Finite Group Databasebeta

← #7035594

Subgroups — #7035594

Order 512.

1285 conjugacy classes of subgroups.

The subgroup lattice has 1169 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59243C211yesmaximal, characteristic
2#40011C211yesmaximal, characteristic
3#32312C211yesmaximal, characteristic, complemented
4#32310C211yesmaximal, characteristic, complemented
5#32291C211yesmaximal, characteristic, complemented
6#32287C211yesmaximal, characteristic, complemented
7#32009C211yesmaximal, characteristic, complemented
8#32007C211yesmaximal, characteristic, complemented
9#31437C211yesmaximal, characteristic, complemented
10#31435C211yesmaximal, characteristic, complemented
11#29158C211yesmaximal, characteristic, complemented
12#27951C211yesmaximal, characteristic, complemented
13#27837C211yesmaximal, characteristic, complemented
14#27836C211yesmaximal, characteristic, complemented
15#27700C211yesmaximal, characteristic, complemented
16#27700C211yesmaximal, characteristic, complemented
17#27364C211yesmaximal, characteristic, complemented
18#27362C211yesmaximal, characteristic, complemented
19#26211C211yesmaximal, characteristic, complemented
20#26207C211yesmaximal, characteristic, complemented
21#25239C211yesmaximal, characteristic, complemented
22#25233C211yesmaximal, characteristic, complemented
23#24948C211yesmaximal, characteristic, complemented
24#24946C211yesmaximal, characteristic, complemented
25#24944C211yesmaximal, characteristic, complemented
26#24942C211yesmaximal, characteristic, complemented
27#23744C211yesmaximal, characteristic, complemented
28#23116C211yesmaximal, characteristic
29#22708C211yesmaximal, characteristic, complemented
30#22707C211yesmaximal, characteristic, complemented
31#22077C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic
33C2×C8×D4C2211yescharacteristic
34C2×C8×D4C2211yescharacteristic
35#2851C2211yescharacteristic
36#2796—21no—
37#2787—21no—
38#2786—21no—
39#2786—21no—
40#2757—21no—
41#2711—21no—
42#2651—21no—
43#2596—21no—
44#2594—21no—
45#2594—21no—
46#2594—21no—
47#2552C2211yescharacteristic
48#2538C2211yescharacteristic
49#2513—21no—
50#2507C2211yescharacteristic
51#2506C2211yescharacteristic
52#2499C2211yescharacteristic
53#2499C2211yescharacteristic
54#2495C2211yescharacteristic
55#2494—21no—
56#2494C2211yescharacteristic
57#2494C2211yescharacteristic
58#2494C2211yescharacteristic
59#2490—21no—
60#2485C2211yescharacteristic
61#2485C2211yescharacteristic
62#2485C2211yescharacteristic
63#2485C2211yescharacteristic
64#2441C2211yescharacteristic
65#2441C2211yescharacteristic
66#2415C2211yescharacteristic
67#2415C2211yescharacteristic
68#2370—21no—
69#2355C2211yescharacteristic
70#2354C2211yescharacteristic
71#2354C2211yescharacteristic
72#2354C2211yescharacteristic
73#2354C2211yescharacteristic
74#2354C2211yescharacteristic
75#2336—21no—
76C4×C22⋊Q8C2211yescharacteristic
77C4×#121C2211yescharacteristic
78#2296C2211yescharacteristic
79#2285C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2097C2211yescharacteristic
94#2088C2211yescharacteristic
95#2086C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2076C2211yescharacteristic
107#2076C2211yescharacteristic
108#2075C2211yescharacteristic
109#2075C2211yescharacteristic
110#2072C2211yescharacteristic
111#2072C2211yescharacteristic
112#2068C2211yescharacteristic
113#2066C2211yescharacteristic
114#2059C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2026C2211yescharacteristic
120#1991C2211yescharacteristic
121#1991C2211yescharacteristic
122#1948C2211yescharacteristic
123#1948C2211yescharacteristic
124#1947C2211yescharacteristic
125#1947C2211yescharacteristic
126#1942C2211yescharacteristic
127#1942C2211yescharacteristic
128#1941C2211yescharacteristic
129#1941C2211yescharacteristic
130#1933C2211yescharacteristic
131#1933C2211yescharacteristic
132#1933C2211yescharacteristic
133#1933C2211yescharacteristic
134#1928C2211yescharacteristic
135#1927C2211yescharacteristic
136#1923C2211yescharacteristic
137#1923C2211yescharacteristic
138#1921C2211yescharacteristic
139#1921C2211yescharacteristic
140#1920C2211yescharacteristic
141#1920C2211yescharacteristic
142#1919C2211yescharacteristic
143#1919C2211yescharacteristic
144#1919C2211yescharacteristic
145#1918C2211yescharacteristic
146#1918C2211yescharacteristic
147#1918C2211yescharacteristic
148#1916C2211yescharacteristic
149#1916C2211yescharacteristic
150#1892C2211yescharacteristic
151#1892C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1873C2211yescharacteristic
155#1873C2211yescharacteristic
156#1873C2211yescharacteristic
157#1869C2211yescharacteristic
158#1869C2211yescharacteristic
159#1869C2211yescharacteristic
160#1869C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1846C2211yescharacteristic
177#1846C2211yescharacteristic
178#1834C2211yescharacteristic
179#1834C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic
188#1807C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191C4×#107C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C8×C22⋊C4C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C4×C22⋊C8C2211yescharacteristic
196#1735C2211yescharacteristic
197#1735C2211yescharacteristic
198#1735C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#125—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×#121D411yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#485—24no—
228C8×D4—24no—
229C8×D4—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268#401—21no—
269#401—21no—
270#401—21no—
271#400—21no—
272#400—21no—
273#399—21no—
274#399—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#397—21no—
281#397—21no—
282#397—21no—
283#397—21no—
284#397—21no—
285#397—21no—
286#397—21no—
287#397—21no—
288#397—21no—
289#397—21no—
290#397—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#396—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#394—21no—
299#394—21no—
300#394—21no—
301#394—21no—
302#394—21no—
303#394—21no—
