Finite Group Databasebeta

← #7039310

Subgroups — #7039310

Order 512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59231C211yesmaximal, characteristic, complemented
2#39030C211yesmaximal, characteristic
3#32256C211yesmaximal, characteristic, complemented
4#31999C211yesmaximal, characteristic, complemented
5#31348C211yesmaximal, characteristic, complemented
6#31335C211yesmaximal, characteristic, complemented
7#31271C211yesmaximal, characteristic, complemented
8#30971C211yesmaximal, characteristic, complemented
9#30582C211yesmaximal, characteristic, complemented
10#30408C211yesmaximal, characteristic, complemented
11#29482C211yesmaximal, characteristic, complemented
12#28714C211yesmaximal, characteristic, complemented
13#28566C211yesmaximal, characteristic, complemented
14#28078C211yesmaximal, characteristic, complemented
15#27865C211yesmaximal, characteristic, complemented
16#27800C211yesmaximal, characteristic, complemented
17#27510C211yesmaximal, characteristic, complemented
18#27473C211yesmaximal, characteristic, complemented
19#27451C211yesmaximal, characteristic, complemented
20#27357C211yesmaximal, characteristic, complemented
21#27238C211yesmaximal, characteristic, complemented
22#26746C211yesmaximal, characteristic, complemented
23#25351C211yesmaximal, characteristic, complemented
24#25128C211yesmaximal, characteristic, complemented
25#24934C211yesmaximal, characteristic, complemented
26#24873C211yesmaximal, characteristic, complemented
27#23764C211yesmaximal, characteristic, complemented
28#23119C211yesmaximal, characteristic, complemented
29#22935C211yesmaximal, characteristic, complemented
30#22566C211yesmaximal, characteristic, complemented
31#22191C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#482C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#435C2211yescharacteristic, complemented
40C22×#102C2211yescharacteristic
41#2854C2211yescharacteristic
42#2779—21no—
43#2744—21no—
44#2703—21no—
45#2697—21no—
46#2686—21no—
47#2685—21no—
48#2648—21no—
49#2612—21no—
50#2562C2211yescharacteristic
51#2562C2211yescharacteristic, complemented
52#2550C2211yescharacteristic, complemented
53#2547C2211yescharacteristic
54#2537C2211yescharacteristic
55#2536C2211yescharacteristic
56#2532—21no—
57#2531—21no—
58#2518—21no—
59#2512C2211yescharacteristic
60#2497C2211yescharacteristic
61#2495—21no—
62#2492C2211yescharacteristic, complemented
63#2490C2211yescharacteristic
64#2489C2211yescharacteristic
65#2485C2211yescharacteristic
66#2467—21no—
67#2454C2211yescharacteristic
68#2424—21no—
69#2417C2211yescharacteristic
70#2415C2211yescharacteristic, complemented
71#2414C2211yescharacteristic
72#2408C2211yescharacteristic
73#2408C2211yescharacteristic
74#2372—21no—
75#2363C2211yescharacteristic
76#2356C2211yescharacteristic, complemented
77#2352C2211yescharacteristic
78#2346C2211yescharacteristic, complemented
79#2345C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81#2312—21no—
82C4×C22⋊Q8C2211yescharacteristic, complemented
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85#2283C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2096C2211yescharacteristic, complemented
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2067C2211yescharacteristic
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2036C2211yescharacteristic, complemented
113#2035C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic, complemented
121#2025C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1987C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1947C2211yescharacteristic, complemented
132#1943C2211yescharacteristic, complemented
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1935C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1894C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1873C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1825C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1809C2211yescharacteristic, complemented
185#1809C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic, complemented
189#1807C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic, complemented
200#1749C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121D411yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×#120—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C22⋊C4—21no—
238C22×C42C2311yescharacteristic
239#501—42no—
240#482—24no—
241#478—42no—
242#468—24no—
243#465—42no—
244#450—42no—
245#435—42no—
246#435—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102—24no—
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#399—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#393—21no—
329#392—21no—
330#392—21no—
331#392—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#390—21no—
339#390—21no—
340#390—21no—
341#390D411yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389D411yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388D411yescharacteristic
380#388D411yescharacteristic
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386D411yescharacteristic
397#386D411yescharacteristic
398#385—21no—
399#385—21no—
400#384C2311yescharacteristic
401#383—21no—
402#383—21no—
403#382—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#381—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380D411yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427#379—21no—
428#379—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446#376—21no—
447#376—21no—
448#376—21no—
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×M16—22no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542#126—82no—
543#125—41no—
544#125—41no—
545#125—41no—
546#125—41no—
547#124—44no—
548#123—82no—
549C22⋊Q8—22no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555#121—22no—
556#121—22no—
557#121—42no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—82no—
565#120—82no—
566#120—82no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—82no—
580#117—22no—
581#117—41no—
582#117—41no—
583#117—41no—
584C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
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—44no—
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×C42—21no—
679C2×C42—21no—
680C2×C42—41no—
681C2×C42—41no—
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688#107—22no—
689#107—22no—
690#107—22no—
