Finite Group Databasebeta

← #49133093

Subgroups — #49133093

Order 36224.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827153C211yesmaximal, characteristic, complemented
2#31827110C211yesmaximal, characteristic
3#31826822C211yesmaximal, characteristic, complemented
4#31826797C211yesmaximal, characteristic, complemented
5#31826792C211yesmaximal, characteristic, complemented
6#31826707C211yesmaximal, characteristic, complemented
7#31826695C211yesmaximal, characteristic, complemented
8#31826688C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic, complemented
10#31826617C211yesmaximal, characteristic, complemented
11C4×#17985380C211yesmaximal, characteristic, complemented
12#31826530C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#478×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic, complemented
19C2×#17985381C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic, complemented
23#22583605—21no—
24#22583601—21no—
25#22583598C2211yescharacteristic
26#22583595—21no—
27#22583594—21no—
28#22583590C2211yescharacteristic
29#22583590C2211yescharacteristic
30#22583590C2211yescharacteristic, complemented
31#22583585C2211yescharacteristic
32#22583584—21no—
33#22583580—21no—
34C4×Dic566C2211yescharacteristic, complemented
35C4×D1132C2211yescharacteristic
36#22583568—21no—
37#22583568C2211yescharacteristic, complemented
38C4⋊C4×D283C2211yescharacteristic
39C2×(C2×D283)⋊C4—21no—
40#22583541C2211yescharacteristic, complemented
41#22583535C2211yescharacteristic, complemented
42#22583533C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51C4×C283⋊C8C2211yescharacteristic, complemented
52#125×C283C2211yescharacteristic, complemented
53C4×D4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56C4⋊C8×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60#17985391—22no—
61#17985391—41no—
62C2×Dic566C2311yescharacteristic
63C2×Dic566C2311yescharacteristic
64C2×D1132—21no—
65C2×D1132D411yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69D4×D283—22no—
70D4×D283—41no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74C2×C4×D283C2311yescharacteristic
75Dic1132—41no—
76#17985381—41no—
77#17985380—22no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—41no—
81C8×D283—41no—
82C4⋊Dic283—21no—
83C4⋊Dic283—21no—
84C4⋊Dic283—21no—
85C4⋊Dic283D411yescharacteristic
86C4⋊Dic283C2311yescharacteristic
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97(C2×D283)⋊C4D411yescharacteristic
98C4×Dic283—21no—
99C4×Dic283—21no—
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283—21no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—42no—
113C22×D283—42no—
114C22×D283—81no—
115C22×D283C2×D411yescharacteristic
116C22×D283C2×D411yescharacteristic
117Dic566—21no—
118Dic566—21no—
119Dic566—21no—
120Dic566—21no—
121D1132—22no—
122D1132—21no—
123D1132—21no—
124D1132—81no—
125C22⋊D283—42no—
126C22⋊D283—42no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—42no—
131C2×Dic283C2×D411yescharacteristic
132C2×Dic283C2×D411yescharacteristic
133C4×D283—21no—
134C4×D283—21no—
135C4×D283—21no—
136C4×D283—21no—
137C4×D283—42no—
138C283⋊C8—21no—
139C283⋊C8—21no—
140C23×C283—21no—
141D4×C283—21no—
142D4×C283#4112yes—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—22no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—41no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—84no—
165C2×D283#13512yes—
166C4×C283—21no—
167C4×C283—21no—
168C4×C283—41no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283C2×#4111yescharacteristic
172C4×C283H(5,𝔽2)11yescharacteristic
173Dic283—21no—
174Dic283—21no—
175Dic283—41no—
176Dic283—41no—
177Dic283—41no—
178C2×C283—42no—
179C2×C283#54611yescharacteristic
180C2×C283C2×#13511yescharacteristic
181C2×C283#57711yescharacteristic
182D283—22no—
183D283—41no—
184D283—81no—
185C283#329611yescharacteristic, complemented, Sylow
186#3296—2831nomaximal, Sylow
187#552—2831no—
188#546—2831no—
189#488—2831no—
190#483—2831no—
191#482—2831no—
192#478D28311yescharacteristic, complemented
193#467—2831no—
194#465—2831no—
195#464—2831no—
196#452—2831no—
197#450—2831no—
198C4×SD16—2831no—
199C8×D4—2831no—
200#416—2831no—
201C2×#102—2831no—
