Finite Group Databasebeta

← #7011082

Subgroups — #7011082

Order 512.

1446 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45214C211yesmaximal, characteristic, complemented
2#42757C211yesmaximal, characteristic, complemented
3#32276C211yesmaximal, characteristic, complemented
4#31697C211yesmaximal, characteristic, complemented
5#31633C211yesmaximal, characteristic, complemented
6#31609C211yesmaximal, characteristic, complemented
7#31557C211yesmaximal, characteristic, complemented
8#31479C211yesmaximal, characteristic, complemented
9#31247C211yesmaximal, characteristic, complemented
10#30416C211yesmaximal, characteristic
11#29174C211yesmaximal, characteristic, complemented
12#28958C211yesmaximal, characteristic, complemented
13#28866C211yesmaximal, characteristic, complemented
14#28100C211yesmaximal, characteristic, complemented
15#27843C211yesmaximal, characteristic, complemented
16#27539C211yesmaximal, characteristic, complemented
17#27450C211yesmaximal, characteristic, complemented
18#27372C211yesmaximal, characteristic, complemented
19#27055C211yesmaximal, characteristic, complemented
20#26380C211yesmaximal, characteristic, complemented
21#26103C211yesmaximal, characteristic, complemented
22#25974C211yesmaximal, characteristic, complemented
23#25354C211yesmaximal, characteristic, complemented
24#25038C211yesmaximal, characteristic, complemented
25#24897C211yesmaximal, characteristic, complemented
26#24716C211yesmaximal, characteristic, complemented
27#23703C211yesmaximal, characteristic, complemented
28#22903C211yesmaximal, characteristic, complemented
29#22880C211yesmaximal, characteristic, complemented
30#22764C211yesmaximal, characteristic, complemented
31#22202C211yesmaximal, characteristic, complemented
32C2×#476C2211yescharacteristic
33C2×#476C2211yescharacteristic, complemented
34C2×#469C2211yescharacteristic
35C2×#447C2211yescharacteristic
36C2×C4×D8C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#433C2211yescharacteristic, complemented
40C2×#418C2211yescharacteristic
41#2824—21no—
42#2796—21no—
43#2749—21no—
44#2749—21no—
45#2745—21no—
46#2735—21no—
47#2728—21no—
48#2723—21no—
49#2705—21no—
50#2652—21no—
51#2643—21no—
52#2628C2211yescharacteristic, complemented
53#2572—21no—
54#2571C2211yescharacteristic, complemented
55#2547C2211yescharacteristic
56#2535C2211yescharacteristic
57#2509C2211yescharacteristic, complemented
58#2496C2211yescharacteristic
59#2495C2211yescharacteristic
60#2495C2211yescharacteristic
61#2494C2211yescharacteristic, complemented
62#2488—21no—
63#2485C2211yescharacteristic
64#2483—21no—
65#2472—21no—
66#2472—21no—
67#2452C2211yescharacteristic
68#2452C2211yescharacteristic
69#2452C2211yescharacteristic, complemented
70#2439C2211yescharacteristic
71#2422C2211yescharacteristic, complemented
72#2420C2211yescharacteristic
73#2420C2211yescharacteristic
74#2420C2211yescharacteristic
75#2408C2211yescharacteristic
76#2395C2211yescharacteristic
77#2363C2211yescharacteristic
78#2357C2211yescharacteristic
79#2357C2211yescharacteristic
80#2349C2211yescharacteristic, complemented
81D4×C22⋊C4C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2324C2211yescharacteristic
85#2324C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2058C2211yescharacteristic, complemented
116#2057C2211yescharacteristic, complemented
117#2054C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#1999C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1988C2211yescharacteristic, complemented
128#1972C2211yescharacteristic
129#1949C2211yescharacteristic, complemented
130#1949C2211yescharacteristic, complemented
131#1949C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1943C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1940C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic, complemented
144#1925C2211yescharacteristic
145#1924C2211yescharacteristic
146#1923C2211yescharacteristic
147#1920C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1917C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic, complemented
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1870C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic, complemented
