Finite Group Databasebeta

← #6493372

Subgroups — #6493372

Order 512.

1669 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37292C211yesmaximal, characteristic, complemented
2#34190C211yesmaximal, characteristic, complemented
3#33203C211yesmaximal, characteristic, complemented
4#33038C211yesmaximal, characteristic, complemented
5#32959C211yesmaximal, characteristic, complemented
6#32902C211yesmaximal, characteristic
7#29990C211yesmaximal, characteristic, complemented
8#29940C211yesmaximal, characteristic, complemented
9#29925C211yesmaximal, characteristic, complemented
10#29834C211yesmaximal, characteristic, complemented
11#27574C211yesmaximal, characteristic, complemented
12#27560C211yesmaximal, characteristic, complemented
13#27513C211yesmaximal, characteristic, complemented
14#27495C211yesmaximal, characteristic, complemented
15#27447C211yesmaximal, characteristic, complemented
16#27431C211yesmaximal, characteristic, complemented
17#27347C211yesmaximal, characteristic, complemented
18#27333C211yesmaximal, characteristic, complemented
19#27240C211yesmaximal, characteristic, complemented
20#27222C211yesmaximal, characteristic, complemented
21#27174C211yesmaximal, characteristic, complemented
22#27158C211yesmaximal, characteristic, complemented
23#26388C211yesmaximal, characteristic, complemented
24#26370C211yesmaximal, characteristic, complemented
25#24913C211yesmaximal, characteristic, complemented
26#24897C211yesmaximal, characteristic, complemented
27#22158C211yesmaximal, characteristic, complemented
28#22126C211yesmaximal, characteristic, complemented
29#21928C211yesmaximal, characteristic, complemented
30#21619C211yesmaximal, characteristic, complemented
31#21513C211yesmaximal, characteristic, complemented
32C22×C4×D4C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43#2856C2211yescharacteristic
44#2851C2211yescharacteristic
45#2761—21no—
46#2757—21no—
47#2737—21no—
48#2723—21no—
49#2701—21no—
50#2691—21no—
51#2686—21no—
52#2672—21no—
53#2660C2211yescharacteristic, complemented
54#2641C2211yescharacteristic, complemented
55#2513C2211yescharacteristic, complemented
56#2512C2211yescharacteristic, complemented
57#2491C2211yescharacteristic
58#2490C2211yescharacteristic
59#2454C2211yescharacteristic, complemented
60#2452C2211yescharacteristic, complemented
61#2422C2211yescharacteristic
62#2420C2211yescharacteristic
63#2357C2211yescharacteristic
64#2357C2211yescharacteristic
65#2353—21no—
66#2353—21no—
67#2349C2211yescharacteristic
68#2349C2211yescharacteristic
69#2344C2211yescharacteristic
70#2344C2211yescharacteristic
71#2342—21no—
72#2342—21no—
73D4×C22⋊C4C2211yescharacteristic
74D4×C22⋊C4C2211yescharacteristic
75#2330C2211yescharacteristic, complemented
76#2328C2211yescharacteristic, complemented
77#2319C2211yescharacteristic
78#2319C2211yescharacteristic
79#2318—21no—
80#2318—21no—
81#2283C2211yescharacteristic
82#2283C2211yescharacteristic
83#2280—21no—
84C2×#381—21no—
85#2275C2211yescharacteristic
86#2275C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic, complemented
94#2092C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2058C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2025C2211yescharacteristic
118#2023C2211yescharacteristic
119#1989C2211yescharacteristic, complemented
120#1989C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1987C2211yescharacteristic, complemented
123#1982C2211yescharacteristic, complemented
124#1982C2211yescharacteristic, complemented
125#1972C2211yescharacteristic
126#1970C2211yescharacteristic
127#1949C2211yescharacteristic, complemented
128#1949C2211yescharacteristic, complemented
129#1949C2211yescharacteristic, complemented
130#1948C2211yescharacteristic, complemented
131#1947C2211yescharacteristic, complemented
132#1947C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic, complemented
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic, complemented
139#1926C2211yescharacteristic, complemented
140#1926C2211yescharacteristic, complemented
141#1926C2211yescharacteristic, complemented
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic, complemented
145#1925C2211yescharacteristic, complemented
146#1925C2211yescharacteristic, complemented
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1921C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1917C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1843C2211yescharacteristic, complemented
184#1832C2211yescharacteristic, complemented
