Finite Group Databasebeta

← #6773906

Subgroups — #6773906

Order 512.

1439 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38054C211yesmaximal, characteristic
2#35239C211yesmaximal, characteristic, complemented
3#33100C211yesmaximal, characteristic, complemented
4#32378C211yesmaximal, characteristic, complemented
5#32253C211yesmaximal, characteristic, complemented
6#31590C211yesmaximal, characteristic, complemented
7#31583C211yesmaximal, characteristic, complemented
8#31483C211yesmaximal, characteristic, complemented
9#30954C211yesmaximal, characteristic, complemented
10#30824C211yesmaximal, characteristic, complemented
11#30819C211yesmaximal, characteristic, complemented
12#30163C211yesmaximal, characteristic, complemented
13#30074C211yesmaximal, characteristic, complemented
14#29524C211yesmaximal, characteristic, complemented
15#29400C211yesmaximal, characteristic, complemented
16#28776C211yesmaximal, characteristic, complemented
17#28662C211yesmaximal, characteristic, complemented
18#28212C211yesmaximal, characteristic, complemented
19#27855C211yesmaximal, characteristic, complemented
20#27585C211yesmaximal, characteristic
21#27262C211yesmaximal, characteristic
22#27256C211yesmaximal, characteristic
23#26416C211yesmaximal, characteristic, complemented
24#26340C211yesmaximal, characteristic, complemented
25#26060C211yesmaximal, characteristic, complemented
26#25960C211yesmaximal, characteristic
27#25958C211yesmaximal, characteristic
28#22595C211yesmaximal, characteristic, complemented
29#22227C211yesmaximal, characteristic, complemented
30#22122C211yesmaximal, characteristic, complemented
31C2×#1926C211yesmaximal, characteristic
32C2×#498C2211yescharacteristic, complemented
33C2×#489C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#475C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C22×#106C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2857—21no—
42#2855C2211yescharacteristic
43#2851—21no—
44#2761—21no—
45#2757—21no—
46#2737—21no—
47#2723—21no—
48#2666—21no—
49#2666—21no—
50#2644C2211yescharacteristic
51#2640C2211yescharacteristic
52#2571C2211yescharacteristic, complemented
53#2570—21no—
54#2561—21no—
55#2552C2211yescharacteristic, complemented
56#2552C2211yescharacteristic, complemented
57#2551C2211yescharacteristic, complemented
58#2550—21no—
59#2512C2211yescharacteristic
60#2483—21no—
61#2480—21no—
62#2452C2211yescharacteristic
63#2448C2211yescharacteristic
64#2447C2211yescharacteristic
65#2442C2211yescharacteristic
66#2442C2211yescharacteristic
67#2440C2211yescharacteristic
68#2440C2211yescharacteristic
69#2440C2211yescharacteristic
70#2438—21no—
71#2438—21no—
72#2437—21no—
73#2435C2211yescharacteristic
74#2360C2211yescharacteristic
75D4×C22⋊C4C2211yescharacteristic
76#2331C2211yescharacteristic, complemented
77#2331C2211yescharacteristic, complemented
78#2330C2211yescharacteristic, complemented
79#2330C2211yescharacteristic, complemented
80#2326C2211yescharacteristic
81#2319C2211yescharacteristic
82C2×#390C2211yescharacteristic
83#2285C2211yescharacteristic
84#2283C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2096C2211yescharacteristic, complemented
89#2096C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2072C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic, complemented
113#2058C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2058C2211yescharacteristic, complemented
116#2058C2211yescharacteristic, complemented
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1992C2211yescharacteristic, complemented
128#1989C2211yescharacteristic, complemented
129#1959C2211yescharacteristic
130#1958C2211yescharacteristic
131#1948C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1943C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1920C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1918C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1844C2211yescharacteristic, complemented
187#1840C2211yescharacteristic, complemented
188#1832C2211yescharacteristic, complemented
189#1817C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1768C2211yescharacteristic, complemented
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1746C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117—21no—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230C22×C22⋊C4—21no—
231C22×C42—21no—
232C22×C42C2311yescharacteristic
233#498—42no—
234#489—42no—
235#488—24no—
236#478—24no—
237#476—42no—
238#475—42no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106—42no—
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#102—24no—
269C2×#102—42no—
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×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#399—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#394—21no—
324#394—21no—
325#393—21no—
326#393—21no—
327#393—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#390—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
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#389C2311yescharacteristic
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#386—21no—
386#386—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384—21no—
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383D411yescharacteristic
405#383D411yescharacteristic
406#382—21no—
407#382—21no—
408#382D411yescharacteristic
409#382D411yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381—21no—
414#381—21no—
415#381D411yescharacteristic
416#381D411yescharacteristic
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380D411yescharacteristic
422#380D411yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427#379—21no—
428#379—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444#376C2311yescharacteristic
445#376C2311yescharacteristic
446C2×#95—21no—
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
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2×D411yescharacteristic
507C23×C4C2×D411yescharacteristic
508C23×C4C2411yescharacteristic
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—82no—
530#126—82no—
531#125—22no—
532#125—22no—
533#125—41no—
534#125—41no—
535#125—82no—
536#124—22no—
537#124—41no—
538#124—41no—
539#124—41no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—82no—
543C22⋊Q8—82no—
544C22⋊Q8—82no—
545C22⋊Q8—82no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×D4—22no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552#117—82no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—82no—
