Finite Group Databasebeta

← #6589313

Subgroups — #6589313

Order 512.

1657 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36017C211yesmaximal, characteristic, complemented
2#35730C211yesmaximal, characteristic
3#33219C211yesmaximal, characteristic, complemented
4#33155C211yesmaximal, characteristic, complemented
5#32966C211yesmaximal, characteristic, complemented
6#28870C211yesmaximal, characteristic, complemented
7#28866C211yesmaximal, characteristic, complemented
8#28110C211yesmaximal, characteristic, complemented
9#28110C211yesmaximal, characteristic, complemented
10#27728C211yesmaximal, characteristic, complemented
11#27170C211yesmaximal, characteristic, complemented
12#27166C211yesmaximal, characteristic, complemented
13#27033C211yesmaximal, characteristic, complemented
14#27031C211yesmaximal, characteristic, complemented
15#26103C211yesmaximal, characteristic, complemented
16#25709C211yesmaximal, characteristic, complemented
17#25466C211yesmaximal, characteristic, complemented
18#25344C211yesmaximal, characteristic, complemented
19#25023C211yesmaximal, characteristic, complemented
20#24936C211yesmaximal, characteristic, complemented
21#24934C211yesmaximal, characteristic, complemented
22#24873C211yesmaximal, characteristic, complemented
23#24869C211yesmaximal, characteristic, complemented
24#23065C211yesmaximal, characteristic, complemented
25#22946C211yesmaximal, characteristic, complemented
26#22944C211yesmaximal, characteristic, complemented
27#22716C211yesmaximal, characteristic, complemented
28#22714C211yesmaximal, characteristic, complemented
29#22500C211yesmaximal, characteristic, complemented
30#21494C211yesmaximal, characteristic, complemented
31#20416C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#436C2211yescharacteristic, complemented
42C2×#418C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C2×#405C2211yescharacteristic
45#2648—21no—
46#2638—21no—
47#2629C2211yescharacteristic
48#2628C2211yescharacteristic
49#2594—21no—
50#2593—21no—
51#2571C2211yescharacteristic, complemented
52#2563C2211yescharacteristic
53#2562C2211yescharacteristic, complemented
54#2561—21no—
55#2535C2211yescharacteristic
56#2529—21no—
57#2524—21no—
58#2518—21no—
59#2518—21no—
60#2495C2211yescharacteristic, complemented
61#2494C2211yescharacteristic, complemented
62#2485C2211yescharacteristic
63#2485C2211yescharacteristic
64#2457—21no—
65#2457—21no—
66#2420C2211yescharacteristic
67#2420C2211yescharacteristic
68#2418—21no—
69#2418—21no—
70#2408C2211yescharacteristic
71#2408C2211yescharacteristic
72#2404—21no—
73#2401—21no—
74#2392C2211yescharacteristic
75#2388—21no—
76#2370C2211yescharacteristic, complemented
77#2361C2211yescharacteristic
78#2361C2211yescharacteristic
79#2357C2211yescharacteristic
80#2354C2211yescharacteristic, complemented
81#2352C2211yescharacteristic
82#2352C2211yescharacteristic
83#2352C2211yescharacteristic
84#2352C2211yescharacteristic
85#2347C2211yescharacteristic, complemented
86#2346C2211yescharacteristic, complemented
87#2274C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2075C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2034C2211yescharacteristic
105#2034C2211yescharacteristic
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#1991C2211yescharacteristic, complemented
113#1990C2211yescharacteristic, complemented
114#1988C2211yescharacteristic, complemented
115#1987C2211yescharacteristic, complemented
116#1955C2211yescharacteristic, complemented
117#1949C2211yescharacteristic, complemented
118#1949C2211yescharacteristic, complemented
119#1949C2211yescharacteristic, complemented
120#1949C2211yescharacteristic, complemented
121#1949C2211yescharacteristic, complemented
122#1949C2211yescharacteristic, complemented
123#1944C2211yescharacteristic, complemented
124#1943C2211yescharacteristic, complemented
125#1942C2211yescharacteristic, complemented
126#1941C2211yescharacteristic, complemented
127#1940C2211yescharacteristic, complemented
128#1934C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic
136#1923C2211yescharacteristic, complemented
137#1923C2211yescharacteristic, complemented
138#1921C2211yescharacteristic, complemented
139#1921C2211yescharacteristic, complemented
140#1920C2211yescharacteristic, complemented
141#1920C2211yescharacteristic, complemented
142#1919C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1918C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1895C2211yescharacteristic
147#1895C2211yescharacteristic
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1875C2211yescharacteristic
151#1875C2211yescharacteristic
152#1869C2211yescharacteristic
153#1869C2211yescharacteristic
154#1864C2211yescharacteristic
155#1864C2211yescharacteristic
156#1862C2211yescharacteristic
157#1862C2211yescharacteristic
158#1854C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic, complemented
161#1854C2211yescharacteristic, complemented
162#1853C2211yescharacteristic
