Finite Group Databasebeta

← #7545260

Subgroups — #7545260

Order 512.

1492 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59922C211yesmaximal, characteristic, complemented
2#36117C211yesmaximal, characteristic
3#32628C211yesmaximal, characteristic, complemented
4#32600C211yesmaximal, characteristic, complemented
5#32326C211yesmaximal, characteristic, complemented
6#31472C211yesmaximal, characteristic, complemented
7#29337C211yesmaximal, characteristic
8#29101C211yesmaximal, characteristic, complemented
9#28580C211yesmaximal, characteristic
10#28046C211yesmaximal, characteristic, complemented
11#27719C211yesmaximal, characteristic, complemented
12#27709C211yesmaximal, characteristic, complemented
13#27578C211yesmaximal, characteristic, complemented
14#27445C211yesmaximal, characteristic, complemented
15#27381C211yesmaximal, characteristic, complemented
16#27154C211yesmaximal, characteristic, complemented
17#26913C211yesmaximal, characteristic, complemented
18#26770C211yesmaximal, characteristic, complemented
19#26424C211yesmaximal, characteristic, complemented
20#26366C211yesmaximal, characteristic, complemented
21#26276C211yesmaximal, characteristic, complemented
22#25217C211yesmaximal, characteristic, complemented
23#25217C211yesmaximal, characteristic, complemented
24#24994C211yesmaximal, characteristic, complemented
25#23242C211yesmaximal, characteristic, complemented
26#23141C211yesmaximal, characteristic, complemented
27#23076C211yesmaximal, characteristic, complemented
28#23040C211yesmaximal, characteristic, complemented
29#22781C211yesmaximal, characteristic, complemented
30#21581C211yesmaximal, characteristic, complemented
31#21033C211yesmaximal, characteristic, complemented
32C2×#529—21no—
33C2×#484C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#428C2211yescharacteristic
39#2856C2211yescharacteristic
40#2854—21no—
41#2768—21no—
42#2729—21no—
43#2590—21no—
44#2589—21no—
45#2587—21no—
46#2585—21no—
47#2582C2211yescharacteristic
48#2552C2211yescharacteristic
49#2548C2211yescharacteristic
50#2546C2211yescharacteristic
51#2520—21no—
52#2512C2211yescharacteristic
53#2512C2211yescharacteristic
54#2509C2211yescharacteristic
55#2507C2211yescharacteristic
56#2501C2211yescharacteristic
57#2501C2211yescharacteristic
58#2479—21no—
59#2479—21no—
60#2454—21no—
61#2453C2211yescharacteristic
62#2451C2211yescharacteristic
63#2448—21no—
64#2441C2211yescharacteristic
65#2439C2211yescharacteristic
66#2425—21no—
67#2425—21no—
68#2370C2211yescharacteristic
69#2369—21no—
70#2366C2211yescharacteristic
71#2362C2211yescharacteristic
72#2362C2211yescharacteristic
73#2361C2211yescharacteristic
74#2361C2211yescharacteristic
75#2354C2211yescharacteristic
76#2354C2211yescharacteristic
77#2351C2211yescharacteristic
78Q8×C4⋊C4C2211yescharacteristic
79C4×C22⋊Q8C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81#2296C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2094C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2073C2211yescharacteristic
97#2072C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2071C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic
111#2025C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#2014C2211yescharacteristic
115#1992C2211yescharacteristic
116#1990C2211yescharacteristic
117#1988C2211yescharacteristic
118#1984C2211yescharacteristic
119#1984C2211yescharacteristic
120#1968C2211yescharacteristic
121#1948C2211yescharacteristic
122#1947C2211yescharacteristic
123#1947C2211yescharacteristic
124#1943C2211yescharacteristic
125#1936C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1935C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1927C2211yescharacteristic
136#1927C2211yescharacteristic
137#1927C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1872C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic
178#1853C2211yescharacteristic
179#1851C2211yescharacteristic
180#1851C2211yescharacteristic
181#1836C2211yescharacteristic
182#1834C2211yescharacteristic
183#1824C2211yescharacteristic
184#1804C2211yescharacteristic
185#1803C2211yescharacteristic
186#1803C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#107C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1749C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210#529—48no—
211C2×#126—21no—
212C2×#126—21no—
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8D411yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121—21no—
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×C4×Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C42—21no—
243C22×C42C2311yescharacteristic
244#484—24no—
245#478—24no—
246#468—24no—
247#468—24no—
248#440—24no—
249#428—24no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#400—21no—
293#400—21no—
294#400—21no—
295#399—21no—
296#399—21no—
297#399—21no—
298#399—21no—
299#399—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#394—21no—
318#394—21no—
319#393—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391D411yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389D411yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387D411yescharacteristic
390#387D411yescharacteristic
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385D411yescharacteristic
401#385D411yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#382—21no—
409#382C2311yescharacteristic
410#380—21no—
411#380—21no—
412#380D411yescharacteristic
413#380C2311yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C2×#95—21no—
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8C2×D411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2411yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—44no—
