Finite Group Databasebeta

← #7536929

Subgroups — #7536929

Order 512.

1605 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59637C211yesmaximal, characteristic, complemented
2#36487C211yesmaximal, characteristic, complemented
3#32674C211yesmaximal, characteristic, complemented
4#32599C211yesmaximal, characteristic, complemented
5#32384C211yesmaximal, characteristic, complemented
6#31573C211yesmaximal, characteristic, complemented
7#28877C211yesmaximal, characteristic, complemented
8#28573C211yesmaximal, characteristic, complemented
9#28329C211yesmaximal, characteristic
10#28303C211yesmaximal, characteristic, complemented
11#28013C211yesmaximal, characteristic, complemented
12#27926C211yesmaximal, characteristic, complemented
13#27497C211yesmaximal, characteristic, complemented
14#27489C211yesmaximal, characteristic, complemented
15#27199C211yesmaximal, characteristic, complemented
16#27076C211yesmaximal, characteristic, complemented
17#27065C211yesmaximal, characteristic, complemented
18#26593C211yesmaximal, characteristic, complemented
19#26323C211yesmaximal, characteristic, complemented
20#25214C211yesmaximal, characteristic, complemented
21#25080C211yesmaximal, characteristic, complemented
22#25064C211yesmaximal, characteristic, complemented
23#24578C211yesmaximal, characteristic, complemented
24#24527C211yesmaximal, characteristic, complemented
25#23237C211yesmaximal, characteristic, complemented
26#23095C211yesmaximal, characteristic, complemented
27#22922C211yesmaximal, characteristic, complemented
28#22870C211yesmaximal, characteristic, complemented
29#22810C211yesmaximal, characteristic, complemented
30C4×#480C211yesmaximal, characteristic, complemented
31C2×#1926C211yesmaximal, characteristic, complemented
32C2×#484C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#466C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×#102C2211yescharacteristic
44#2853—21no—
45#2850C2211yescharacteristic
46#2797—21no—
47#2752—21no—
48#2602—21no—
49#2596—21no—
50#2596—21no—
51#2592C2211yescharacteristic, complemented
52#2589—21no—
53#2580C2211yescharacteristic
54#2575—21no—
55#2570C2211yescharacteristic, complemented
56#2557—21no—
57#2548C2211yescharacteristic
58#2513C2211yescharacteristic
59#2513C2211yescharacteristic
60#2513C2211yescharacteristic, complemented
61#2511C2211yescharacteristic, complemented
62#2504C2211yescharacteristic
63#2503C2211yescharacteristic
64#2501C2211yescharacteristic
65#2488—21no—
66#2472—21no—
67#2445C2211yescharacteristic
68#2445C2211yescharacteristic
69#2433C2211yescharacteristic
70#2419—21no—
71#2418—21no—
72#2412—21no—
73#2367C2211yescharacteristic, complemented
74#2366C2211yescharacteristic
75#2361C2211yescharacteristic
76#2360C2211yescharacteristic
77#2358—21no—
78#2357C2211yescharacteristic
79#2357C2211yescharacteristic, complemented
80#2355C2211yescharacteristic, complemented
81#2355C2211yescharacteristic, complemented
82#2345C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×#123—21no—
86C4×#121C2211yescharacteristic
87C2×#390C2211yescharacteristic
88C2×C4×C4⋊C4C2211yescharacteristic
89#2097C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic, complemented
96#2092C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2073C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2041C2211yescharacteristic
115#2014C2211yescharacteristic
116#2012C2211yescharacteristic
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic, complemented
119#2011C2211yescharacteristic
120#2011C2211yescharacteristic
121#1984C2211yescharacteristic, complemented
122#1984C2211yescharacteristic, complemented
123#1982C2211yescharacteristic
124#1970C2211yescharacteristic
125#1970C2211yescharacteristic
126#1970C2211yescharacteristic
127#1970C2211yescharacteristic
128#1970C2211yescharacteristic
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic, complemented
132#1968C2211yescharacteristic, complemented
133#1957C2211yescharacteristic
134#1957C2211yescharacteristic
135#1949C2211yescharacteristic, complemented
136#1948C2211yescharacteristic, complemented
137#1948C2211yescharacteristic, complemented
138#1942C2211yescharacteristic, complemented
139#1934C2211yescharacteristic
140#1933C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1926C2211yescharacteristic, complemented
