Finite Group Databasebeta

← #6857294

Subgroups — #6857294

Order 512.

1408 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39823C211yesmaximal, characteristic
2#39819C211yesmaximal, characteristic, complemented
3#33188C211yesmaximal, characteristic, complemented
4#32404C211yesmaximal, characteristic, complemented
5#32397C211yesmaximal, characteristic, complemented
6#32175C211yesmaximal, characteristic, complemented
7#32166C211yesmaximal, characteristic, complemented
8#31578C211yesmaximal, characteristic, complemented
9#31571C211yesmaximal, characteristic, complemented
10#30762C211yesmaximal, characteristic, complemented
11#30757C211yesmaximal, characteristic, complemented
12#30254C211yesmaximal, characteristic
13#30244C211yesmaximal, characteristic, complemented
14#28590C211yesmaximal, characteristic, complemented
15#28588C211yesmaximal, characteristic, complemented
16#28587C211yesmaximal, characteristic
17#28583C211yesmaximal, characteristic, complemented
18#27501C211yesmaximal, characteristic, complemented
19#27496C211yesmaximal, characteristic, complemented
20#27219C211yesmaximal, characteristic, complemented
21#27216C211yesmaximal, characteristic, complemented
22#27084C211yesmaximal, characteristic, complemented
23#27081C211yesmaximal, characteristic, complemented
24#26589C211yesmaximal, characteristic, complemented
25#26586C211yesmaximal, characteristic, complemented
26#24759C211yesmaximal, characteristic, complemented
27#24757C211yesmaximal, characteristic, complemented
28#22192C211yesmaximal, characteristic, complemented
29#22180C211yesmaximal, characteristic, complemented
30#21523C211yesmaximal, characteristic, complemented
31#21027C211yesmaximal, characteristic, complemented
32C2×#497C2211yescharacteristic
33C2×#470C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#464C2211yescharacteristic
43C2×#461C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45C2×#423C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2857C2211yescharacteristic
48#2850C2211yescharacteristic
49#2802—21no—
50#2800—21no—
51#2797—21no—
52#2787—21no—
53#2776—21no—
54#2770—21no—
55#2757—21no—
56#2749—21no—
57#2621C2211yescharacteristic
58#2621C2211yescharacteristic
59#2620C2211yescharacteristic
60#2619C2211yescharacteristic
61#2606—21no—
62#2603—21no—
63#2600—21no—
64#2590—21no—
65#2577—21no—
66#2570C2211yescharacteristic
67#2570C2211yescharacteristic
68#2548C2211yescharacteristic
69#2546C2211yescharacteristic
70#2530—21no—
71#2526—21no—
72#2514C2211yescharacteristic
73#2513C2211yescharacteristic
74#2512C2211yescharacteristic
75#2511C2211yescharacteristic
76#2466—21no—
77#2447C2211yescharacteristic
78#2447C2211yescharacteristic
79#2446C2211yescharacteristic
80#2446C2211yescharacteristic
81#2366C2211yescharacteristic
82#2365C2211yescharacteristic
83#2356C2211yescharacteristic
84#2356C2211yescharacteristic
85#2324C2211yescharacteristic
86#2323C2211yescharacteristic
87#2323C2211yescharacteristic
88#2323C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C4×#121C2211yescharacteristic
91#2296C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2093C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2083C2211yescharacteristic
104#2074C2211yescharacteristic
105#2074C2211yescharacteristic
106#2073C2211yescharacteristic
107#2072C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2065C2211yescharacteristic
112#2056C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2043C2211yescharacteristic
117#2043C2211yescharacteristic
118#2042C2211yescharacteristic
119#2041C2211yescharacteristic
120#2016C2211yescharacteristic
121#2016C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2013C2211yescharacteristic
129#2013C2211yescharacteristic
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic
132#1983C2211yescharacteristic
133#1981C2211yescharacteristic
134#1973C2211yescharacteristic
135#1971C2211yescharacteristic
136#1969C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1958C2211yescharacteristic
140#1956C2211yescharacteristic
141#1949C2211yescharacteristic
142#1947C2211yescharacteristic
143#1941C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1917C2211yescharacteristic
163#1917C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1895C2211yescharacteristic
171#1894C2211yescharacteristic
172#1894C2211yescharacteristic
173#1894C2211yescharacteristic
174#1893C2211yescharacteristic
175#1892C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1878C2211yescharacteristic
184#1878C2211yescharacteristic
185#1877C2211yescharacteristic
186#1877C2211yescharacteristic
187#1877C2211yescharacteristic
188#1865C2211yescharacteristic
189#1865C2211yescharacteristic
190#1865C2211yescharacteristic
191#1864C2211yescharacteristic
192#1847C2211yescharacteristic
193#1807C2211yescharacteristic
194#1805C2211yescharacteristic
195#1802C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1763C2211yescharacteristic
198#1762C2211yescharacteristic
199#1729C2211yescharacteristic