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1797C2211yescharacteristic
192#1797C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196C4×#106C2211yescharacteristic, complemented
197#1768C2211yescharacteristic, complemented
198#1768C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×D4—24no—
222C2×C4×D4—24no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117—21no—
236C2×#117—21no—
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C42C2311yescharacteristic
242#478—24no—
243#478—24no—
244#478—42no—
245#474—42no—
246#459—24no—
247#459—24no—
248#447—42no—
249#447—42no—
250#442—42no—
251C4×D8—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#399—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#393—21no—
327#393—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#389—21no—
344#389—21no—
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#383—21no—
395#383D411yescharacteristic
396#383D411yescharacteristic
397#382D411yescharacteristic
398#382D411yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#381—21no—
404#381—21no—
405#381—21no—
406#381—21no—
407#381—21no—
408#381—21no—
409#381—21no—
410#381—21no—
411#381D411yescharacteristic
412#381D411yescharacteristic
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380D411yescharacteristic
419#380D411yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#379—21no—
425#379—21no—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447#376—21no—
448#376C2311yescharacteristic
449#376C2311yescharacteristic
450C2×#95—21no—
451C2×#95—21no—
452C2×#95—21no—
453C2×#95—21no—
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#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—28no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—82no—
520C23×C4—82no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546#127—22no—
547#127—22no—
548#126—82no—
549#125—22no—
550#125—22no—
551#125—41no—
552#125—41no—
553#124—82no—
554#123—82no—
555C22⋊Q8—82no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—82no—
561#121—82no—
562C4×D4—28no—
563C4×D4—28no—
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—22no—
573C4×D4—22no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4#4114yes—
583C4×D4#4114yes—
584#117—82no—
585#117—82no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C22⋊C4—28no—
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—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—82no—
664C2×C22⋊C4—82no—
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—22no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735#97—41no—
736#97—41no—
737C4×C8—41no—
738C4×C8—41no—
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#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783C24—21no—
784C24—24no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—42no—
789C24—42no—
790C24—42no—
791C24—42no—
792C24—81no—
793C24—81no—
794C24C22×D411yescharacteristic
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×D4—24no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
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—21no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4C2×#4112yes—
838C2×D4C2×#4112yes—
839C2×D4H(5,𝔽2)12yes—
840C2×D42−1+412yes—
841C22×C4—24no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
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×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—816no—
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C2511yescharacteristic
913D8—44no—
914D8—44no—
915D8—82no—
916D8—82no—
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—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C4⋊C4—24no—
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—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
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⋊C4C2×#4112yes—
986C4⋊C4C2×#4112yes—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
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—
1031C42—22no—
1032C42—22no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C42C2×#4112yes—
1052C42C2×#4112yes—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—22no—
1057C23—21no—
1058C23—22no—
1059C23—21no—
1060C23—22no—
1061C23—21no—
1062C23—22no—
1063C23—48no—
1064C23—48no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
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—41no—
1088C23—41no—
1089C23—84no—
1090C23—84no—
1091C23—84no—
1092C23—84no—
1093C23—84no—
1094C23#57612yes—
