Finite Group Databasebeta

← #7045582

Subgroups — #7045582

Order 512.

1439 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59424C211yesmaximal, characteristic
2#59325C211yesmaximal, characteristic, complemented
3#32624C211yesmaximal, characteristic, complemented
4#32556C211yesmaximal, characteristic, complemented
5#32502C211yesmaximal, characteristic, complemented
6#32453C211yesmaximal, characteristic, complemented
7#32256C211yesmaximal, characteristic, complemented
8#31979C211yesmaximal, characteristic, complemented
9#31655C211yesmaximal, characteristic, complemented
10#30831C211yesmaximal, characteristic, complemented
11#28123C211yesmaximal, characteristic
12#27715C211yesmaximal, characteristic, complemented
13#27686C211yesmaximal, characteristic, complemented
14#27578C211yesmaximal, characteristic, complemented
15#27376C211yesmaximal, characteristic, complemented
16#27262C211yesmaximal, characteristic
17#26777C211yesmaximal, characteristic, complemented
18#26329C211yesmaximal, characteristic, complemented
19#26181C211yesmaximal, characteristic, complemented
20#25994C211yesmaximal, characteristic, complemented
21#25952C211yesmaximal, characteristic
22#25337C211yesmaximal, characteristic, complemented
23#25206C211yesmaximal, characteristic, complemented
24#25084C211yesmaximal, characteristic
25#25007C211yesmaximal, characteristic, complemented
26#24690C211yesmaximal, characteristic, complemented
27C2×#2073C211yesmaximal, characteristic
28#22932C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic
30#22295C211yesmaximal, characteristic, complemented
31#22182C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#467C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2786—21no—
42#2774—21no—
43#2755—21no—
44#2740—21no—
45#2601—21no—
46#2592C2211yescharacteristic
47#2581C2211yescharacteristic, complemented
48#2568C2211yescharacteristic, complemented
49#2565C2211yescharacteristic, complemented
50#2560—21no—
51#2550C2211yescharacteristic, complemented
52#2549—21no—
53#2538C2211yescharacteristic
54#2520—21no—
55#2512C2211yescharacteristic
56#2512C2211yescharacteristic
57#2509C2211yescharacteristic, complemented
58#2508—21no—
59#2508C2211yescharacteristic, complemented
60#2505—21no—
61#2505—21no—
62#2502C2211yescharacteristic
63#2480—21no—
64#2480—21no—
65#2448C2211yescharacteristic
66#2447C2211yescharacteristic
67#2442C2211yescharacteristic
68#2440C2211yescharacteristic
69#2437—21no—
70#2435C2211yescharacteristic
71#2368—21no—
72#2367C2211yescharacteristic
73#2360C2211yescharacteristic
74#2360C2211yescharacteristic
75#2355C2211yescharacteristic, complemented
76#2354C2211yescharacteristic
77#2351C2211yescharacteristic, complemented
78#2345C2211yescharacteristic
79#2342—21no—
80D4×C22⋊C4C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C2×#390C2211yescharacteristic
85C2×#382C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2087C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2072C2211yescharacteristic, complemented
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2065C2211yescharacteristic
114#2057C2211yescharacteristic, complemented
115#2056C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2026C2211yescharacteristic, complemented
123#2025C2211yescharacteristic
124#2023C2211yescharacteristic
125#2015C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1987C2211yescharacteristic, complemented
128#1985C2211yescharacteristic, complemented
129#1985C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1973C2211yescharacteristic
132#1959C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1947C2211yescharacteristic, complemented
136#1947C2211yescharacteristic, complemented
137#1943C2211yescharacteristic, complemented
138#1940C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1921C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1877C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1836C2211yescharacteristic, complemented
187#1824C2211yescharacteristic
188#1808C2211yescharacteristic
189#1805C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic, complemented
193#1797C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8D411yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C22⋊C4—21no—
232C22×C22⋊C4—21no—
233C22×C22⋊C4—21no—
234C22×C42C2311yescharacteristic
235#489—42no—
236#484—24no—
237#478—42no—
238#467—24no—
239#464—42no—
240#450—24no—
241#440—42no—
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102—42no—
270C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#399—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#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#394—21no—
321#394—21no—
322#393—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391D411yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390—21no—
335#390—21no—
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389D411yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387D411yescharacteristic
386#387D411yescharacteristic
387#386—21no—
388#386—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385D411yescharacteristic
400#385D411yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#382—21no—
405#382—21no—
406#382—21no—
407#382—21no—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#381—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380D411yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#379—21no—
422#379—21no—
423#379—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
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
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445C2×#95—21no—
446C2×#95—21no—
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×Q8—21no—
489C22×Q8C2×D411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2×D411yescharacteristic
507C23×C4C2×D411yescharacteristic
508C23×C4C2411yescharacteristic