200#1729C2211yescharacteristic
201#1729C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#126—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C42C2311yescharacteristic
240#497—42no—
241#470—42no—
242#468—42no—
243#468—42no—
244#468—42no—
245#467—24no—
246#467—42no—
247#465—24no—
248#465—24no—
249#465—42no—
250#464—42no—
251#461—42no—
252C4×SD16—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264#423—42no—
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299#405—42no—
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#401—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#392—21no—
343#392—21no—
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389D411yescharacteristic
375#389D411yescharacteristic
376#389D411yescharacteristic
377#389D411yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385D411yescharacteristic
429#385D411yescharacteristic
430#385D411yescharacteristic
431#385D411yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383—21no—
435#383—21no—
436#383—21no—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#380—21no—
444#380—21no—
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461#376—21no—
462#376—21no—
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×Q16—41no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8#4114yes—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561#127—41no—
562#127—41no—
563#126—82no—
564#124—41no—
565#124—41no—
566#124—41no—
567#124—41no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—82no—
593C4×D4—82no—
594#117—41no—
595#117—41no—
596#117—41no—
597#117—41no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—41no—
685C2×C42—41no—
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#107—22no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#106—22no—
700#106—22no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#97—22no—
740#97—41no—
741C4×C8—22no—
742C4×C8—41no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24C22×D411yescharacteristic
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—42no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C2×#4112yes—
892C22×C4H(5,𝔽2)12yes—
893C22×C4C2511yescharacteristic
894Q16—82no—
895Q16—82no—
896Q16—82no—
897SD16—44no—
898SD16—82no—
899SD16—82no—
900SD16—82no—
901SD16—82no—
902SD16—82no—
903M16—44no—
904M16—82no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—44no—
927C2×C8—82no—
928C2×C8C2×#4112yes—
929C2×C8C2×#4112yes—
930C2×C8H(5,𝔽2)12yes—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—41no—
1030C42—41no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—42no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23#55012yes—
1062C23C23×D411yescharacteristic
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—84no—
1088D4—84no—
1089D4—162no—
1090D4—162no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—82no—
1175C2×C4—82no—
1176C2×C4—162no—
1177C2×C4—162no—
1178C2×C4#55012yes—
1179C2×C4#57712yes—
1180C2×C4C22×#4111yescharacteristic
1181C2×C4C2×H(5,𝔽2)11yescharacteristic
1182C2×C4C2×H(5,𝔽2)11yescharacteristic
1183C2×C4#58511yescharacteristic
1184C2×C4#58511yescharacteristic
1185C2×C4#58511yescharacteristic
1186C8—22no—
1187C8—22no—
1188C8—22no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22#344911yescharacteristic
1216C22C2×#55011yescharacteristic
1217C22#349611yescharacteristic
1218C22C2×#57711yescharacteristic
1219C22#358411yescharacteristic
1220C22#358611yescharacteristic
1221C22#358611yescharacteristic
1222C4—22no—
1223C4—22no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4#350511yescharacteristic
1250C4#351211yescharacteristic
1251C4#353411yescharacteristic
1252C4#356011yescharacteristic
1253C2—42no—
1254C2—161no—
1255C2—161no—
1256C2#3973811yescharacteristic
1257C2#6099111yescharacteristic
1258C2#6099611yescharacteristic
1259C2#6140711yescharacteristic
1260C2#6141811yescharacteristic
1261C2#6230711yescharacteristic
1262C2#6232211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2619C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39819C2semidirect
3. #33188C2semidirect
4. #32404C2semidirect
5. #32397C2semidirect
6. #32175C2semidirect
7. #32166C2semidirect
8. #31578C2semidirect
9. #31571C2semidirect
10. #30762C2semidirect
11. #30757C2semidirect
13. #30244C2semidirect
14. #28590C2semidirect
15. #28588C2semidirect
17. #28583C2semidirect
18. #27501C2semidirect
19. #27496C2semidirect
20. #27219C2semidirect
21. #27216C2semidirect
22. #27084C2semidirect
23. #27081C2semidirect
24. #26589C2semidirect
25. #26586C2semidirect
26. #24759C2semidirect
27. #24757C2semidirect
28. #22192C2semidirect
29. #22180C2semidirect
30. #21523C2semidirect
31. #21027C2semidirect

Maximal subgroups

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

subgroupindex
#398232
#398192
#331882
#324042
#323972
#321752
#321662
#315782
#315712
#307622
#307572
#302542
#302442
#285902
#285882
#285872
#285832
#275012
#274962
#272192
#272162
#270842
#270812
#265892
#265862
#247592
#247572
#221922
#221802
#215232
#210272