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#390—21no—
308#390—21no—
309#390—21no—
310#390—21no—
311#390—21no—
312#390—21no—
313#390D411yescharacteristic
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389D411yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388D411yescharacteristic
356#388D411yescharacteristic
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—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#386D411yescharacteristic
378#386D411yescharacteristic
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#383—21no—
391#382—21no—
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#380—21no—
396#380—21no—
397#380D411yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2411yescharacteristic
482C22×D4C2×D411yescharacteristic
483C22×D4C2×D411yescharacteristic
484C22×D4C2×D411yescharacteristic
485C23×C4C2×D411yescharacteristic
486C23×C4C2×D411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8—41no—
496C22×C8—41no—
497C22×C8—41no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8—41no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510#125—41no—
511#125—41no—
512#125—44no—
513#125—44no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518C22⋊Q8—41no—
519C22⋊Q8—41no—
520#121—24no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—41no—
528C4×D4—41no—
529#117—22no—
530#117—22no—
531#117—41no—
532#117—41no—
533#117—41no—
534#117—41no—
535#117—41no—
536#117—41no—
537#117—41no—
538#117—41no—
539#117—41no—
540#117—41no—
541#117—41no—
542#117—41no—
543#117—41no—
544#117—41no—
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⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—41no—
645C2×C42—41no—
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107—22no—
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—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670#103—22no—
671#103—22no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681C22⋊C8—41no—
682C22⋊C8—41no—
683C22⋊C8—41no—
684C22⋊C8—41no—
685C22⋊C8#4114yes—
686C4×C8—22no—
687C4×C8—22no—
688C4×C8—41no—
689C4×C8—41no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
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#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24C22×D411yescharacteristic
740C24C22×D411yescharacteristic
741C24C22×D411yescharacteristic
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—41no—
791C22×C4—41no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C2×#4112yes—
807C22×C42−1+412yes—
808C22×C4C2511yescharacteristic
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
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—82no—
832C2×C8—82no—
833C2×C8—82no—
834C2×C8—82no—
835C2×C8C2×#4112yes—
836C2×C8C2×#4112yes—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
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—41no—
870C4⋊C4—41no—
871C4⋊C4—42no—
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—81no—
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#13514yes—
903C22⋊C4—22no—
904C22⋊C4—22no—
905C22⋊C4—22no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4—41no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C22⋊C4—81no—
919C22⋊C4—81no—
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—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—41no—
946C42—41no—
947C42—42no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23#54712yes—
982C23C23×D411yescharacteristic
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987D4—44no—
988D4—44no—
989D4—82no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
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—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
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—82no—
1080C2×C4—82no—
1081C2×C4#54712yes—
1082C2×C4C2×#13512yes—
1083C2×C4C2×#13512yes—
1084C2×C4C2×#13512yes—
1085C2×C4C22×#4111yescharacteristic
1086C2×C4C2×2−1+411yescharacteristic
1087C2×C4#58511yescharacteristic
1088C2×C4#58511yescharacteristic
1089C2×C4#58511yescharacteristic
1090C2×C4#58511yescharacteristic
1091C8—22no—
1092C8—22no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—41no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—41no—
1117C22—41no—
1118C22—41no—
1119C22—41no—
1120C22C2×#54711yescharacteristic
1121C22#348511yescharacteristic
1122C22#350011yescharacteristic
1123C22C22×#13511yescharacteristic
1124C22#358411yescharacteristic
1125C22#358411yescharacteristic
1126C22#358611yescharacteristic
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4#352111yescharacteristic
1155C4#352111yescharacteristic
1156C4#355311yescharacteristic
1157C4#355311yescharacteristic
1158C2—42no—
1159C2—81no—
1160C2—81no—
1161C2#4349511yescharacteristic
1162C2#6123411yescharacteristic
1163C2#6128011yescharacteristic
1164C2#6170111yescharacteristic
1165C2#6176811yescharacteristic
1166C2#6253411yescharacteristic
1167C2#6260611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121D4
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
3. #32312C2semidirect
4. #32310C2semidirect
5. #32291C2semidirect
6. #32287C2semidirect
7. #32009C2semidirect
8. #32007C2semidirect
9. #31437C2semidirect
10. #31435C2semidirect
11. #29158C2semidirect
12. #27951C2semidirect
13. #27837C2semidirect
14. #27836C2semidirect
15. #27700C2semidirect
16. #27700C2semidirect
17. #27364C2semidirect
18. #27362C2semidirect
19. #26211C2semidirect
20. #26207C2semidirect
21. #25239C2semidirect
22. #25233C2semidirect
23. #24948C2semidirect
24. #24946C2semidirect
25. #24944C2semidirect
26. #24942C2semidirect
27. #23744C2semidirect
29. #22708C2semidirect
30. #22707C2semidirect
31. #22077C2semidirect

Maximal subgroups

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

subgroupindex
#592432
#400112
#323122
#323102
#322912
#322872
#320092
#320072
#314372
#314352
#291582
#279512
#278372
#278362
#277002
#273642
#273622
#262112
#262072
#252392
#252332
#249482
#249462
#249442
#249422
#237442
#231162
#227082
#227072
#220772