Finite Group Databasebeta

← #6813423

Subgroups — #6813423

Order 512.

1347 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42924C211yesmaximal, characteristic
2#42451C211yesmaximal, characteristic
3#33141C211yesmaximal, characteristic, complemented
4#32396C211yesmaximal, characteristic, complemented
5#32392C211yesmaximal, characteristic, complemented
6#32350C211yesmaximal, characteristic, complemented
7#32346C211yesmaximal, characteristic, complemented
8#32291C211yesmaximal, characteristic, complemented
9#32280C211yesmaximal, characteristic, complemented
10#31107C211yesmaximal, characteristic, complemented
11#31097C211yesmaximal, characteristic, complemented
12#29919C211yesmaximal, characteristic, complemented
13#29919C211yesmaximal, characteristic, complemented
14#28829C211yesmaximal, characteristic, complemented
15#28550C211yesmaximal, characteristic, complemented
16#28012C211yesmaximal, characteristic, complemented
17#27999C211yesmaximal, characteristic, complemented
18#27940C211yesmaximal, characteristic, complemented
19#27842C211yesmaximal, characteristic, complemented
20#26349C211yesmaximal, characteristic, complemented
21#26340C211yesmaximal, characteristic, complemented
22#26139C211yesmaximal, characteristic
23#26128C211yesmaximal, characteristic
24#26078C211yesmaximal, characteristic, complemented
25#26076C211yesmaximal, characteristic, complemented
26#25047C211yesmaximal, characteristic, complemented
27#24793C211yesmaximal, characteristic
28#23038C211yesmaximal, characteristic, complemented
29#22663C211yesmaximal, characteristic
30#21571C211yesmaximal, characteristic
31#20802C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×#441C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#427C2211yescharacteristic
45C22×#106C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2838—21no—
48#2834—21no—
49#2807—21no—
50#2787—21no—
51#2787—21no—
52#2776—21no—
53#2757—21no—
54#2726—21no—
55#2723—21no—
56#2690—21no—
57#2666—21no—
58#2664—21no—
59#2652—21no—
60#2633—21no—
61#2625C2211yescharacteristic
62#2625C2211yescharacteristic
63#2585—21no—
64#2567C2211yescharacteristic
65#2565C2211yescharacteristic
66#2552C2211yescharacteristic
67#2552C2211yescharacteristic
68#2514C2211yescharacteristic
69#2514C2211yescharacteristic
70#2508C2211yescharacteristic
71#2506C2211yescharacteristic
72#2502C2211yescharacteristic
73#2499C2211yescharacteristic
74#2496C2211yescharacteristic
75#2494C2211yescharacteristic
76#2460—21no—
77#2442C2211yescharacteristic
78#2441C2211yescharacteristic
79#2440C2211yescharacteristic
80#2439C2211yescharacteristic
81#2423C2211yescharacteristic
82#2423C2211yescharacteristic
83#2417C2211yescharacteristic
84#2415C2211yescharacteristic
85#2395C2211yescharacteristic
86#2362C2211yescharacteristic
87#2360C2211yescharacteristic
88#2354C2211yescharacteristic
89D4×C4⋊C4C2211yescharacteristic
90#2317C2211yescharacteristic
91#2317C2211yescharacteristic
92#2101C2211yescharacteristic
93#2101C2211yescharacteristic
94#2100C2211yescharacteristic
95#2100C2211yescharacteristic
96#2097C2211yescharacteristic
97#2097C2211yescharacteristic
98#2096C2211yescharacteristic
99#2096C2211yescharacteristic
100#2096C2211yescharacteristic
101#2096C2211yescharacteristic
102#2095C2211yescharacteristic
103#2095C2211yescharacteristic
104#2088C2211yescharacteristic
105#2087C2211yescharacteristic
106#2085C2211yescharacteristic
107#2085C2211yescharacteristic
108#2084C2211yescharacteristic
109#2084C2211yescharacteristic
110#2084C2211yescharacteristic
111#2084C2211yescharacteristic
112#2084C2211yescharacteristic
113#2083C2211yescharacteristic
114#2077C2211yescharacteristic
115#2076C2211yescharacteristic
116#2074C2211yescharacteristic
117#2074C2211yescharacteristic
118#2072C2211yescharacteristic
119#2072C2211yescharacteristic
120#2068C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2058C2211yescharacteristic
127#2058C2211yescharacteristic
128#2036C2211yescharacteristic
129#2035C2211yescharacteristic
130#2035C2211yescharacteristic
131#2035C2211yescharacteristic
132#1971C2211yescharacteristic
133#1969C2211yescharacteristic
134#1969C2211yescharacteristic
135#1969C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1947C2211yescharacteristic
140#1944C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1916C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1873C2211yescharacteristic
165#1873C2211yescharacteristic
166#1872C2211yescharacteristic
167#1872C2211yescharacteristic
168#1869C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1863C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1850C2211yescharacteristic
182#1847C2211yescharacteristic
183#1847C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1846C2211yescharacteristic
187#1846C2211yescharacteristic
188#1844C2211yescharacteristic
189#1844C2211yescharacteristic
190#1844C2211yescharacteristic
191#1844C2211yescharacteristic
192#1818C2211yescharacteristic
193#1809C2211yescharacteristic
194#1809C2211yescharacteristic
195#1809C2211yescharacteristic
196C4×#107C2211yescharacteristic
197C4×#106C2211yescharacteristic
198#1771C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229#501—42no—
230#485—42no—
231#483—42no—
232#479—42no—
233#475—42no—
234#470—24no—
235#470—42no—
236#441—42no—
237#436—24no—
238#428—42no—
239#428—42no—
240#428—42no—
241#427—42no—
