Finite Group Databasebeta

← #24909108

Subgroups — #24909108

Order 10624.

280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128262C211yesmaximal, characteristic
2#100×D83C211yesmaximal, characteristic, complemented
3#99×D83C211yesmaximal, characteristic, complemented
4#19127491C211yesmaximal, characteristic, complemented
5#19127489C211yesmaximal, characteristic, complemented
6#19127487C211yesmaximal, characteristic, complemented
7#352×C83C211yesmaximal, characteristic, complemented
8C22×D332C411yescharacteristic, complemented
9C2×D4×D83C2211yescharacteristic
10M16×D83—21no—
11#14581777—21no—
12#14581775C411yescharacteristic, complemented
13#14581767—21no—
14#14581765—21no—
15#14581762—21no—
16#14581762C411yescharacteristic, complemented
17#14581760C2211yescharacteristic
18C22⋊C4×D83—21no—
19C22⋊C4×D83C411yescharacteristic, complemented
20#14581709C2211yescharacteristic
21#14581708—21no—
22#14581707C2211yescharacteristic
23#14581706—21no—
24#123×C83C2211yescharacteristic
25#100×C83C2211yescharacteristic
26#99×C83C2211yescharacteristic
27C23×D83C2×C411yescharacteristic
28C23×D83C2×C411yescharacteristic, complemented
29C23×D83D411yescharacteristic
30C2×D332—21no—
31C2×D332—21no—
32C2×D332—21no—
33C2×D332—41no—
34C2×D332—41no—
35C2×D332D411yescharacteristic
36C2×C22⋊D83—21no—
37C2×C22⋊D83C2×C411yescharacteristic
38C2×C22⋊D83D411yescharacteristic
39D4×D83—41no—
40D4×D83—41no—
41C2×C4×D83—21no—
42C2×C4×D83—41no—
43C2×C4×D83D411yescharacteristic
44#13050574—21no—
45#13050573—41no—
46C8×D83—41no—
47Dic83⋊C4—21no—
48C22⋊Dic83—21no—
49C22⋊Dic83C2×C411yescharacteristic, complemented
50(C2×D83)⋊C4—21no—
51(C2×D83)⋊C4—21no—
52(C2×D83)⋊C4—21no—
53(C2×D83)⋊C4—21no—
54(C2×D83)⋊C4—41no—
55C2×D4×C83C2311yescharacteristic
56C22×C4×C83C2×C411yescharacteristic, complemented
57M16×C83—21no—
58C4⋊C4×C83—21no—
59C22⋊C4×C83—21no—
60C22⋊C4×C83—21no—
61C22⋊C4×C83C2×C411yescharacteristic, complemented
62C23×C83C22×C411yescharacteristic
63C23×C83C2×D411yescharacteristic
64C22×D83—21no—
65C22×D83—21no—
66C22×D83—21no—
67C22×D83—21no—
68C22×D83—21no—
69C22×D83—41no—
70C22×D83—81no—
71C22×D83—81no—
72C22×D83—81no—
73C22×D83C22⋊C411yescharacteristic
74C22×D83C22⋊C411yescharacteristic
75C22×D83C22⋊C411yescharacteristic
76D4×C83—41no—
77C2×C4×C83—21no—
78C2×C4×C83—21no—
79C2×C4×C83—41no—
80C2×C4×C83—41no—
81C2×C4×C83C2×D411yescharacteristic
82C22⋊D83—41no—
83C22⋊D83—41no—
84C22⋊D83—81no—
85C2×Dic83—21no—
86C2×Dic83—41no—
87C2×Dic83C22⋊C411yescharacteristic
88D332—41no—
89D332—42no—
90D332—41no—
91D332—41no—
92D332—81no—
93C4×D83—21no—
94C4×D83—21no—
95C4×D83—81no—
96C4×D83—82no—
97C8×C83—41no—
98C83⋊C8—41no—
99C22×C83—21no—
100C22×C83—21no—
101C22×C83—41no—
102C22×C83—41no—
103C22×C83C2×C22⋊C411yescharacteristic
104C2×D83—21no—
105C2×D83—21no—
106C2×D83—41no—
107C2×D83—42no—
108C2×D83—41no—
109C2×D83—41no—
110C2×D83—41no—
111C2×D83—41no—
112C2×D83—41no—
113C2×D83—81no—
114C2×D83—81no—
115C2×D83—81no—
116C2×D83—82no—
117C2×D83#9911yescharacteristic
118C2×D83#9911yescharacteristic
119C4×C83—21no—
120C4×C83—41no—
121C4×C83—41no—
122C4×C83—81no—
123Dic83—21no—
124Dic83—41no—
125Dic83—81no—
126C2×C83—21no—
127C2×C83—41no—
128C2×C83—41no—
129C2×C83C2×#9911yescharacteristic
130D83—21no—
131D83—21no—
132D83—41no—
133D83—41no—