154#1926C2211yescharacteristic, complemented
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic, complemented
158#1925C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic, complemented
173#1879C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1874C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1852C2211yescharacteristic
181#1850C2211yescharacteristic
182#1850C2211yescharacteristic
183#1846C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1823C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic, complemented
189C4×#107C2211yescharacteristic, complemented
190C4×#107C2211yescharacteristic, complemented
191C4×#107C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8D411yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#120—21no—
225C2×#120—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C42—21no—
242C22×C42C2311yescharacteristic
243#484—24no—
244#481—42no—
245#480—24no—
246#466—42no—
247#465—42no—
248#460—24no—
249#450—42no—
250#447—24no—
251C4×D8—24no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106—42no—
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102—24no—
277C2×#102—42no—
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#393—21no—
334#393—21no—
335#392—21no—
336#392—21no—
337#391—21no—
338#391D411yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#390—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#389—21no—
363#389D411yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—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#387D411yescharacteristic
399#387D411yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385D411yescharacteristic
418#385D411yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#381—21no—
429#381—21no—
430#381—21no—
431#380—21no—
432#380D411yescharacteristic
433#380C2311yescharacteristic
434#379—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C2×#95—21no—
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#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8C2×D411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552#127—22no—
553#127—41no—
554#127—41no—
555#127—41no—
556#124—41no—
557#124—41no—
558#124—82no—
559#123—44no—
560#123—82no—
561#123—82no—
562#123—82no—
563C22⋊Q8—24no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—22no—
570#120—44no—
571#120—82no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—82no—
585C4×D4—82no—
586C4×D4—82no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
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—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
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—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—82no—
668C2×C22⋊C4—82no—
669C2×C22⋊C4—82no—
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—41no—
685C2×C42—41no—
686C2×C42—82no—
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#107—22no—
696#107—22no—
697#107—22no—
698#107—22no—
699#107—22no—
700#107—41no—
701#107—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709C4⋊C8—22no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713#103—22no—
714#103—22no—
715#103—41no—
716#103—41no—
717#103—41no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102#4114yes—
741C22⋊C8—22no—
742C22⋊C8#4114yes—
743C4×C8—22no—
744C4×C8—41no—
745C4×C8—41no—
746C4×C8—41no—
747C4×C8—41no—
748C4×C8—41no—
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#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C2×Q8—22no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—41no—
812C2×Q8—41no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4C2×#4112yes—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C2×#4112yes—
919C22×C4H(5,𝔽2)12yes—
920C22×C4C2511yescharacteristic
921SD16—82no—
922SD16—82no—
923SD16—82no—
924D8—44no—
925D8—82no—
926D8—82no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—44no—
949C2×C8—82no—
950C2×C8C2×#4112yes—
951C2×C8C2×#4112yes—
952C2×C8C2×#4112yes—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4C2×#4112yes—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4#13514yes—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—41no—
1055C42—41no—
1056C42—42no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—22no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—84no—
1099C23—84no—
1100C23—84no—
