Finite Group Databasebeta

← #6603207

Subgroups — #6603207

Order 512.

1625 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36370C211yesmaximal, characteristic, complemented
2C4×#559C211yesmaximal, characteristic, complemented
3#33080C211yesmaximal, characteristic, complemented
4#33078C211yesmaximal, characteristic, complemented
5#33071C211yesmaximal, characteristic, complemented
6#29503C211yesmaximal, characteristic, complemented
7#29497C211yesmaximal, characteristic, complemented
8#29373C211yesmaximal, characteristic, complemented
9#29372C211yesmaximal, characteristic, complemented
10#29195C211yesmaximal, characteristic, complemented
11#28156C211yesmaximal, characteristic
12#27388C211yesmaximal, characteristic, complemented
13#27369C211yesmaximal, characteristic, complemented
14#27218C211yesmaximal, characteristic, complemented
15#27199C211yesmaximal, characteristic, complemented
16#26778C211yesmaximal, characteristic, complemented
17#26763C211yesmaximal, characteristic, complemented
18#26608C211yesmaximal, characteristic, complemented
19#26593C211yesmaximal, characteristic, complemented
20#25069C211yesmaximal, characteristic, complemented
21#25003C211yesmaximal, characteristic, complemented
22#24198C211yesmaximal, characteristic, complemented
23#24198C211yesmaximal, characteristic, complemented
24#23108C211yesmaximal, characteristic, complemented
25#23008C211yesmaximal, characteristic, complemented
26#22830C211yesmaximal, characteristic, complemented
27#22819C211yesmaximal, characteristic, complemented
28#22776C211yesmaximal, characteristic, complemented
29#21505C211yesmaximal, characteristic, complemented
30#21122C211yesmaximal, characteristic, complemented
31#21113C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#460C2211yescharacteristic
34C2×#459C2211yescharacteristic
35C2×#459C2211yescharacteristic
36C2×#442C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×D8C2211yescharacteristic
40#2864C2211yescharacteristic
41#2860C2211yescharacteristic
42#2860C2211yescharacteristic
43#2580C2211yescharacteristic
44#2580C2211yescharacteristic
45#2507C2211yescharacteristic
46#2507C2211yescharacteristic
47#2479—21no—
48#2479—21no—
49#2468—21no—
50#2468—21no—
51#2458—21no—
52#2458—21no—
53#2445C2211yescharacteristic
54#2445C2211yescharacteristic
55#2374—21no—
56#2374—21no—
57#2367—21no—
58#2367C2211yescharacteristic
59#2367C2211yescharacteristic
60#2366C2211yescharacteristic
61#2359—21no—
62#2359—21no—
63#2357—21no—
64#2357C2211yescharacteristic
65#2357C2211yescharacteristic
66#2357C2211yescharacteristic
67#2355C2211yescharacteristic
68#2355C2211yescharacteristic
69#2349C2211yescharacteristic
70C4×#127C2211yescharacteristic
71C4×#127C2211yescharacteristic
72C4×#124—21no—
73C4×#124C2211yescharacteristic
74C4×#124C2211yescharacteristic
75C4×#123—21no—
76C4×#123—21no—
77#2293C2211yescharacteristic
78#2293C2211yescharacteristic
79C42×Q8C2211yescharacteristic
80C42×Q8C2211yescharacteristic
81C42×D4—21no—
82C42×D4C2211yescharacteristic
83C42×D4C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2073C2211yescharacteristic
91#2073C2211yescharacteristic
92#2071C2211yescharacteristic
93#2071C2211yescharacteristic
94#2067C2211yescharacteristic
95#2067C2211yescharacteristic
96#2065C2211yescharacteristic
97#2065C2211yescharacteristic
98#2042C2211yescharacteristic
99#2042C2211yescharacteristic
100#2042C2211yescharacteristic
101#2042C2211yescharacteristic
102#2012C2211yescharacteristic
103#2012C2211yescharacteristic
104#2012C2211yescharacteristic
105#2012C2211yescharacteristic
106#2011C2211yescharacteristic
107#2011C2211yescharacteristic
108#1985C2211yescharacteristic
109#1985C2211yescharacteristic
110#1982C2211yescharacteristic
111#1973C2211yescharacteristic
112#1972C2211yescharacteristic
113#1970C2211yescharacteristic
114#1968C2211yescharacteristic
115#1961C2211yescharacteristic
116#1961C2211yescharacteristic
117#1949C2211yescharacteristic
118#1949C2211yescharacteristic
119#1947C2211yescharacteristic
120#1936C2211yescharacteristic
121#1935C2211yescharacteristic
122#1934C2211yescharacteristic
123#1933C2211yescharacteristic
124#1928C2211yescharacteristic
