Finite Group Databasebeta

← #6774607

Subgroups — #6774607

Order 512.

1213 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38072C211yesmaximal, characteristic
2#35235C211yesmaximal, characteristic
3#33100C211yesmaximal, characteristic
4#32381C211yesmaximal, characteristic, complemented
5#32334C211yesmaximal, characteristic, complemented
6#32333C211yesmaximal, characteristic, complemented
7#32254C211yesmaximal, characteristic, complemented
8#32140C211yesmaximal, characteristic, complemented
9#32135C211yesmaximal, characteristic, complemented
10#31464C211yesmaximal, characteristic, complemented
11#30964C211yesmaximal, characteristic, complemented
12#30160C211yesmaximal, characteristic, complemented
13#30103C211yesmaximal, characteristic, complemented
14#29526C211yesmaximal, characteristic, complemented
15#29407C211yesmaximal, characteristic, complemented
16#29282C211yesmaximal, characteristic, complemented
17#29185C211yesmaximal, characteristic, complemented
18#28786C211yesmaximal, characteristic
19#27866C211yesmaximal, characteristic
20#27724C211yesmaximal, characteristic
21#27722C211yesmaximal, characteristic
22#27618C211yesmaximal, characteristic
23#26429C211yesmaximal, characteristic
24#26365C211yesmaximal, characteristic
25#26078C211yesmaximal, characteristic
26#26019C211yesmaximal, characteristic
27#26011C211yesmaximal, characteristic
28#22596C211yesmaximal, characteristic
29#22255C211yesmaximal, characteristic, complemented
30#22124C211yesmaximal, characteristic, complemented
31#21033C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#428C2211yescharacteristic
35#2855—21no—
36#2855—21no—
37#2855C2211yescharacteristic
38#2771—21no—
39#2765—21no—
40#2739—21no—
41#2738—21no—
42#2666—21no—
43#2666—21no—
44#2647C2211yescharacteristic
45#2645C2211yescharacteristic
46#2606—21no—
47#2605—21no—
48#2570C2211yescharacteristic
49#2570C2211yescharacteristic
50#2569—21no—
51#2550C2211yescharacteristic
52#2550C2211yescharacteristic
53#2549—21no—
54#2533—21no—
55#2528—21no—
56#2524—21no—
57#2511C2211yescharacteristic
58#2509C2211yescharacteristic
59#2508—21no—
60#2507C2211yescharacteristic
61#2499C2211yescharacteristic
62#2453C2211yescharacteristic
63#2442C2211yescharacteristic
64#2442C2211yescharacteristic
65#2441C2211yescharacteristic
66#2440C2211yescharacteristic
67#2440C2211yescharacteristic
68#2362C2211yescharacteristic
69#2346C2211yescharacteristic
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2330C2211yescharacteristic
73#2330C2211yescharacteristic
74#2330C2211yescharacteristic
75#2320C2211yescharacteristic
76#2296C2211yescharacteristic
77#2283C2211yescharacteristic
78#2283C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2087C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2083C2211yescharacteristic
104#2083C2211yescharacteristic
105#2074C2211yescharacteristic
106#2074C2211yescharacteristic
107#2072C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2058C2211yescharacteristic
116#2057C2211yescharacteristic
117#2026C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1991C2211yescharacteristic
123#1990C2211yescharacteristic
124#1989C2211yescharacteristic
125#1988C2211yescharacteristic
126#1987C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1947C2211yescharacteristic
130#1944C2211yescharacteristic
131#1943C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1933C2211yescharacteristic
137#1933C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1894C2211yescharacteristic
173#1894C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1853C2211yescharacteristic
181#1852C2211yescharacteristic
182#1851C2211yescharacteristic
183#1851C2211yescharacteristic
184#1844C2211yescharacteristic
185#1840C2211yescharacteristic
186#1836C2211yescharacteristic
187#1836C2211yescharacteristic
188#1832C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1817C2211yescharacteristic
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic
194#1803C2211yescharacteristic
195#1768C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1746C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C42—21no—
219C22×C42C2311yescharacteristic
220#501—24no—
221#479—24no—
222#428—24no—
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×C22⋊C8C2311yescharacteristic
252C2×C22⋊C8C2311yescharacteristic
253C2×#97C2311yescharacteristic
254C2×#97C2311yescharacteristic
255C2×C4×C8C2311yescharacteristic
256C2×C4×C8C2311yescharacteristic
257#401—21no—
258#400—21no—
259#400—21no—
260#400—21no—
261#400—21no—
262#400—21no—
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#399—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#397—21no—
287#397—21no—
288#396—21no—
289#395—21no—
290#395—21no—
291#395—21no—
292#395—21no—
293#391—21no—
294#391—21no—
295#391—21no—
296#391—21no—
297#391—21no—
298#391—21no—
299#391C2311yescharacteristic
300#391C2311yescharacteristic
301#391C2311yescharacteristic
302#391C2311yescharacteristic
303#391C2311yescharacteristic
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
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#387—21no—
340#387—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
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#385—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#385—21no—
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#384C2311yescharacteristic
377#383—21no—
378#383—21no—
379#383D411yescharacteristic
380#383D411yescharacteristic
381#382—21no—
382#382—21no—
383#382D411yescharacteristic
384#382D411yescharacteristic
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#381—21no—
391#381—21no—
