Finite Group Databasebeta

← #7083047

Subgroups — #7083047

Order 512.

1521 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59257C211yesmaximal, characteristic, complemented
2#39189C211yesmaximal, characteristic
3#32405C211yesmaximal, characteristic, complemented
4#32389C211yesmaximal, characteristic, complemented
5#32289C211yesmaximal, characteristic, complemented
6#32288C211yesmaximal, characteristic, complemented
7#32054C211yesmaximal, characteristic, complemented
8#32054C211yesmaximal, characteristic, complemented
9#30579C211yesmaximal, characteristic, complemented
10#30570C211yesmaximal, characteristic, complemented
11#29164C211yesmaximal, characteristic, complemented
12#28086C211yesmaximal, characteristic, complemented
13#28067C211yesmaximal, characteristic, complemented
14#27951C211yesmaximal, characteristic, complemented
15#27946C211yesmaximal, characteristic, complemented
16#27926C211yesmaximal, characteristic, complemented
17#27508C211yesmaximal, characteristic, complemented
18#27490C211yesmaximal, characteristic, complemented
19#26150C211yesmaximal, characteristic, complemented
20#26148C211yesmaximal, characteristic, complemented
21#26142C211yesmaximal, characteristic, complemented
22#26130C211yesmaximal, characteristic, complemented
23#25136C211yesmaximal, characteristic, complemented
24#25120C211yesmaximal, characteristic, complemented
25#24882C211yesmaximal, characteristic, complemented
26#24878C211yesmaximal, characteristic, complemented
27#23731C211yesmaximal, characteristic, complemented
28#23118C211yesmaximal, characteristic, complemented
29#22666C211yesmaximal, characteristic, complemented
30#22659C211yesmaximal, characteristic, complemented
31#22043C211yesmaximal, characteristic, complemented
32C2×#484C2211yescharacteristic, complemented
33C2×#481C2211yescharacteristic
34C2×#485C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#428C2211yescharacteristic, complemented
44C22×#106C2211yescharacteristic, complemented
45C2×#418C2211yescharacteristic
46C2×#418C2211yescharacteristic
47#2851C2211yescharacteristic
48#2803—21no—
49#2800—21no—
50#2797—21no—
51#2750—21no—
52#2750—21no—
53#2714—21no—
54#2622—21no—
55#2573—21no—
56#2573—21no—
57#2571C2211yescharacteristic, complemented
58#2538C2211yescharacteristic, complemented
59#2513C2211yescharacteristic
60#2512C2211yescharacteristic
61#2509—21no—
62#2504C2211yescharacteristic
63#2503C2211yescharacteristic, complemented
64#2503C2211yescharacteristic, complemented
65#2500C2211yescharacteristic
66#2495—21no—
67#2495C2211yescharacteristic, complemented
68#2495C2211yescharacteristic, complemented
69#2490C2211yescharacteristic
70#2490C2211yescharacteristic
71#2480—21no—
72#2424—21no—
73#2420—21no—
74#2416C2211yescharacteristic
75#2415C2211yescharacteristic
76#2415C2211yescharacteristic
77#2414C2211yescharacteristic
78#2408C2211yescharacteristic
79#2408C2211yescharacteristic
80#2357—21no—
81#2355C2211yescharacteristic, complemented
82#2352C2211yescharacteristic
83#2352C2211yescharacteristic
84#2352C2211yescharacteristic
85D4×C4⋊C4C2211yescharacteristic
86D4×C4⋊C4C2211yescharacteristic, complemented
87#2321—21no—
88C4×C22⋊Q8C2211yescharacteristic
89C4×#121C2211yescharacteristic
90C2×#390C2211yescharacteristic
91#2285C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2096C2211yescharacteristic, complemented
96#2094C2211yescharacteristic
97#2094C2211yescharacteristic
98#2093C2211yescharacteristic
99#2093C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2092C2211yescharacteristic
104#2092C2211yescharacteristic
105#2092C2211yescharacteristic
106#2085C2211yescharacteristic, complemented
107#2084C2211yescharacteristic, complemented
108#2084C2211yescharacteristic, complemented
109#2083C2211yescharacteristic, complemented
110#2083C2211yescharacteristic, complemented
111#2083C2211yescharacteristic, complemented
112#2077C2211yescharacteristic, complemented
113#2077C2211yescharacteristic, complemented
114#2073C2211yescharacteristic
115#2073C2211yescharacteristic
116#2067C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic, complemented
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2036C2211yescharacteristic, complemented
122#2036C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2026C2211yescharacteristic, complemented
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1991C2211yescharacteristic, complemented
133#1991C2211yescharacteristic, complemented