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1851C2211yescharacteristic
179#1850C2211yescharacteristic, complemented
180#1847C2211yescharacteristic, complemented
181#1835C2211yescharacteristic, complemented
182#1825C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1807C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194C4×#107C2211yescharacteristic, complemented
195#1770C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199#1762C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#124—21no—
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C22×C22⋊C4—21no—
233C22×C22⋊C4—21no—
234#476—42no—
235#476—42no—
236#469—24no—
237#447—24no—
238C4×D8—24no—
239C4×D8—42no—
240#435—42no—
241#433—42no—
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
261#418—42no—
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×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#401—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400D411yescharacteristic
302#399—21no—
303#399D411yescharacteristic
304#398D411yescharacteristic
305#397—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#397—21no—
316#397—21no—
317#397D411yescharacteristic
318#397D411yescharacteristic
319#397D411yescharacteristic
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#395—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394D411yescharacteristic
332#394D411yescharacteristic
333#393—21no—
334#393—21no—
335#393—21no—
336#393—21no—
337#393—21no—
338#392—21no—
339#392—21no—
340#391—21no—
341#391—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
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#388—21no—
379#388—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384C2311yescharacteristic
408#383—21no—
409#383—21no—
410#382—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#381—21no—
420#381—21no—
421#380—21no—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379—21no—
433#379—21no—
434#379—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C2×#95—21no—
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#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
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×D4—22no—
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×D8—41no—
518C2×D8—41no—
519C2×D8#4114yes—
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#126—82no—
542#124—82no—
543#123—82no—
544C22⋊Q8—82no—
545C22⋊Q8—82no—
546C22⋊Q8—82no—
547#121—22no—
548#121—22no—
549#121—22no—
550#121—22no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#120—82no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572#117—41no—
573#117—41no—
574#117—41no—
575#117—41no—
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⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—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—82no—
651C2×C22⋊C4—82no—
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#107—22no—
674#107—41no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#106—22no—
680#106—22no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686#106—41no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712C22⋊C8—22no—
713C22⋊C8—22no—
714C22⋊C8—41no—
715C22⋊C8—41no—
716C22⋊C8—41no—
717#97—41no—
718#97—41no—
719#97—41no—
720C4×C8—22no—
721C4×C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24—21no—
771C24—21no—
772C24—42no—
773C24—42no—
774C24—42no—
775C24—81no—
776C24—81no—
777C24—81no—
778C24—81no—
779C24C22×D411yescharacteristic
780C24C22×D411yescharacteristic
781C2×Q8—42no—
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—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4—41no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—81no—
813C2×D4—82no—
814C2×D4—82no—
815C2×D4—82no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4C2×#4112yes—
825C2×D4C2×#4112yes—
826C2×D42−1+412yes—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C2511yescharacteristic
886D8—44no—
887D8—44no—
888M16—82no—
889M16—82no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—82no—
913C2×C8C2×#4112yes—
914C2×C8H(5,𝔽2)12yes—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C42—81no—
1026C42—81no—
1027C42—81no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—22no—
1037C23—22no—
1038C23—21no—
1039C23—21no—