163#1853C2211yescharacteristic, complemented
164#1853C2211yescharacteristic, complemented
165#1852C2211yescharacteristic
166#1852C2211yescharacteristic, complemented
167#1852C2211yescharacteristic, complemented
168#1847C2211yescharacteristic, complemented
169#1835C2211yescharacteristic, complemented
170#1835C2211yescharacteristic, complemented
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic
173#1824C2211yescharacteristic, complemented
174#1824C2211yescharacteristic, complemented
175#1809C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic, complemented
178#1809C2211yescharacteristic, complemented
179#1808C2211yescharacteristic
180#1807C2211yescharacteristic
181#1802C2211yescharacteristic
182#1802C2211yescharacteristic
183#1798C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186C4×#107C2211yescharacteristic, complemented
187C4×#106C2211yescharacteristic, complemented
188C8×C4⋊C4C2211yescharacteristic, complemented
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1735C2211yescharacteristic
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#547—24no—
210#547—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×C22⋊Q8—21no—
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×#120—21no—
222#518—24no—
223#518—42no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245#501—42no—
246#482—24no—
247#482—24no—
248#478—24no—
249#478—42no—
250#436—24no—
251#436—24no—
252#436—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—24no—
274C2×#102—24no—
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299#405—42no—
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#401—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#398D411yescharacteristic
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397D411yescharacteristic
324#396—21no—
325#396—21no—
326#396D411yescharacteristic
327#396D411yescharacteristic
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394D411yescharacteristic
337#394D411yescharacteristic
338#394D411yescharacteristic
339#393—21no—
340#393—21no—
341#393—21no—
342#392—21no—
343#392—21no—
344#392—21no—
345#392D411yescharacteristic
346#390—21no—
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
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#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—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#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#384C2311yescharacteristic
403#383—21no—
404#383—21no—
405#382—21no—
406#382—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381—21no—
414#381—21no—
415#380—21no—
416#380—21no—
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376—21no—
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—44no—
495C2×#41—82no—
496C2×#41—82no—
497C22×Q8—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C2×M16—41no—
529C2×M16—41no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16#4114yescomplemented
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546#125—22no—
547#125—22no—
548#123—44no—
549#123—44no—
550C22⋊Q8—44no—
551#121—22no—
552#121—22no—
553#121—22no—
554#121—22no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#120—82no—
560#120—82no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—44no—
575C4×D4—44no—
576C4×D4—82no—
577C4×D4—82no—
578C4×D4#4114yes—
579#117—22no—
580#117—22no—
581#117—22no—
582#117—22no—
583#117—22no—
584#117—22no—
585#117—22no—
586#117—41no—
587#117—41no—
588#117—41no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4—44no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#107—22no—
695#107—22no—
696#107—22no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#106—22no—
703#106—22no—
704#106—22no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710C4⋊C8—22no—
711C4⋊C8—22no—
712C4⋊C8—22no—
713C4⋊C8—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102#4114yescomplemented
730C22⋊C8—22no—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738#97—22no—
739#97—41no—
740C4×C8—22no—
741C4×C8—22no—
742C4×C8—22no—
743C4×C8—41no—
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#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788C24—21no—
789C24—21no—
790C24—42no—
791C24—42no—
792C24—42no—
793C24—81no—
794C24—81no—
795C24—81no—
796C24—81no—
797C24C22×D411yescharacteristic
798C24C22×D411yescharacteristic
799C24C22×D411yescharacteristic
800#41—816no—
801C2×Q8—42no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×D4—28no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—44no—
825C2×D4—41no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4C2×#4112yes—
843C2×D4C2×#4112yes—
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—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—24no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C2×#4112yes—
907C22×C42−1+412yes—
908C22×C4C2511yescharacteristic
909M16—44no—
910M16—82no—
911M16—82no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—44no—
934C2×C8C2×#4112yes—
935C2×C8C2×#4112yes—