509C2×Q16—22no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—41no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534#126—82no—
535#126—82no—
536#125—41no—
537#125—41no—
538#124—22no—
539#124—41no—
540#124—41no—
541#124—41no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—42no—
546C22⋊Q8—44no—
547C22⋊Q8—82no—
548C22⋊Q8#4114yes—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563#117—82no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—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—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊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—44no—
646C2×C22⋊C4—82no—
647C2×C22⋊C4—82no—
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—41no—
663C2×C42—41no—
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#107—22no—
673#107—22no—
674#107—22no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#106—41no—
680#106—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713C22⋊C8—22no—
714C22⋊C8—22no—
715#97—41no—
716#97—41no—
717#97—41no—
718#97—41no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24—21no—
771C24—42no—
772C24—42no—
773C24—42no—
774C24—42no—
775C24—81no—
776C24—81no—
777C24—81no—
778C24C22×D411yescharacteristic
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—41no—
791C2×Q8—41no—
792C2×Q8—41no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8C2×#4112yes—
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—44no—
809C2×D4—44no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—82no—
813C2×D4—82no—
814C2×D4—81no—
815C2×D4H(5,𝔽2)12yes—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C2×#4112yes—
869C22×C42−1+412yes—
870C22×C4C2511yescharacteristic
871Q16—82no—
872SD16—44no—
873SD16—82no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—82no—
899C2×C8—82no—
900C4⋊C4—24no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4C2×#4112yes—
961C22⋊C4—24no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—41no—
1004C42—41no—
1005C42—42no—
1006C42—42no—
1007C42—81no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—22no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—84no—
1034C23—84no—
1035C23—84no—
1036C23—84no—
1037C23—162no—
1038C23—162no—
1039C23—162no—
1040C23#54812yes—
1041C23#57512yes—
1042C23#57812yes—
1043C23C23×D411yescharacteristic
1044Q8—22no—
1045Q8—22no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—41no—
1052Q8—82no—
1053Q8—162no—
1054D4—22no—
1055D4—22no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—41no—
1062D4—84no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—82no—
1148C2×C4—82no—
1149C2×C4—84no—
1150C2×C4—162no—
1151C2×C4—162no—
1152C2×C4—162no—
1153C2×C4—162no—
1154C2×C4#54812yes—
1155C2×C4C22×#4111yescharacteristic
1156C2×C4C2×H(5,𝔽2)11yescharacteristic
1157C2×C4C2×2−1+411yescharacteristic
1158C2×C4#58511yescharacteristic
1159C2×C4#58511yescharacteristic
1160C2×C4#58511yescharacteristic
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8—41no—
1166C8—41no—
1167C8—41no—
1168C8—41no—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—42no—
1176C22—42no—
1177C22—42no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—168no—
1190C22#337714yes—
1191C22C2×#54811yescharacteristic
1192C22#348511yescharacteristic
1193C22#348811yescharacteristic
1194C22C2×#57511yescharacteristic
1195C22C2×#57811yescharacteristic
1196C22#358511yescharacteristic
1197C22#358511yescharacteristic
1198C4—22no—
1199C4—42no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—42no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4#351311yescharacteristic
1226C4#352111yescharacteristic
1227C4#353511yescharacteristic
1228C4#356411yescharacteristic
1229C2—24no—
1230C2—82no—
1231C2—161no—
1232C2#4353311yescharacteristic
1233C2C2×#337711yescharacteristic
1234C2#6133711yescharacteristic
1235C2#6171411yescharacteristic
1236C2#6175411yescharacteristic
1237C2#6197111yescharacteristic
1238C2#6201711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59325C2semidirect
3. #32624C2semidirect
4. #32556C2semidirect
5. #32502C2semidirect
6. #32453C2semidirect
7. #32256C2semidirect
8. #31979C2semidirect
9. #31655C2semidirect
10. #30831C2semidirect
12. #27715C2semidirect
13. #27686C2semidirect
14. #27578C2semidirect
15. #27376C2semidirect
17. #26777C2semidirect
18. #26329C2semidirect
19. #26181C2semidirect
20. #25994C2semidirect
22. #25337C2semidirect
23. #25206C2semidirect
25. #25007C2semidirect
26. #24690C2semidirect
28. #22932C2semidirect
30. #22295C2semidirect
31. #22182C2semidirect
47. #2581C22semidirect
48. #2568C22semidirect
49. #2565C22semidirect
51. #2550C22semidirect
57. #2509C22semidirect
59. #2508C22semidirect
75. #2355C22semidirect
77. #2351C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
94. #2087C22semidirect
95. #2087C22semidirect
96. #2083C22semidirect
97. #2074C22semidirect
106. #2072C22semidirect
108. #2068C22semidirect
114. #2057C22semidirect
115. #2056C22semidirect
122. #2026C22semidirect
126. #1992C22semidirect
127. #1987C22semidirect
128. #1985C22semidirect
129. #1985C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
135. #1947C22semidirect
136. #1947C22semidirect
137. #1943C22semidirect
138. #1940C22semidirect
139. #1940C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1928C22semidirect
147. #1928C22semidirect
148. #1928C22semidirect
149. #1927C22semidirect
154. #1921C22semidirect
155. #1921C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
176. #1865C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
186. #1836C22semidirect
189. #1805C22semidirect
190. #1805C22semidirect
192. #1803C22semidirect
195. #1776C22semidirect
196. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#594242
#593252
#326242
#325562
#325022
#324532
#322562
#319792
#316552
#308312
#281232
#277152
#276862
#275782
#273762
#272622
#267772
#263292
#261812
#259942
#259522
#253372
#252062
#250842
#250072
#246902
C2×#20732
#229322
#228542
#222952
#221822