Finite Group Databasebeta

← #6654414

Subgroups — #6654414

Order 512.

1274 conjugacy classes of subgroups.

The subgroup lattice has 1177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37292C211yesmaximal, characteristic
2#35202C211yesmaximal, characteristic, complemented
3#33152C211yesmaximal, characteristic, complemented
4#33113C211yesmaximal, characteristic
5#32390C211yesmaximal, characteristic, complemented
6#32374C211yesmaximal, characteristic, complemented
7#32253C211yesmaximal, characteristic, complemented
8#32241C211yesmaximal, characteristic, complemented
9#31755C211yesmaximal, characteristic, complemented
10#31739C211yesmaximal, characteristic, complemented
11#31470C211yesmaximal, characteristic, complemented
12#31454C211yesmaximal, characteristic, complemented
13#31367C211yesmaximal, characteristic, complemented
14#31359C211yesmaximal, characteristic, complemented
15#31106C211yesmaximal, characteristic, complemented
16#31084C211yesmaximal, characteristic, complemented
17#30967C211yesmaximal, characteristic, complemented
18#30959C211yesmaximal, characteristic, complemented
19#30796C211yesmaximal, characteristic, complemented
20#30788C211yesmaximal, characteristic, complemented
21#29943C211yesmaximal, characteristic, complemented
22#29920C211yesmaximal, characteristic
23#29360C211yesmaximal, characteristic, complemented
24#29360C211yesmaximal, characteristic, complemented
25#29294C211yesmaximal, characteristic, complemented
26#29285C211yesmaximal, characteristic, complemented
27#29265C211yesmaximal, characteristic, complemented
28#29216C211yesmaximal, characteristic, complemented
29#28698C211yesmaximal, characteristic, complemented
30#28292C211yesmaximal, characteristic, complemented
31#21928C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38#2864—21no—
39#2859—21no—
40#2856C2211yescharacteristic
41#2851C2211yescharacteristic
42#2761—21no—
43#2757—21no—
44#2737—21no—
45#2723—21no—
46#2701—21no—
47#2691—21no—
48#2686—21no—
49#2672—21no—
50#2667—21no—
51#2667—21no—
52#2660C2211yescharacteristic
53#2641C2211yescharacteristic
54#2606—21no—
55#2606—21no—
56#2552C2211yescharacteristic
57#2552C2211yescharacteristic
58#2552C2211yescharacteristic
59#2552C2211yescharacteristic
60#2513C2211yescharacteristic
61#2512C2211yescharacteristic
62#2491C2211yescharacteristic
63#2490C2211yescharacteristic
64#2454C2211yescharacteristic
65#2452C2211yescharacteristic
66#2441—21no—
67#2441—21no—
68#2441C2211yescharacteristic
69#2441C2211yescharacteristic
70#2441C2211yescharacteristic
71#2441C2211yescharacteristic
72#2422C2211yescharacteristic
73#2420C2211yescharacteristic
74#2330C2211yescharacteristic
75#2330C2211yescharacteristic
76#2330C2211yescharacteristic
77#2330C2211yescharacteristic
78#2330C2211yescharacteristic
79#2328C2211yescharacteristic
80#2285C2211yescharacteristic
81#2283C2211yescharacteristic
82C4×#117C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2094C2211yescharacteristic
88#2093C2211yescharacteristic
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2071C2211yescharacteristic
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2057C2211yescharacteristic
120#2057C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#1992C2211yescharacteristic
132#1992C2211yescharacteristic
133#1991C2211yescharacteristic
134#1990C2211yescharacteristic
135#1989C2211yescharacteristic
136#1989C2211yescharacteristic
137#1989C2211yescharacteristic
138#1989C2211yescharacteristic
139#1989C2211yescharacteristic
140#1989C2211yescharacteristic
141#1982C2211yescharacteristic
142#1982C2211yescharacteristic
143#1982C2211yescharacteristic
144#1982C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1948C2211yescharacteristic
150#1947C2211yescharacteristic
151#1947C2211yescharacteristic
152#1947C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic
157#1936C2211yescharacteristic
158#1936C2211yescharacteristic
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1924C2211yescharacteristic
168#1924C2211yescharacteristic
169#1923C2211yescharacteristic
170#1923C2211yescharacteristic
171#1921C2211yescharacteristic
172#1921C2211yescharacteristic
173#1920C2211yescharacteristic
174#1920C2211yescharacteristic
175#1919C2211yescharacteristic
176#1919C2211yescharacteristic
177#1918C2211yescharacteristic
178#1918C2211yescharacteristic
179#1917C2211yescharacteristic
180#1917C2211yescharacteristic
181#1916C2211yescharacteristic
182#1916C2211yescharacteristic
183#1875C2211yescharacteristic
184#1875C2211yescharacteristic
185#1864C2211yescharacteristic
186#1864C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1854C2211yescharacteristic
190#1854C2211yescharacteristic
191#1847C2211yescharacteristic
192#1845C2211yescharacteristic
193#1843C2211yescharacteristic
194#1832C2211yescharacteristic
195#1825C2211yescharacteristic
196#1825C2211yescharacteristic
197#1802C2211yescharacteristic
198#1802C2211yescharacteristic
199#1797C2211yescharacteristic
200#1797C2211yescharacteristic
201#1768C2211yescharacteristic
202#1768C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#127C2311yescharacteristic
205C2×#126—21no—
206C2×#125—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#501—42no—
228#499—42no—
229#482—42no—
230#482—42no—
231#478—42no—
232#478—42no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#399—21no—
282#399—21no—
283#399—21no—
284#399—21no—
285#399—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#395—21no—
310#395—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#393—21no—
