Finite Group Databasebeta

← #6761265

Subgroups — #6761265

Order 512.

1322 conjugacy classes of subgroups.

The subgroup lattice has 1203 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37953C211yesmaximal, characteristic
2#35163C211yesmaximal, characteristic, complemented
3#33112C211yesmaximal, characteristic, complemented
4#32075C211yesmaximal, characteristic, complemented
5#32049C211yesmaximal, characteristic, complemented
6#32023C211yesmaximal, characteristic, complemented
7#31997C211yesmaximal, characteristic
8#30792C211yesmaximal, characteristic, complemented
9#30788C211yesmaximal, characteristic, complemented
10#30576C211yesmaximal, characteristic
11#30572C211yesmaximal, characteristic, complemented
12#29993C211yesmaximal, characteristic, complemented
13#29932C211yesmaximal, characteristic, complemented
14#29269C211yesmaximal, characteristic, complemented
15#28698C211yesmaximal, characteristic, complemented
16#28075C211yesmaximal, characteristic, complemented
17#28062C211yesmaximal, characteristic, complemented
18#27796C211yesmaximal, characteristic, complemented
19#27789C211yesmaximal, characteristic, complemented
20#27642C211yesmaximal, characteristic, complemented
21#27628C211yesmaximal, characteristic, complemented
22#27501C211yesmaximal, characteristic, complemented
23#27488C211yesmaximal, characteristic, complemented
24#27366C211yesmaximal, characteristic, complemented
25#27363C211yesmaximal, characteristic, complemented
26#24765C211yesmaximal, characteristic, complemented
27#24655C211yesmaximal, characteristic, complemented
28#22752C211yesmaximal, characteristic, complemented
29#22163C211yesmaximal, characteristic, complemented
30#21966C211yesmaximal, characteristic, complemented
31#21362C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#431C2211yescharacteristic
40C2×#424C2211yescharacteristic
41#2866—21no—
42#2864—21no—
43#2850C2211yescharacteristic
44#2784—21no—
45#2781—21no—
46#2775—21no—
47#2756—21no—
48#2660C2211yescharacteristic
49#2652—21no—
50#2649—21no—
51#2620C2211yescharacteristic
52#2610—21no—
53#2609—21no—
54#2538C2211yescharacteristic
55#2535C2211yescharacteristic
56#2533—21no—
57#2529—21no—
58#2529—21no—
59#2518—21no—
60#2517—21no—
61#2511C2211yescharacteristic
62#2508C2211yescharacteristic
63#2499C2211yescharacteristic
64#2497C2211yescharacteristic
65#2492C2211yescharacteristic
66#2491C2211yescharacteristic
67#2490C2211yescharacteristic
68#2489C2211yescharacteristic
69#2489C2211yescharacteristic
70#2485C2211yescharacteristic
71#2474—21no—
72#2441C2211yescharacteristic
73#2415C2211yescharacteristic
74#2356C2211yescharacteristic
75#2354C2211yescharacteristic
76#2330C2211yescharacteristic
77#2326C2211yescharacteristic
78#2323C2211yescharacteristic
79#2320C2211yescharacteristic
80#2314C2211yescharacteristic
81#2314C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83#2290C2211yescharacteristic
84#2285C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2096C2211yescharacteristic
91#2096C2211yescharacteristic
92#2094C2211yescharacteristic
93#2094C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2074C2211yescharacteristic
103#2073C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2056C2211yescharacteristic
109#2055C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic
121#2026C2211yescharacteristic
122#2025C2211yescharacteristic
123#2024C2211yescharacteristic
124#2001C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic
127#1990C2211yescharacteristic
128#1983C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1973C2211yescharacteristic
132#1969C2211yescharacteristic
133#1969C2211yescharacteristic
134#1968C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1948C2211yescharacteristic
143#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1947C2211yescharacteristic
148#1935C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1926C2211yescharacteristic
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1923C2211yescharacteristic
162#1921C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1894C2211yescharacteristic
169#1893C2211yescharacteristic
170#1878C2211yescharacteristic
171#1877C2211yescharacteristic
172#1875C2211yescharacteristic
173#1873C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic
181#1862C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1832C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic
196C4×#107C2211yescharacteristic
197C4×#107C2211yescharacteristic
198C4×#106C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1768C2211yescharacteristic
201#1753C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124—21no—
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117—21no—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C42C2311yescharacteristic
228#501—42no—
229#499—42no—
230#485—42no—
231#482—42no—
232#468—42no—
233#467—42no—
234#464—24no—
235#431—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254#424—24no—
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#399—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#393—21no—
325#393—21no—
326#392—21no—
327#391—21no—
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#390—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388D411yescharacteristic
373#388D411yescharacteristic
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
