Finite Group Databasebeta

← #24910439

Subgroups — #24910439

Order 10624.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581762C211yesmaximal, characteristic
2C2×#14581754C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D83C211yesmaximal, characteristic, complemented
4C22×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D83C211yesmaximal, characteristic, complemented
6#19127602C211yesmaximal, characteristic, complemented
7#19127591C211yesmaximal, characteristic, complemented
8#19127590C211yesmaximal, characteristic, complemented
9#19127579C211yesmaximal, characteristic, complemented
10#19127579C211yesmaximal, characteristic, complemented
11#19127578C211yesmaximal, characteristic, complemented
12#19127572C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic83C211yesmaximal, characteristic, complemented
14#19127548C211yesmaximal, characteristic, complemented
15#385×C83C211yesmaximal, characteristic, complemented
16C24×D83C2211yescharacteristic
17C22×D332C2211yescharacteristic
18C22×D332C2211yescharacteristic
19C22×C22⋊D83C2211yescharacteristic
20C23×Dic83C2211yescharacteristic
21C22×C4×D83C2211yescharacteristic
22C22×C4×D83C2211yescharacteristic
23C22×C4×D83C2211yescharacteristic, complemented
24#14581762C418yescomplemented
25#14581754—24no—
26C4×C22⋊D83—24no—
27C2×Dic83⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic83C2211yescharacteristic
29C2×(C2×D83)⋊C4—24no—
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C2×(C2×D83)⋊C4C2211yescharacteristic
37C2×(C2×D83)⋊C4C2211yescharacteristic
38C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D83—24no—
42C2×C4×Dic83C2211yescharacteristic, complemented
43C2×C4×Dic83C2211yescharacteristic, complemented
44C2×C4×Dic83C2211yescharacteristic, complemented
45C83⋊#95C2211yescharacteristic, complemented
46C83⋊#95C2211yescharacteristic, complemented
47C83⋊#95C2211yescharacteristic, complemented
48C83⋊#95C2211yescharacteristic, complemented
49C23×C4×C83C2211yescharacteristic
50C2×C4⋊C4×C83C2211yescharacteristic, complemented
51C2×C4⋊C4×C83C2211yescharacteristic, complemented
52C2×C22⋊C4×C83C2211yescharacteristic
53C2×C22⋊C4×C83C2211yescharacteristic
54#95×C83C2211yescharacteristic, complemented
55#95×C83C2211yescharacteristic, complemented
56C23×D83—22no—
57C23×D83—22no—
58C23×D83—22no—
59C23×D83—22no—
60C23×D83—41no—
61C23×D83—41no—
62C23×D83C2×C414yescomplemented
63C23×D83C2311yescharacteristic
64C23×D83C2311yescharacteristic
65C23×D83C2311yescharacteristic
66C2×D332—22no—
67C2×D332—22no—
68C2×D332—41no—
69C2×D332—41no—
70C2×D332C2×C414yescomplemented
71C2×D332C2×C414yescomplemented
72C2×C22⋊D83—22no—
73C2×C22⋊D83—22no—
74C2×C22⋊D83C2×C414yescomplemented
75C22×Dic83—22no—
76C22×Dic83—22no—
77C22×Dic83—41no—
78C22×Dic83C2311yescharacteristic
79C22×Dic83C2311yescharacteristic
80C22×Dic83C2311yescharacteristic
81C22×Dic83C2311yescharacteristic
82C22×Dic83C2311yescharacteristic
83C2×C4×D83—22no—
84C2×C4×D83—22no—
85C2×C4×D83—22no—
86C2×C4×D83—22no—
87C2×C4×D83—22no—
88C2×C4×D83—22no—
89C2×C4×D83—41no—
90C2×C4×D83—41no—
91C2×C4×D83—41no—
92Dic83⋊C4—22no—
93C22⋊Dic83D414yescomplemented
94(C2×D83)⋊C4—22no—
95(C2×D83)⋊C4—22no—
96(C2×D83)⋊C4—22no—
97(C2×D83)⋊C4—22no—
98(C2×D83)⋊C4—22no—
99(C2×D83)⋊C4—22no—
100(C2×D83)⋊C4—22no—