134#1973C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1927C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1923C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic
165#1893C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1872C2211yescharacteristic
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic
173#1870C2211yescharacteristic, complemented
174#1869C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic, complemented
185#1853C2211yescharacteristic, complemented
186#1853C2211yescharacteristic, complemented
187#1852C2211yescharacteristic, complemented
188#1847C2211yescharacteristic, complemented
189#1846C2211yescharacteristic, complemented
190#1846C2211yescharacteristic, complemented
191#1846C2211yescharacteristic, complemented
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic
194#1809C2211yescharacteristic, complemented
195#1808C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198C4×#106C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic, complemented
201C4×C22⋊C8C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121—21no—
216C2×#121D411yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222C2×#120—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C42C2311yescharacteristic
239#485—42no—
240#484—42no—
241#481—42no—
242#480—42no—
243#468—42no—
244#465—42no—
245#450—24no—
246#436—24no—
247#435—24no—
248#428—42no—
249#428—42no—
250#428—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106—42no—
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—42no—
277#418—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#392—21no—
344#392—21no—
345#392—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390D411yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389D411yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388D411yescharacteristic
392#388D411yescharacteristic
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386D411yescharacteristic
408#386D411yescharacteristic
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#380—21no—
434#380—21no—
435#380D411yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4C2×D411yescharacteristic
507C22×D4C2×D411yescharacteristic
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2×D411yescharacteristic
516C23×C4C2×D411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546#126—82no—
547#125—41no—
548#125—41no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555#121—42no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—82no—
565#120—44no—
566#120—82no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—44no—
576C4×D4—82no—
577#117—41no—
578#117—41no—
579#117—41no—
580#117—41no—
581#117—41no—
582#117—41no—
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⋊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—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
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×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—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4—82no—
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×C42—21no—
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—41no—
687C2×C42—41no—
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
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#107—41no—
703#107—41no—
704#106—22no—
705#106—22no—
706#106—22no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716C4⋊C8—22no—
717C4⋊C8—22no—
718#103—22no—
719#103—22no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8#4114yes—
746#97—22no—
747C4×C8—22no—
748C4×C8—41no—
749C4×C8—41no—
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#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—42no—
796C24—42no—
797C24—42no—
798C24—81no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24C22×D411yescharacteristic
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—82no—
838C2×D4—82no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
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—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
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—81no—
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×C4C2×#4112yes—
911C22×C42−1+412yes—
912C22×C4C2511yescharacteristic
913SD16—82no—
914SD16—82no—
915M16—44no—
916M16—44no—
917M16—44no—
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—44no—
939C2×C8C2×#4112yes—
940C2×C8C2×#4112yes—
941C2×C8H(5,𝔽2)12yes—
942C2×C8H(5,𝔽2)12yes—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
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—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