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106—42no—
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292#405—24no—
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#401—21no—
301#401—21no—
302#401—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400D411yescharacteristic
312#399—21no—
313#399—21no—
314#399—21no—
315#399D411yescharacteristic
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398D411yescharacteristic
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397D411yescharacteristic
344#397D411yescharacteristic
345#397D411yescharacteristic
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#395—21no—
351#395—21no—
352#394—21no—
353#394D411yescharacteristic
354#394D411yescharacteristic
355#393—21no—
356#391—21no—
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
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#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—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#386—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383—21no—
435#383—21no—
436#382—21no—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#380—21no—
442#380—21no—
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4C2×D411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C2411yescharacteristic
501C23×C4C2411yescharacteristic
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×M16—22no—
506C2×M16—22no—
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—22no—
510C2×M16#4114yes—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524#126—82no—
525#125—41no—
526#125—41no—
527#125—82no—
528#125—82no—
529#125—82no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—41no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C22⋊Q8—41no—
538C22⋊Q8—82no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—82no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552#117—41no—
553#117—41no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#107—22no—
659#107—22no—
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#106—22no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—22no—
672#106—22no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702C22⋊C8—22no—
703C22⋊C8—22no—
704C22⋊C8—22no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707#97—22no—
708#97—22no—
709#97—22no—
710C4×C8—22no—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8—22no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
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#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770C24C22×D411yescharacteristic
771C24C22×D411yescharacteristic
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—41no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C2×#4112yes—
838C22×C42−1+412yes—
839C22×C4C2511yescharacteristic
840Q16—44no—
841M16—28no—
842M16—44no—
843C2×C8—28no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8C2×#4112yes—
863C2×C8C2×#4112yes—
864C2×C8H(5,𝔽2)12yes—
865C2×C8H(5,𝔽2)12yes—
866C2×C82−1+412yes—
867C2×C82−1+412yes—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—41no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23#54712yes—
999C23C23×D411yescharacteristic
1000Q8—41no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—41no—
1006Q8—41no—
1007Q8—41no—
1008Q8—162no—
1009D4—44no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—162no—
1100C2×C4—162no—
1101C2×C4—162no—
1102C2×C4#54712yes—
1103C2×C4#57712yes—
1104C2×C4#57712yes—
1105C2×C4C22×#4111yescharacteristic
1106C2×C4C2×H(5,𝔽2)11yescharacteristic
1107C2×C4C2×H(5,𝔽2)11yescharacteristic
1108C2×C4C2×2−1+411yescharacteristic
1109C2×C4C2×2−1+411yescharacteristic
1110C2×C4C2×2−1+411yescharacteristic
1111C8—22no—
1112C8—22no—
1113C8—22no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C8#53914yes—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22C2×#54711yescharacteristic
1134C22#349811yescharacteristic
1135C22#349911yescharacteristic
1136C22C2×#57711yescharacteristic
1137C22C2×#57711yescharacteristic
1138C22#358611yescharacteristic
1139C22#358611yescharacteristic
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4C2×#53911yescharacteristic
1169C4#349211yescharacteristic
1170C4#355211yescharacteristic
1171C4#355211yescharacteristic
1172C2—42no—
1173C2—81no—
1174C2#3934811yescharacteristic
1175C2#6127111yescharacteristic
1176C2#6128111yescharacteristic
1177C2#6246611yescharacteristic
1178C2#6246611yescharacteristic
1179C2#6248611yescharacteristic
1180C2#6250211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33141C2semidirect
4. #32396C2semidirect
5. #32392C2semidirect
6. #32350C2semidirect
7. #32346C2semidirect
8. #32291C2semidirect
9. #32280C2semidirect
10. #31107C2semidirect
11. #31097C2semidirect
12. #29919C2semidirect
13. #29919C2semidirect
14. #28829C2semidirect
15. #28550C2semidirect
16. #28012C2semidirect
17. #27999C2semidirect
18. #27940C2semidirect
19. #27842C2semidirect
20. #26349C2semidirect
21. #26340C2semidirect
24. #26078C2semidirect
25. #26076C2semidirect
26. #25047C2semidirect
28. #23038C2semidirect
31. #20802C2semidirect

Maximal subgroups

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

subgroupindex
#429242
#424512
#331412
#323962
#323922
#323502
#323462
#322912
#322802
#311072
#310972
#299192
#288292
#285502
#280122
#279992
#279402
#278422
#263492
#263402
#261392
#261282
#260782
#260762
#250472
#247932
#230382
#226632
#215712
#208022