1040C23—22no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—84no—
1064C23—84no—
1065C23—84no—
1066C23—162no—
1067C23—162no—
1068C23—162no—
1069C23—162no—
1070C23C23×D411yescharacteristic
1071Q8—162no—
1072Q8—162no—
1073D4—22no—
1074D4—22no—
1075D4—22no—
1076D4—22no—
1077D4—22no—
1078D4—22no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—82no—
1086D4—84no—
1087D4—162no—
1088D4—162no—
1089D4—162no—
1090D4—162no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—162no—
1175C2×C4—162no—
1176C2×C4—162no—
1177C2×C4—162no—
1178C2×C4—162no—
1179C2×C4—162no—
1180C2×C4—162no—
1181C2×C4C22×#4111yescharacteristic
1182C2×C4C2×H(5,𝔽2)11yescharacteristic
1183C2×C4C2×2−1+411yescharacteristic
1184C2×C4#58511yescharacteristic
1185C2×C4#58511yescharacteristic
1186C2×C4#58511yescharacteristic
1187C8—22no—
1188C8—22no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C22—41no—
1196C22—41no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—41no—
1201C22—42no—
1202C22—41no—
1203C22—42no—
1204C22—42no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—42no—
1212C22—42no—
1213C22—41no—
1214C22—41no—
1215C22—42no—
1216C22—41no—
1217C22—41no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—168no—
1231C22D4×#4111yescharacteristic
1232C22#348911yescharacteristic
1233C22#349611yescharacteristic
1234C22#358411yescharacteristic
1235C22#358511yescharacteristic
1236C22#358511yescharacteristic
1237C22#358511yescharacteristic
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4#349111yescharacteristic
1264C4#352011yescharacteristic
1265C4#356011yescharacteristic
1266C4#356411yescharacteristic
1267C2—81no—
1268C2—81no—
1269C2—82no—
1270C2—82no—
1271C2—82no—
1272C2#4303111yescharacteristic
1273C2#6150511yescharacteristic
1274C2#6152911yescharacteristic
1275C2#6217611yescharacteristic
1276C2#6223511yescharacteristic
1277C2#6228611yescharacteristic
1278C2#6234711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45214C2semidirect
2. #42757C2semidirect
3. #32276C2semidirect
4. #31697C2semidirect
5. #31633C2semidirect
6. #31609C2semidirect
7. #31557C2semidirect
8. #31479C2semidirect
9. #31247C2semidirect
11. #29174C2semidirect
12. #28958C2semidirect
13. #28866C2semidirect
14. #28100C2semidirect
15. #27843C2semidirect
16. #27539C2semidirect
17. #27450C2semidirect
18. #27372C2semidirect
19. #27055C2semidirect
20. #26380C2semidirect
21. #26103C2semidirect
22. #25974C2semidirect
23. #25354C2semidirect
24. #25038C2semidirect
25. #24897C2semidirect
26. #24716C2semidirect
27. #23703C2semidirect
28. #22903C2semidirect
29. #22880C2semidirect
30. #22764C2semidirect
31. #22202C2semidirect
33. C2×#476C22semidirect
39. C2×#433C22semidirect
52. #2628C22semidirect
54. #2571C22semidirect
57. #2509C22semidirect
61. #2494C22semidirect
69. #2452C22semidirect
71. #2422C22semidirect
80. #2349C22semidirect
85. #2324C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
103. #2076C22semidirect
105. #2073C22semidirect
109. #2067C22semidirect
113. #2065C22semidirect
114. #2058C22semidirect
115. #2058C22semidirect
116. #2057C22semidirect
123. #2033C22semidirect
126. #1993C22semidirect
127. #1988C22semidirect
129. #1949C22semidirect
130. #1949C22semidirect
131. #1949C22semidirect
132. #1944C22semidirect
133. #1943C22semidirect
134. #1941C22semidirect
135. #1941C22semidirect
136. #1940C22semidirect
143. #1926C22semidirect
147. #1920C22semidirect
148. #1920C22semidirect
149. #1920C22semidirect
150. #1919C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
153. #1918C22semidirect
154. #1917C22semidirect
155. #1916C22semidirect
160. #1893C22semidirect
172. #1864C22semidirect
175. #1862C22semidirect
179. #1850C22semidirect
180. #1847C22semidirect
181. #1835C22semidirect
185. #1809C22semidirect
186. #1809C22semidirect
187. #1807C22semidirect
190. #1804C22semidirect
194. C4×#107C22semidirect
195. #1770C22semidirect
198. #1762C22semidirect
199. #1762C22semidirect
201. #1753C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#452142
#427572
#322762
#316972
#316332
#316092
#315572
#314792
#312472
#304162
#291742
#289582
#288662
#281002
#278432
#275392
#274502
#273722
#270552
#263802
#261032
#259742
#253542
#250382
#248972
#247162
#237032
#229032
#228802
#227642
#222022