638C2×C22⋊C4—82no—
639C2×C22⋊C4—82no—
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C42—22no—
645C2×C42—22no—
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×C42—82no—
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663#107—22no—
664#107—41no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102#4114yes—
707C22⋊C8—22no—
708C22⋊C8—22no—
709#97—41no—
710#97—41no—
711C4×C8—22no—
712C4×C8—41no—
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#95—21no—
745#95—21no—
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
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
762C24—21no—
763C24—21no—
764C24—42no—
765C24—42no—
766C24—42no—
767C24—42no—
768C24—81no—
769C24—81no—
770C24—81no—
771C24C22×D411yescharacteristic
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—82no—
803C2×D4—82no—
804C2×D4—81no—
805C2×D4C2×#4112yes—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—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—41no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
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×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C42−1+412yes—
859C22×C42−1+412yes—
860C22×C4C2511yescharacteristic
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×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—44no—
885C2×C8—82no—
886C2×C8C2×#4112yes—
887C4⋊C4—22no—
888C4⋊C4—22no—
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—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
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—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4C2×#4112yes—
951C4⋊C4H(5,𝔽2)12yes—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
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—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
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—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C42—22no—
983C42—22no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—42no—
997C42—42no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—22no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—84no—
1023C23—84no—
1024C23—84no—
1025C23—84no—
1026C23—162no—
1027C23—162no—
1028C23—162no—
1029C23#53612yes—
1030C23#57712yes—
1031C23#57712yes—
1032C23C23×D411yescharacteristic
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—41no—
1037Q8—162no—
1038Q8—162no—
1039Q8—162no—
1040D4—22no—
1041D4—22no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—84no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
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—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
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—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—44no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—44no—
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—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—84no—
1135C2×C4—84no—
1136C2×C4—162no—
1137C2×C4—162no—
1138C2×C4—162no—
1139C2×C4#53612yes—
1140C2×C4#57712yes—
1141C2×C4C22×#4111yescharacteristic
1142C2×C4C2×H(5,𝔽2)11yescharacteristic
1143C2×C4C2×2−1+411yescharacteristic
1144C2×C4C2×2−1+411yescharacteristic
1145C2×C4#58511yescharacteristic
1146C2×C4#58511yescharacteristic
1147C8—22no—
1148C8—41no—
1149C8—41no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C22—22no—
1156C22—22no—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—168no—
1176C22#324414yes—
1177C22C2×#53611yescharacteristic
1178C22D4×#4111yescharacteristic
1179C22#348811yescharacteristic
1180C22C2×#57711yescharacteristic
1181C22C2×#57711yescharacteristic
1182C22C2×#57711yescharacteristic
1183C22#358511yescharacteristic
1184C4—22no—
1185C4—22no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—42no—
1191C4—41no—
1192C4—41no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4#349511yescharacteristic
1212C4#352011yescharacteristic
1213C4#356111yescharacteristic
1214C4#356411yescharacteristic
1215C2—24no—
1216C2—82no—
1217C2—161no—
1218C2#3837011yescharacteristic
1219C2C2×#324411yescharacteristic
1220C2#6087311yescharacteristic
1221C2#6148311yescharacteristic
1222C2#6152211yescharacteristic
1223C2#6201611yescharacteristic
1224C2#6205511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35239C2semidirect
3. #33100C2semidirect
4. #32378C2semidirect
5. #32253C2semidirect
6. #31590C2semidirect
7. #31583C2semidirect
8. #31483C2semidirect
9. #30954C2semidirect
10. #30824C2semidirect
11. #30819C2semidirect
12. #30163C2semidirect
13. #30074C2semidirect
14. #29524C2semidirect
15. #29400C2semidirect
16. #28776C2semidirect
17. #28662C2semidirect
18. #28212C2semidirect
19. #27855C2semidirect
23. #26416C2semidirect
24. #26340C2semidirect
25. #26060C2semidirect
28. #22595C2semidirect
29. #22227C2semidirect
30. #22122C2semidirect
32. C2×#498C22semidirect
35. C2×#475C22semidirect
52. #2571C22semidirect
55. #2552C22semidirect
56. #2552C22semidirect
57. #2551C22semidirect
76. #2331C22semidirect
77. #2331C22semidirect
78. #2330C22semidirect
79. #2330C22semidirect
86. #2101C22semidirect
87. #2099C22semidirect
88. #2096C22semidirect
89. #2096C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2084C22semidirect
99. #2084C22semidirect
100. #2084C22semidirect
102. #2072C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
112. #2059C22semidirect
113. #2058C22semidirect
114. #2058C22semidirect
115. #2058C22semidirect
116. #2058C22semidirect
121. #2026C22semidirect
126. #1993C22semidirect
127. #1992C22semidirect
128. #1989C22semidirect
131. #1948C22semidirect
132. #1944C22semidirect
133. #1943C22semidirect
134. #1941C22semidirect
135. #1941C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
142. #1927C22semidirect
143. #1927C22semidirect
144. #1927C22semidirect
145. #1927C22semidirect
158. #1920C22semidirect
159. #1920C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1919C22semidirect
163. #1919C22semidirect
164. #1918C22semidirect
165. #1918C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
186. #1844C22semidirect
187. #1840C22semidirect
188. #1832C22semidirect
192. #1805C22semidirect
197. #1768C22semidirect
200. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#380542
#352392
#331002
#323782
#322532
#315902
#315832
#314832
#309542
#308242
#308192
#301632
#300742
#295242
#294002
#287762
#286622
#282122
#278552
#275852
#272622
#272562
#264162
#263402
#260602
#259602
#259582
#225952
#222272
#221222
C2×#19262