Finite Group Databasebeta

← #6826398

Subgroups — #6826398

Order 512.

1205 conjugacy classes of subgroups.

The subgroup lattice has 1095 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42733C211yesmaximal, characteristic, complemented
2#42638C211yesmaximal, characteristic
3#33274C211yesmaximal, characteristic
4#32494C211yesmaximal, characteristic, complemented
5#32490C211yesmaximal, characteristic
6#32235C211yesmaximal, characteristic, complemented
7#32226C211yesmaximal, characteristic
8#31887C211yesmaximal, characteristic
9#31884C211yesmaximal, characteristic, complemented
10#31467C211yesmaximal, characteristic
11#31456C211yesmaximal, characteristic, complemented
12#30164C211yesmaximal, characteristic, complemented
13#30157C211yesmaximal, characteristic
14#28835C211yesmaximal, characteristic, complemented
15#28817C211yesmaximal, characteristic, complemented
16#28026C211yesmaximal, characteristic
17#28025C211yesmaximal, characteristic
18#28010C211yesmaximal, characteristic
19#28006C211yesmaximal, characteristic, complemented
20#28000C211yesmaximal, characteristic, complemented
21#27994C211yesmaximal, characteristic, complemented
22#27373C211yesmaximal, characteristic, complemented
23#27358C211yesmaximal, characteristic
24#27141C211yesmaximal, characteristic, complemented
25#27130C211yesmaximal, characteristic
26#26498C211yesmaximal, characteristic
27#26498C211yesmaximal, characteristic
28#23169C211yesmaximal, characteristic, complemented
29#22820C211yesmaximal, characteristic
30#21730C211yesmaximal, characteristic, complemented
31#21679C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#440C2211yescharacteristic
35#2836—21no—
36#2833—21no—
37#2762—21no—
38#2758—21no—
39#2747—21no—
40#2725—21no—
41#2722—21no—
42#2721—21no—
43#2719—21no—
44#2713—21no—
45#2666—21no—
46#2664—21no—
47#2645C2211yescharacteristic
48#2644C2211yescharacteristic
49#2642—21no—
50#2629—21no—
51#2571C2211yescharacteristic
52#2552C2211yescharacteristic
53#2552C2211yescharacteristic
54#2551C2211yescharacteristic
55#2528—21no—
56#2514C2211yescharacteristic
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic
59#2512C2211yescharacteristic
60#2511C2211yescharacteristic
61#2511C2211yescharacteristic
62#2508C2211yescharacteristic
63#2507C2211yescharacteristic
64#2507C2211yescharacteristic
65#2506C2211yescharacteristic
66#2506C2211yescharacteristic
67#2506C2211yescharacteristic
68#2478—21no—
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic
71#2451C2211yescharacteristic
72#2451C2211yescharacteristic
73#2402C2211yescharacteristic
74#2370C2211yescharacteristic
75#2369C2211yescharacteristic
76#2356C2211yescharacteristic
77#2354C2211yescharacteristic
78#2331C2211yescharacteristic
79#2330C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2099C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2086C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2073C2211yescharacteristic
97#2072C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#1991C2211yescharacteristic
121#1990C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1973C2211yescharacteristic
125#1973C2211yescharacteristic
126#1973C2211yescharacteristic
127#1968C2211yescharacteristic
128#1968C2211yescharacteristic
129#1968C2211yescharacteristic
130#1948C2211yescharacteristic
131#1948C2211yescharacteristic
132#1947C2211yescharacteristic
133#1947C2211yescharacteristic
134#1944C2211yescharacteristic
135#1944C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1941C2211yescharacteristic
146#1940C2211yescharacteristic
147#1940C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1928C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1921C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1918C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1918C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1916C2211yescharacteristic
177#1916C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1847C2211yescharacteristic
183#1847C2211yescharacteristic
184#1845C2211yescharacteristic
185#1844C2211yescharacteristic
186#1832C2211yescharacteristic
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#107C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199#1770C2211yescharacteristic
200#1770C2211yescharacteristic
201C8×C4⋊C4C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×#117—21no—
219#501—24no—
220#501—24no—
221#440—24no—
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271#401—21no—
272#401—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400D411yescharacteristic
288#400D411yescharacteristic
289#400D411yescharacteristic
290#400D411yescharacteristic
291#399—21no—
292#399—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398D411yescharacteristic
308#398D411yescharacteristic
309#398D411yescharacteristic
310#398D411yescharacteristic
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#385—21no—
402#385—21no—
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#383—21no—
411#383—21no—
412#382—21no—
413#382—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#380—21no—
417#380—21no—
418#380—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437#376—21no—
438#376C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×D4C2411yescharacteristic
