311yescharacteristic
282#389C2316yes—
283#389C2313yes—
284#389C2312yes—
285#389C2316yes—
286#389C2312yes—
287#389C2313yes—
288#389C2313yes—
289#388C23112yes—
290#388C23112yes—
291#388C2316yes—
292#388C23112yes—
293#388C2316yes—
294#388C2316yes—
295#388C2316yes—
296#388C23112yes—
297#388C2316yes—
298#388C2316yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C2316yes—
304#388C2316yes—
305#388C2316yes—
306#388C2316yes—
307#388C2316yes—
308#388C2316yes—
309#387C23112yes—
310#387C23112yes—
311#387C2316yes—
312#387C23112yes—
313#387C23112yes—
314#387C2316yes—
315#387C2316yes—
316#387C2316yes—
317#387C2312yes—
318#387C2316yes—
319#387C2312yes—
320#387C2316yes—
321#386C23112yes—
322#386C23112yes—
323#386C23112yes—
324#386C23112yes—
325#386C23112yes—
326#386C23112yes—
327#386C2316yes—
328#386C23112yes—
329#386C2316yes—
330#385C23112yes—
331#385C23112yes—
332#385C23112yes—
333#385C23112yes—
334#385C2316yes—
335#385C23112yes—
336#385C23112yes—
337#385C23112yes—
338#385C2316yes—
339#385C2316yes—
340#385C2316yes—
341#385C2316yes—
342#385C2316yes—
343#384C2313yes—
344#384C2313yes—
345#384C2316yes—
346#384C2316yes—
347#384C2316yes—
348#384C2313yes—
349#384C2311yescharacteristic
350#383C2316yes—
351#382C2316yes—
352#382C2313yes—
353#382C2316yes—
354#382C2313yes—
355#381C23112yes—
356#381C2316yes—
357#380C23112yes—
358#380C23112yes—
359#380C2316yes—
360#380C2316yes—
361#380C23112yes—
362#380C2313yes—
363#380C2313yes—
364#380C2313yes—
365#380C2313yes—
366#380C2316yes—
367C4×C4⋊C4C2316yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2311yescharacteristic
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2311yescharacteristic
378C4×C4⋊C4C2316yes—
379C4×C4⋊C4C2313yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2316yes—
382C4×C4⋊C4C2313yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2316yes—
386C4×C4⋊C4C2313yes—
387C4×C4⋊C4C2313yes—
388C4×C4⋊C4C2316yes—
389C4×C4⋊C4C2313yes—
390C4×C4⋊C4C2313yes—
391C4×C4⋊C4C2313yes—
392C4×C4⋊C4C2316yes—
393C4×C4⋊C4C2316yes—
394C4×C4⋊C4C2313yes—
395C4×C4⋊C4C2313yes—
396C4×C22⋊C4C23112yes—
397C4×C22⋊C4C2316yes—
398C4×C22⋊C4C23112yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C2313yes—
401C4×C22⋊C4C2313yes—
402C4×C22⋊C4C2316yes—
403C4×C22⋊C4C2316yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C2313yes—
406C4×C22⋊C4C2313yes—
407#376C2316yes—
408#376C2311yescharacteristic
409#376C2313yes—
410C2×#95C23112yes—
411C43C2316yes—
412C43C2313yes—
413C43C2313yes—
414C2×#41—28no—
415C2×#41—24no—
416C2×#41—28no—
417C2×#41—24no—
418C2×#41—412no—
419C2×#41—412no—
420C2×#41C22×C418yes—
421C2×#41C22×C4116yes—
422C2×#41C22×C4148yes—
423C22×Q8C2413yes—
424C22×Q8C2411yescharacteristic