524#127—41no—
525#127—41no—
526#126—44no—
527#126—44no—
528#125—22no—
529#125—41no—
530#125—44no—
531#124—44no—
532#123—44no—
533#123—44no—
534#123—82no—
535#123—82no—
536C22⋊Q8—24no—
537C22⋊Q8—22no—
538C22⋊Q8#4114yes—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—44no—
544#121—82no—
545C4×Q8—22no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—44no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—44no—
559C4×D4—44no—
560C4×D4—44no—
561#117—22no—
562#117—41no—
563#117—44no—
564#117—44no—
565#117—41no—
566#117—41no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
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—41no—
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
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⋊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×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—41no—
670C2×C42—41no—
671C2×C42—44no—
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680#107—22no—
681#107—22no—
682#107—22no—
683#107—22no—
684#107—22no—
685#107#4114yes—
686#106—22no—
687#106—22no—
688#106—22no—
689#106—41no—
690C4⋊C8—22no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693C4⋊C8—41no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—41no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714C22⋊C8—22no—
715C22⋊C8—22no—
716#97—22no—
717#97—41no—
718#97—41no—
719#97—41no—
720C4×C8—41no—
721C4×C8—41no—
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#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763C24—21no—
764C24—21no—
765C24C22×D411yescharacteristic
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—41no—
772C2×Q8—41no—
773C2×Q8—42no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8AGL(1,ℤ/8)14yes—
777C2×Q8C2×#4112yes—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—81no—
801C2×D4—81no—
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—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
852C22×C42−1+412yes—
853C22×C4C2511yescharacteristic
854SD16—44no—
855SD16—82no—
856M16—44no—
857M16—82no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
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×C8C2×#4112yes—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
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—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
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—42no—
931C4⋊C4—42no—
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⋊C4C2×#4112yes—
949C4⋊C4C2×#4112yes—
950C4⋊C4C2×#4112yes—
951C22⋊C4—24no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—41no—
992C42—41no—
993C42—42no—
994C42—42no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23#54812yes—
1028C23C23×D411yescharacteristic
1029Q8—22no—
1030Q8—22no—
1031Q8—44no—
1032Q8—41no—
1033Q8—41no—
1034Q8—162no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—84no—
1044D4—84no—
1045D4—84no—
1046D4—162no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
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—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—44no—
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—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—82no—
1130C2×C4—84no—
1131C2×C4—84no—
1132C2×C4—84no—
1133C2×C4—84no—
1134C2×C4#54812yes—
1135C2×C4C2×AGL(1,ℤ/8)12yes—
1136C2×C4C2×AGL(1,ℤ/8)12yes—
1137C2×C4C2×AGL(1,ℤ/8)12yes—
1138C2×C4C22×#4111yescharacteristic
1139C2×C4C22×#4111yescharacteristic
1140C2×C4C2×2−1+411yescharacteristic
1141C2×C4#58511yescharacteristic
1142C2×C4#58511yescharacteristic
1143C2×C4#58511yescharacteristic
1144C8—22no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C8—41no—
1151C8—41no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22C2×#54811yescharacteristic
1174C22D4×#4111yescharacteristic
1175C22#348511yescharacteristic
1176C22C22×AGL(1,ℤ/8)11yescharacteristic
1177C22#358511yescharacteristic
1178C22#358611yescharacteristic
1179C22#358611yescharacteristic
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—42no—
1188C4—42no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—42no—
1196C4—42no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4#347511yescharacteristic
1208C4#351611yescharacteristic
1209C4#352111yescharacteristic
1210C4#355311yescharacteristic
1211C2—42no—
1212C2—161no—
1213C2—161no—
1214C2#5907711yescharacteristic
1215C2#6132111yescharacteristic
1216C2#6133511yescharacteristic
1217C2#6146611yescharacteristic
1218C2#6151611yescharacteristic
1219C2#6170611yescharacteristic
1220C2#6178211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59922C2semidirect
3. #32628C2semidirect
4. #32600C2semidirect
5. #32326C2semidirect
6. #31472C2semidirect
8. #29101C2semidirect
10. #28046C2semidirect
11. #27719C2semidirect
12. #27709C2semidirect
13. #27578C2semidirect
14. #27445C2semidirect
15. #27381C2semidirect
16. #27154C2semidirect
17. #26913C2semidirect
18. #26770C2semidirect
19. #26424C2semidirect
20. #26366C2semidirect
21. #26276C2semidirect
22. #25217C2semidirect
23. #25217C2semidirect
24. #24994C2semidirect
25. #23242C2semidirect
26. #23141C2semidirect
27. #23076C2semidirect
28. #23040C2semidirect
29. #22781C2semidirect
30. #21581C2semidirect
31. #21033C2semidirect

Maximal subgroups

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

subgroupindex
#599222
#361172
#326282
#326002
#323262
#314722
#293372
#291012
#285802
#280462
#277192
#277092
#275782
#274452
#273812
#271542
#269132
#267702
#264242
#263662
#262762
#252172
#249942
#232422
#231412
#230762
#230402
#227812
#215812
#210332