101(C2×D83)⋊C4—41no—
102(C2×D83)⋊C4C2×C414yescomplemented
103(C2×D83)⋊C4C2×C414yescomplemented
104(C2×D83)⋊C4D414yescomplemented
105C4×Dic83—22no—
106C4×Dic83—22no—
107C4×Dic83—41no—
108C24×C83C2311yescharacteristic
109C22×C4×C83—22no—
110C22×C4×C83—22no—
111C22×C4×C83—41no—
112C22×C4×C83C2311yescharacteristic
113C22×C4×C83C2311yescharacteristic
114C22×C4×C83C2311yescharacteristic
115C22×C4×C83C2311yescharacteristic
116C22×C4×C83C2311yescharacteristic
117C22×C4×C83C2311yescharacteristic
118C4⋊C4×C83—22no—
119C4⋊C4×C83—41no—
120C22⋊C4×C83—22no—
121C22⋊C4×C83C2×C414yescomplemented
122C23×C83—21no—
123C23×C83—21no—
124C23×C83—21no—
125C23×C83—21no—
126C23×C83C22×C412yes—
127C23×C83C2×D412yes—
128C23×C83#4112yes—
129C23×C83C2411yescharacteristic
130C22×D83—21no—
131C22×D83—21no—
132C22×D83—21no—
133C22×D83—21no—
134C22×D83—28no—
135C22×D83—21no—
136C22×D83—21no—
137C22×D83—21no—
138C22×D83—21no—
139C22×D83—21no—
140C22×D83—21no—
141C22×D83—21no—
142C22×D83—21no—
143C22×D83—21no—
144C22×D83—21no—
145C22×D83—21no—
146C22×D83—21no—
147C22×D83—28no—
148C22×D83—44no—
149C22×D83—44no—
150C22×D83—44no—
151C22×D83—44no—
152C22×D83—44no—
153C22×D83C22×C412yes—
154C22×D83C22×C412yes—
155C22×D83C22×C412yes—
156C22×D83C2×D412yes—
157C22×D83#4112yes—
158C2×C4×C83—21no—
159C2×C4×C83—21no—
160C2×C4×C83—21no—
161C2×C4×C83—21no—
162C2×C4×C83—21no—
163C2×C4×C83—21no—
164C2×C4×C83—21no—
165C2×C4×C83—21no—
166C2×C4×C83—21no—
167C2×C4×C83—21no—
168C2×C4×C83—21no—
169C2×C4×C83—21no—
170C2×C4×C83—21no—
171C2×C4×C83—21no—
172C2×C4×C83—21no—
173C2×C4×C83—44no—
174C2×C4×C83C22×C412yes—
175C2×C4×C83C22×C412yes—
176C2×C4×C83C2×D412yes—
177C22⋊D83—28no—
178C2×Dic83—21no—
179C2×Dic83—21no—
180C2×Dic83—21no—
181C2×Dic83—21no—
182C2×Dic83—21no—
183C2×Dic83—21no—
184C2×Dic83—21no—
185C2×Dic83—21no—
186C2×Dic83—21no—
187C2×Dic83—21no—
188C2×Dic83—21no—
189C2×Dic83—44no—
190C2×Dic83C22×C412yes—
191C2×Dic83C2×D412yes—
192C2×Dic83C2×D412yes—
193C2×Dic83C2×D412yes—
194D332—28no—
195D332—44no—
196C4×D83—44no—
197C4×D83—44no—
198C4×D83—44no—
199C22×C83—22no—
200C22×C83—22no—
201C22×C83—22no—
202C22×C83—22no—
203C22×C83—22no—
204C22×C83—22no—
205C22×C83C4×D414yescomplemented
206C22×C83C23×C411yescharacteristic
207C22×C83C22×D411yescharacteristic
208C22×C83C22×D411yescharacteristic
209C22×C83C2×#4111yescharacteristic
210C22×C83C2×#4111yescharacteristic
211C22×C83H(5,𝔽2)11yescharacteristic
212C22×C83H(5,𝔽2)11yescharacteristic
213C2×D83—22no—
214C2×D83—22no—
215C2×D83—22no—
216C2×D83—22no—
217C2×D83—22no—
218C2×D83—22no—
219C2×D83—22no—
220C2×D83—22no—
221C2×D83—22no—
222C2×D83—22no—
223C2×D83—22no—
224C2×D83—22no—
225C2×D83—416no—
226C2×D83—41no—
227C2×D83—41no—
228C2×D83—41no—
229C2×D83—41no—
230C2×D83—41no—
231C2×D83—41no—
232C2×D83—41no—
233C2×D83—41no—
234C2×D83C4×D414yescomplemented
235C4×C83—22no—
236C4×C83—22no—
237C4×C83—22no—
238C4×C83—41no—
239C4×C83—41no—
240C4×C83—41no—
241Dic83—22no—
242Dic83—22no—
243Dic83—22no—
244Dic83—22no—
245Dic83—41no—
246C2×C83—24no—
247C2×C83C2×C4×D411yescharacteristic
248C2×C83C2×C4×D411yescharacteristic
249C2×C83#51811yescharacteristic
250C2×C83D4211yescharacteristic
251C2×C83#54611yescharacteristic
252C2×C83#54611yescharacteristic
253C2×C83#55111yescharacteristic
254D83—24no—