1095C23C23×D411yescharacteristic
1096Q8—162no—
1097D4—22no—
1098D4—22no—
1099D4—22no—
1100D4—22no—
1101D4—22no—
1102D4—48no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—162no—
1114D4—162no—
1115D4—162no—
1116D4—162no—
1117D4#54214yes—
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—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—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—44no—
1158C2×C4—48no—
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—41no—
1197C2×C4—82no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4#52512yes—
1209C2×C4#52512yes—
1210C2×C4C22×#4111yescharacteristic
1211C2×C4C22×#4111yescharacteristic
1212C2×C4C2×H(5,𝔽2)11yescharacteristic
1213C2×C4C2×2−1+411yescharacteristic
1214C2×C4#58511yescharacteristic
1215C2×C4#58511yescharacteristic
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—24no—
1228C22—42no—
1229C22—42no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—41no—
1234C22—42no—
1235C22—41no—
1236C22—42no—
1237C22—41no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—816no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22C2×#52511yescharacteristic
1261C22#348811yescharacteristic
1262C22#348911yescharacteristic
1263C22C2×#57611yescharacteristic
1264C22#358411yescharacteristic
1265C22#358511yescharacteristic
1266C22#358511yescharacteristic
1267C4—22no—
1268C4—22no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—42no—
1280C4—41no—
1281C4—41no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4C2×#54211yescharacteristic
1293C4#345511yescharacteristic
1294C4#349411yescharacteristic
1295C4#349511yescharacteristic
1296C2—42no—
1297C2—44no—
1298C2—82no—
1299C2—161no—
1300C2—161no—
1301C2#3526011yescharacteristic
1302C2#6057811yescharacteristic
1303C2#6058711yescharacteristic
1304C2#6200711yescharacteristic
1305C2#6202811yescharacteristic
1306C2#6221111yescharacteristic
1307C2#6223111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32902C2
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
1. #37292C2semidirect
2. #34190C2semidirect
3. #33203C2semidirect
4. #33038C2semidirect
5. #32959C2semidirect
7. #29990C2semidirect
8. #29940C2semidirect
9. #29925C2semidirect
10. #29834C2semidirect
11. #27574C2semidirect
12. #27560C2semidirect
13. #27513C2semidirect
14. #27495C2semidirect
15. #27447C2semidirect
16. #27431C2semidirect
17. #27347C2semidirect
18. #27333C2semidirect
19. #27240C2semidirect
20. #27222C2semidirect
21. #27174C2semidirect
22. #27158C2semidirect
23. #26388C2semidirect
24. #26370C2semidirect
25. #24913C2semidirect
26. #24897C2semidirect
27. #22158C2semidirect
28. #22126C2semidirect
29. #21928C2semidirect
30. #21619C2semidirect
31. #21513C2semidirect
53. #2660C22semidirect
54. #2641C22semidirect
55. #2513C22semidirect
56. #2512C22semidirect
59. #2454C22semidirect
60. #2452C22semidirect
75. #2330C22semidirect
76. #2328C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2099C22semidirect
93. #2092C22semidirect
94. #2092C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
101. #2073C22semidirect
102. #2073C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2065C22semidirect
106. #2065C22semidirect
107. #2059C22semidirect
108. #2058C22semidirect
119. #1989C22semidirect
120. #1989C22semidirect
121. #1989C22semidirect
122. #1987C22semidirect
123. #1982C22semidirect
124. #1982C22semidirect
127. #1949C22semidirect
128. #1949C22semidirect
129. #1949C22semidirect
130. #1948C22semidirect
131. #1947C22semidirect
132. #1947C22semidirect
133. #1944C22semidirect
134. #1942C22semidirect
136. #1936C22semidirect
138. #1934C22semidirect
139. #1926C22semidirect
140. #1926C22semidirect
141. #1926C22semidirect
144. #1925C22semidirect
145. #1925C22semidirect
146. #1925C22semidirect
151. #1921C22semidirect
152. #1919C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1917C22semidirect
156. #1917C22semidirect
157. #1916C22semidirect
158. #1916C22semidirect
177. #1864C22semidirect
180. #1862C22semidirect
183. #1843C22semidirect
184. #1832C22semidirect
195. #1776C22semidirect
196. C4×#106C22semidirect
197. #1768C22semidirect
198. #1768C22semidirect
200. #1762C22semidirect
202. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#372922
#341902
#332032
#330382
#329592
#329022
#299902
#299402
#299252
#298342
#275742
#275602
#275132
#274952
#274472
#274312
#273472
#273332
#272402
#272222
#271742
#271582
#263882
#263702
#249132
#248972
#221582
#221262
#219282
#216192
#215132