Finite Group Databasebeta

← #7610677

Subgroups — #7610677

Order 512.

1573 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45188C211yesmaximal, characteristic, complemented
2#45096C211yesmaximal, characteristic, complemented
3#32227C211yesmaximal, characteristic, complemented
4#31847C211yesmaximal, characteristic, complemented
5#31645C211yesmaximal, characteristic, complemented
6#31355C211yesmaximal, characteristic, complemented
7#29078C211yesmaximal, characteristic, complemented
8#28992C211yesmaximal, characteristic, complemented
9#28893C211yesmaximal, characteristic, complemented
10#27826C211yesmaximal, characteristic, complemented
11#27705C211yesmaximal, characteristic, complemented
12#27703C211yesmaximal, characteristic, complemented
13#27619C211yesmaximal, characteristic, complemented
14#27581C211yesmaximal, characteristic, complemented
15#27449C211yesmaximal, characteristic, complemented
16#26969C211yesmaximal, characteristic, complemented
17#26748C211yesmaximal, characteristic, complemented
18#26672C211yesmaximal, characteristic, complemented
19#26409C211yesmaximal, characteristic, complemented
20#26205C211yesmaximal, characteristic, complemented
21#25136C211yesmaximal, characteristic, complemented
22#24527C211yesmaximal, characteristic, complemented
23#23963C211yesmaximal, characteristic
24#23945C211yesmaximal, characteristic, complemented
25#23141C211yesmaximal, characteristic, complemented
26#22880C211yesmaximal, characteristic, complemented
27#22772C211yesmaximal, characteristic, complemented
28#22501C211yesmaximal, characteristic, complemented
29#21571C211yesmaximal, characteristic, complemented
30#21412C211yesmaximal, characteristic, complemented
31#21091C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38C2×#436C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2786—21no—
43#2751—21no—
44#2736—21no—
45#2718—21no—
46#2701—21no—
47#2698—21no—
48#2686—21no—
49#2684—21no—
50#2563C2211yescharacteristic
51#2557—21no—
52#2550C2211yescharacteristic, complemented
53#2534—21no—
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic
56#2504C2211yescharacteristic
57#2503C2211yescharacteristic
58#2496—21no—
59#2491C2211yescharacteristic
60#2488—21no—
61#2480—21no—
62#2467—21no—
63#2453C2211yescharacteristic, complemented
64#2447—21no—
65#2447C2211yescharacteristic, complemented
66#2439C2211yescharacteristic
67#2439C2211yescharacteristic, complemented
68#2427C2211yescharacteristic, complemented
69#2422C2211yescharacteristic
70#2420C2211yescharacteristic, complemented
71#2419—21no—
72#2415C2211yescharacteristic
73#2408C2211yescharacteristic
74#2395C2211yescharacteristic
75#2363C2211yescharacteristic
76#2362C2211yescharacteristic, complemented
77#2361C2211yescharacteristic
78#2357C2211yescharacteristic
79#2352C2211yescharacteristic
80#2349C2211yescharacteristic, complemented
81D4×C22⋊C4C2211yescharacteristic
82#2317C2211yescharacteristic
83#2314C2211yescharacteristic
84#2309C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2083C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2067C2211yescharacteristic
100#2065C2211yescharacteristic, complemented
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2036C2211yescharacteristic, complemented
105#2034C2211yescharacteristic
106#2025C2211yescharacteristic
107#2025C2211yescharacteristic
108#2024C2211yescharacteristic, complemented
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic, complemented
112#2012C2211yescharacteristic
113#2012C2211yescharacteristic
114#2000C2211yescharacteristic
115#1999C2211yescharacteristic
116#1999C2211yescharacteristic
117#1993C2211yescharacteristic, complemented
118#1993C2211yescharacteristic, complemented
119#1991C2211yescharacteristic, complemented
120#1990C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1988C2211yescharacteristic, complemented
123#1972C2211yescharacteristic
124#1968C2211yescharacteristic
125#1959C2211yescharacteristic, complemented
126#1958C2211yescharacteristic, complemented
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1935C2211yescharacteristic, complemented
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1933C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1925C2211yescharacteristic
141#1924C2211yescharacteristic, complemented
142#1923C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1921C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic, complemented
154#1894C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic, complemented
171#1873C2211yescharacteristic
172#1872C2211yescharacteristic, complemented
173#1869C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1850C2211yescharacteristic
179#1835C2211yescharacteristic, complemented
180#1825C2211yescharacteristic, complemented
181#1824C2211yescharacteristic
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic, complemented
184#1818C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic, complemented
202#1735C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—24no—
212#553—42no—
213#542—24no—
214#542—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252#468—24no—
253#450—42no—
254#447—24no—
255C4×D8—24no—
256#436—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264#418—24no—
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295#405—42no—
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400D411yescharacteristic
307#399D411yescharacteristic
308#398—21no—
309#398—21no—
310#398D411yescharacteristic
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397D411yescharacteristic
323#397D411yescharacteristic
324#397D411yescharacteristic
325#396—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394D411yescharacteristic
336#394D411yescharacteristic
337#393—21no—
338#393—21no—
339#393—21no—
340#393—21no—
341#393—21no—
342#392—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#384—21no—
410#384C2311yescharacteristic
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#381—21no—
418#381—21no—
419#381—21no—
420#381—21no—
421#381—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#379—21no—
431#379—21no—
432#379—21no—
433#379—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C2×#95—21no—
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
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×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—22no—
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×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—22no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551#126—44no—
552#126—44no—
553#126—82no—
554#125—22no—
555#125—41no—
556#124—22no—
557#124—41no—
558#124—44no—
559#124—82no—
560#123—44no—
561#123—44no—
562#123—82no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—41no—
572#121—41no—
573#121—44no—
574#121—41no—
575#121—41no—
576#121#4114yes—
577#120—82no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—44no—
593C4×D4—82no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—41no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
