Finite Group Databasebeta

← #6601472

Subgroups — #6601472

Order 512.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38112C211yesmaximal, characteristic, complemented
2#34305C211yesmaximal, characteristic, complemented
3#33150C211yesmaximal, characteristic, complemented
4#33102C211yesmaximal, characteristic, complemented
5#33086C211yesmaximal, characteristic, complemented
6#29530C211yesmaximal, characteristic, complemented
7#29484C211yesmaximal, characteristic, complemented
8#29418C211yesmaximal, characteristic, complemented
9#29406C211yesmaximal, characteristic, complemented
10#29161C211yesmaximal, characteristic, complemented
11#28114C211yesmaximal, characteristic, complemented
12#27504C211yesmaximal, characteristic, complemented
13#27427C211yesmaximal, characteristic, complemented
14#27357C211yesmaximal, characteristic, complemented
15#27166C211yesmaximal, characteristic, complemented
16#27140C211yesmaximal, characteristic, complemented
17#27027C211yesmaximal, characteristic, complemented
18#26723C211yesmaximal, characteristic, complemented
19#26562C211yesmaximal, characteristic, complemented
20#24937C211yesmaximal, characteristic, complemented
21#24861C211yesmaximal, characteristic, complemented
22#24091C211yesmaximal, characteristic, complemented
23#23963C211yesmaximal, characteristic
24#22916C211yesmaximal, characteristic, complemented
25#22858C211yesmaximal, characteristic, complemented
26#22791C211yesmaximal, characteristic, complemented
27#22615C211yesmaximal, characteristic, complemented
28#22574C211yesmaximal, characteristic, complemented
29#21586C211yesmaximal, characteristic, complemented
30#21126C211yesmaximal, characteristic, complemented
31C2×#1926C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#447C2211yescharacteristic
36C2×#442C2211yescharacteristic
37C22×#106C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40#2851C2211yescharacteristic
41#2797—21no—
42#2786—21no—
43#2752—21no—
44#2740—21no—
45#2644C2211yescharacteristic
46#2624C2211yescharacteristic
47#2513C2211yescharacteristic
48#2490C2211yescharacteristic
49#2486C2211yescharacteristic
50#2483—21no—
51#2482—21no—
52#2454C2211yescharacteristic
53#2420C2211yescharacteristic
54#2412—21no—
55#2411—21no—
56#2408C2211yescharacteristic
57#2373—21no—
58#2370C2211yescharacteristic, complemented
59#2364—21no—
60#2361C2211yescharacteristic
61#2361C2211yescharacteristic, complemented
62#2359—21no—
63#2354C2211yescharacteristic, complemented
64#2349—21no—
65D4×C4⋊C4C2211yescharacteristic
66#2346C2211yescharacteristic, complemented
67#2345C2211yescharacteristic
68#2344C2211yescharacteristic
69D4×C22⋊C4C2211yescharacteristic
70#2335—21no—
71#2334—21no—
72#2330C2211yescharacteristic, complemented
73#2324C2211yescharacteristic
74#2324C2211yescharacteristic, complemented
75#2319C2211yescharacteristic
76C4×#121—21no—
77C4×#121C2211yescharacteristic
78C2×#390C2211yescharacteristic
79#2290—21no—
80#2290C2211yescharacteristic
81#2275C2211yescharacteristic, complemented
82#2274C2211yescharacteristic, complemented
83C2×C4×C4⋊C4C2211yescharacteristic
84#2101C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2093C2211yescharacteristic
87#2092C2211yescharacteristic, complemented
88#2084C2211yescharacteristic, complemented
89#2077C2211yescharacteristic, complemented
90#2077C2211yescharacteristic, complemented
91#2071C2211yescharacteristic
92#2067C2211yescharacteristic
93#2067C2211yescharacteristic
94#2059C2211yescharacteristic, complemented
95#2059C2211yescharacteristic, complemented
96#2059C2211yescharacteristic, complemented
97#2054C2211yescharacteristic
98#2054C2211yescharacteristic
99#2034C2211yescharacteristic, complemented
100#2034C2211yescharacteristic, complemented
101#2033C2211yescharacteristic
102#2033C2211yescharacteristic
103#2025C2211yescharacteristic
104#2025C2211yescharacteristic
105#2025C2211yescharacteristic, complemented
106#1999C2211yescharacteristic
107#1999C2211yescharacteristic
108#1989C2211yescharacteristic, complemented
109#1989C2211yescharacteristic, complemented
110#1972C2211yescharacteristic
111#1949C2211yescharacteristic, complemented
112#1949C2211yescharacteristic, complemented
113#1944C2211yescharacteristic, complemented
114#1944C2211yescharacteristic, complemented
115#1942C2211yescharacteristic, complemented
116#1936C2211yescharacteristic
117#1934C2211yescharacteristic
118#1934C2211yescharacteristic
119#1934C2211yescharacteristic, complemented
120#1926C2211yescharacteristic
121#1926C2211yescharacteristic
122#1926C2211yescharacteristic
123#1926C2211yescharacteristic
124#1926C2211yescharacteristic
125#1926C2211yescharacteristic
126#1926C2211yescharacteristic
127#1926C2211yescharacteristic
128#1926C2211yescharacteristic
129#1926C2211yescharacteristic
130#1926C2211yescharacteristic
131#1925C2211yescharacteristic
132#1925C2211yescharacteristic
133#1925C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic, complemented