485C23×C4—21no—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—22no—
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501C4⋊Q8—82no—
502#126—82no—
503#126—82no—
504#126—82no—
505#125—22no—
506#125—22no—
507#125—41no—
508#125—41no—
509#125—82no—
510#125—82no—
511#125—82no—
512#125—82no—
513C4×Q8—22no—
514C4×Q8—41no—
515C4×D4—22no—
516C4×D4—41no—
517#117—82no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
584C2×C22⋊C4—21no—
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⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C42—21no—
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×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614#107—22no—
615#107—22no—
616#107—22no—
617#107—22no—
618#107—22no—
619#107—41no—
620#107—41no—
621#107—41no—
622#107—41no—
623#107#4114yes—
624#106—22no—
625#106—22no—
626#106—22no—
627#106—22no—
628#106—22no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633C4⋊C8—22no—
634C4⋊C8—22no—
635C4⋊C8—41no—
636C4⋊C8—41no—
637C4⋊C8—41no—
638C4⋊C8—41no—
639#103—22no—
640#103—22no—
641#103—41no—
642#103—41no—
643#103—41no—
644#103—41no—
645#103—41no—
646#102—22no—
647#102—22no—
648#102—41no—
649#102—41no—
650#102—41no—
651#102—41no—
652#102—41no—
653#97—22no—
654#97—22no—
655#97—22no—
656#97—22no—
657#97—41no—
658C4×C8—22no—
659C4×C8—22no—
660C4×C8—22no—
661C4×C8—22no—
662C4×C8—41no—
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#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
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
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725C24—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—42no—
733C2×Q8—42no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—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—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—81no—
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
777SD16—44no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
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×C8C2×#4112yes—
799C2×C82−1+412yes—
800C2×C82−1+412yes—
801C2×C82−1+412yes—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
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—21no—
834C4⋊C4—41no—
835C4⋊C4—41no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
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—42no—
851C4⋊C4—42no—
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⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4C2×#4112yes—
880C4⋊C4C2×#4112yes—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—81no—
885C22⋊C4—81no—
886C22⋊C4—81no—
887C22⋊C4—81no—
888C22⋊C4—81no—
889C22⋊C4—81no—
890C22⋊C4—81no—
891C22⋊C4—81no—
892C22⋊C4—81no—
893C22⋊C4—81no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—42no—
909C42—42no—
910C42—42no—
911C42—42no—
912C42—42no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23C23×D411yescharacteristic
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8—41no—
931Q8—162no—
932Q8—162no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
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—22no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
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—41no—
1021C2×C4—41no—
1022C2×C4—84no—
1023C2×C4#57612yes—
1024C2×C4#57712yes—
1025C2×C4C22×#4111yescharacteristic
1026C2×C4C2×2−1+411yescharacteristic
1027C2×C4C2×2−1+411yescharacteristic
1028C2×C4C2×2−1+411yescharacteristic
1029C2×C4#58511yescharacteristic
1030C2×C4#58511yescharacteristic
1031C8—22no—
1032C8—41no—
1033C8—41no—
1034C8—41no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C8#54114yes—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22D4×#4111yescharacteristic
1047C22#349711yescharacteristic
1048C22#349911yescharacteristic
1049C22C2×#57611yescharacteristic
1050C22C2×#57711yescharacteristic
1051C22#358611yescharacteristic
1052C22#358611yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—41no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—41no—
1060C4—41no—
1061C4—41no—
1062C4—42no—
1063C4—42no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
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—81no—
1082C4C2×#54111yescharacteristic
1083C4#351611yescharacteristic
1084C4#355511yescharacteristic
1085C4#356511yescharacteristic
1086C2—161no—
1087C2#3939911yescharacteristic
1088C2#6155311yescharacteristic
1089C2#6155611yescharacteristic
1090C2#6238111yescharacteristic
1091C2#6239111yescharacteristic
1092C2#6251311yescharacteristic
1093C2#6251511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42733C2semidirect
4. #32494C2semidirect
6. #32235C2semidirect
9. #31884C2semidirect
11. #31456C2semidirect
12. #30164C2semidirect
14. #28835C2semidirect
15. #28817C2semidirect
19. #28006C2semidirect
20. #28000C2semidirect
21. #27994C2semidirect
22. #27373C2semidirect
24. #27141C2semidirect
28. #23169C2semidirect
30. #21730C2semidirect
31. #21679C2semidirect

Maximal subgroups

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

subgroupindex
#427332
#426382
#332742
#324942
#324902
#322352
#322262
#318872
#318842
#314672
#314562
#301642
#301572
#288352
#288172
#280262
#280252
#280102
#280062
#280002
#279942
#273732
#273582
#271412
#271302
#264982
#231692
#228202
#217302
#216792