Finite Group Databasebeta

← #6554144

Subgroups — #6554144

Order 512.

1390 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39069C211yesmaximal, characteristic
2#38265C211yesmaximal, characteristic, complemented
3#30386C211yesmaximal, characteristic, complemented
4#30353C211yesmaximal, characteristic, complemented
5#29787C211yesmaximal, characteristic, complemented
6#29454C211yesmaximal, characteristic, complemented
7#29435C211yesmaximal, characteristic, complemented
8#29194C211yesmaximal, characteristic, complemented
9#29033C211yesmaximal, characteristic, complemented
10#29015C211yesmaximal, characteristic, complemented
11#28971C211yesmaximal, characteristic, complemented
12#28880C211yesmaximal, characteristic, complemented
13#28667C211yesmaximal, characteristic, complemented
14#28366C211yesmaximal, characteristic
15#28037C211yesmaximal, characteristic, complemented
16#28024C211yesmaximal, characteristic, complemented
17#27699C211yesmaximal, characteristic, complemented
18#27257C211yesmaximal, characteristic
19#26832C211yesmaximal, characteristic, complemented
20#26497C211yesmaximal, characteristic, complemented
21#26079C211yesmaximal, characteristic, complemented
22#24618C211yesmaximal, characteristic, complemented
23#24515C211yesmaximal, characteristic, complemented
24#23788C211yesmaximal, characteristic, complemented
25#23687C211yesmaximal, characteristic, complemented
26#23616C211yesmaximal, characteristic, complemented
27#23040C211yesmaximal, characteristic, complemented
28#22936C211yesmaximal, characteristic, complemented
29#22861C211yesmaximal, characteristic, complemented
30#22579C211yesmaximal, characteristic, complemented
31#20553C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#452C2211yescharacteristic
37C2×#441C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#433C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#424C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#416C2211yescharacteristic
44#2864C2211yescharacteristic
45#2860C2211yescharacteristic
46#2794—21no—
47#2762—21no—
48#2756—21no—
49#2753—21no—
50#2745—21no—
51#2741—21no—
52#2741—21no—
53#2739—21no—
54#2645C2211yescharacteristic
55#2641C2211yescharacteristic
56#2625C2211yescharacteristic
57#2624C2211yescharacteristic
58#2602—21no—
59#2578—21no—
60#2573—21no—
61#2553—21no—
62#2528—21no—
63#2527—21no—
64#2514C2211yescharacteristic
65#2513C2211yescharacteristic
66#2511—21no—
67#2509C2211yescharacteristic
68#2509C2211yescharacteristic
69#2503C2211yescharacteristic
70#2467—21no—
71#2453C2211yescharacteristic
72#2451C2211yescharacteristic
73#2448C2211yescharacteristic
74#2445C2211yescharacteristic
75#2442C2211yescharacteristic
76#2439C2211yescharacteristic
77#2431C2211yescharacteristic
78#2362C2211yescharacteristic
79#2361C2211yescharacteristic
80#2345C2211yescharacteristic
81#2341C2211yescharacteristic
82#2331C2211yescharacteristic
83#2320C2211yescharacteristic
84#2317C2211yescharacteristic
85#2311C2211yescharacteristic
86C4×#124C2211yescharacteristic
87#2298C2211yescharacteristic
88#2295C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2097C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2087C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2074C2211yescharacteristic
100#2073C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2059C2211yescharacteristic
118#2057C2211yescharacteristic
119#2056C2211yescharacteristic
120#2055C2211yescharacteristic
121#2055C2211yescharacteristic
122#2055C2211yescharacteristic
123#2042C2211yescharacteristic
124#2041C2211yescharacteristic
125#2026C2211yescharacteristic
126#2024C2211yescharacteristic
127#2015C2211yescharacteristic
128#2014C2211yescharacteristic
129#1991C2211yescharacteristic
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1971C2211yescharacteristic
133#1969C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1961C2211yescharacteristic
137#1958C2211yescharacteristic
138#1958C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1927C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1920C2211yescharacteristic
164#1919C2211yescharacteristic
165#1893C2211yescharacteristic
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic
169#1875C2211yescharacteristic
170#1872C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1852C2211yescharacteristic
179#1846C2211yescharacteristic
180#1835C2211yescharacteristic
181#1823C2211yescharacteristic
182#1809C2211yescharacteristic
183#1788C2211yescharacteristic
184#1776C2211yescharacteristic
185C4×#107C2211yescharacteristic
186#1771C2211yescharacteristic
187#1771C2211yescharacteristic
188#1770C2211yescharacteristic
189C8×C4⋊C4C2211yescharacteristic
190#1768C2211yescharacteristic
191#1768C2211yescharacteristic
192#1767C2211yescharacteristic
193C4×C4⋊C8C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226#501—42no—
227#486—42no—
228#481—24no—
229#468—24no—
230#452—24no—
231#441—42no—
232#440—42no—
233#433—24no—
234#428—42no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248#424—24no—
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255#417—24no—
256#416—42no—
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295#401—21no—
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#400—21no—
310#399—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#395—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#393—21no—
333#392—21no—
334#392—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#390—21no—