136#1924C2211yescharacteristic, complemented
137#1923C2211yescharacteristic, complemented
138#1921C2211yescharacteristic, complemented
139#1920C2211yescharacteristic, complemented
140#1920C2211yescharacteristic, complemented
141#1920C2211yescharacteristic, complemented
142#1920C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1918C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1917C2211yescharacteristic, complemented
153#1916C2211yescharacteristic, complemented
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1869C2211yescharacteristic
166#1869C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic, complemented
171#1864C2211yescharacteristic, complemented
172#1864C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1862C2211yescharacteristic, complemented
175#1854C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic, complemented
179#1852C2211yescharacteristic
180#1840C2211yescharacteristic, complemented
181#1824C2211yescharacteristic
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic, complemented
184#1823C2211yescharacteristic
185#1818C2211yescharacteristic, complemented
186#1808C2211yescharacteristic
187#1807C2211yescharacteristic
188#1797C2211yescharacteristic
189#1786C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192C4×#107C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1750C2211yescharacteristic, complemented
200#1746C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#553—24no—
209#553—24no—
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#121—21no—
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C42—21no—
244C22×C42C2311yescharacteristic
245#480—24no—
246#480—24no—
247#447—24no—
248#442—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106—24no—
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#102—24no—
267C2×#102—24no—
268C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#399—21no—
299#399—21no—
300#398—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#396—21no—
311#396—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#392—21no—
318#390—21no—
319#390—21no—
320#390—21no—
321#390—21no—
322#390—21no—
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388D411yescharacteristic
362#388D411yescharacteristic
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387D411yescharacteristic
374#387D411yescharacteristic
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386D411yescharacteristic
384#386D411yescharacteristic
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385D411yescharacteristic
395#385D411yescharacteristic
396#384C2311yescharacteristic
397#382—21no—
398#382C2311yescharacteristic
399#381—21no—
400#381—21no—
401#381—21no—
402#381—21no—
403#380—21no—
404#380—21no—
405#380—21no—
406#380—21no—
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#379—21no—
414#379—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442#376C2311yescharacteristic
443C2×#95—21no—
444C2×#95—21no—
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#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C2×D411yescharacteristic
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536#126—28no—
537#125—22no—
538#125—22no—
539#125—41no—
540#125—41no—
541#123—28no—
542#123—82no—
543#121—28no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—41no—
550#121—41no—
551#121#4114yes—
552#120—82no—
553C4×D4—28no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—82no—
567C4×D4—82no—
568C4×D4—82no—
569C4×D4—82no—
570#117—22no—
571#117—22no—
572#117—41no—
573#117—41no—
574#117—82no—
575#117—82no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4#4114yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—82no—
659C2×C22⋊C4—82no—
660C2×C22⋊C4—82no—
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42—82no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—22no—
693#107—22no—
694#107—22no—
695#107—41no—
696#107—41no—
697#106—22no—
698#106—22no—
699#106—22no—
700#106—22no—
701#106—22no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102#4114yes—
727C22⋊C8—22no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733#97—22no—
734#97—41no—
735C4×C8—41no—
736C4×C8—41no—
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#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—21no—
779C24—42no—
780C24—42no—
781C24—42no—
782C24—42no—
783C24—81no—
784C24—81no—
785C24—81no—
786C24C22×D411yescharacteristic
787C24C22×D411yescharacteristic
788C2×D4—22no—
789C2×D4—24no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—24no—
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—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—82no—
817C2×D4—82no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4C2×#4112yes—
827C2×D4C2×#4112yes—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4C2511yescharacteristic
899D8—44no—
900D8—82no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—44no—
925C2×C8—82no—
926C2×C8C2×#4112yes—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—22no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4C2×#4112yes—