255D83—42no—
256D83—42no—
257#2358—831nomaximal, Sylow
258C83#235811yescharacteristic, complemented, Sylow
259C2×#120—831no—
260C2×C4×D4—831no—
261C2×C4×D4—831no—
262C22×C22⋊C4—831no—
263C22×C22⋊C4—831no—
264#390—831no—
265#388—831no—
266#388—831no—
267#386—831no—
268#386—831no—
269#386—831no—
270#385—831no—
271#385D8311yescharacteristic, complemented
272C4×C22⋊C4—831no—
273C4×C22⋊C4—831no—
274C25—831no—
275C22×D4—831no—
276C22×D4—831no—
277C22×D4—831no—
278C23×C4—831no—
279C23×C4—831no—
280C23×C4—831no—
281C23×C4—831no—
282C23×C4C2×D8311yescharacteristic
283#120—838no—
284C4×D4—1664no—
285C4×D4—1664no—
286C2×C4⋊C4—831no—
287C2×C4⋊C4C2×D8311yescharacteristic, complemented
288C2×C4⋊C4C2×D8311yescharacteristic, complemented
289C2×C22⋊C4—831no—
290C2×C22⋊C4—831no—
291C2×C22⋊C4—831no—
292C2×C22⋊C4—831no—
293C2×C22⋊C4—831no—
294C2×C22⋊C4—831no—
295C2×C22⋊C4—831no—
296C2×C22⋊C4—831no—
297C2×C22⋊C4—831no—
298C2×C22⋊C4—831no—
299C2×C22⋊C4—831no—
300C2×C22⋊C4—831no—
301C2×C22⋊C4—1664no—
302C2×C22⋊C4—1664no—
303C2×C22⋊C4C2×D8311yescharacteristic
304C2×C22⋊C4C2×D8311yescharacteristic
305C2×C42—831no—
306C2×C42—831no—
307C2×C42—831no—
308#95—831no—
309#95—831no—
310#95—831no—
311#95—831no—
312#95C2×D8311yescharacteristic, complemented
313#95C2×D8311yescharacteristic, complemented
314C24—3321no—
315C24—3321no—
316C24—834no—
317C24—831no—
318C24—831no—
319C24—831no—
320C24—1662no—
321C24—1662no—
322C24—1662no—
323C24—1662no—
324C24C22×D8311yescharacteristic
325C2×D4—3321no—
326C2×D4—3321no—
327C2×D4—834no—
328C2×D4—834no—
329C2×D4—834no—
330C2×D4—1662no—
331C2×D4—1662no—
332C2×D4—1662no—
333C2×D4—1662no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—3321no—
338C22×C4—3321no—
339C22×C4—3321no—
340C22×C4—3321no—
341C22×C4—831no—
342C22×C4—831no—
343C22×C4—831no—
344C22×C4—831no—
345C22×C4—831no—
346C22×C4—1662no—
347C22×C4—1662no—
348C22×C4—1662no—
349C22×C4—1662no—
350C22×C4—1662no—
351C22×C4—1662no—
352C22×C4—1662no—
353C22×C4—1662no—
354C22×C4C22×D8311yescharacteristic
355C22×C4C22×D8311yescharacteristic
356C22×C4C22×D8311yescharacteristic
357C22×C4C22×D8311yescharacteristic
358C22×C4C22×D8311yescharacteristic
359C22×C4C22×D8311yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—41no—
362C4⋊C4—1662no—
363C22⋊C4—22no—
364C22⋊C4—3321no—
365C22⋊C4—834no—
366C22⋊C4—834no—
367C22⋊C4—834no—
368C22⋊C4—834no—
369C22⋊C4—1662no—
370C22⋊C4—1662no—
371C22⋊C4—1662no—
372C22⋊C4—1662no—
373C22⋊C4—1662no—
374C22⋊C4—1662no—
375C22⋊C4—1662no—
376C22⋊C4C4×D8314yescomplemented
377C42—3321no—
378C42—1662no—
379C42—1662no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—3324no—
385C23—3324no—
386C23—3324no—
387C23—3324no—
388C23—3324no—
389C23—832no—
390C23—832no—
391C23—832no—
392C23—832no—
393C23—832no—
394C23—1668no—
395C23—1661no—
396C23—1661no—
397C23—1661no—
398C23—1661no—
399C23—1661no—
400C23—1661no—
401C23—1661no—
402C23—1661no—
403C23—1661no—
404C23—1661no—
405C23—1661no—
406C23—1661no—
407C23—1668no—
408C23—1661no—
409C23—1661no—
410C23—1661no—
411C23—1661no—
412C23C2×C4×D8312yes—
413C23D4×D8312yes—
414C23#1305059112yes—
415C23C23×D8311yescharacteristic
416D4—3324no—
417D4—1668no—
418D4—1668no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—3324no—
436C2×C4—3324no—
437C2×C4—3324no—
