Finite Group Databasebeta

← #7566672

Subgroups — #7566672

Order 512.

1380 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44961C211yesmaximal, characteristic
2#35783C211yesmaximal, characteristic, complemented
3#32638C211yesmaximal, characteristic, complemented
4#32593C211yesmaximal, characteristic, complemented
5#32243C211yesmaximal, characteristic, complemented
6#30809C211yesmaximal, characteristic, complemented
7#29170C211yesmaximal, characteristic, complemented
8#29116C211yesmaximal, characteristic
9#29025C211yesmaximal, characteristic, complemented
10#28058C211yesmaximal, characteristic, complemented
11#27714C211yesmaximal, characteristic, complemented
12#27386C211yesmaximal, characteristic, complemented
13#27271C211yesmaximal, characteristic
14#27135C211yesmaximal, characteristic, complemented
15#27129C211yesmaximal, characteristic, complemented
16#26766C211yesmaximal, characteristic, complemented
17#26710C211yesmaximal, characteristic, complemented
18#26704C211yesmaximal, characteristic, complemented
19#26331C211yesmaximal, characteristic, complemented
20#26001C211yesmaximal, characteristic, complemented
21#25966C211yesmaximal, characteristic
22#25007C211yesmaximal, characteristic, complemented
23#24588C211yesmaximal, characteristic, complemented
24#24479C211yesmaximal, characteristic
25#23245C211yesmaximal, characteristic, complemented
26#23225C211yesmaximal, characteristic, complemented
27#23079C211yesmaximal, characteristic, complemented
28#22621C211yesmaximal, characteristic, complemented
29#22562C211yesmaximal, characteristic
30#21585C211yesmaximal, characteristic, complemented
31#21063C211yesmaximal, characteristic
32C2×#488C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#428C2211yescharacteristic
36C2×#418C2211yescharacteristic
37C22×#102C2211yescharacteristic
38#2761—21no—
39#2735—21no—
40#2735—21no—
41#2723—21no—
42#2665—21no—
43#2628C2211yescharacteristic
44#2607—21no—
45#2592C2211yescharacteristic
46#2588—21no—
47#2586—21no—
48#2567C2211yescharacteristic, complemented
49#2561—21no—
50#2550C2211yescharacteristic, complemented
51#2538C2211yescharacteristic
52#2531—21no—
53#2526—21no—
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic
56#2511—21no—
57#2509C2211yescharacteristic, complemented
58#2506C2211yescharacteristic, complemented
59#2499C2211yescharacteristic
60#2480—21no—
61#2462—21no—
62#2448C2211yescharacteristic
63#2447C2211yescharacteristic
64#2441—21no—
65#2441C2211yescharacteristic
66#2439C2211yescharacteristic
67#2435C2211yescharacteristic
68#2396—21no—
69#2396C2211yescharacteristic
70#2370C2211yescharacteristic, complemented
71#2369C2211yescharacteristic, complemented
72#2367C2211yescharacteristic
73#2365C2211yescharacteristic, complemented
74#2357C2211yescharacteristic
75#2355C2211yescharacteristic, complemented
76#2346C2211yescharacteristic
77#2345C2211yescharacteristic
78#2344C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2323C2211yescharacteristic
81#2309C2211yescharacteristic
82#2274C2211yescharacteristic
83#2101C2211yescharacteristic, complemented
84#2101C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2097C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2074C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2025C2211yescharacteristic
110#2024C2211yescharacteristic, complemented
111#2024C2211yescharacteristic, complemented
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#1993C2211yescharacteristic, complemented
116#1989C2211yescharacteristic, complemented
117#1985C2211yescharacteristic, complemented
118#1985C2211yescharacteristic, complemented
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1959C2211yescharacteristic
122#1949C2211yescharacteristic, complemented
123#1948C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1943C2211yescharacteristic, complemented
126#1942C2211yescharacteristic, complemented
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1935C2211yescharacteristic, complemented
133#1935C2211yescharacteristic, complemented
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1928C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1894C2211yescharacteristic
168#1892C2211yescharacteristic
169#1873C2211yescharacteristic
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1854C2211yescharacteristic
177#1851C2211yescharacteristic
178#1850C2211yescharacteristic
179#1836C2211yescharacteristic, complemented
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1823C2211yescharacteristic
183#1809C2211yescharacteristic
184#1807C2211yescharacteristic
185#1804C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189#1776C2211yescharacteristic, complemented
190C4×#107C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1750C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×#117—21no—
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C22⋊C4—21no—
226#488—24no—
227#484—24no—
228#474—24no—
229#428—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246#418—24no—
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#102—24no—
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400D411yescharacteristic
285#399—21no—
286#399—21no—
287#399—21no—
288#399D411yescharacteristic
289#398—21no—
290#398—21no—
291#398D411yescharacteristic
292#398D411yescharacteristic
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396D411yescharacteristic
308#396D411yescharacteristic
309#395—21no—
310#395—21no—
311#395—21no—
312#395—21no—
313#395D411yescharacteristic
314#394—21no—
315#394—21no—
316#393—21no—
317#393—21no—
318#393—21no—
319#393D411yescharacteristic
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
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#389C2311yescharacteristic
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#388—21no—
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#388—21no—
373#388—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#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#386—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#384—21no—
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#382—21no—
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#381—21no—
403#381—21no—
404#381—21no—
405#380—21no—
406#380—21no—
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#379—21no—
411#379—21no—
412#379—21no—
413#379—21no—
414#379—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
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
441#376—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
484C25—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×D4—22no—
490C22×D4—21no—
