Finite Group Databasebeta

← #6745257

Subgroups — #6745257

Order 512.

1293 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42614C211yesmaximal, characteristic, complemented
2#35968C211yesmaximal, characteristic, complemented
3#33089C211yesmaximal, characteristic, complemented
4#32427C211yesmaximal, characteristic, complemented
5#32370C211yesmaximal, characteristic, complemented
6#32091C211yesmaximal, characteristic, complemented
7#31899C211yesmaximal, characteristic, complemented
8#31583C211yesmaximal, characteristic, complemented
9#31177C211yesmaximal, characteristic, complemented
10#30903C211yesmaximal, characteristic
11#30824C211yesmaximal, characteristic, complemented
12#30349C211yesmaximal, characteristic
13#30069C211yesmaximal, characteristic, complemented
14#28034C211yesmaximal, characteristic, complemented
15#28017C211yesmaximal, characteristic, complemented
16#27514C211yesmaximal, characteristic, complemented
17#27504C211yesmaximal, characteristic, complemented
18#27431C211yesmaximal, characteristic, complemented
19#27144C211yesmaximal, characteristic, complemented
20#27090C211yesmaximal, characteristic, complemented
21#27079C211yesmaximal, characteristic
22#27007C211yesmaximal, characteristic, complemented
23#26887C211yesmaximal, characteristic, complemented
24#26782C211yesmaximal, characteristic, complemented
25#26754C211yesmaximal, characteristic, complemented
26#26103C211yesmaximal, characteristic, complemented
27#26024C211yesmaximal, characteristic, complemented
28#23228C211yesmaximal, characteristic, complemented
29#23098C211yesmaximal, characteristic, complemented
30#22378C211yesmaximal, characteristic, complemented
31#21626C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#475C2211yescharacteristic
34C2×#463C2211yescharacteristic
35#2831—21no—
36#2783—21no—
37#2716—21no—
38#2689—21no—
39#2689—21no—
40#2652—21no—
41#2651—21no—
42#2644C2211yescharacteristic
43#2641C2211yescharacteristic
44#2637—21no—
45#2597—21no—
46#2593—21no—
47#2571C2211yescharacteristic
48#2565C2211yescharacteristic
49#2551C2211yescharacteristic
50#2548C2211yescharacteristic
51#2531—21no—
52#2526—21no—
53#2513C2211yescharacteristic
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic
56#2512C2211yescharacteristic
57#2512C2211yescharacteristic
58#2509C2211yescharacteristic
59#2507C2211yescharacteristic
60#2507C2211yescharacteristic
61#2479—21no—
62#2468—21no—
63#2452C2211yescharacteristic
64#2452C2211yescharacteristic
65#2448C2211yescharacteristic
66#2448C2211yescharacteristic
67#2429—21no—
68#2402C2211yescharacteristic
69#2395—21no—
70#2370C2211yescharacteristic
71#2367C2211yescharacteristic
72#2367C2211yescharacteristic
73#2366C2211yescharacteristic
74#2365C2211yescharacteristic
75#2357C2211yescharacteristic
76#2357C2211yescharacteristic
77#2354C2211yescharacteristic
78#2331C2211yescharacteristic
79#2276C2211yescharacteristic
80#2101C2211yescharacteristic
81#2096C2211yescharacteristic
82#2094C2211yescharacteristic
83#2093C2211yescharacteristic
84#2092C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic
88#2085C2211yescharacteristic
89#2084C2211yescharacteristic
90#2073C2211yescharacteristic
91#2072C2211yescharacteristic
92#2071C2211yescharacteristic
93#2068C2211yescharacteristic
94#2067C2211yescharacteristic
95#2067C2211yescharacteristic
96#2065C2211yescharacteristic
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2058C2211yescharacteristic
104#2055C2211yescharacteristic
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2025C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#2012C2211yescharacteristic
119#2011C2211yescharacteristic
120#1987C2211yescharacteristic
121#1987C2211yescharacteristic
122#1983C2211yescharacteristic
123#1972C2211yescharacteristic
124#1972C2211yescharacteristic
125#1972C2211yescharacteristic
126#1970C2211yescharacteristic
127#1968C2211yescharacteristic
128#1958C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1943C2211yescharacteristic
134#1941C2211yescharacteristic
135#1940C2211yescharacteristic
136#1939C2211yescharacteristic
137#1936C2211yescharacteristic
138#1935C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic
185#1863C2211yescharacteristic
186#1847C2211yescharacteristic
187#1840C2211yescharacteristic
188#1834C2211yescharacteristic
189#1805C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#106C2211yescharacteristic
195#1771C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197#1768C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227#489—24no—
228#475—24no—
229#463—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400D411yescharacteristic
286#400D411yescharacteristic
287#400D411yescharacteristic
288#400D411yescharacteristic
289#399—21no—
290#399—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398D411yescharacteristic
298#398D411yescharacteristic
299#398D411yescharacteristic
300#398D411yescharacteristic
301#397—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#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#395—21no—
320#395—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#393—21no—
328#393—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390—21no—
335#390—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
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#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#382—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#381—21no—
416#380—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441#376—21no—