125#1927C2211yescharacteristic
126#1926C2211yescharacteristic
127#1926C2211yescharacteristic
128#1926C2211yescharacteristic
129#1926C2211yescharacteristic
130#1925C2211yescharacteristic
131#1925C2211yescharacteristic
132#1925C2211yescharacteristic
133#1925C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic
136#1921C2211yescharacteristic
137#1921C2211yescharacteristic
138#1920C2211yescharacteristic
139#1919C2211yescharacteristic
140#1919C2211yescharacteristic
141#1919C2211yescharacteristic
142#1918C2211yescharacteristic
143#1918C2211yescharacteristic
144#1918C2211yescharacteristic
145#1918C2211yescharacteristic
146#1917C2211yescharacteristic
147#1917C2211yescharacteristic
148#1916C2211yescharacteristic
149#1916C2211yescharacteristic
150#1880C2211yescharacteristic
151#1880C2211yescharacteristic
152#1879C2211yescharacteristic
153#1879C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1847C2211yescharacteristic
181#1839C2211yescharacteristic
182#1839C2211yescharacteristic
183#1836C2211yescharacteristic
184#1831C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1803C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#107C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1767C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1745C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#559—24no—
210#559—24no—
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C4×Q8D411yescharacteristic
223C2×C4×Q8D411yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C22×C42—21no—
247C22×C42—21no—
248#460—24no—
249#459—24no—
250#459—24no—
251#442—24no—
252#440—24no—
253#440—24no—
254C4×D8—24no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#399—21no—
304#399—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#393—21no—
314#393—21no—
315#391—21no—
316#391C2311yescharacteristic
317#391C2311yescharacteristic
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#390C2311yescharacteristic
334#390C2311yescharacteristic
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#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#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
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#384C2311yescharacteristic
394#384C2311yescharacteristic
395#382—21no—
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#381—21no—
401#381—21no—
402#381—21no—
403#380—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4D411yescharacteristic
410C4×C4⋊C4D411yescharacteristic
411C4×C4⋊C4D411yescharacteristic
412C4×C4⋊C4D411yescharacteristic
413C4×C4⋊C4D411yescharacteristic
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
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⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C2×#95—21no—
445C43—21no—
446C43C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533#127—22no—
534#127—22no—
535#127—41no—
536#127#4114yes—
537#126—82no—
538#126—82no—
539#124—28no—
540#124—22no—
541#124—22no—
542#124—22no—
543#124—22no—
544#123—28no—
545#123—28no—
546#123—44no—
547#123—44no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—42no—
553C4×Q8—42no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8#4114yes—
558C4×D4—28no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—44no—
580C4×D4—44no—
581C4×D4—82no—
582C4×D4—82no—
583C4×D4—82no—
584#117—82no—
585#117—82no—
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—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—82no—
674C2×C42—82no—
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#107—22no—
695#107—22no—
696#107—22no—
697#107—41no—
698#107—41no—
699#107—41no—
700#106—22no—
701#106—41no—
702#106—41no—
703#106—41no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708#103—22no—
709#103—22no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
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#4114yes—
736#97—22no—
737#97—22no—
738#97—22no—
739#97—41no—
740C4×C8—22no—
741C4×C8—41no—
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#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C2×Q8—22no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8C2×#4112yes—
792C2×D4—24no—
793C2×D4—24no—