202C2×#41—2831no—
203C22×D4—2831no—
204C2×Q16—2831no—
205C2×SD16—2831no—
206C2×SD16—2831no—
207C22×C8—2831no—
208C22×C8—2831no—
209#126—5661no—
210#125—5661no—
211#125C2×D28311yescharacteristic, complemented
212#124—2831no—
213#123—5661no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—2831no—
217C22⋊Q8—2831no—
218#121—2831no—
219#121—5661no—
220#120—5661no—
221C4×Q8—2831no—
222C4×D4—2831no—
223C4×D4C2×D28311yescharacteristic
224#117—2831no—
225#117—5661no—
226C2×C4⋊C4—2831no—
227C2×C22⋊C4—5661no—
228#107C2×D28311yescharacteristic, complemented
229#106—2831no—
230#106C2×D28311yescharacteristic, complemented
231C4⋊C8C2×D28311yescharacteristic, complemented
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102C2×D28311yescharacteristic
241#102C2×D28311yescharacteristic
242C22⋊C8—2831no—
243C22⋊C8—2831no—
244C4×C8—2831no—
245C24—5661no—
246#41—5662no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—2831no—
250C2×D4—2831no—
251C2×D4—2831no—
252C2×D4—5661no—
253C2×D4—5661no—
254C2×D4—5662no—
255C2×D4—5661no—
256C2×D4—11321no—
257C2×D4C22×D28311yescharacteristic
258C22×C4—21no—
259C22×C4—2831no—
260C22×C4—2831no—
261C22×C4—5661no—
262C22×C4—5661no—
263Q16—11321no—
264SD16—5662no—
265SD16—11321no—
266C2×C8—2831no—
267C2×C8—2831no—
268C2×C8—11321no—
269C2×C8—11321no—
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4C22×D28311yescharacteristic
282C4⋊C4C22×D28311yescharacteristic
283C4⋊C4C22×D28311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—2831no—
286C22⋊C4—2831no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C42—5661no—
295C42—5661no—
296C42C22×D28311yescharacteristic
297C23—21no—
298C23—2831no—
299C23—2831no—
300C23—5661no—
301C23—11322no—
302C23—11322no—
303C23—22641no—
304Q8—5661no—
305Q8—5661no—
306Q8—5661no—
307Q8—5661no—
308D4—21no—
309D4—5662no—
310D4—5661no—
311D4—5661no—
312D4—11322no—
313D4—11322no—
314D4—22641no—
315D4#1798539312yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—2831no—
321C2×C4—2831no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—5661no—
329C2×C4—11322no—
330C2×C4—11322no—
331C2×C4D4×D28311yescharacteristic
332C2×C4D4×D28311yescharacteristic
333C2×C4C23×D28311yescharacteristic
334C8—21no—
335C8—21no—
336C8—5661no—
337C8—5661no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—2832no—
342C22—5661no—
343C22—5661no—
344C22—5661no—
345C22—5661no—
346C22—5661no—
347C22—11321no—
348C22—11321no—
349C22—11321no—
350C22—22644no—
351C22C2×D4×D28311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—5661no—
358C4—5661no—
359C4—11321no—
360C4—11321no—
361C4—11321no—
362C4C2×#1798539311yescharacteristic
363C4#2258365611yescharacteristic
364C2—42no—
365C2—5662no—
366C2—11321no—
367C2—22641no—
368C2#3182710611yescharacteristic
369C2#135×D28311yescharacteristic
370C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#478×C283C2
socleC22×C283C22×D4
prime radical#31827110C2
hypercenter#478D283
hypocenterC283#3296
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31827153C2semidirect
3. #31826822C2semidirect
4. #31826797C2semidirect
5. #31826792C2semidirect
6. #31826707C2semidirect
7. #31826695C2semidirect
8. #31826688C2semidirect
9. #31826628C2semidirect
10. #31826617C2semidirect
11. C4×#17985380C2semidirect
12. #31826530C2semidirect
13. #31826458C2semidirect
14. #102×D283C2semidirect
15. #478×C283C2semidirect
18. C2×Dic1132C22semidirect
22. C2×C8×D283C22semidirect
30. #22583590C22semidirect
34. C4×Dic566C22semidirect
37. #22583568C22semidirect
40. #22583541C22semidirect
41. #22583535C22semidirect
42. #22583533C22semidirect
43. #22583533C22semidirect
44. #22583533C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C4×C283⋊C8C22semidirect
52. #125×C283C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. C4⋊C8×C283C22semidirect
185. C283#3296semidirect
192. #478D283semidirect
211. #125C2×D283semidirect
228. #107C2×D283semidirect
230. #106C2×D283semidirect
231. C4⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271532
#318271102
#318268222
#318267972
#318267922
#318267072
#318266952
#318266882
#318266282
#318266172
C4×#179853802
#318265302
#318264582
#102×D2832
#478×C2832
#3296283