320#393—21no—
321#390—21no—
322#390—21no—
323#390—21no—
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
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#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#384—21no—
394#384—21no—
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383D411yescharacteristic
404#383D411yescharacteristic
405#382—21no—
406#382D411yescharacteristic
407#382D411yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#381D411yescharacteristic
412#381D411yescharacteristic
413#380—21no—
414#380—21no—
415#380D411yescharacteristic
416#380D411yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376—21no—
437#376C2311yescharacteristic
438#376C2311yescharacteristic
439C43—21no—
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4C2×D411yescharacteristic
494C23×C4C2×D411yescharacteristic
495C23×C4C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506#127—22no—
507#127—22no—
508#126—82no—
509#125—22no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—22no—
514#125—22no—
515#125—41no—
516#125—41no—
517#125—41no—
518#125—41no—
519#125—41no—
520#125—41no—
521#125—82no—
522#125—82no—
523#124—82no—
524#123—82no—
525C22⋊Q8—82no—
526#121—41no—
527#121—41no—
528#121—41no—
529#121—41no—
530#121—82no—
531#121—82no—
532C4×D4—41no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—41no—
536#117—22no—
537#117—22no—
538#117—41no—
539#117—41no—
540#117—82no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
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×C42—22no—
631C2×C42—22no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650#107—22no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107—41no—
655#107—41no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#106—22no—
661#106—22no—
662#106—22no—
663#106—41no—
664#106—41no—
665#106—41no—
666C4⋊C8—22no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690C22⋊C8—41no—
691C22⋊C8—41no—
692C22⋊C8—41no—
693C22⋊C8—41no—
694#97—41no—
695#97—41no—
696C4×C8—41no—
697C4×C8—41no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
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#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742C24—21no—
743C24—21no—
744C24C22×D411yescharacteristic
745C2×Q8—81no—
746C2×Q8—81no—
747C2×Q8—81no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—81no—
765C2×D4—81no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—81no—
769C2×D4—81no—
770C2×D4—81no—
771C2×D4—81no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C2511yescharacteristic
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4H(5,𝔽2)12yes—
914C4⋊C42−1+412yes—
915C22⋊C4—41no—
916C22⋊C4—41no—
917C22⋊C4—41no—
918C22⋊C4—41no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C42—22no—
946C42—22no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C422−1+412yes—
968C422−1+412yes—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23C23×D411yescharacteristic
991Q8—162no—
992D4—41no—
993D4—41no—
994D4—41no—
995D4—41no—
996D4—41no—
997D4—41no—
998D4—41no—
999D4—41no—
1000D4—162no—
1001D4—162no—
1002D4—162no—
1003D4—162no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—44no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
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—82no—
1088C2×C4—162no—
1089C2×C4—162no—
1090C2×C4#53612yes—
1091C2×C4#53612yes—
1092C2×C4#57612yes—
1093C2×C4C2×H(5,𝔽2)11yescharacteristic
1094C2×C4C2×2−1+411yescharacteristic
1095C2×C4C2×2−1+411yescharacteristic
1096C2×C4C2×2−1+411yescharacteristic
1097C2×C4#58511yescharacteristic
1098C2×C4#58511yescharacteristic
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C8—41no—
1103C8—41no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22C2×#53611yescharacteristic
1129C22#348811yescharacteristic
1130C22#348911yescharacteristic
1131C22C2×#57611yescharacteristic
1132C22#358411yescharacteristic
1133C22#358511yescharacteristic
1134C22#358611yescharacteristic
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—42no—
1143C4—41no—
1144C4—41no—
1145C4—42no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4#355011yescharacteristic
1163C4#355411yescharacteristic
1164C4#355511yescharacteristic
1165C4#355711yescharacteristic
1166C2—81no—
1167C2—161no—
1168C2—161no—
1169C2#3727511yescharacteristic
1170C2#6087111yescharacteristic
1171C2#6087511yescharacteristic
1172C2#6201211yescharacteristic
1173C2#6203711yescharacteristic
1174C2#6222211yescharacteristic
1175C2#6223811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35202C2semidirect
3. #33152C2semidirect
5. #32390C2semidirect
6. #32374C2semidirect
7. #32253C2semidirect
8. #32241C2semidirect
9. #31755C2semidirect
10. #31739C2semidirect
11. #31470C2semidirect
12. #31454C2semidirect
13. #31367C2semidirect
14. #31359C2semidirect
15. #31106C2semidirect
16. #31084C2semidirect
17. #30967C2semidirect
18. #30959C2semidirect
19. #30796C2semidirect
20. #30788C2semidirect
21. #29943C2semidirect
23. #29360C2semidirect
24. #29360C2semidirect
25. #29294C2semidirect
26. #29285C2semidirect
27. #29265C2semidirect
28. #29216C2semidirect
29. #28698C2semidirect
30. #28292C2semidirect
31. #21928C2semidirect

Maximal subgroups

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

subgroupindex
#372922
#352022
#331522
#331132
#323902
#323742
#322532
#322412
#317552
#317392
#314702
#314542
#313672
#313592
#311062
#310842
#309672
#309592
#307962
#307882
#299432
#299202
#293602
#292942
#292852
#292652
#292162
#286982
#282922
#219282