438C2×C4—3324no—
439C2×C4—832no—
440C2×C4—832no—
441C2×C4—832no—
442C2×C4—832no—
443C2×C4—1661no—
444C2×C4—1661no—
445C2×C4—1661no—
446C2×C4—1661no—
447C2×C4—1661no—
448C2×C4—1661no—
449C2×C4—1661no—
450C2×C4—1661no—
451C2×C4—1661no—
452C2×C4—1661no—
453C2×C4—1661no—
454C2×C4C2×C4×D8312yes—
455C2×C4C2×C4×D8312yes—
456C2×C4D4×D8312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—33216no—
464C22—3321no—
465C22—3321no—
466C22—3321no—
467C22—3321no—
468C22—3321no—
469C22—3321no—
470C22—3321no—
471C22—3321no—
472C22—834no—
473C22—1662no—
474C22—1662no—
475C22—1662no—
476C22—1662no—
477C22—1662no—
478C22—1662no—
479C22—1662no—
480C22—1662no—
481C22—1662no—
482C22—1662no—
483C22—1662no—
484C22—1662no—
485C22#1458175414yescomplemented
486C22C22×C4×D8311yescharacteristic
487C22C2×D4×D8311yescharacteristic
488C22C2×D4×D8311yescharacteristic
489C22#41×D8311yescharacteristic
490C22C2×#1305059111yescharacteristic
491C22#1458183711yescharacteristic
492C22#1458183811yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—3321no—
500C4—1662no—
501C4—1662no—
502C4—1662no—
503C4—1662no—
504C2—24no—
505C2—3322no—
506C2—3322no—
507C2—1664no—
508C2C4×D4×D8311yescharacteristic
509C2C2×#1458175411yescharacteristic
510C2#1912817311yescharacteristic
511C2#1912833311yescharacteristic
512C2#1912834211yescharacteristic
513C2#1912834311yescharacteristic
514C2#1912837811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutatorC22×C83C23×C4
Fitting#385×C83C2
socle, cosocleC23×C83C24
prime radicalC2×#14581762C2
hypercenter#385D83
hypocenterC83#2358
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#14581754C2semidirect
3. C2×C4×C22⋊D83C2semidirect
4. C22×(C2×D83)⋊C4C2semidirect
5. C2×C22⋊C4×D83C2semidirect
6. #19127602C2semidirect
7. #19127591C2semidirect
8. #19127590C2semidirect
9. #19127579C2semidirect
10. #19127579C2semidirect
11. #19127578C2semidirect
12. #19127572C2semidirect
13. C22⋊C4×Dic83C2semidirect
14. #19127548C2semidirect
15. #385×C83C2semidirect
23. C22×C4×D83C22semidirect
24. #14581762C4semidirect
27. C2×Dic83⋊C4C22semidirect
38. C2×(C2×D83)⋊C4C22semidirect
39. C2×(C2×D83)⋊C4C22semidirect
40. C2×(C2×D83)⋊C4C22semidirect
42. C2×C4×Dic83C22semidirect
43. C2×C4×Dic83C22semidirect
44. C2×C4×Dic83C22semidirect
45. C83⋊#95C22semidirect
46. C83⋊#95C22semidirect
47. C83⋊#95C22semidirect
48. C83⋊#95C22semidirect
50. C2×C4⋊C4×C83C22semidirect
51. C2×C4⋊C4×C83C22semidirect
54. #95×C83C22semidirect
55. #95×C83C22semidirect
62. C23×D83C2×C4semidirect
70. C2×D332C2×C4semidirect
71. C2×D332C2×C4semidirect
74. C2×C22⋊D83C2×C4semidirect
93. C22⋊Dic83D4semidirect
102. (C2×D83)⋊C4C2×C4semidirect
103. (C2×D83)⋊C4C2×C4semidirect
104. (C2×D83)⋊C4D4semidirect
121. C22⋊C4×C83C2×C4semidirect
205. C22×C83C4×D4semidirect
234. C2×D83C4×D4semidirect
258. C83#2358semidirect
271. #385D83semidirect
287. C2×C4⋊C4C2×D83semidirect
288. C2×C4⋊C4C2×D83semidirect
312. #95C2×D83semidirect
313. #95C2×D83semidirect
376. C22⋊C4C4×D83semidirect
485. C22#14581754semidirect

Maximal subgroups

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

subgroupindex
C2×#145817622
C2×#145817542
C2×C4×C22⋊D832
C22×(C2×D83)⋊C42
C2×C22⋊C4×D832
#191276022
#191275912
#191275902
#191275792
#191275782
#191275722
C22⋊C4×Dic832
#191275482
#385×C832
#235883