Finite Group Databasebeta

← #6875536

Subgroups — #6875536

Order 512.

1256 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38926C211yesmaximal, characteristic
2#35235C211yesmaximal, characteristic, complemented
3#33150C211yesmaximal, characteristic, complemented
4#31716C211yesmaximal, characteristic, complemented
5#31708C211yesmaximal, characteristic, complemented
6#31436C211yesmaximal, characteristic, complemented
7#31424C211yesmaximal, characteristic, complemented
8#31376C211yesmaximal, characteristic
9#31372C211yesmaximal, characteristic
10#31088C211yesmaximal, characteristic
11#31086C211yesmaximal, characteristic
12#30103C211yesmaximal, characteristic, complemented
13#30100C211yesmaximal, characteristic, complemented
14#29404C211yesmaximal, characteristic, complemented
15#29400C211yesmaximal, characteristic, complemented
16#29187C211yesmaximal, characteristic, complemented
17#29185C211yesmaximal, characteristic, complemented
18#28831C211yesmaximal, characteristic, complemented
19#28796C211yesmaximal, characteristic, complemented
20#27879C211yesmaximal, characteristic, complemented
21#27817C211yesmaximal, characteristic, complemented
22#27733C211yesmaximal, characteristic, complemented
23#27633C211yesmaximal, characteristic
24#26514C211yesmaximal, characteristic, complemented
25#26449C211yesmaximal, characteristic, complemented
26#26117C211yesmaximal, characteristic, complemented
27#26051C211yesmaximal, characteristic, complemented
28#22640C211yesmaximal, characteristic, complemented
29#22123C211yesmaximal, characteristic, complemented
30#22122C211yesmaximal, characteristic, complemented
31C4×#481C211yesmaximal, characteristic
32C2×#481C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#476C2211yescharacteristic
35#2855—21no—
36#2855—21no—
37#2851C2211yescharacteristic
38#2765—21no—
39#2750—21no—
40#2744—21no—
41#2695—21no—
42#2666—21no—
43#2666—21no—
44#2647C2211yescharacteristic
45#2647C2211yescharacteristic
46#2606—21no—
47#2605—21no—
48#2577—21no—
49#2570C2211yescharacteristic
50#2570C2211yescharacteristic
51#2570C2211yescharacteristic
52#2569—21no—
53#2566C2211yescharacteristic
54#2550C2211yescharacteristic
55#2550C2211yescharacteristic
56#2549—21no—
57#2496C2211yescharacteristic
58#2494C2211yescharacteristic
59#2493—21no—
60#2468—21no—
61#2442C2211yescharacteristic
62#2442C2211yescharacteristic
63#2440C2211yescharacteristic
64#2440C2211yescharacteristic
65#2422C2211yescharacteristic
66#2420C2211yescharacteristic
67#2419—21no—
68#2370C2211yescharacteristic
69#2349C2211yescharacteristic
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2330C2211yescharacteristic
73#2330C2211yescharacteristic
74#2319C2211yescharacteristic
75#2319C2211yescharacteristic
76C4×#121C2211yescharacteristic
77#2283C2211yescharacteristic
78#2283C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic
108#2073C2211yescharacteristic
109#2071C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2058C2211yescharacteristic
114#2058C2211yescharacteristic
115#2057C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2023C2211yescharacteristic
120#1993C2211yescharacteristic
121#1992C2211yescharacteristic
122#1991C2211yescharacteristic
123#1991C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1988C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1944C2211yescharacteristic
137#1943C2211yescharacteristic
138#1941C2211yescharacteristic
139#1941C2211yescharacteristic
140#1939C2211yescharacteristic
141#1939C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1923C2211yescharacteristic
153#1923C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1919C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1874C2211yescharacteristic
171#1864C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1846C2211yescharacteristic
179#1846C2211yescharacteristic
180#1844C2211yescharacteristic
181#1840C2211yescharacteristic
182#1840C2211yescharacteristic
183#1836C2211yescharacteristic
184#1836C2211yescharacteristic
185#1835C2211yescharacteristic
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic
188#1824C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1802C2211yescharacteristic
193#1797C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1768C2211yescharacteristic
199#1768C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#126—21no—
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#123—21no—
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—21no—
212C2×#121C2311yescharacteristic
213C2×C4×D4—21no—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C42—21no—
220C22×C42C2311yescharacteristic
221#481—24no—
222#478—24no—
223#476—24no—
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×C22⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264#401—21no—
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—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#398—21no—
287#398—21no—
288#397—21no—
289#397—21no—
290#397—21no—
291#397—21no—
292#396—21no—
293#396—21no—
294#395—21no—
295#395—21no—
296#395—21no—
297#395—21no—
298#394—21no—
299#394—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#390C2311yescharacteristic
307#390C2311yescharacteristic
308#390C2311yescharacteristic
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#388—21no—
334#388—21no—
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#386—21no—
360#386—21no—
361#385—21no—
362#385—21no—
363#385—21no—
364#385—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#384C2311yescharacteristic
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#383—21no—
377#383D411yescharacteristic
378#383D411yescharacteristic
379#382D411yescharacteristic
380#382D411yescharacteristic
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#382C2311yescharacteristic
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#381—21no—
389#381—21no—
390#381—21no—
391#381—21no—
392#381D411yescharacteristic
393#381D411yescharacteristic
394#380—21no—
395#380—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380D411yescharacteristic
400#380D411yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2311yescharacteristic