975C4⋊C4C2×#4112yes—
976C4⋊C4C2×#4112yes—
977C4⋊C4C2×#4112yes—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C42—24no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—41no—
1034C42—41no—
1035C42—42no—
1036C42—42no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—22no—
1054C23—22no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—84no—
1079C23—84no—
1080C23—84no—
1081C23—84no—
1082C23—162no—
1083C23—162no—
1084C23—162no—
1085C23#52512yes—
1086C23#57612yes—
1087C23#57712yes—
1088C23C23×D411yescharacteristic
1089D4—22no—
1090D4—22no—
1091D4—22no—
1092D4—22no—
1093D4—44no—
1094D4—48no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—84no—
1104D4—84no—
1105D4—162no—
1106D4—162no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—44no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—82no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—162no—
1196C2×C4—162no—
1197C2×C4—162no—
1198C2×C4—162no—
1199C2×C4—162no—
1200C2×C4#52512yes—
1201C2×C4C22×#4111yescharacteristic
1202C2×C4C22×#4111yescharacteristic
1203C2×C4C22×#4111yescharacteristic
1204C2×C4#58511yescharacteristic
1205C2×C4#58511yescharacteristic
1206C2×C4#58511yescharacteristic
1207C8—22no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—42no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—42no—
1227C22—41no—
1228C22—42no—
1229C22—42no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—41no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—168no—
1250C22#311914yes—
1251C22C2×#52511yescharacteristic
1252C22D4×#4111yescharacteristic
1253C22#348511yescharacteristic
1254C22C2×#57611yescharacteristic
1255C22C2×#57711yescharacteristic
1256C22#358411yescharacteristic
1257C22#358511yescharacteristic
1258C4—22no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—42no—
1268C4—41no—
1269C4—41no—
1270C4—42no—
1271C4—41no—
1272C4—42no—
1273C4—42no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4#347511yescharacteristic
1284C4#347511yescharacteristic
1285C4#351011yescharacteristic
1286C4#352111yescharacteristic
1287C2—24no—
1288C2—81no—
1289C2—82no—
1290C2—82no—
1291C2—161no—
1292C2#3622411yescharacteristic
1293C2C2×#311911yescharacteristic
1294C2#6059211yescharacteristic
1295C2#6149011yescharacteristic
1296C2#6151911yescharacteristic
1297C2#6174611yescharacteristic
1298C2#6177211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23963C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38112C2semidirect
2. #34305C2semidirect
3. #33150C2semidirect
4. #33102C2semidirect
5. #33086C2semidirect
6. #29530C2semidirect
7. #29484C2semidirect
8. #29418C2semidirect
9. #29406C2semidirect
10. #29161C2semidirect
11. #28114C2semidirect
12. #27504C2semidirect
13. #27427C2semidirect
14. #27357C2semidirect
15. #27166C2semidirect
16. #27140C2semidirect
17. #27027C2semidirect
18. #26723C2semidirect
19. #26562C2semidirect
20. #24937C2semidirect
21. #24861C2semidirect
22. #24091C2semidirect
24. #22916C2semidirect
25. #22858C2semidirect
26. #22791C2semidirect
27. #22615C2semidirect
28. #22574C2semidirect
29. #21586C2semidirect
30. #21126C2semidirect
31. C2×#1926C2semidirect
58. #2370C22semidirect
61. #2361C22semidirect
63. #2354C22semidirect
66. #2346C22semidirect
72. #2330C22semidirect
74. #2324C22semidirect
81. #2275C22semidirect
82. #2274C22semidirect
84. #2101C22semidirect
85. #2100C22semidirect
87. #2092C22semidirect
88. #2084C22semidirect
89. #2077C22semidirect
90. #2077C22semidirect
94. #2059C22semidirect
95. #2059C22semidirect
96. #2059C22semidirect
99. #2034C22semidirect
100. #2034C22semidirect
105. #2025C22semidirect
108. #1989C22semidirect
109. #1989C22semidirect
111. #1949C22semidirect
112. #1949C22semidirect
113. #1944C22semidirect
114. #1944C22semidirect
115. #1942C22semidirect
119. #1934C22semidirect
135. #1925C22semidirect
136. #1924C22semidirect
137. #1923C22semidirect
138. #1921C22semidirect
139. #1920C22semidirect
140. #1920C22semidirect
141. #1920C22semidirect
142. #1920C22semidirect
143. #1919C22semidirect
144. #1919C22semidirect
145. #1919C22semidirect
146. #1919C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1918C22semidirect
150. #1918C22semidirect
151. #1918C22semidirect
152. #1917C22semidirect
153. #1916C22semidirect
170. #1864C22semidirect
171. #1864C22semidirect
172. #1864C22semidirect
173. #1862C22semidirect
174. #1862C22semidirect
175. #1854C22semidirect
176. #1854C22semidirect
178. #1853C22semidirect
180. #1840C22semidirect
183. #1824C22semidirect
185. #1818C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. C4×#107C22semidirect
196. C4×#102C22semidirect
199. #1750C22semidirect
200. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#381122
#343052
#331502
#331022
#330862
#295302
#294842
#294182
#294062
#291612
#281142
#275042
#274272
#273572
#271662
#271402
#270272
#267232
#265622
#249372
#248612
#240912
#239632
#229162
#228582
#227912
#226152
#225742
#215862
#211262
C2×#19262