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#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387D411yescharacteristic
395#387D411yescharacteristic
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386D411yescharacteristic
401#386D411yescharacteristic
402#385—21no—
403#385—21no—
404#385—21no—
405#385D411yescharacteristic
406#385D411yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#383—21no—
413#383—21no—
414#382—21no—
415#382—21no—
416#382—21no—
417#382—21no—
418#382—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#376—21no—
450#376—21no—
451#376C2311yescharacteristic
452C43—21no—
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
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×D411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4C2×D411yescharacteristic
496C23×C4C2×D411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C2×Q16—22no—
500C2×Q16—41no—
501C2×Q16—41no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×M16—22no—
506C2×M16—41no—
507C2×M16—41no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521#125—22no—
522#125—41no—
523#125—41no—
524#125—41no—
525#124—22no—
526#124—22no—
527#124—82no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530C22⋊Q8—41no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534C22⋊Q8—41no—
535C22⋊Q8—41no—
536#121—41no—
537#121—41no—
538#121—41no—
539#121—41no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548#117—22no—
549#117—22no—
550#117—22no—
551#117—41no—
552#117—41no—
553#117—41no—
554#117—82no—
555#117—82no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656#107—22no—
657#107—22no—
658#107—22no—
659#107—41no—
660#107—41no—
661#107—41no—
662#107—41no—
663#106—22no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8#4114yes—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#102—22no—
694#102—22no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700C22⋊C8—22no—
701C22⋊C8—22no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C22⋊C8—41no—
705C22⋊C8—41no—
706#97—41no—
707C4×C8—22no—
708C4×C8—22no—
709C4×C8—41no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
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#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763C24—21no—
764C24C22×D411yescharacteristic
765C24C22×D411yescharacteristic
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—42no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C2511yescharacteristic
845Q16—82no—
846SD16—82no—
847M16—82no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—82no—
871C2×C8C2×#4112yes—
872C2×C8C2×#4112yes—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4H(5,𝔽2)12yes—
931C22⋊C4—22no—
932C22⋊C4—22no—
933C22⋊C4—22no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—41no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C42—22no—
965C42—22no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42C2×#4112yes—
988C422−1+412yes—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23C23×D411yescharacteristic
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—162no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—82no—
1025D4—162no—
1026D4—162no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—84no—
1116C2×C4#54712yes—
1117C2×C4#54712yes—
1118C2×C4#57712yes—
1119C2×C4C22×#4111yescharacteristic
1120C2×C4C2×H(5,𝔽2)11yescharacteristic
1121C2×C4C2×2−1+411yescharacteristic
1122C2×C4#58511yescharacteristic
1123C2×C4#58511yescharacteristic
1124C2×C4#58511yescharacteristic
1125C8—22no—
1126C8—22no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22#344911yescharacteristic
1155C22C2×#54711yescharacteristic
1156C22#348811yescharacteristic
1157C22C2×#57711yescharacteristic
1158C22#358411yescharacteristic
1159C22#358411yescharacteristic
1160C22#358611yescharacteristic
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—42no—
1172C4—41no—
1173C4—41no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4#351411yescharacteristic
1189C4#352411yescharacteristic
1190C4#354711yescharacteristic
1191C4#356511yescharacteristic
1192C2—81no—
1193C2—81no—
1194C2—161no—
1195C2#3805011yescharacteristic
1196C2#6095611yescharacteristic
1197C2#6098711yescharacteristic
1198C2#6126111yescharacteristic
1199C2#6127111yescharacteristic
1200C2#6205011yescharacteristic
1201C2#6207011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35163C2semidirect
3. #33112C2semidirect
4. #32075C2semidirect
5. #32049C2semidirect
6. #32023C2semidirect
8. #30792C2semidirect
9. #30788C2semidirect
11. #30572C2semidirect
12. #29993C2semidirect
13. #29932C2semidirect
14. #29269C2semidirect
15. #28698C2semidirect
16. #28075C2semidirect
17. #28062C2semidirect
18. #27796C2semidirect
19. #27789C2semidirect
20. #27642C2semidirect
21. #27628C2semidirect
22. #27501C2semidirect
23. #27488C2semidirect
24. #27366C2semidirect
25. #27363C2semidirect
26. #24765C2semidirect
27. #24655C2semidirect
28. #22752C2semidirect
29. #22163C2semidirect
30. #21966C2semidirect
31. #21362C2semidirect

Maximal subgroups

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

subgroupindex
#379532
#351632
#331122
#320752
#320492
#320232
#319972
#307922
#307882
#305762
#305722
#299932
#299322
#292692
#286982
#280752
#280622
#277962
#277892
#276422
#276282
#275012
#274882
#273662
#273632
#247652
#246552
#227522
#221632
#219662
#213622