1101C23—84no—
1102C23—162no—
1103C23—162no—
1104C23—162no—
1105C23#55012yes—
1106C23C2×#13512yes—
1107C23#57612yes—
1108C23C23×D411yescharacteristic
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—82no—
1114D4—22no—
1115D4—22no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—84no—
1131D4—84no—
1132D4—84no—
1133D4—84no—
1134D4—162no—
1135D4—162no—
1136D4—162no—
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—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—44no—
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—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—82no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4#55012yes—
1222C2×C4C2×#13512yes—
1223C2×C4C2×#13512yes—
1224C2×C4#57712yes—
1225C2×C4C22×#4111yescharacteristic
1226C2×C4C22×#4111yescharacteristic
1227C2×C4C2×H(5,𝔽2)11yescharacteristic
1228C2×C4#58511yescharacteristic
1229C2×C4#58511yescharacteristic
1230C2×C4#58511yescharacteristic
1231C8—22no—
1232C8—22no—
1233C8—22no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—168no—
1274C22#339614yes—
1275C22C2×#55011yescharacteristic
1276C22D4×#4111yescharacteristic
1277C22#348511yescharacteristic
1278C22C22×#13511yescharacteristic
1279C22C2×#57611yescharacteristic
1280C22C2×#57711yescharacteristic
1281C22#358511yescharacteristic
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4#347511yescharacteristic
1308C4#351311yescharacteristic
1309C4#352111yescharacteristic
1310C4#354511yescharacteristic
1311C2—24no—
1312C2—82no—
1313C2—161no—
1314C2—161no—
1315C2—161no—
1316C2#5904811yescharacteristic
1317C2C2×#339611yescharacteristic
1318C2#6142111yescharacteristic
1319C2#6143211yescharacteristic
1320C2#6151911yescharacteristic
1321C2#6170211yescharacteristic
1322C2#6176611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28329C2
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
1. #59637C2semidirect
2. #36487C2semidirect
3. #32674C2semidirect
4. #32599C2semidirect
5. #32384C2semidirect
6. #31573C2semidirect
7. #28877C2semidirect
8. #28573C2semidirect
10. #28303C2semidirect
11. #28013C2semidirect
12. #27926C2semidirect
13. #27497C2semidirect
14. #27489C2semidirect
15. #27199C2semidirect
16. #27076C2semidirect
17. #27065C2semidirect
18. #26593C2semidirect
19. #26323C2semidirect
20. #25214C2semidirect
21. #25080C2semidirect
22. #25064C2semidirect
23. #24578C2semidirect
24. #24527C2semidirect
25. #23237C2semidirect
26. #23095C2semidirect
27. #22922C2semidirect
28. #22870C2semidirect
29. #22810C2semidirect
30. C4×#480C2semidirect
31. C2×#1926C2semidirect
51. #2592C22semidirect
55. #2570C22semidirect
60. #2513C22semidirect
61. #2511C22semidirect
73. #2367C22semidirect
79. #2357C22semidirect
80. #2355C22semidirect
81. #2355C22semidirect
89. #2097C22semidirect
90. #2097C22semidirect
95. #2092C22semidirect
96. #2092C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2084C22semidirect
103. #2073C22semidirect
104. #2073C22semidirect
106. #2065C22semidirect
107. #2065C22semidirect
108. #2065C22semidirect
112. #2054C22semidirect
113. #2042C22semidirect
118. #2012C22semidirect
121. #1984C22semidirect
122. #1984C22semidirect
131. #1968C22semidirect
132. #1968C22semidirect
135. #1949C22semidirect
136. #1948C22semidirect
137. #1948C22semidirect
138. #1942C22semidirect
140. #1933C22semidirect
141. #1928C22semidirect
142. #1928C22semidirect
152. #1926C22semidirect
153. #1926C22semidirect
154. #1926C22semidirect
155. #1926C22semidirect
157. #1925C22semidirect
158. #1925C22semidirect
159. #1921C22semidirect
160. #1921C22semidirect
161. #1918C22semidirect
162. #1918C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
172. #1879C22semidirect
173. #1879C22semidirect
176. #1877C22semidirect
178. #1863C22semidirect
183. #1846C22semidirect
184. #1846C22semidirect
188. #1804C22semidirect
189. C4×#107C22semidirect
190. C4×#107C22semidirect
191. C4×#107C22semidirect
192. C8×C4⋊C4C22semidirect
193. C8×C4⋊C4C22semidirect
194. C4×#103C22semidirect
196. C4×#102C22semidirect
197. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#596372
#364872
#326742
#325992
#323842
#315732
#288772
#285732
#283292
#283032
#280132
#279262
#274972
#274892
#271992
#270762
#270652
#265932
#263232
#252142
#250802
#250642
#245782
#245272
#232372
#230952
#229222
#228702
#228102
C4×#4802
C2×#19262