Finite Group Databasebeta

← #6563843

Subgroups — #6563843

Order 512.

1542 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38069C211yesmaximal, characteristic, complemented
2#34398C211yesmaximal, characteristic
3#30159C211yesmaximal, characteristic, complemented
4#30084C211yesmaximal, characteristic, complemented
5#29913C211yesmaximal, characteristic, complemented
6#29504C211yesmaximal, characteristic, complemented
7#29402C211yesmaximal, characteristic, complemented
8#29325C211yesmaximal, characteristic, complemented
9#28210C211yesmaximal, characteristic, complemented
10#27516C211yesmaximal, characteristic, complemented
11#27497C211yesmaximal, characteristic, complemented
12#27383C211yesmaximal, characteristic, complemented
13#27370C211yesmaximal, characteristic, complemented
14#27325C211yesmaximal, characteristic, complemented
15#27304C211yesmaximal, characteristic, complemented
16#26396C211yesmaximal, characteristic, complemented
17#26372C211yesmaximal, characteristic, complemented
18#26338C211yesmaximal, characteristic, complemented
19#26336C211yesmaximal, characteristic, complemented
20#25495C211yesmaximal, characteristic
21#25212C211yesmaximal, characteristic, complemented
22#25212C211yesmaximal, characteristic, complemented
23#24060C211yesmaximal, characteristic
24#23842C211yesmaximal, characteristic, complemented
25#23690C211yesmaximal, characteristic, complemented
26C2×#2085C211yesmaximal, characteristic, complemented
27#23032C211yesmaximal, characteristic, complemented
28#23022C211yesmaximal, characteristic, complemented
29#22938C211yesmaximal, characteristic, complemented
30#22916C211yesmaximal, characteristic, complemented
31#22595C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C22×#107C2211yescharacteristic
42C22×#106C2211yescharacteristic
43#2855C2211yescharacteristic
44#2774—21no—
45#2767—21no—
46#2766—21no—
47#2758—21no—
48#2647C2211yescharacteristic
49#2645C2211yescharacteristic
50#2511C2211yescharacteristic
51#2509C2211yescharacteristic
52#2508C2211yescharacteristic
53#2503—21no—
54#2503C2211yescharacteristic
55#2493—21no—
56#2484—21no—
57#2451C2211yescharacteristic
58#2440C2211yescharacteristic
59#2438—21no—
60#2379—21no—
61#2379—21no—
62#2361C2211yescharacteristic
63#2361C2211yescharacteristic
64#2361C2211yescharacteristic
65#2361C2211yescharacteristic
66#2360C2211yescharacteristic
67#2357C2211yescharacteristic
68#2357C2211yescharacteristic
69#2349C2211yescharacteristic
70#2349C2211yescharacteristic
71#2344C2211yescharacteristic
72#2339—21no—
73#2339—21no—
74#2331C2211yescharacteristic
75#2331C2211yescharacteristic
76#2331C2211yescharacteristic
77#2328C2211yescharacteristic
78#2328C2211yescharacteristic
79#2325—21no—
80#2325—21no—
81#2320C2211yescharacteristic
82#2318—21no—
83#2318—21no—
84C2×#389C2211yescharacteristic
85#2283C2211yescharacteristic
86C2×#382C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic
93#2088C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2085C2211yescharacteristic
105#2085C2211yescharacteristic
106#2085C2211yescharacteristic
107#2074C2211yescharacteristic
108#2074C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2067C2211yescharacteristic
114#2065C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2055C2211yescharacteristic
121#2055C2211yescharacteristic
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2041C2211yescharacteristic
125#2024C2211yescharacteristic
126#2014C2211yescharacteristic
127#1973C2211yescharacteristic
128#1968C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1948C2211yescharacteristic
132#1947C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1942C2211yescharacteristic
136#1941C2211yescharacteristic
137#1936C2211yescharacteristic
138#1934C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1927C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1918C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1917C2211yescharacteristic
154#1917C2211yescharacteristic
155#1916C2211yescharacteristic
156#1916C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1872C2211yescharacteristic
166#1872C2211yescharacteristic
167#1865C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic
185#1840C2211yescharacteristic
186#1832C2211yescharacteristic
187#1817C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1768C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1746C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41—21no—
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#532—24no—
209#532—24no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#124—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121—21no—
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C22×C4⋊C4—21no—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#480—24no—
239#480—24no—
240#476—42no—
241#474—42no—
242#465—24no—
243#465—24no—
244#440—42no—
245C4×SD16—42no—
246C2×#107—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106—42no—
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#401—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#395—21no—
315#395—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—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#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#384C2311yescharacteristic
401#383—21no—
402#383D411yescharacteristic
403#383D411yescharacteristic
404#382—21no—
405#382—21no—
406#382—21no—
407#382—21no—
408#382D411yescharacteristic
409#382D411yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#381—21no—