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—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4C2×#4112yes—
826C2×D4C2×#4112yes—
827C2×D4C2×#4112yes—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C2511yescharacteristic
885SD16—44no—
886SD16—44no—
887D8—44no—
888D8—44no—
889D8—82no—
890D8—82no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
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×C8C2×#4112yes—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
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—41no—
944C4⋊C4—41no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
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⋊C4—81no—
961C4⋊C4C2×#4112yes—
962C4⋊C4C2×#4112yes—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—24no—
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—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C42—24no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—41no—
1020C42—41no—
1021C42—41no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42C2×#4112yes—
1038C42C2×#4112yes—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23C23×D411yescharacteristic
1068Q8—22no—
1069Q8—22no—
1070Q8—44no—
1071Q8—41no—
1072Q8—41no—
1073D4—22no—
1074D4—22no—
1075D4—22no—
1076D4—22no—
1077D4—22no—
1078D4—22no—
1079D4—48no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—84no—
1091D4—84no—
1092D4—84no—
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—21no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
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—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
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—84no—
1167C2×C4—84no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—84no—
1171C2×C4—84no—
1172C2×C4—84no—
1173C2×C4—84no—
1174C2×C4—162no—
1175C2×C4—162no—
1176C2×C4#52512yes—
1177C2×C4#52512yes—
1178C2×C4#57512yes—
1179C2×C4#57512yes—
1180C2×C4#57612yes—
1181C2×C4C22×#4111yescharacteristic
1182C2×C4C22×#4111yescharacteristic
1183C2×C4C22×#4111yescharacteristic
1184C2×C4#58511yescharacteristic
1185C2×C4#58511yescharacteristic
1186C2×C4#58511yescharacteristic
1187C8—22no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22C2×#52511yescharacteristic
1224C22D4×#4111yescharacteristic
1225C22#348711yescharacteristic
1226C22C2×#57511yescharacteristic
1227C22C2×#57511yescharacteristic
1228C22C2×#57611yescharacteristic
1229C22#358511yescharacteristic
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—41no—
1236C4—41no—
1237C4—42no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—42no—
1246C4—41no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4#347511yescharacteristic
1257C4#347511yescharacteristic
1258C4#351211yescharacteristic
1259C4#352111yescharacteristic
1260C2—82no—
1261C2—82no—
1262C2—82no—
1263C2—161no—
1264C2#3622811yescharacteristic
1265C2#6055911yescharacteristic
1266C2#6059011yescharacteristic
1267C2#6144411yescharacteristic
1268C2#6145611yescharacteristic
1269C2#6189611yescharacteristic
1270C2#6189811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28156C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36370C2semidirect
2. C4×#559C2semidirect
3. #33080C2semidirect
4. #33078C2semidirect
5. #33071C2semidirect
6. #29503C2semidirect
7. #29497C2semidirect
8. #29373C2semidirect
9. #29372C2semidirect
10. #29195C2semidirect
12. #27388C2semidirect
13. #27369C2semidirect
14. #27218C2semidirect
15. #27199C2semidirect
16. #26778C2semidirect
17. #26763C2semidirect
18. #26608C2semidirect
19. #26593C2semidirect
20. #25069C2semidirect
21. #25003C2semidirect
22. #24198C2semidirect
23. #24198C2semidirect
24. #23108C2semidirect
25. #23008C2semidirect
26. #22830C2semidirect
27. #22819C2semidirect
28. #22776C2semidirect
29. #21505C2semidirect
30. #21122C2semidirect
31. #21113C2semidirect

Maximal subgroups

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

subgroupindex
#363702
C4×#5592
#330802
#330782
#330712
#295032
#294972
#293732
#293722
#291952
#281562
#273882
#273692
#272182
#271992
#267782
#267632
#266082
#265932
#250692
#250032
#241982
#231082
#230082
#228302
#228192
#227762
#215052
#211222
#211132