Finite Group Databasebeta

← #7566221

Subgroups — #7566221

Order 512.

1427 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59754C211yesmaximal, characteristic
2#36564C211yesmaximal, characteristic, complemented
3#32647C211yesmaximal, characteristic, complemented
4#32575C211yesmaximal, characteristic, complemented
5#32226C211yesmaximal, characteristic, complemented
6#30832C211yesmaximal, characteristic, complemented
7#29163C211yesmaximal, characteristic, complemented
8#29107C211yesmaximal, characteristic, complemented
9#29011C211yesmaximal, characteristic, complemented
10#28041C211yesmaximal, characteristic, complemented
11#27720C211yesmaximal, characteristic, complemented
12#27364C211yesmaximal, characteristic, complemented
13#27282C211yesmaximal, characteristic
14#27147C211yesmaximal, characteristic, complemented
15#27133C211yesmaximal, characteristic, complemented
16#26763C211yesmaximal, characteristic, complemented
17#26695C211yesmaximal, characteristic, complemented
18#26692C211yesmaximal, characteristic, complemented
19#26316C211yesmaximal, characteristic, complemented
20#26005C211yesmaximal, characteristic, complemented
21#25975C211yesmaximal, characteristic, complemented
22#25004C211yesmaximal, characteristic, complemented
23#24591C211yesmaximal, characteristic, complemented
24#24490C211yesmaximal, characteristic
25#23239C211yesmaximal, characteristic, complemented
26#23232C211yesmaximal, characteristic, complemented
27#23063C211yesmaximal, characteristic, complemented
28#22623C211yesmaximal, characteristic, complemented
29#22579C211yesmaximal, characteristic, complemented
30C4×#480C211yesmaximal, characteristic, complemented
31#21059C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#428C2211yescharacteristic
36C2×#417C2211yescharacteristic
37C2×#417C2211yescharacteristic
38#2857—21no—
39#2857C2211yescharacteristic
40#2797—21no—
41#2753—21no—
42#2586—21no—
43#2586—21no—
44#2581C2211yescharacteristic
45#2578—21no—
46#2567C2211yescharacteristic
47#2551C2211yescharacteristic
48#2549—21no—
49#2549—21no—
50#2548C2211yescharacteristic
51#2521—21no—
52#2518—21no—
53#2513C2211yescharacteristic
54#2512C2211yescharacteristic
55#2507—21no—
56#2507C2211yescharacteristic
57#2507C2211yescharacteristic
58#2500C2211yescharacteristic
59#2467—21no—
60#2461—21no—
61#2451—21no—
62#2448C2211yescharacteristic
63#2445C2211yescharacteristic
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2431C2211yescharacteristic
67#2374—21no—
68#2369C2211yescharacteristic
69#2369C2211yescharacteristic
70#2369C2211yescharacteristic
71#2367C2211yescharacteristic
72#2355C2211yescharacteristic
73Q8×C4⋊C4C2211yescharacteristic
74#2347C2211yescharacteristic
75#2345C2211yescharacteristic
76#2345C2211yescharacteristic
77#2341C2211yescharacteristic
78C4×C22⋊Q8—21no—
79C4×C22⋊Q8C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2297C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic
89#2088C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2083C2211yescharacteristic
93#2072C2211yescharacteristic
94#2072C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic
104#2057C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2024C2211yescharacteristic
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#1990C2211yescharacteristic
116#1988C2211yescharacteristic
117#1985C2211yescharacteristic
118#1984C2211yescharacteristic
119#1983C2211yescharacteristic
120#1982C2211yescharacteristic
121#1957C2211yescharacteristic
122#1949C2211yescharacteristic
123#1947C2211yescharacteristic
124#1947C2211yescharacteristic
125#1944C2211yescharacteristic
126#1941C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1933C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1927C2211yescharacteristic
141#1927C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1895C2211yescharacteristic
168#1895C2211yescharacteristic
169#1874C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1852C2211yescharacteristic
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1836C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1823C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1803C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#107C2211yescharacteristic
192#1771C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1763C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#124—21no—
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8D411yescharacteristic
219C2×#121C2311yescharacteristic
220C2×C4×Q8—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C42—21no—
230C22×C42C2311yescharacteristic
231#489—24no—
232#480—24no—
233#477—24no—
234#428—24no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251#417—24no—
252#417—24no—
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#400—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#396—21no—
298#395—21no—
299#395—21no—
300#395—21no—
301#395—21no—
302#395—21no—
303#395—21no—
304#395—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#392—21no—
312#392—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391D411yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#390—21no—
326#390—21no—
327#390—21no—
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389D411yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387D411yescharacteristic
383#387D411yescharacteristic
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385D411yescharacteristic
394#385D411yescharacteristic
395#384—21no—
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#383—21no—
401#382—21no—
402#382C2311yescharacteristic
403#380—21no—