425C22×D4C2413yes—
426C22×D4C2416yes—
427C22×D4C2413yes—
428C22×D4C2416yes—
429C22×D4C2416yes—
430C22×D4C24112yes—
431C23×C4C2416yes—
432C23×C4C2413yes—
433C23×C4C2413yes—
434C23×C4C2416yes—
435C23×C4C24112yes—
436C23×C4C24112yes—
437C23×C4C2416yes—
438C23×C4C24112yes—
439C23×C4C2413yes—
440C4⋊Q8C22×C4124yes—
441#127C22×C4124yes—
442#127C22×C4148yes—
443#126C22×C4148yes—
444#125C22×C418yes—
445#125C22×C4148yes—
446#124C22×C4124yes—
447#123C22×C4148yes—
448#123C22×C4196yes—
449C22⋊Q8C22×C4124yes—
450#121C22×C4124yes—
451#121C22×C4148yes—
452#121C22×C4148yes—
453#121C22×C4148yes—
454#121C22×C4196yes—
455#121C22×C4148yes—
456C4×Q8—24no—
457C4×Q8—28no—
458C4×Q8—24no—
459C4×Q8—28no—
460C4×Q8—24no—
461C4×Q8—24no—
462C4×Q8—212no—
463C4×Q8—46no—
464C4×Q8—412no—
465C4×Q8C22×C418yes—
466C4×Q8C22×C418yes—
467C4×Q8C22×C4116yes—
468C4×Q8C22×C4124yes—
469C4×D4—212no—
470C4×D4—424no—
471C4×D4—46no—
472C4×D4—412no—
473C4×D4—412no—
474C4×D4—412no—
475C4×D4—412no—
476C4×D4—412no—
477C4×D4—412no—
478C4×D4—412no—
479C4×D4—424no—
480C4×D4—86no—
481C4×D4—86no—
482C4×D4—812no—
483C4×D4C22×C4124yes—
484C4×D4C22×C4124yes—
485C4×D4C22×C4148yes—
486C4×D4C22×C4148yes—
487C4×D4C22×C4124yes—
488C4×D4C22×C4148yes—
489C4×D4C22×C4148yes—
490#117—212no—
491#117—46no—
492#117—412no—
493#117—412no—
494#117—424no—
495#117—412no—
496#117C22×C4124yes—
497#117C22×C4148yes—
498C2×C4⋊C4—424no—
499C2×C4⋊C4—412no—
500C2×C4⋊C4—412no—
501C2×C4⋊C4—412no—
502C2×C4⋊C4—86no—
503C2×C4⋊C4C22×C4148yes—
504C2×C4⋊C4C2413yes—
505C2×C4⋊C4C2413yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2413yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2413yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2413yes—
512C2×C4⋊C4C2413yes—
513C2×C4⋊C4C2411yescharacteristic
514C2×C4⋊C4C2411yescharacteristic
515C2×C4⋊C4C2413yes—
516C2×C4⋊C4C2413yes—
517C2×C4⋊C4C24112yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C2416yes—
521C2×C4⋊C4C24112yes—
522C2×C4⋊C4C2416yes—
523C2×C4⋊C4C2416yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2413yes—
527C2×C4⋊C4C2413yes—
528C2×C4⋊C4C2416yes—
529C2×C4⋊C4C2416yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2413yes—
533C2×C4⋊C4C2416yes—
534C2×C4⋊C4C2416yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2413yes—
537C2×C4⋊C4C2411yescharacteristic
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2416yes—
540C2×C4⋊C4C2411yescharacteristic
541C2×C4⋊C4C2416yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2413yes—
544C2×C22⋊C4C2413yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C24112yes—
547C2×C22⋊C4C2416yes—
548C2×C22⋊C4C2416yes—
549C2×C22⋊C4C2416yes—
550C2×C22⋊C4C24112yes—
551C2×C22⋊C4C2413yes—
552C2×C22⋊C4C2413yes—