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#106—22no—
697#106—22no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702C4⋊C8—22no—
703C4⋊C8—41no—
704#103—22no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102#4114yes—
724C22⋊C8—22no—
725C22⋊C8—22no—
726C22⋊C8—22no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732#97—22no—
733#97—41no—
734#97—41no—
735#97—41no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#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
779C24—21no—
780C24—21no—
781C24—42no—
782C24—42no—
783C24—81no—
784C24—81no—
785C24—81no—
786C24—81no—
787C24—81no—
788C24C22×D411yescharacteristic
789C24C22×D411yescharacteristic
790C24C22×D411yescharacteristic
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—42no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×D4—22no—
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—41no—
814C2×D4—41no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—42no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—82no—
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×D4C2×#4112yes—
840C22×C4—21no—
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—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2511yescharacteristic
899SD16—82no—
900SD16—82no—
901M16—82no—
902M16—82no—
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—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—82no—
926C2×C8—82no—
927C2×C8C2×#4112yes—
928C2×C8H(5,𝔽2)12yes—
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—21no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
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—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4C2×#4112yes—
979C22⋊C4—22no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—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—
1024C22⋊C4—81no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—41no—
1034C42—41no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—84no—
1080C23—84no—
1081C23—162no—
1082C23—162no—
1083C23—162no—
1084C23—162no—
1085C23—162no—
1086C23#57512yes—
1087C23C23×D411yescharacteristic
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—162no—
1093D4—22no—
1094D4—22no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—82no—
1102D4—82no—
1103D4—82no—
1104D4—84no—
1105D4—84no—
1106D4—162no—
1107D4—162no—
1108D4—162no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
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—22no—
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—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—82no—
1197C2×C4—82no—
1198C2×C4—162no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4C22×#4111yescharacteristic
1202C2×C4C2×H(5,𝔽2)11yescharacteristic
1203C2×C4#58511yescharacteristic
1204C2×C4#58511yescharacteristic
1205C2×C4#58511yescharacteristic
1206C2×C4#58511yescharacteristic
1207C8—22no—
1208C8—22no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—42no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—42no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—42no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—168no—
1251C22D4×#4111yescharacteristic
1252C22#348511yescharacteristic
1253C22#349611yescharacteristic
1254C22C2×#57511yescharacteristic
1255C22#358511yescharacteristic
1256C22#358511yescharacteristic
1257C22#358611yescharacteristic
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4#349311yescharacteristic
1284C4#351411yescharacteristic
1285C4#354511yescharacteristic
1286C4#356611yescharacteristic
1287C2—42no—
1288C2—81no—
1289C2—81no—
1290C2—82no—
1291C2—161no—
1292C2#4350411yescharacteristic
1293C2#6145511yescharacteristic
1294C2#6150611yescharacteristic
1295C2#6171411yescharacteristic
1296C2#6178011yescharacteristic
1297C2#6229811yescharacteristic
1298C2#6233311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39030C2
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. #59231C2semidirect
3. #32256C2semidirect
4. #31999C2semidirect
5. #31348C2semidirect
6. #31335C2semidirect
7. #31271C2semidirect
8. #30971C2semidirect
9. #30582C2semidirect
10. #30408C2semidirect
11. #29482C2semidirect
12. #28714C2semidirect
13. #28566C2semidirect
14. #28078C2semidirect
15. #27865C2semidirect
16. #27800C2semidirect
17. #27510C2semidirect
18. #27473C2semidirect
19. #27451C2semidirect
20. #27357C2semidirect
21. #27238C2semidirect
22. #26746C2semidirect
23. #25351C2semidirect
24. #25128C2semidirect
25. #24934C2semidirect
26. #24873C2semidirect
27. #23764C2semidirect
28. #23119C2semidirect
29. #22935C2semidirect
30. #22566C2semidirect
31. #22191C2semidirect
32. C2×#501C22semidirect
39. C2×#435C22semidirect
51. #2562C22semidirect
52. #2550C22semidirect
62. #2492C22semidirect
70. #2415C22semidirect
76. #2356C22semidirect
78. #2346C22semidirect
82. C4×C22⋊Q8C22semidirect
85. #2283C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2096C22semidirect
91. #2088C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
94. #2083C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
100. #2076C22semidirect
102. #2075C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
111. #2036C22semidirect
112. #2036C22semidirect
120. #2026C22semidirect
126. #1992C22semidirect
127. #1989C22semidirect
128. #1987C22semidirect
131. #1947C22semidirect
132. #1943C22semidirect
136. #1935C22semidirect
137. #1935C22semidirect
138. #1928C22semidirect
139. #1927C22semidirect
148. #1924C22semidirect
149. #1921C22semidirect
150. #1919C22semidirect
151. #1919C22semidirect
152. #1918C22semidirect
153. #1918C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1917C22semidirect
161. #1894C22semidirect
169. #1873C22semidirect
171. #1870C22semidirect
174. #1865C22semidirect
175. #1863C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
182. #1825C22semidirect
184. #1809C22semidirect
185. #1809C22semidirect
186. #1809C22semidirect
188. #1808C22semidirect
192. #1776C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
199. #1752C22semidirect
200. #1749C22semidirect
201. #1735C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#592312
#390302
#322562
#319992
#313482
#313352
#312712
#309712
#305822
#304082
#294822
#287142
#285662
#280782
#278652
#278002
#275102
#274732
#274512
#273572
#272382
#267462
#253512
#251282
#249342
#248732
#237642
#231192
#229352
#225662
#221912