420#381—21no—
421#381—21no—
422#381D411yescharacteristic
423#381D411yescharacteristic
424#380—21no—
425#380—21no—
426#380D411yescharacteristic
427#380D411yescharacteristic
428#380C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376C2311yescharacteristic
444#376C2311yescharacteristic
445C2×#95—21no—
446C2×#95—21no—
447C2×#95—21no—
448C2×#95—21no—
449C2×#95—21no—
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—28no—
491C2×#41—82no—
492C2×#41—82no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C22×C8—22no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C4⋊Q8—22no—
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539#127—22no—
540#127—22no—
541#124—28no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—82no—
545#121—28no—
546#121—22no—
547#121—22no—
548#121#4114yes—
549#121#4114yes—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×D4—28no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—82no—
566C4×D4—82no—
567C4×D4—82no—
568C4×D4—82no—
569#117—82no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
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⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—82no—
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#107—22no—
662#107—22no—
663#107—22no—
664#107—22no—
665#107—22no—
666#107—22no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#106—22no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703C22⋊C8—22no—
704C22⋊C8—22no—
705#97—22no—
706#97—41no—
707C4×C8—22no—
708C4×C8—41no—
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#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#95—21no—
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
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770C24—21no—
771C24—21no—
772C24C22×D411yescharacteristic
773#41—816no—
774C2×Q8—24no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—42no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4C2×#4112yes—
809C2×D4C2×#4112yes—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C2×#4112yes—
878C22×C4C2×#4112yes—
879C22×C4C2511yescharacteristic
880SD16—44no—
881SD16—44no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—44no—
905C2×C8—44no—
906C2×C82−1+412yes—
907C2×C82−1+412yes—
908C4⋊C4—24no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4C2×#4112yes—
961C4⋊C4C2×#4112yes—
962C4⋊C4H(5,𝔽2)12yes—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C42—22no—
986C42—22no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—42no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—22no—
1012C23—22no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23#52512yes—
1026C23#57612yes—
1027C23#57712yes—
1028C23C23×D411yescharacteristic
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—84no—
1034Q8—162no—
1035D4—22no—
1036D4—22no—
1037D4—22no—
1038D4—22no—
1039D4—48no—
1040D4—48no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—84no—
1046D4—84no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—41no—
1093C2×C4—44no—
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—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—82no—
1133C2×C4—84no—
1134C2×C4—84no—
1135C2×C4—84no—
1136C2×C4—84no—
1137C2×C4—162no—
1138C2×C4—162no—
1139C2×C4—162no—
1140C2×C4—162no—
1141C2×C4—162no—
1142C2×C4—162no—
1143C2×C4#52512yes—
1144C2×C4C22×#4111yescharacteristic
1145C2×C4C22×#4111yescharacteristic
1146C2×C4C2×H(5,𝔽2)11yescharacteristic
1147C2×C4C2×2−1+411yescharacteristic
1148C2×C4C2×2−1+411yescharacteristic
1149C2×C4#58511yescharacteristic
1150C8—22no—
1151C8—22no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22#311814yes—
1179C22C2×#52511yescharacteristic
1180C22#348811yescharacteristic
1181C22#349911yescharacteristic
1182C22C2×#57611yescharacteristic
1183C22C2×#57711yescharacteristic
1184C22#358411yescharacteristic
1185C22#358611yescharacteristic
1186C4—22no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—42no—
1196C4—41no—
1197C4—41no—
1198C4—42no—
1199C4—42no—
1200C4—41no—
1201C4—41no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4#351511yescharacteristic
1214C4#351511yescharacteristic
1215C4#352011yescharacteristic
1216C4#352011yescharacteristic
1217C2—24no—
1218C2—82no—
1219C2—82no—
1220C2#3600111yescharacteristic
1221C2C2×#311811yescharacteristic
1222C2#6058611yescharacteristic
1223C2#6201911yescharacteristic
1224C2#6206411yescharacteristic
1225C2#6249111yescharacteristic
1226C2#6251511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
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
1. #38069C2semidirect
3. #30159C2semidirect
4. #30084C2semidirect
5. #29913C2semidirect
6. #29504C2semidirect
7. #29402C2semidirect
8. #29325C2semidirect
9. #28210C2semidirect
10. #27516C2semidirect
11. #27497C2semidirect
12. #27383C2semidirect
13. #27370C2semidirect
14. #27325C2semidirect
15. #27304C2semidirect
16. #26396C2semidirect
17. #26372C2semidirect
18. #26338C2semidirect
19. #26336C2semidirect
21. #25212C2semidirect
22. #25212C2semidirect
24. #23842C2semidirect
25. #23690C2semidirect
26. C2×#2085C2semidirect
27. #23032C2semidirect
28. #23022C2semidirect
29. #22938C2semidirect
30. #22916C2semidirect
31. #22595C2semidirect

Maximal subgroups

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

subgroupindex
#380692
#343982
#301592
#300842
#299132
#295042
#294022
#293252
#282102
#275162
#274972
#273832
#273702
#273252
#273042
#263962
#263722
#263382
#263362
#254952
#252122
#240602
#238422
#236902
C2×#20852
#230322
#230222
#229382
#229162
#225952