392#381D411yescharacteristic
393#381D411yescharacteristic
394#380—21no—
395#380—21no—
396#380D411yescharacteristic
397#380D411yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4C2311yescharacteristic
419C4×C22⋊C4C2311yescharacteristic
420#376—21no—
421#376—21no—
422#376C2311yescharacteristic
423#376C2311yescharacteristic
424C2×#95—21no—
425#340C2311yescharacteristic
426#340C2311yescharacteristic
427#340C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
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#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
484C23×C4—21no—
485C23×C4—21no—
486C23×C4C2×D411yescharacteristic
487C23×C4C2×D411yescharacteristic
488C23×C4C2411yescharacteristic
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C4⋊Q8—22no—
504C4⋊Q8—22no—
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507#125—22no—
508#125—22no—
509#125—22no—
510#125—41no—
511#125—41no—
512#125—41no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—82no—
516C22⋊Q8—82no—
517C4×Q8—22no—
518C4×Q8—41no—
519#117—22no—
520#117—22no—
521#117—22no—
522#117—41no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4C2×D411yescharacteristic
592C2×C22⋊C4C2×D411yescharacteristic
593C2×C22⋊C4C2×D411yescharacteristic
594C2×C22⋊C4C2×D411yescharacteristic
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—82no—
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618#107—22no—
619#107—22no—
620#107—22no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#107#4114yes—
626#106—22no—
627#106—22no—
628#106—22no—
629#106—22no—
630#106—22no—
631#106—41no—
632#106—41no—
633#106—41no—
634C4⋊C8—22no—
635C4⋊C8—41no—
636C4⋊C8—41no—
637C4⋊C8—41no—
638#103—22no—
639#103—22no—
640#103—22no—
641#103—41no—
642#103—41no—
643#103—41no—
644#103—41no—
645#103—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648#97—22no—
649#97—41no—
650C4×C8—41no—
651C4×C8—41no—
652#95—21no—
653#95—21no—
654#95—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
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#95C2×D411yescharacteristic
704#95C2×D411yescharacteristic
705#95C2×D411yescharacteristic
706#95C2×D411yescharacteristic
707#95C2×D411yescharacteristic
708#95C2×D411yescharacteristic
709#95C2×D411yescharacteristic
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719C24C22×D411yescharacteristic
720C2×Q8—21no—
721C2×Q8—21no—
722C2×Q8—21no—
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—21no—
726C2×Q8—42no—
727C2×Q8—42no—
728C2×Q8—81no—
729C2×Q8—81no—
730C2×Q8—81no—
731C2×Q8—81no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—81no—
763C22×C4—81no—
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C42−1+412yes—
778C22×C42−1+412yes—
779C22×C4C2511yescharacteristic
780M16—44no—
781M16—82no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8C2×#4112yes—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—41no—
834C4⋊C4—41no—
835C4⋊C4—41no—
836C4⋊C4—41no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4C2×#4112yes—
877C4⋊C4C2×#4112yes—
878C4⋊C42−1+412yes—
879C22⋊C4—41no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—41no—
883C22⋊C4—42no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—81no—
889C42—22no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—42no—
904C42—42no—
905C42—42no—
906C42—81no—
907C42—81no—
908C42—81no—
909C42—81no—
910C42—81no—
911C42—81no—
912C42—81no—
913C42—81no—
914C42—81no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23#53612yes—
922C23C23×D411yescharacteristic
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8—162no—
928Q8—162no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—82no—
1021C2×C4—84no—
1022C2×C4—84no—
1023C2×C4#53612yes—
1024C2×C4C22×#4111yescharacteristic
1025C2×C4C2×2−1+411yescharacteristic
1026C2×C4C2×2−1+411yescharacteristic
1027C2×C4C2×2−1+411yescharacteristic
1028C2×C4#58511yescharacteristic
1029C2×C4#58511yescharacteristic
1030C8—22no—
1031C8—41no—
1032C8—41no—
1033C8—41no—
1034C8—41no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22C2×#53611yescharacteristic
1046C22D4×#4111yescharacteristic
1047C22#348911yescharacteristic
1048C22#358411yescharacteristic
1049C22#358511yescharacteristic
1050C22#358611yescharacteristic
1051C22#358611yescharacteristic
1052C4—22no—
1053C4—41no—
1054C4—41no—
1055C4—41no—
1056C4—41no—
1057C4—42no—
1058C4—42no—
1059C4—41no—
1060C4—41no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—42no—
1068C4—81no—
1069C4—81no—
1070C4—81no—
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4#349511yescharacteristic
1082C4#352311yescharacteristic
1083C4#356311yescharacteristic
1084C4#356411yescharacteristic
1085C2—42no—
1086C2#3837111yescharacteristic
1087C2#6086711yescharacteristic
1088C2#6087611yescharacteristic
1089C2#6150911yescharacteristic
1090C2#6154911yescharacteristic
1091C2#6217611yescharacteristic
1092C2#6223411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
4. #32381C2semidirect
5. #32334C2semidirect
6. #32333C2semidirect
7. #32254C2semidirect
8. #32140C2semidirect
9. #32135C2semidirect
10. #31464C2semidirect
11. #30964C2semidirect
12. #30160C2semidirect
13. #30103C2semidirect
14. #29526C2semidirect
15. #29407C2semidirect
16. #29282C2semidirect
17. #29185C2semidirect
29. #22255C2semidirect
30. #22124C2semidirect

Maximal subgroups

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

subgroupindex
#380722
#352352
#331002
#323812
#323342
#323332
#322542
#321402
#321352
#314642
#309642
#301602
#301032
#295262
#294072
#292822
#291852
#287862
#278662
#277242
#277222
#276182
#264292
#263652
#260782
#260192
#260112
#225962
#222552
#221242
#210332