348#390—21no—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
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#388D411yescharacteristic
389#388D411yescharacteristic
390#388D411yescharacteristic
391#388D411yescharacteristic
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#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387D411yescharacteristic
412#387D411yescharacteristic
413#387D411yescharacteristic
414#387D411yescharacteristic
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384—21no—
426#383—21no—
427#383—21no—
428#382—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#376—21no—
458#376C2311yescharacteristic
459C43C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2411yescharacteristic
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—41no—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×M16—41no—
520C2×M16—41no—
521C2×M16#4114yes—
522C22×C8—22no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535#127—41no—
536#127—41no—
537#126—82no—
538#125—41no—
539#125—41no—
540#124—22no—
541#124—41no—
542#123—82no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545#121—22no—
546#121—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—82no—
556#117—22no—
557#117—22no—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655#107—22no—
656#107—22no—
657#107—22no—
658#107—41no—
659#107—41no—
660#107—41no—
661#107—41no—
662#106—22no—
663#106—22no—
664#106—22no—
665#106—41no—
666#106—41no—
667#106—41no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700C22⋊C8—22no—
701C22⋊C8#4114yes—
702#97—22no—
703#97—41no—
704#97—41no—
705#97—41no—
706#97—41no—
707C4×C8—22no—
708C4×C8—41no—
709C4×C8—41no—
710C4×C8—41no—
711C4×C8—41no—
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#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
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—44no—
774#41—44no—
775#41—82no—
776#41—82no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—42no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×Q82−1+412yes—
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—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C2×#4112yes—
860C22×C4C2×#4112yes—
861C22×C4C2511yescharacteristic
862Q16—44no—
863SD16—44no—
864SD16—82no—
865M16—44no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—82no—
887C2×C8C2×#4112yes—
888C2×C8C2×#4112yes—
889C2×C8C2×#4112yes—
890C2×C8C2×#4112yes—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4H(5,𝔽2)12yes—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—41no—
989C42—41no—
990C42—41no—
991C42—41no—
992C42—42no—
993C42—42no—
994C42—42no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23#53212yes—
1021C23C23×D411yescharacteristic
1022Q8—22no—
1023Q8—22no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—162no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—84no—
1040D4—84no—
1041D4—162no—
1042D4—162no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
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—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—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—84no—
1128C2×C4—162no—
1129C2×C4—162no—
1130C2×C4—162no—
1131C2×C4#53212yes—
1132C2×C4C22×#4111yescharacteristic
1133C2×C4C22×#4111yescharacteristic
1134C2×C4C2×H(5,𝔽2)11yescharacteristic
1135C2×C4C2×2−1+411yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C8—22no—
1139C8—22no—
1140C8—22no—
1141C8—22no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C22—22no—
1147C22—22no—
1148C22—22no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22C2×#53211yescharacteristic
1168C22#348811yescharacteristic
1169C22#348911yescharacteristic
1170C22#358411yescharacteristic
1171C22#358411yescharacteristic
1172C22#358511yescharacteristic
1173C22#358611yescharacteristic
1174C4—22no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—42no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—42no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4#349511yescharacteristic
1202C4#350511yescharacteristic
1203C4#352011yescharacteristic
1204C4#352111yescharacteristic
1205C2—42no—
1206C2—161no—
1207C2—161no—
1208C2#3582511yescharacteristic
1209C2#6069711yescharacteristic
1210C2#6072411yescharacteristic
1211C2#6203011yescharacteristic
1212C2#6204711yescharacteristic
1213C2#6216211yescharacteristic
1214C2#6217411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2431C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #38265C2semidirect
3. #30386C2semidirect
4. #30353C2semidirect
5. #29787C2semidirect
6. #29454C2semidirect
7. #29435C2semidirect
8. #29194C2semidirect
9. #29033C2semidirect
10. #29015C2semidirect
11. #28971C2semidirect
12. #28880C2semidirect
13. #28667C2semidirect
15. #28037C2semidirect
16. #28024C2semidirect
17. #27699C2semidirect
19. #26832C2semidirect
20. #26497C2semidirect
21. #26079C2semidirect
22. #24618C2semidirect
23. #24515C2semidirect
24. #23788C2semidirect
25. #23687C2semidirect
26. #23616C2semidirect
27. #23040C2semidirect
28. #22936C2semidirect
29. #22861C2semidirect
30. #22579C2semidirect
31. #20553C2semidirect

Maximal subgroups

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

subgroupindex
#390692
#382652
#303862
#303532
#297872
#294542
#294352
#291942
#290332
#290152
#289712
#288802
#286672
#283662
#280372
#280242
#276992
#272572
#268322
#264972
#260792
#246182
#245152
#237882
#236872
#236162
#230402
#229362
#228612
#225792
#205532