442#376C2311yescharacteristic
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#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×D8—22no—
496C2×D8—41no—
497C2×D8—41no—
498C2×D8—41no—
499C2×D8—41no—
500C2×D8—41no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—82no—
514#127—41no—
515#127—41no—
516#126—82no—
517#126—82no—
518#126—82no—
519#125—41no—
520#125—41no—
521#124—22no—
522#124—22no—
523#124—41no—
524#124—41no—
525C22⋊Q8—82no—
526C22⋊Q8—82no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—82no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—82no—
541#117—82no—
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⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
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×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#106—22no—
651#106—22no—
652#106—22no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665#103—22no—
666#103—22no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103#4114yes—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
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—
690#102—41no—
691#97—22no—
692#97—41no—
693#97—41no—
694C4×C8—41no—
695C4×C8—41no—
696C4×C8—41no—
697#95—21no—
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#95—21no—
727#95—21no—
728#95—21no—
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
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745C24—21no—
746C24—21no—
747C24—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8C2×#4112yes—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—81no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4—81no—
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—21no—
796C22×C4—21no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4—81no—
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×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C2511yescharacteristic
821SD16—82no—
822D8—82no—
823D8—82no—
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—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8C2×#4112yes—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
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—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
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⋊C4C2×#4112yes—
908C4⋊C42−1+412yes—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
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—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
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—
990C23—41no—
991C23—41no—
992C23C23×D411yescharacteristic
993Q8—22no—
994Q8—22no—
995Q8—41no—
996Q8—41no—
997Q8—84no—
998Q8—162no—
999D4—41no—
1000D4—41no—
1001D4—41no—
1002D4—41no—
1003D4—41no—
1004D4—41no—
1005D4—41no—
1006D4—41no—
1007D4—41no—
1008D4—41no—
1009D4—41no—
1010D4—41no—
1011D4—84no—
1012D4—162no—
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—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—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
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—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—84no—
1094C2×C4—162no—
1095C2×C4—162no—
1096C2×C4#57712yes—
1097C2×C4C22×#4111yescharacteristic
1098C2×C4C2×2−1+411yescharacteristic
1099C2×C4#58511yescharacteristic
1100C2×C4#58511yescharacteristic
1101C2×C4#58511yescharacteristic
1102C2×C4#58511yescharacteristic
1103C8—22no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C8—41no—
1110C8—41no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
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—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22D4×#4111yescharacteristic
1133C22#348711yescharacteristic
1134C22#348911yescharacteristic
1135C22C2×#57711yescharacteristic
1136C22#358411yescharacteristic
1137C22#358511yescharacteristic
1138C22#358511yescharacteristic
1139C4—22no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—42no—
1147C4—42no—
1148C4—41no—
1149C4—41no—
1150C4—42no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4#346111yescharacteristic
1167C4#352111yescharacteristic
1168C4#356511yescharacteristic
1169C4#356611yescharacteristic
1170C2—161no—
1171C2—161no—
1172C2—161no—
1173C2#3783111yescharacteristic
1174C2#6149511yescharacteristic
1175C2#6150411yescharacteristic
1176C2#6191311yescharacteristic
1177C2#6192411yescharacteristic
1178C2#6215611yescharacteristic
1179C2#6219711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2011C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42614C2semidirect
2. #35968C2semidirect
3. #33089C2semidirect
4. #32427C2semidirect
5. #32370C2semidirect
6. #32091C2semidirect
7. #31899C2semidirect
8. #31583C2semidirect
9. #31177C2semidirect
11. #30824C2semidirect
13. #30069C2semidirect
14. #28034C2semidirect
15. #28017C2semidirect
16. #27514C2semidirect
17. #27504C2semidirect
18. #27431C2semidirect
19. #27144C2semidirect
20. #27090C2semidirect
22. #27007C2semidirect
23. #26887C2semidirect
24. #26782C2semidirect
25. #26754C2semidirect
26. #26103C2semidirect
27. #26024C2semidirect
28. #23228C2semidirect
29. #23098C2semidirect
30. #22378C2semidirect
31. #21626C2semidirect

Maximal subgroups

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

subgroupindex
#426142
#359682
#330892
#324272
#323702
#320912
#318992
#315832
#311772
#309032
#308242
#303492
#300692
#280342
#280172
#275142
#275042
#274312
#271442
#270902
#270792
#270072
#268872
#267822
#267542
#261032
#260242
#232282
#230982
#223782
#216262