553C2×C22⋊C4C2416yes—
554C2×C22⋊C4C24112yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C2416yes—
557C2×C22⋊C4C2416yes—
558C2×C22⋊C4C2416yes—
559C2×C22⋊C4C2416yes—
560C2×C22⋊C4C2416yes—
561C2×C22⋊C4C2416yes—
562C2×C22⋊C4C2416yes—
563C2×C22⋊C4C2416yes—
564C2×C22⋊C4C2416yes—
565C2×C42—412no—
566C2×C42C22×C4124yes—
567C2×C42C2411yescharacteristic
568C2×C42C2413yes—
569C2×C42C2416yes—
570C2×C42C2416yes—
571C2×C42C2413yes—
572C2×C42C2416yes—
573C2×C42C2413yes—
574C2×C42C2413yes—
575C2×C42C2413yes—
576C2×C42C2413yes—
577C2×C42C2416yes—
578C2×C42C24112yes—
579C2×C42C2413yes—
580C2×C42C2413yes—
581C2×C42C2416yes—
582C2×C42C2416yes—
583C2×C42C2412yes—
584C2×C42C2413yes—
585C2×C42C2413yes—
586C2×C42C2412yes—
587C2×C42C2413yes—
588C2×C42C2413yes—
589C2×C42C2416yes—
590C2×C42C2413yes—
591C2×C42C2411yescharacteristic
592C2×C42C2411yescharacteristic
593#95C2416yes—
594#95C2416yes—
595#95C2416yes—
596#95C24112yes—
597#95C2412yes—
598#95C2411yescharacteristic
599#95C2411yescharacteristic
600#95C2411yescharacteristic
601#95C2411yescharacteristic
602#95C2413yes—
603#95C2413yes—
604#95C2413yes—
605#95C2413yes—
606#95C2416yes—
607#95C2416yes—
608#95C2416yes—
609#95C2412yes—
610#95C2416yes—
611#95C2416yes—
612#95C2412yes—
613#95C2416yes—
614#95C2416yes—
615#95C2416yes—
616#95C2412yes—
617#95C2416yes—
618#95C24112yes—
619#95C2416yes—
620#95C2416yes—
621#95C2416yes—
622#95C2416yes—
623C24C2513yes—
624C24C2516yes—
625#41—264no—
626#41—232no—
627#41—496no—
628C2×Q8—26no—
629C2×Q8—26no—
630C2×Q8C23×C4112yes—
631C2×Q8C23×C414yes—
632C2×Q8H(5,𝔽2)14yes—
633C2×Q82−1+414yes—
634C2×D4—26no—
635C2×D4—212no—
636C2×D4—26no—
637C2×D4—26no—
638C2×D4—212no—
639C2×D4—26no—
640C2×D4—412no—
641C2×D4—46no—
642C2×D4—46no—
643C2×D4—46no—
644C2×D4—46no—
645C2×D4—412no—
646C2×D4C23×C4112yes—
647C2×D4C23×C4124yes—
648C2×D4C23×C4112yes—
649C2×D4C23×C4124yes—
650C2×D4C23×C4124yes—
651C2×D4C23×C4148yes—
652C22×C4—212no—
653C22×C4—26no—
654C22×C4—26no—
655C22×C4—212no—
656C22×C4—26no—
657C22×C4—26no—
658C22×C4—212no—
659C22×C4—412no—
660C22×C4—43no—
661C22×C4—43no—
662C22×C4—412no—
663C22×C4—46no—
664C22×C4—46no—
665C22×C4—46no—
666C22×C4—46no—
667C22×C4—46no—
668C22×C4—412no—
669C22×C4—412no—
670C22×C4—412no—
671C22×C4—412no—
672C22×C4—412no—
673C22×C4—412no—
674C22×C4C23×C4112yes—
675C22×C4C23×C4112yes—
676C22×C4C23×C4124yes—
677C22×C4C23×C4112yes—
678C22×C4C23×C4148yes—
679C22×C4C2512yes—
680C22×C4C2513yes—
681C22×C4C2511yescharacteristic
682C22×C4C2513yes—
683C22×C4C2513yes—
684C22×C4C2511yescharacteristic
685C22×C4C2512yes—
686C22×C4C2513yes—
687C22×C4C2516yes—
688C22×C4C2516yes—
689C22×C4C2512yes—
690C22×C4C2513yes—
691C22×C4C2516yes—
