Finite Group Databasebeta

← #6825674

Subgroups — #6825674

Order 512.

1312 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42850C211yesmaximal, characteristic, complemented
2#42830C211yesmaximal, characteristic
3#33276C211yesmaximal, characteristic, complemented
4#32092C211yesmaximal, characteristic
5#32084C211yesmaximal, characteristic, complemented
6#31911C211yesmaximal, characteristic
7#31904C211yesmaximal, characteristic, complemented
8#31644C211yesmaximal, characteristic
9#31635C211yesmaximal, characteristic, complemented
10#31161C211yesmaximal, characteristic
11#31149C211yesmaximal, characteristic, complemented
12#30143C211yesmaximal, characteristic
13#30140C211yesmaximal, characteristic, complemented
14#28538C211yesmaximal, characteristic, complemented
15#28477C211yesmaximal, characteristic
16#28018C211yesmaximal, characteristic
17#27998C211yesmaximal, characteristic, complemented
18#26918C211yesmaximal, characteristic
19#26910C211yesmaximal, characteristic, complemented
20#26493C211yesmaximal, characteristic, complemented
21#26481C211yesmaximal, characteristic
22#26269C211yesmaximal, characteristic
23#26265C211yesmaximal, characteristic, complemented
24#26259C211yesmaximal, characteristic
25#26256C211yesmaximal, characteristic
26#26183C211yesmaximal, characteristic, complemented
27#26177C211yesmaximal, characteristic
28#23184C211yesmaximal, characteristic, complemented
29#22679C211yesmaximal, characteristic, complemented
30#21703C211yesmaximal, characteristic
31#21678C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#497C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#494C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#462C2211yescharacteristic
40C2×#441C2211yescharacteristic
41C2×#441C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×C4×Q16C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47#2839—21no—
48#2836—21no—
49#2810—21no—
50#2807—21no—
51#2802—21no—
52#2794—21no—
53#2791—21no—
54#2787—21no—
55#2765—21no—
56#2744—21no—
57#2655—21no—
58#2655—21no—
59#2654—21no—
60#2654—21no—
61#2645C2211yescharacteristic
62#2645C2211yescharacteristic
63#2596—21no—
64#2590—21no—
65#2565C2211yescharacteristic
66#2565C2211yescharacteristic
67#2546C2211yescharacteristic
68#2545C2211yescharacteristic
69#2513C2211yescharacteristic
70#2511C2211yescharacteristic
71#2509C2211yescharacteristic
72#2507C2211yescharacteristic
73#2454C2211yescharacteristic
74#2453C2211yescharacteristic
75#2453C2211yescharacteristic
76#2453C2211yescharacteristic
77#2448C2211yescharacteristic
78#2448C2211yescharacteristic
79#2447C2211yescharacteristic
80#2446C2211yescharacteristic
81#2446C2211yescharacteristic
82#2446C2211yescharacteristic
83#2446C2211yescharacteristic
84#2446C2211yescharacteristic
85#2402C2211yescharacteristic
86#2365C2211yescharacteristic
87#2365C2211yescharacteristic
88#2351C2211yescharacteristic
89Q8×C4⋊C4C2211yescharacteristic
90#2327C2211yescharacteristic
91#2326C2211yescharacteristic
92#2101C2211yescharacteristic
93#2099C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2095C2211yescharacteristic
97#2095C2211yescharacteristic
98#2088C2211yescharacteristic
99#2086C2211yescharacteristic
100#2074C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2056C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2056C2211yescharacteristic
112#2056C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2043C2211yescharacteristic
117#2043C2211yescharacteristic
118#2043C2211yescharacteristic
119#2043C2211yescharacteristic
120#2043C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2026C2211yescharacteristic
125#2026C2211yescharacteristic
126#2026C2211yescharacteristic
127#2025C2211yescharacteristic
128#2016C2211yescharacteristic
129#2016C2211yescharacteristic
130#2015C2211yescharacteristic
131#2013C2211yescharacteristic
132#1981C2211yescharacteristic
133#1981C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1971C2211yescharacteristic
137#1971C2211yescharacteristic
138#1971C2211yescharacteristic
139#1971C2211yescharacteristic
140#1969C2211yescharacteristic
141#1969C2211yescharacteristic
142#1969C2211yescharacteristic
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1958C2211yescharacteristic
147#1956C2211yescharacteristic
148#1944C2211yescharacteristic
149#1944C2211yescharacteristic
150#1943C2211yescharacteristic
151#1943C2211yescharacteristic
152#1941C2211yescharacteristic
153#1941C2211yescharacteristic
154#1939C2211yescharacteristic
155#1939C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1933C2211yescharacteristic
162#1928C2211yescharacteristic
163#1926C2211yescharacteristic
164#1921C2211yescharacteristic
165#1919C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1877C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1862C2211yescharacteristic
190#1847C2211yescharacteristic
191#1847C2211yescharacteristic
192#1832C2211yescharacteristic
193#1805C2211yescharacteristic
194#1803C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1770C2211yescharacteristic
201C8×C4⋊C4C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230#499—42no—
231#497—24no—