404#380—21no—
405#380—21no—
406#380—21no—
407#380D411yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C2×#95—21no—
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#336C2311yescharacteristic
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
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—82no—
529#127—41no—
530#127—41no—
531#126—82no—
532#124—22no—
533#124—41no—
534#124—82no—
535#123—44no—
536C22⋊Q8—24no—
537C22⋊Q8—82no—
538C22⋊Q8—82no—
539C22⋊Q8—82no—
540#121—22no—
541#121—22no—
542C4×Q8—22no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—82no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—82no—
552#117—22no—
553#117—22no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
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—41no—
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4#4114yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42—82no—
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#107—22no—
662#107—22no—
663#107—22no—
664#107—22no—
665#107—22no—
666#107—22no—
667#107—41no—
668#107—41no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673C4⋊C8—22no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103#4114yes—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701C22⋊C8—22no—
702C22⋊C8—22no—
703#97—22no—
704#97—41no—
705C4×C8—41no—
706C4×C8—41no—
707C4×C8—41no—
708C4×C8—41no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
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#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754C24—21no—
755C24—21no—
756C24C22×D411yescharacteristic
757#41—44no—
758#41—44no—
759#41—82no—
760#41—82no—
761C2×Q8—22no—
762C2×Q8—22no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—41no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8C2×#4112yes—
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—21no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
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—24no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
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×C4C2×#4112yes—
853C22×C42−1+412yes—
854C22×C4C2511yescharacteristic
855M16—44no—
856M16—82no—
857C2×C8—21no—
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×C8C2×#4112yes—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
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—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
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#13714yes—
941C4⋊C4C2×#4112yes—
942C4⋊C4C2×#4112yes—
943C4⋊C4C2×#4112yes—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
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—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—41no—
985C42—41no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23#54812yes—
1021C23C23×D411yescharacteristic
1022Q8—22no—
1023Q8—22no—
1024Q8—44no—
1025Q8—41no—
1026Q8—41no—
1027Q8—162no—
1028Q8—162no—
1029Q8—162no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—84no—
1039D4—84no—
1040D4—162no—
1041D4—162no—
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—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
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—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—44no—
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—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—84no—
1124C2×C4—84no—
1125C2×C4—82no—
1126C2×C4—84no—
1127C2×C4—162no—
1128C2×C4#54812yes—
1129C2×C4C2×#13712yes—
1130C2×C4C2×#13712yes—
1131C2×C4C2×#13712yes—
1132C2×C4#57612yes—
1133C2×C4C22×#4111yescharacteristic
1134C2×C4C22×#4111yescharacteristic
1135C2×C4C2×2−1+411yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C2×C4#58511yescharacteristic
1139C8—22no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22C2×#54811yescharacteristic
1169C22D4×#4111yescharacteristic
1170C22#348511yescharacteristic
1171C22C22×#13711yescharacteristic
1172C22C2×#57611yescharacteristic
1173C22#358411yescharacteristic
1174C22#358511yescharacteristic
1175C4—22no—
1176C4—22no—
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4#347511yescharacteristic
1203C4#349511yescharacteristic
1204C4#351011yescharacteristic
1205C4#356411yescharacteristic
1206C2—42no—
1207C2—161no—
1208C2—161no—
1209C2#5913211yescharacteristic
1210C2#6131911yescharacteristic
1211C2#6132511yescharacteristic
1212C2#6144011yescharacteristic
1213C2#6155511yescharacteristic
1214C2#6172611yescharacteristic
1215C2#6176211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2431C22
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
2. #36564C2semidirect
3. #32647C2semidirect
4. #32575C2semidirect
5. #32226C2semidirect
6. #30832C2semidirect
7. #29163C2semidirect
8. #29107C2semidirect
9. #29011C2semidirect
10. #28041C2semidirect
11. #27720C2semidirect
12. #27364C2semidirect
14. #27147C2semidirect
15. #27133C2semidirect
16. #26763C2semidirect
17. #26695C2semidirect
18. #26692C2semidirect
19. #26316C2semidirect
20. #26005C2semidirect
21. #25975C2semidirect
22. #25004C2semidirect
23. #24591C2semidirect
25. #23239C2semidirect
26. #23232C2semidirect
27. #23063C2semidirect
28. #22623C2semidirect
29. #22579C2semidirect
30. C4×#480C2semidirect
31. #21059C2semidirect

Maximal subgroups

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

subgroupindex
#597542
#365642
#326472
#325752
#322262
#308322
#291632
#291072
#290112
#280412
#277202
#273642
#272822
#271472
#271332
#267632
#266952
#266922
#263162
#260052
#259752
#250042
#245912
#244902
#232392
#232322
#230632
#226232
#225792
C4×#4802
#210592