Finite Group Databasebeta

← #7079175

Subgroups — #7079175

Order 512.

1490 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45188C211yesmaximal, characteristic, complemented
2#42465C211yesmaximal, characteristic, complemented
3#32529C211yesmaximal, characteristic, complemented
4#32457C211yesmaximal, characteristic, complemented
5#32388C211yesmaximal, characteristic, complemented
6#32371C211yesmaximal, characteristic, complemented
7#32292C211yesmaximal, characteristic, complemented
8#31933C211yesmaximal, characteristic, complemented
9#30778C211yesmaximal, characteristic, complemented
10#30689C211yesmaximal, characteristic, complemented
11#28857C211yesmaximal, characteristic, complemented
12#28528C211yesmaximal, characteristic, complemented
13#28032C211yesmaximal, characteristic, complemented
14#27942C211yesmaximal, characteristic, complemented
15#27874C211yesmaximal, characteristic, complemented
16#27500C211yesmaximal, characteristic, complemented
17#26546C211yesmaximal, characteristic, complemented
18#26354C211yesmaximal, characteristic, complemented
19#26354C211yesmaximal, characteristic, complemented
20#26131C211yesmaximal, characteristic, complemented
21#26094C211yesmaximal, characteristic, complemented
22#26064C211yesmaximal, characteristic, complemented
23#25974C211yesmaximal, characteristic, complemented
24#25132C211yesmaximal, characteristic
25#24869C211yesmaximal, characteristic, complemented
26#24512C211yesmaximal, characteristic, complemented
27#23735C211yesmaximal, characteristic, complemented
28#22915C211yesmaximal, characteristic, complemented
29#22870C211yesmaximal, characteristic, complemented
30#22664C211yesmaximal, characteristic, complemented
31#21992C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic, complemented
33C2×#482C2211yescharacteristic
34C2×#480C2211yescharacteristic, complemented
35C2×#476C2211yescharacteristic
36C2×#476C2211yescharacteristic, complemented
37C2×#469C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×C4×D8C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#433C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#428C2211yescharacteristic, complemented
44C2×#427C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2824—21no—
48#2808—21no—
49#2798—21no—
50#2787—21no—
51#2786—21no—
52#2751—21no—
53#2736—21no—
54#2694—21no—
55#2684—21no—
56#2653—21no—
57#2630—21no—
58#2624C2211yescharacteristic
59#2570C2211yescharacteristic, complemented
60#2563C2211yescharacteristic
61#2563C2211yescharacteristic, complemented
62#2557—21no—
63#2534—21no—
64#2513C2211yescharacteristic
65#2513C2211yescharacteristic, complemented
66#2512C2211yescharacteristic
67#2506C2211yescharacteristic, complemented
68#2504C2211yescharacteristic
69#2500C2211yescharacteristic, complemented
70#2494C2211yescharacteristic, complemented
71#2491C2211yescharacteristic
72#2480—21no—
73#2467—21no—
74#2460—21no—
75#2439C2211yescharacteristic
76#2439C2211yescharacteristic
77#2439C2211yescharacteristic, complemented
78#2422C2211yescharacteristic
79#2422C2211yescharacteristic, complemented
80#2414C2211yescharacteristic
81#2408C2211yescharacteristic
82#2395C2211yescharacteristic
83#2361C2211yescharacteristic
84#2361C2211yescharacteristic
85#2357C2211yescharacteristic
86#2352C2211yescharacteristic
87#2352C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2317C2211yescharacteristic
90#2314C2211yescharacteristic
91#2309C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2094C2211yescharacteristic
95#2093C2211yescharacteristic
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2092C2211yescharacteristic, complemented
104#2092C2211yescharacteristic, complemented
105#2092C2211yescharacteristic, complemented
106#2086C2211yescharacteristic, complemented
107#2085C2211yescharacteristic, complemented
108#2085C2211yescharacteristic, complemented
109#2085C2211yescharacteristic, complemented
110#2083C2211yescharacteristic, complemented
111#2076C2211yescharacteristic, complemented
112#2073C2211yescharacteristic
113#2071C2211yescharacteristic, complemented
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic, complemented
120#2058C2211yescharacteristic, complemented
121#2058C2211yescharacteristic, complemented
122#2058C2211yescharacteristic, complemented
123#2054C2211yescharacteristic
124#2054C2211yescharacteristic
125#2054C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic, complemented
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic
130#2023C2211yescharacteristic
131#1999C2211yescharacteristic