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—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—82no—
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—22no—
708#106—41no—
709#106—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713#103—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102#4114yes—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742#97—41no—
743#97—41no—
744#97—41no—
745C4×C8—22no—
746C4×C8—41no—
747C4×C8—41no—
748C4×C8—41no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791C24—21no—
792C24—21no—
793C24—21no—
794C24—42no—
795C24—42no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24—81no—
801C24C22×D411yescharacteristic
802C24C22×D411yescharacteristic
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—42no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×D4—22no—
816C2×D4—24no—
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—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—41no—
836C2×D4—41no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—82no—
844C2×D4—82no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4C2×#4112yes—
854C2×D4C2×#4112yes—
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—21no—
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—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
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—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×C4C22×D411yescharacteristic
911C22×C4C2×#4112yes—
912C22×C4H(5,𝔽2)12yes—
913C22×C4C2511yescharacteristic
914SD16—82no—
915SD16—82no—
916D8—44no—
917D8—82no—
918M16—44no—
919M16—82no—
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—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—44no—
944C2×C8C2×#4112yes—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
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—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
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⋊C4C2×#4112yes—
994C4⋊C4C2×#4112yes—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—24no—
999C22⋊C4—22no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
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—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
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—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—21no—
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—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—84no—
1096C23—84no—
1097C23—162no—
1098C23—162no—
1099C23—162no—
1100C23—162no—
1101C23—162no—
1102C23#54612yes—
1103C23C23×D411yescharacteristic
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—162no—
1109Q8—162no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—22no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—84no—
1123D4—82no—
1124D4—84no—
1125D4—84no—
1126D4—162no—
1127D4—162no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
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—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
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—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4#54612yes—
1218C2×C4C22×#4111yescharacteristic
1219C2×C4C22×#4111yescharacteristic
1220C2×C4C2×H(5,𝔽2)11yescharacteristic
1221C2×C4#58511yescharacteristic
1222C2×C4#58511yescharacteristic
1223C2×C4#58511yescharacteristic
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—42no—
1240C22—41no—
1241C22—42no—
1242C22—41no—
1243C22—41no—
1244C22—42no—
1245C22—42no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—42no—
1251C22—42no—
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—81no—
1265C22—81no—
1266C22—81no—
1267C22—168no—
1268C22C2×#54611yescharacteristic
1269C22D4×#4111yescharacteristic
1270C22#350011yescharacteristic
1271C22#358411yescharacteristic
1272C22#358411yescharacteristic
1273C22#358511yescharacteristic
1274C22#358511yescharacteristic
1275C4—22no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—42no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—42no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4#347511yescharacteristic
1301C4#351311yescharacteristic
1302C4#352111yescharacteristic
1303C4#353311yescharacteristic
1304C2—42no—
1305C2—81no—
1306C2—82no—
1307C2—82no—
1308C2—161no—
1309C2#5980511yescharacteristic
1310C2#6118711yescharacteristic
1311C2#6120811yescharacteristic
1312C2#6150011yescharacteristic
1313C2#6150611yescharacteristic
1314C2#6261411yescharacteristic
1315C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23963C2
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. #45096C2semidirect
3. #32227C2semidirect
4. #31847C2semidirect
5. #31645C2semidirect
6. #31355C2semidirect
7. #29078C2semidirect
8. #28992C2semidirect
9. #28893C2semidirect
10. #27826C2semidirect
11. #27705C2semidirect
12. #27703C2semidirect
13. #27619C2semidirect
14. #27581C2semidirect
15. #27449C2semidirect
16. #26969C2semidirect
17. #26748C2semidirect
18. #26672C2semidirect
19. #26409C2semidirect
20. #26205C2semidirect
21. #25136C2semidirect
22. #24527C2semidirect
24. #23945C2semidirect
25. #23141C2semidirect
26. #22880C2semidirect
27. #22772C2semidirect
28. #22501C2semidirect
29. #21571C2semidirect
30. #21412C2semidirect
31. #21091C2semidirect
52. #2550C22semidirect
63. #2453C22semidirect
65. #2447C22semidirect
67. #2439C22semidirect
68. #2427C22semidirect
70. #2420C22semidirect
76. #2362C22semidirect
80. #2349C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2088C22semidirect
92. #2084C22semidirect
93. #2083C22semidirect
94. #2077C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
100. #2065C22semidirect
104. #2036C22semidirect
108. #2024C22semidirect
111. #2023C22semidirect
117. #1993C22semidirect
118. #1993C22semidirect
119. #1991C22semidirect
120. #1990C22semidirect
121. #1989C22semidirect
122. #1988C22semidirect
125. #1959C22semidirect
126. #1958C22semidirect
131. #1935C22semidirect
138. #1933C22semidirect
139. #1927C22semidirect
141. #1924C22semidirect
142. #1923C22semidirect
143. #1921C22semidirect
144. #1921C22semidirect
145. #1921C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1916C22semidirect
153. #1895C22semidirect
170. #1874C22semidirect
172. #1872C22semidirect
175. #1862C22semidirect
179. #1835C22semidirect
180. #1825C22semidirect
183. #1823C22semidirect
187. #1804C22semidirect
188. #1804C22semidirect
189. #1771C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1763C22semidirect
193. #1762C22semidirect
194. C4×#103C22semidirect
195. C4×#102C22semidirect
196. C4×#102C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
201. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#451882
#450962
#322272
#318472
#316452
#313552
#290782
#289922
#288932
#278262
#277052
#277032
#276192
#275812
#274492
#269692
#267482
#266722
#264092
#262052
#251362
#245272
#239632
#239452
#231412
#228802
#227722
#225012
#215712
#214122
#210912