424#376—21no—
425#376C2311yescharacteristic
426#376C2311yescharacteristic
427C2×#95—21no—
428C2×#95—21no—
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#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×D4—21no—
484C22×D4C2411yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C2×D411yescharacteristic
491C23×C4C2×D411yescharacteristic
492C23×C4C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C4⋊Q8—22no—
502C4⋊Q8—22no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505#126—82no—
506#125—22no—
507#125—22no—
508#125—22no—
509#125—22no—
510#125—41no—
511#125—41no—
512#123—82no—
513C22⋊Q8—82no—
514C22⋊Q8—82no—
515#121—22no—
516#121—41no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—41no—
522C4×D4—41no—
523C4×D4—82no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
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—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
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×C22⋊C4—21no—
597C2×C22⋊C4C2×D411yescharacteristic
598C2×C22⋊C4C2×D411yescharacteristic
599C2×C22⋊C4C2×D411yescharacteristic
600C2×C22⋊C4C2×D411yescharacteristic
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—82no—
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621#107—22no—
622#107—41no—
623#107—41no—
624#107—41no—
625#107—41no—
626#107—41no—
627#106—22no—
628#106—22no—
629#106—22no—
630#106—22no—
631#106—22no—
632#106—22no—
633#106—41no—
634#106—41no—
635#106—41no—
636#106—41no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—41no—
642C4⋊C8—41no—
643#102—22no—
644#102—22no—
645#102—22no—
646#102—22no—
647#102—41no—
648#102—41no—
649#102—41no—
650#102#4114yes—
651C22⋊C8—22no—
652C22⋊C8—41no—
653C22⋊C8—41no—
654C22⋊C8—41no—
655#97—41no—
656#97—41no—
657C4×C8—22no—
658C4×C8—22no—
659C4×C8—41no—
660C4×C8—41no—
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#95—21no—
704#95—21no—
705#95—21no—
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
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722C24—21no—
723C24C22×D411yescharacteristic
724C2×Q8—42no—
725C2×Q8—42no—
726C2×Q8—81no—
727C2×Q8—81no—
728C2×Q8—81no—
729C2×Q8—81no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—81no—
738C2×D4C2×#4112yes—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—22no—
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—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—81no—
774C22×C4—81no—
775C22×C4—81no—
776C22×C4—81no—
777C22×C4—81no—
778C22×C4—81no—
779C22×C4—81no—
780C22×C4—81no—
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C2511yescharacteristic
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×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8C2×#4112yes—
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—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
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⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4C2×#4112yes—
887C4⋊C42−1+412yes—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C22⋊C4—42no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—42no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C42—22no—
908C42—22no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—81no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C422−1+412yes—
929C422−1+412yes—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—22no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23#57712yes—
944C23C23×D411yescharacteristic
945Q8—162no—
946Q8—162no—
947D4—22no—
948D4—22no—
949D4—41no—
950D4—41no—
951D4—84no—
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—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—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—44no—
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—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—82no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4—162no—
1043C2×C4—162no—
1044C2×C4—162no—
1045C2×C4#53612yes—
1046C2×C4#53612yes—
1047C2×C4C22×#4111yescharacteristic
1048C2×C4C2×2−1+411yescharacteristic
1049C2×C4C2×2−1+411yescharacteristic
1050C2×C4C2×2−1+411yescharacteristic
1051C2×C4#58511yescharacteristic
1052C2×C4#58511yescharacteristic
1053C8—22no—
1054C8—41no—
1055C8—41no—
1056C8—41no—
1057C8—41no—
1058C8—41no—
1059C8—41no—
1060C8—41no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22C2×#53611yescharacteristic
1076C22D4×#4111yescharacteristic
1077C22#348911yescharacteristic
1078C22C2×#57711yescharacteristic
1079C22#358411yescharacteristic
1080C22#358411yescharacteristic
1081C22#358511yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—42no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—41no—
1096C4—42no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4#350911yescharacteristic
1111C4#351511yescharacteristic
1112C4#355511yescharacteristic
1113C4#356511yescharacteristic
1114C2—42no—
1115C2—82no—
1116C2#3989011yescharacteristic
1117C2#6085911yescharacteristic
1118C2#6087311yescharacteristic
1119C2#6147211yescharacteristic
1120C2#6154811yescharacteristic
1121C2#6217611yescharacteristic
1122C2#6221311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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
2. #35235C2semidirect
3. #33150C2semidirect
4. #31716C2semidirect
5. #31708C2semidirect
6. #31436C2semidirect
7. #31424C2semidirect
12. #30103C2semidirect
13. #30100C2semidirect
14. #29404C2semidirect
15. #29400C2semidirect
16. #29187C2semidirect
17. #29185C2semidirect
18. #28831C2semidirect
19. #28796C2semidirect
20. #27879C2semidirect
21. #27817C2semidirect
22. #27733C2semidirect
24. #26514C2semidirect
25. #26449C2semidirect
26. #26117C2semidirect
27. #26051C2semidirect
28. #22640C2semidirect
29. #22123C2semidirect
30. #22122C2semidirect

Maximal subgroups

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

subgroupindex
#389262
#352352
#331502
#317162
#317082
#314362
#314242
#313762
#313722
#310882
#310862
#301032
#301002
#294042
#294002
#291872
#291852
#288312
#287962
#278792
#278172
#277332
#276332
#265142
#264492
#261172
#260512
#226402
#221232
#221222
C4×#4812