132#1972C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1970C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1947C2211yescharacteristic, complemented
143#1942C2211yescharacteristic, complemented
144#1942C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic, complemented
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic, complemented
155#1925C2211yescharacteristic, complemented
156#1923C2211yescharacteristic, complemented
157#1923C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1893C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1869C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic, complemented
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic, complemented
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1846C2211yescharacteristic, complemented
189#1846C2211yescharacteristic, complemented
190#1836C2211yescharacteristic, complemented
191#1834C2211yescharacteristic, complemented
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic, complemented
194#1808C2211yescharacteristic
195#1804C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#107C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#125—21no—
213C2×#124—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C22⋊C4—21no—
234#500—42no—
235#482—42no—
236#480—42no—
237#476—42no—
238#476—42no—
239#469—42no—
240#447—24no—
241C4×D8—42no—
242#436—24no—
243#433—24no—
244#428—42no—
245#428—42no—
246#427—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
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
273C2×C4⋊C8C2311yescharacteristic
274#418—42no—
275C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#401—21no—
307#400—21no—
308#400—21no—
309#400D411yescharacteristic
310#399—21no—
311#399D411yescharacteristic
312#398—21no—
313#398—21no—
314#398D411yescharacteristic
315#397—21no—
316#397—21no—
317#397—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#397D411yescharacteristic
327#397D411yescharacteristic
328#397D411yescharacteristic
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#394D411yescharacteristic
343#394D411yescharacteristic
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#392—21no—
353#392—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
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#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
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×Q8—21no—
495C22×Q8—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—22no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—41no—
529C2×M16—41no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545#126—82no—
546#125—82no—
547#124—82no—
548#123—82no—
549#123—82no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#120—82no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—82no—
568C4×D4—82no—
569#117—22no—
570#117—22no—
571#117—41no—
572#117—41no—
573#117—41no—
574#117—41no—
575#117—41no—
576#117—41no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—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—82no—
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—22no—
684#107—22no—
685#107—22no—
686#107—22no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#106—22no—
696#106—22no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—22no—
709C4⋊C8—41no—
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—
730C22⋊C8—22no—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—41no—
734C22⋊C8#4114yes—
735#97—22no—
736C4×C8—22no—
737C4×C8—22no—
738C4×C8—22no—
739C4×C8—41no—
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#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
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—21no—
785C24—21no—
786C24—42no—
787C24—42no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24—81no—
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×D4—22no—
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—44no—
820C2×D4—44no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—82no—
830C2×D4—82no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D42−1+412yes—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—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—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C2×#4112yes—
892C22×C42−1+412yes—
893C22×C4C2511yescharacteristic
894D8—44no—
895D8—82no—
896M16—44no—
897M16—44no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—44no—
919C2×C8C2×#4112yes—
920C2×C8C2×#4112yes—
921C2×C8H(5,𝔽2)12yes—
922C2×C8H(5,𝔽2)12yes—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