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—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—41no—
1049C42—41no—
1050C42—42no—
1051C42—42no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23—162no—
1096C23—162no—
1097C23—162no—
1098C23—162no—
1099C23#54712yes—
1100C23#57512yes—
1101C23C23×D411yescharacteristic
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106D4—44no—
1107D4—44no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—84no—
1117D4—82no—
1118D4—162no—
1119D4—162no—
1120D4—162no—
1121D4—162no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
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—21no—
1141C2×C4—21no—
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—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—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—82no—
1208C2×C4—82no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4#54712yes—
1214C2×C4#57712yes—
1215C2×C4C22×#4111yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4C2×H(5,𝔽2)11yescharacteristic
1218C2×C4C2×2−1+411yescharacteristic
1219C2×C4#58511yescharacteristic
1220C2×C4#58511yescharacteristic
1221C8—22no—
1222C8—22no—
1223C8—22no—
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—168no—
1265C22C2×#54711yescharacteristic
1266C22#348511yescharacteristic
1267C22#349811yescharacteristic
1268C22C2×#57511yescharacteristic
1269C22C2×#57711yescharacteristic
1270C22#358411yescharacteristic
1271C22#358511yescharacteristic
1272C4—22no—
1273C4—22no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4#351311yescharacteristic
1298C4#351311yescharacteristic
1299C4#354111yescharacteristic
1300C4#354111yescharacteristic
1301C2—42no—
1302C2—42no—
1303C2—81no—
1304C2—161no—
1305C2—161no—
1306C2#4408211yescharacteristic
1307C2#6125511yescharacteristic
1308C2#6128511yescharacteristic
1309C2#6172911yescharacteristic
1310C2#6174911yescharacteristic
1311C2#6242811yescharacteristic
1312C2#6246511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39189C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59257C2semidirect
3. #32405C2semidirect
4. #32389C2semidirect
5. #32289C2semidirect
6. #32288C2semidirect
7. #32054C2semidirect
8. #32054C2semidirect
9. #30579C2semidirect
10. #30570C2semidirect
11. #29164C2semidirect
12. #28086C2semidirect
13. #28067C2semidirect
14. #27951C2semidirect
15. #27946C2semidirect
16. #27926C2semidirect
17. #27508C2semidirect
18. #27490C2semidirect
19. #26150C2semidirect
20. #26148C2semidirect
21. #26142C2semidirect
22. #26130C2semidirect
23. #25136C2semidirect
24. #25120C2semidirect
25. #24882C2semidirect
26. #24878C2semidirect
27. #23731C2semidirect
28. #23118C2semidirect
29. #22666C2semidirect
30. #22659C2semidirect
31. #22043C2semidirect
32. C2×#484C22semidirect
34. C2×#485C22semidirect
43. C2×#428C22semidirect
44. C22×#106C22semidirect
57. #2571C22semidirect
58. #2538C22semidirect
63. #2503C22semidirect
64. #2503C22semidirect
67. #2495C22semidirect
68. #2495C22semidirect
81. #2355C22semidirect
86. D4×C4⋊C4C22semidirect
92. #2101C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2096C22semidirect
106. #2085C22semidirect
107. #2084C22semidirect
108. #2084C22semidirect
109. #2083C22semidirect
110. #2083C22semidirect
111. #2083C22semidirect
112. #2077C22semidirect
113. #2077C22semidirect
118. #2059C22semidirect
121. #2036C22semidirect
122. #2036C22semidirect
129. #2026C22semidirect
132. #1991C22semidirect
133. #1991C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1948C22semidirect
146. #1927C22semidirect
147. #1927C22semidirect
154. #1923C22semidirect
155. #1923C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1919C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
173. #1870C22semidirect
174. #1869C22semidirect
175. #1865C22semidirect
176. #1863C22semidirect
181. #1854C22semidirect
182. #1854C22semidirect
184. #1853C22semidirect
185. #1853C22semidirect
186. #1853C22semidirect
187. #1852C22semidirect
188. #1847C22semidirect
189. #1846C22semidirect
190. #1846C22semidirect
191. #1846C22semidirect
194. #1809C22semidirect
195. #1808C22semidirect
197. #1776C22semidirect
198. C4×#106C22semidirect
199. #1753C22semidirect
200. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#592572
#391892
#324052
#323892
#322892
#322882
#320542
#305792
#305702
#291642
#280862
#280672
#279512
#279462
#279262
#275082
#274902
#261502
#261482
#261422
#261302
#251362
#251202
#248822
#248782
#237312
#231182
#226662
#226592
#220432