692C22×C4C2512yes—
693C22×C4C2511yescharacteristic
694C22×C4C2511yescharacteristic
695C22×C4C2513yes—
696C22×C4C2511yescharacteristic
697C22×C4C2511yescharacteristic
698C22×C4C2513yes—
699C22×C4C2511yescharacteristic
700C4⋊C4—26no—
701C4⋊C4—26no—
702C4⋊C4—212no—
703C4⋊C4—26no—
704C4⋊C4—212no—
705C4⋊C4—26no—
706C4⋊C4—212no—
707C4⋊C4—26no—
708C4⋊C4—26no—
709C4⋊C4—26no—
710C4⋊C4—26no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—46no—
714C4⋊C4—412no—
715C4⋊C4—46no—
716C4⋊C4—412no—
717C4⋊C4—46no—
718C4⋊C4—46no—
719C4⋊C4—46no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—43no—
723C4⋊C4—43no—
724C4⋊C4—42no—
725C4⋊C4—42no—
726C4⋊C4—46no—
727C4⋊C4—46no—
728C4⋊C4C23×C4112yes—
729C4⋊C4C23×C4124yes—
730C4⋊C4C23×C4124yes—
731C4⋊C4C23×C418yes—
732C4⋊C4C23×C4112yes—
733C4⋊C4C23×C414yes—
734C4⋊C4C23×C418yes—
735C4⋊C4C23×C4124yes—
736C4⋊C4C23×C414yes—
737C4⋊C4C23×C4124yes—
738C22⋊C4—26no—
739C22⋊C4—26no—
740C22⋊C4—212no—
741C22⋊C4—46no—
742C22⋊C4—46no—
743C22⋊C4—43no—
744C22⋊C4—43no—
745C22⋊C4—46no—
746C22⋊C4—46no—
747C22⋊C4—46no—
748C22⋊C4—46no—
749C22⋊C4—412no—
750C22⋊C4—412no—
751C22⋊C4—46no—
752C22⋊C4—46no—
753C22⋊C4—46no—
754C22⋊C4—412no—
755C22⋊C4C23×C4124yes—
756C22⋊C4C23×C4124yes—
757C22⋊C4C23×C4124yes—
758C22⋊C4C23×C4124yes—
759C22⋊C4C23×C4124yes—
760C22⋊C4C23×C4124yes—
761C42—26no—
762C42—212no—
763C42—26no—
764C42—212no—
765C42—26no—
766C42—212no—
767C42—26no—
768C42—26no—
769C42—22no—
770C42—26no—
771C42—42no—
772C42—46no—
773C42—43no—
774C42—42no—
775C42—43no—
776C42—412no—
777C42—46no—
778C42—43no—
779C42—43no—
780C42—46no—
781C42C23×C414yes—
782C42C23×C4112yes—
783C42C23×C4112yes—
784C42C23×C4112yes—
785C42C23×C4124yes—
786C42H(5,𝔽2)14yes—
787C23—23no—
788C23—26no—
789C23—26no—
790C23—23no—
791C23—23no—
792C23—26no—
793C23—23no—
794C23—26no—
795C23—26no—
796C23—23no—
797C23—23no—
798C23—26no—
799C23C24×C416yes—
800C23C24×C4112yes—
801C23C2611yescharacteristic
802Q8—224no—
803Q8#520116yescomplemented
804D4—248no—
805D4—224no—
806D4—224no—
807D4—424no—
808D4—424no—
809D4—448no—
810C2×C4—21no—
811C2×C4—26no—
812C2×C4—22no—
813C2×C4—23no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—26no—
819C2×C4—23no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—23no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—23no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—248no—
829C2×C4—224no—
830C2×C4—224no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—22no—
834C2×C4—23no—
835C2×C4—23no—
836C2×C4—26no—
837C2×C4—23no—
838C2×C4—23no—
839C2×C4—26no—
840C2×C4—26no—
841C2×C4—26no—
842C2×C4—21no—
843C2×C4—23no—
844C2×C4—23no—
845C2×C4—23no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—23no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—23no—