491C22×D4—22no—
492C22×D4—22no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2411yescharacteristic
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—41no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520#126—82no—
521#125—22no—
522#125—41no—
523#125—82no—
524#124—22no—
525#124—41no—
526#124—41no—
527#124—41no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—82no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—82no—
536C4×D4—22no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117—82no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4#4114yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
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—82no—
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
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×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107—22no—
653#107—22no—
654#107—22no—
655#107—22no—
656#107—22no—
657#107—22no—
658#106—22no—
659#106—22no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664C4⋊C8—22no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102#4114yes—
692C22⋊C8—22no—
693C22⋊C8—22no—
694#97—41no—
695#97—41no—
696#97—41no—
697#97—41no—
698C4×C8—22no—
699C4×C8—41no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
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#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24—21no—
751C24—42no—
752C24—42no—
753C24—81no—
754C24—81no—
755C24—81no—
756C24—81no—
757C24—81no—
758C24C22×D411yescharacteristic
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—41no—
766C2×Q8—41no—
767C2×Q8—41no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—82no—
790C2×D4—82no—
791C2×D4—81no—
792C2×D4C2×#4112yes—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—24no—
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—42no—
813C22×C4—42no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
834C22×C42−1+412yes—
835C22×C4C2511yescharacteristic
836M16—44no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
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—82no—
861C2×C8C2×#4112yes—
862C4⋊C4—24no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
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—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
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⋊C4C2×#4112yes—
921C4⋊C4C2×#4112yes—
922C4⋊C4C2×#4112yes—
923C22⋊C4—41no—
924C22⋊C4—41no—
925C22⋊C4—41no—
926C22⋊C4—41no—
927C22⋊C4—41no—
928C22⋊C4—41no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—22no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—84no—
1004C23—84no—
1005C23—162no—
1006C23—162no—
1007C23—162no—
1008C23—162no—
1009C23—162no—
1010C23#54812yes—
1011C23C23×D411yescharacteristic
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—82no—
1017Q8—84no—
1018Q8—162no—
1019D4—22no—
1020D4—22no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—84no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
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—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
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—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—84no—
1113C2×C4—162no—
1114C2×C4—162no—
1115C2×C4#54812yes—
1116C2×C4C22×#4111yescharacteristic
1117C2×C4C22×#4111yescharacteristic
1118C2×C4C2×2−1+411yescharacteristic
1119C2×C4#58511yescharacteristic
1120C2×C4#58511yescharacteristic
1121C2×C4#58511yescharacteristic
1122C8—22no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—168no—
1152C22C2×#54811yescharacteristic
1153C22D4×#4111yescharacteristic
1154C22#348511yescharacteristic
1155C22#358411yescharacteristic
1156C22#358511yescharacteristic
1157C22#358511yescharacteristic
1158C22#358611yescharacteristic
1159C4—22no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—42no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—42no—
1174C4—42no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4#347511yescharacteristic
1187C4#349511yescharacteristic
1188C4#351011yescharacteristic
1189C4#356411yescharacteristic
1190C2—42no—
1191C2—82no—
1192C2—161no—
1193C2#5913211yescharacteristic
1194C2#6133211yescharacteristic
1195C2#6134411yescharacteristic
1196C2#6151811yescharacteristic
1197C2#6152911yescharacteristic
1198C2#6178011yescharacteristic
1199C2#6180411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35783C2semidirect
3. #32638C2semidirect
4. #32593C2semidirect
5. #32243C2semidirect
6. #30809C2semidirect
7. #29170C2semidirect
9. #29025C2semidirect
10. #28058C2semidirect
11. #27714C2semidirect
12. #27386C2semidirect
14. #27135C2semidirect
15. #27129C2semidirect
16. #26766C2semidirect
17. #26710C2semidirect
18. #26704C2semidirect
19. #26331C2semidirect
20. #26001C2semidirect
22. #25007C2semidirect
23. #24588C2semidirect
25. #23245C2semidirect
26. #23225C2semidirect
27. #23079C2semidirect
28. #22621C2semidirect
30. #21585C2semidirect
48. #2567C22semidirect
50. #2550C22semidirect
57. #2509C22semidirect
58. #2506C22semidirect
70. #2370C22semidirect
71. #2369C22semidirect
73. #2365C22semidirect
75. #2355C22semidirect
83. #2101C22semidirect
84. #2101C22semidirect
85. #2100C22semidirect
86. #2100C22semidirect
87. #2097C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2085C22semidirect
92. #2083C22semidirect
93. #2074C22semidirect
97. #2068C22semidirect
101. #2066C22semidirect
103. #2059C22semidirect
104. #2058C22semidirect
110. #2024C22semidirect
111. #2024C22semidirect
115. #1993C22semidirect
116. #1989C22semidirect
117. #1985C22semidirect
118. #1985C22semidirect
122. #1949C22semidirect
123. #1948C22semidirect
124. #1947C22semidirect
125. #1943C22semidirect
126. #1942C22semidirect
132. #1935C22semidirect
133. #1935C22semidirect
137. #1928C22semidirect
138. #1928C22semidirect
139. #1927C22semidirect
140. #1927C22semidirect
153. #1921C22semidirect
154. #1921C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
159. #1919C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1918C22semidirect
163. #1917C22semidirect
164. #1917C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
179. #1836C22semidirect
188. #1776C22semidirect
189. #1776C22semidirect
190. C4×#107C22semidirect
191. C4×#106C22semidirect
192. #1771C22semidirect
193. #1770C22semidirect
194. #1763C22semidirect
197. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#449612
#357832
#326382
#325932
#322432
#308092
#291702
#291162
#290252
#280582
#277142
#273862
#272712
#271352
#271292
#267662
#267102
#267042
#263312
#260012
#259662
#250072
#245882
#244792
#232452
#232252
#230792
#226212
#225622
#215852
#210632