936C2×C8C2×#4112yes—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4C2×#4112yes—
987C4⋊C4C2×#4112yes—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—24no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C42C2×#4112yes—
1051C42H(5,𝔽2)12yes—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—22no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—22no—
1074C23—48no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23—162no—
1093C23#54712yes—
1094C23C23×D411yescharacteristic
1095Q8—84no—
1096D4—22no—
1097D4—22no—
1098D4—22no—
1099D4—22no—
1100D4—48no—
1101D4—44no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—82no—
1107D4—82no—
1108D4—84no—
1109D4—84no—
1110D4—84no—
1111D4—84no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
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—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4#54612yes—
1204C2×C4#54612yes—
1205C2×C4#54712yes—
1206C2×C4C22×#4111yescharacteristic
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C22×#4111yescharacteristic
1209C2×C4C2×H(5,𝔽2)11yescharacteristic
1210C2×C4C2×2−1+411yescharacteristic
1211C2×C4#58511yescharacteristic
1212C8—22no—
1213C8—22no—
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—42no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—42no—
1233C22—42no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—42no—
1240C22—41no—
1241C22—41no—
1242C22—42no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—42no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—168no—
1256C22C2×#54611yescharacteristic
1257C22C2×#54711yescharacteristic
1258C22D4×#4111yescharacteristic
1259C22#358411yescharacteristic
1260C22#358411yescharacteristic
1261C22#358511yescharacteristic
1262C22#358511yescharacteristic
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—42no—
1274C4—41no—
1275C4—42no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4#344411yescharacteristic
1289C4#349511yescharacteristic
1290C4#350511yescharacteristic
1291C4#352011yescharacteristic
1292C2—42no—
1293C2—81no—
1294C2—81no—
1295C2—82no—
1296C2—82no—
1297C2#3614311yescharacteristic
1298C2#6117511yescharacteristic
1299C2#6121611yescharacteristic
1300C2#6127411yescharacteristic
1301C2#6127611yescharacteristic
1302C2#6153511yescharacteristic
1303C2#6153611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35730C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36017C2semidirect
3. #33219C2semidirect
4. #33155C2semidirect
5. #32966C2semidirect
6. #28870C2semidirect
7. #28866C2semidirect
8. #28110C2semidirect
9. #28110C2semidirect
10. #27728C2semidirect
11. #27170C2semidirect
12. #27166C2semidirect
13. #27033C2semidirect
14. #27031C2semidirect
15. #26103C2semidirect
16. #25709C2semidirect
17. #25466C2semidirect
18. #25344C2semidirect
19. #25023C2semidirect
20. #24936C2semidirect
21. #24934C2semidirect
22. #24873C2semidirect
23. #24869C2semidirect
24. #23065C2semidirect
25. #22946C2semidirect
26. #22944C2semidirect
27. #22716C2semidirect
28. #22714C2semidirect
29. #22500C2semidirect
30. #21494C2semidirect
31. #20416C2semidirect
34. C2×#501C22semidirect
41. C2×#436C22semidirect
51. #2571C22semidirect
53. #2562C22semidirect
60. #2495C22semidirect
61. #2494C22semidirect
76. #2370C22semidirect
80. #2354C22semidirect
85. #2347C22semidirect
86. #2346C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
94. #2077C22semidirect
95. #2077C22semidirect
96. #2075C22semidirect
97. #2075C22semidirect
112. #1991C22semidirect
113. #1990C22semidirect
114. #1988C22semidirect
115. #1987C22semidirect
116. #1955C22semidirect
117. #1949C22semidirect
118. #1949C22semidirect
119. #1949C22semidirect
120. #1949C22semidirect
121. #1949C22semidirect
122. #1949C22semidirect
123. #1944C22semidirect
124. #1943C22semidirect
125. #1942C22semidirect
126. #1941C22semidirect
127. #1940C22semidirect
136. #1923C22semidirect
137. #1923C22semidirect
138. #1921C22semidirect
139. #1921C22semidirect
140. #1920C22semidirect
141. #1920C22semidirect
142. #1919C22semidirect
143. #1919C22semidirect
144. #1918C22semidirect
145. #1918C22semidirect
160. #1854C22semidirect
161. #1854C22semidirect
163. #1853C22semidirect
164. #1853C22semidirect
166. #1852C22semidirect
167. #1852C22semidirect
168. #1847C22semidirect
169. #1835C22semidirect
170. #1835C22semidirect
173. #1824C22semidirect
174. #1824C22semidirect
177. #1809C22semidirect
178. #1809C22semidirect
186. C4×#107C22semidirect
187. C4×#106C22semidirect
188. C8×C4⋊C4C22semidirect
197. #1753C22semidirect
198. #1753C22semidirect
200. #1736C22semidirect
201. #1736C22semidirect
532. C2×M16#41semidirect
729. #102#41semidirect

Maximal subgroups

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

subgroupindex
#360172
#357302
#332192
#331552
#329662
#288702
#288662
#281102
#277282
#271702
#271662
#270332
#270312
#261032
#257092
#254662
#253442
#250232
#249362
#249342
#248732
#248692
#230652
#229462
#229442
#227162
#227142
#225002
#214942
#204162