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—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
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—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—22no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—84no—
1077C23—84no—
1078C23—162no—
1079C23—162no—
1080C23—162no—
1081C23—162no—
1082C23—162no—
1083C23#54712yes—
1084C23C23×D411yescharacteristic
1085Q8—162no—
1086Q8—162no—
1087D4—22no—
1088D4—22no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—84no—
1100D4—82no—
1101D4—84no—
1102D4—84no—
1103D4—162no—
1104D4—162no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—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—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—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—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4#54712yes—
1192C2×C4#57612yes—
1193C2×C4C22×#4111yescharacteristic
1194C2×C4C2×H(5,𝔽2)11yescharacteristic
1195C2×C4C2×H(5,𝔽2)11yescharacteristic
1196C2×C4C2×2−1+411yescharacteristic
1197C2×C4C2×2−1+411yescharacteristic
1198C2×C4#58511yescharacteristic
1199C8—22no—
1200C8—22no—
1201C8—22no—
1202C8—22no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—42no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—42no—
1221C22—41no—
1222C22—42no—
1223C22—41no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—168no—
1243C22C2×#54711yescharacteristic
1244C22#348911yescharacteristic
1245C22#349811yescharacteristic
1246C22C2×#57611yescharacteristic
1247C22#358411yescharacteristic
1248C22#358411yescharacteristic
1249C22#358511yescharacteristic
1250C4—22no—
1251C4—22no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4#351311yescharacteristic
1276C4#352011yescharacteristic
1277C4#353511yescharacteristic
1278C4#353811yescharacteristic
1279C2—42no—
1280C2—81no—
1281C2—82no—
1282C2—161no—
1283C2—161no—
1284C2#4397611yescharacteristic
1285C2#6127411yescharacteristic
1286C2#6128411yescharacteristic
1287C2#6218711yescharacteristic
1288C2#6220811yescharacteristic
1289C2#6243611yescharacteristic
1290C2#6246811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25132C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45188C2semidirect
2. #42465C2semidirect
3. #32529C2semidirect
4. #32457C2semidirect
5. #32388C2semidirect
6. #32371C2semidirect
7. #32292C2semidirect
8. #31933C2semidirect
9. #30778C2semidirect
10. #30689C2semidirect
11. #28857C2semidirect
12. #28528C2semidirect
13. #28032C2semidirect
14. #27942C2semidirect
15. #27874C2semidirect
16. #27500C2semidirect
17. #26546C2semidirect
18. #26354C2semidirect
19. #26354C2semidirect
20. #26131C2semidirect
21. #26094C2semidirect
22. #26064C2semidirect
23. #25974C2semidirect
25. #24869C2semidirect
26. #24512C2semidirect
27. #23735C2semidirect
28. #22915C2semidirect
29. #22870C2semidirect
30. #22664C2semidirect
31. #21992C2semidirect
32. C2×#500C22semidirect
34. C2×#480C22semidirect
36. C2×#476C22semidirect
43. C2×#428C22semidirect
59. #2570C22semidirect
61. #2563C22semidirect
65. #2513C22semidirect
67. #2506C22semidirect
69. #2500C22semidirect
70. #2494C22semidirect
77. #2439C22semidirect
79. #2422C22semidirect
92. #2101C22semidirect
103. #2092C22semidirect
104. #2092C22semidirect
105. #2092C22semidirect
106. #2086C22semidirect
107. #2085C22semidirect
108. #2085C22semidirect
109. #2085C22semidirect
110. #2083C22semidirect
111. #2076C22semidirect
113. #2071C22semidirect
119. #2065C22semidirect
120. #2058C22semidirect
121. #2058C22semidirect
122. #2058C22semidirect
127. #2034C22semidirect
136. #1949C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1948C22semidirect
142. #1947C22semidirect
143. #1942C22semidirect
144. #1942C22semidirect
145. #1939C22semidirect
151. #1926C22semidirect
154. #1925C22semidirect
155. #1925C22semidirect
156. #1923C22semidirect
157. #1923C22semidirect
158. #1921C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
175. #1862C22semidirect
179. #1854C22semidirect
181. #1853C22semidirect
183. #1852C22semidirect
185. #1851C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1846C22semidirect
189. #1846C22semidirect
190. #1836C22semidirect
191. #1834C22semidirect
193. #1809C22semidirect
197. C4×#107C22semidirect
198. C8×C4⋊C4C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#451882
#424652
#325292
#324572
#323882
#323712
#322922
#319332
#307782
#306892
#288572
#285282
#280322
#279422
#278742
#275002
#265462
#263542
#261312
#260942
#260642
#259742
#251322
#248692
#245122
#237352
#229152
#228702
#226642
#219922