134D83—81no—
135#2121—831nomaximal, Sylow
136C83#212111yescharacteristic, complemented, Sylow
137#534—831no—
138C2×#100—831no—
139C2×#99—831no—
140#352—831no—
141#352D8311yescharacteristic, complemented
142AΣL(1,𝔽16)—831no—
143AΣL(1,𝔽16)—831no—
144C22×D4—831no—
145C22×D4—831no—
146C2×M16—1661no—
147#123—831no—
148#123—1661no—
149#123C2×D8311yescharacteristic
150#121—1661no—
151#121—1661no—
152#120—831no—
153#120—831no—
154#120—1661no—
155C2×C22⋊C4—831no—
156C2×C22⋊C4—1661no—
157#100—831no—
158#100—1661no—
159#100C2×D8311yescharacteristic
160#99—831no—
161#99—1661no—
162#99C2×D8311yescharacteristic
163C24—831no—
164C24—831no—
165C24—831no—
166C2×D4—3321no—
167C2×D4—3321no—
168C2×D4—3321no—
169C2×D4—3321no—
170C2×D4—831no—
171C2×D4—831no—
172C2×D4—831no—
173C2×D4—1661no—
174C2×D4—1661no—
175C2×D4—1661no—
176C2×D4—1661no—
177C2×D4C22×D8311yescharacteristic
178C22×C4—3321no—
179C22×C4—831no—
180C22×C4—1661no—
181C22×C4C4×D8311yescharacteristic, complemented
182M16—21no—
183M16—3321no—
184M16—1661no—
185C2×C8—3321no—
186C4⋊C4—21no—
187C4⋊C4—1661no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—3321no—
191C22⋊C4—831no—
192C22⋊C4—1661no—
193C22⋊C4—1661no—
194C22⋊C4—1661no—
195C22⋊C4—1661no—
196C22⋊C4—1661no—
197C22⋊C4C4×D8311yescharacteristic, complemented
198C23—3321no—
199C23—831no—
200C23—831no—
201C23—831no—
202C23—6641no—
203C23—6641no—
204C23—6641no—
205C23—1661no—
206C23—1661no—
207C23—1661no—
208C23—1661no—
209C23—1661no—
210C23C2×C4×D8311yescharacteristic
211C23D4×D8311yescharacteristic
212D4—41no—
213D4—3321no—
214D4—3321no—
215D4—3321no—
216D4—3322no—
217D4—3321no—
218D4—3321no—
219D4—6641no—
220D4—6641no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—3321no—
226C2×C4—831no—
227C2×C4—6641no—
228C2×C4—6642no—
229C2×C4—1661no—
230C2×C4—1661no—
231C2×C4—1661no—
232C2×C4D4×D8311yescharacteristic
233C8—41no—
234C8—3321no—
235C22—21no—
236C22—21no—
237C22—41no—
238C22—41no—
239C22—3321no—
240C22—3321no—
241C22—3321no—
242C22—3321no—
243C22—3321no—
244C22—3322no—
245C22—3321no—
246C22—831no—
247C22—831no—
248C22—6641no—
249C22—6641no—
250C22—6641no—
251C22—6642no—
252C22—1661no—
253C22—1661no—
254C22C22⋊C4×D8311yescharacteristic
255C4—21no—
256C4—41no—
257C4—41no—
258C4—81no—
259C4—3321no—
260C4—6641no—
261C4—1661no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2—3321no—
266C2—3321no—
267C2—6641no—
268C2—1661no—
269C2—1661no—
270C2#99×D8311yescharacteristic
subgroupG/H
centerC2#99×D83
commutatorC23×C83C22×C4
FrattiniC2×D4C22×D83
Fitting#352×C83C2
socleC2×C83C2×#99
prime radical#19128262C2
cosocleC2×D4×C83C23
hypercenter#352D83
hypocenterC83#2121
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #100×D83C2semidirect
3. #99×D83C2semidirect
4. #19127491C2semidirect
5. #19127489C2semidirect
6. #19127487C2semidirect
7. #352×C83C2semidirect
8. C22×D332C4semidirect
12. #14581775C4semidirect
16. #14581762C4semidirect
19. C22⋊C4×D83C4semidirect
28. C23×D83C2×C4semidirect
49. C22⋊Dic83C2×C4semidirect
56. C22×C4×C83C2×C4semidirect
61. C22⋊C4×C83C2×C4semidirect
136. C83#2121semidirect
141. #352D83semidirect
181. C22×C4C4×D83semidirect
197. C22⋊C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
#191282622
#100×D832
#99×D832
#191274912
#191274892
#191274872
#352×C832
#212183