853C2×C4—23no—
854C2×C4—26no—
855C2×C4—26no—
856C2×C4—21no—
857C2×C4—23no—
858C2×C4—22no—
859C2×C4—23no—
860C2×C4—22no—
861C2×C4—412no—
862C2×C4—448no—
863C2×C4—812no—
864C2×C4—812no—
865C2×C4—1612no—
866C2×C4—1612no—
867C2×C4C24×C412yes—
868C2×C4C24×C412yes—
869C2×C4C24×C414yes—
870C2×C4C24×C416yes—
871C2×C4C24×C416yes—
872C2×C4C24×C4112yes—
873C2×C4C24×C414yes—
874C2×C4C24×C416yes—
875C2×C4C24×C412yes—
876C2×C4C2×H(5,𝔽2)12yes—
877C2×C4C2×H(5,𝔽2)12yes—
878C2×C4C2×H(5,𝔽2)16yes—
879C2×C4C2×H(5,𝔽2)12yes—
880C2×C4C2×2−1+416yes—
881C2×C4#58512yes—
882C22—26no—
883C22—212no—
884C22—26no—
885C22—212no—
886C22—26no—
887C22—212no—
888C22—46no—
889C22—43no—
890C22—46no—
891C22—43no—
892C22—43no—
893C22—46no—
894C22—43no—
895C22—46no—
896C22C25×C411yescharacteristic
897C22C22×H(5,𝔽2)11yescharacteristic
898C22C22×H(5,𝔽2)11yescharacteristic
899C22C22×2−1+411yescharacteristic
900C22C2×#58511yescharacteristic
901C22H(7,𝔽2)11yescharacteristic
902C222−1+611yescharacteristic
903C4—24no—
904C4—22no—
905C4—26no—
906C4—212no—
907C4—22no—
908C4—26no—
909C4—24no—
910C4—22no—
911C4—22no—
912C4—46no—
913C4—43no—
914C4—46no—
915C4—41no—
916C4—42no—
917C4—43no—
918C4—42no—
919C4—43no—
920C4—41no—
921C4—43no—
922C4C2×#520112yes—
923C4C4×H(5,𝔽2)14yes—
924C2—46no—
925C2—412no—
926C2C22×#52011yescharacteristic
927C2C2×C4×H(5,𝔽2)11yescharacteristic
928C2#6265411yescharacteristic
929C2#6291611yescharacteristic
930C2#6292211yescharacteristic
931C2#6294611yescharacteristic
932C2#6295211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3517C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34494C2semidirect
3. #34483C2semidirect
4. #34480C2semidirect
5. #34461C2semidirect
6. #34431C2semidirect
7. #34418C2semidirect
8. #34393C2semidirect
9. #34384C2semidirect
10. #34337C2semidirect
11. #34313C2semidirect
12. #34313C2semidirect
13. #34313C2semidirect
14. #34308C2semidirect
15. #34295C2semidirect
16. #34263C2semidirect
17. #34250C2semidirect
18. #34207C2semidirect
19. #34183C2semidirect
20. C4×#557C2semidirect
21. C4×#550C2semidirect
22. #34125C2semidirect
23. #34084C2semidirect
24. #3517C4semidirect
162. #557C2×C4semidirect
163. #553C2×C4semidirect
164. #550C2×C4semidirect
165. #550C2×C4semidirect
166. #550C2×C4semidirect
167. #547C2×C4semidirect
168. #540C2×C4semidirect
169. #532C2×C4semidirect
173. #529C2×C4semidirect
190. #520C2×C4semidirect
192. C4×#41C2×C4semidirect
803. Q8#520semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
#344942
#344832
#344802
#344612
#344312
#344182
#343932
#343842
#343372
#343132
#343082
#342952
#342632
#342502
#342072
#341832
C4×#5572
C4×#5502
#341252
#340842