232#497—42no—
233#494—24no—
234#479—42no—
235#479—42no—
236#464—42no—
237#462—42no—
238#441—24no—
239#441—42no—
240#441—42no—
241#440—42no—
242C4×Q16—42no—
243C4×Q16—42no—
244C4×SD16—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#401—21no—
303#401—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400D411yescharacteristic
323#400D411yescharacteristic
324#400D411yescharacteristic
325#400D411yescharacteristic
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398D411yescharacteristic
346#398D411yescharacteristic
347#398D411yescharacteristic
348#398D411yescharacteristic
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384—21no—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#382—21no—
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#381—21no—
453#380—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466#376C2311yescharacteristic
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#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×Q8C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C2×Q16—22no—
501C2×Q16—22no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×Q16—41no—
517C2×Q16#4114yes—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C4⋊Q8—22no—
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543#125—41no—
544#125—41no—
545#125—41no—
546#125—41no—
547#124—22no—
548#124—41no—
549#124—41no—
550#124—41no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×D4—41no—
570C4×D4—41no—
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—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C42—21no—
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×C42—21no—
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#107—22no—
662#107—22no—
663#107—22no—
664#107—41no—
665#107—41no—
666#107—41no—
667#106—22no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—41no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#97—22no—
709#97—22no—
710#97—22no—
711#97—22no—
712#97—22no—
713C4×C8—22no—
714C4×C8—22no—
715C4×C8—22no—
716C4×C8—41no—
717C4×C8—41no—
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#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
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×Q8C2×#4112yes—
814C2×Q8C2×#4112yes—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C2511yescharacteristic
854Q16—28no—
855Q16—44no—
856Q16—44no—
857Q16—82no—
858Q16—82no—
859Q16—82no—
860SD16—44no—
861SD16—44no—
862SD16—82no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8C2×#4112yes—
884C2×C8H(5,𝔽2)12yes—
885C2×C8H(5,𝔽2)12yes—
886C2×C82−1+412yes—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
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—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
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—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—42no—
984C42—42no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23C23×D411yescharacteristic
1002Q8—22no—
1003Q8—22no—
1004Q8—22no—
1005Q8—22no—
1006Q8—41no—
1007Q8—41no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
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—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
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—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—162no—
1113C2×C4#57812yes—
1114C2×C4C22×#4111yescharacteristic
1115C2×C4C2×H(5,𝔽2)11yescharacteristic
1116C2×C4C2×H(5,𝔽2)11yescharacteristic
1117C2×C4C2×2−1+411yescharacteristic
1118C2×C4#58511yescharacteristic
1119C2×C4#58511yescharacteristic
1120C8—22no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8#53914yes—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22D4×#4111yescharacteristic
1136C22#349711yescharacteristic
1137C22#349811yescharacteristic
1138C22C2×#57811yescharacteristic
1139C22#358411yescharacteristic
1140C22#358611yescharacteristic
1141C22#358611yescharacteristic
1142C4—22no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—42no—
1154C4—42no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4C2×#53911yescharacteristic
1172C4#351311yescharacteristic
1173C4#355411yescharacteristic
1174C4#356211yescharacteristic
1175C2—161no—
1176C2#3939711yescharacteristic
1177C2#6149111yescharacteristic
1178C2#6151211yescharacteristic
1179C2#6240611yescharacteristic
1180C2#6241211yescharacteristic
1181C2#6246211yescharacteristic
1182C2#6246411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42850C2semidirect
3. #33276C2semidirect
5. #32084C2semidirect
7. #31904C2semidirect
9. #31635C2semidirect
11. #31149C2semidirect
13. #30140C2semidirect
14. #28538C2semidirect
17. #27998C2semidirect
19. #26910C2semidirect
20. #26493C2semidirect
23. #26265C2semidirect
26. #26183C2semidirect
28. #23184C2semidirect
29. #22679C2semidirect
31. #21678C2semidirect

Maximal subgroups

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

subgroupindex
#428502
#428302
#332762
#320922
#320842
#319112
#319042
#316442
#316352
#311612
#311492
#301432
#301402
#285382
#284772
#280182
#279982
#269182
#269102
#264932
#264812
#262692
#262652
#262592
#262562
#261832
#261772
#231842
#226792
#217032
#216782