Finite Group Databasebeta

← #24909101

Subgroups — #24909101

Order 10624.

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

normal subgroups only

This group has 264 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#19128207C211yesmaximal, characteristic
2#19127682C211yesmaximal, characteristic, complemented
3#19127673C211yesmaximal, characteristic, complemented
4#19127492C211yesmaximal, characteristic, complemented
5#19127490C211yesmaximal, characteristic, complemented
6#19127488C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C83C211yesmaximal, characteristic, complemented
8C2×#13050589C2211yescharacteristic
9C23×Dic83C411yescharacteristic, complemented
10M16×D83—21no—
11#14581776C411yescharacteristic, complemented
12#14581773C2211yescharacteristic
13#14581769—21no—
14#14581764—21no—
15#14581761C411yescharacteristic, complemented
16D4×Dic83—21no—
17(C22⋊D83)⋊C4—21no—
18#14581748—21no—
19#14581748C411yescharacteristic, complemented
20#14581710—21no—
21#14581709C2211yescharacteristic
22#14581707C2211yescharacteristic
23#14581706—21no—
24#120×C83C2211yescharacteristic
25#100×C83C2211yescharacteristic
26#99×C83C2211yescharacteristic
27#13050589—41no—
28#13050589—41no—
29C2×Dic166D411yescharacteristic
30C2×C22⋊D83—21no—
31C2×C22⋊D83C2×C411yescharacteristic
32C2×C22⋊D83D411yescharacteristic
33C22×Dic83—21no—
34C22×Dic83—21no—
35C22×Dic83—41no—
36C22×Dic83—41no—
37C22×Dic83C2×C411yescharacteristic
38C22×Dic83C2×C411yescharacteristic
39C22×Dic83D411yescharacteristic
40C2×C4×D83D411yescharacteristic
41#13050574—21no—
42#13050573—41no—
43C8×D83—41no—
44C4⋊Dic83—21no—
45Dic83⋊C4—21no—
46Dic83⋊C4—21no—
47Dic83⋊C4—41no—
48C22⋊Dic83—21no—
49C22⋊Dic83—21no—
50C22⋊Dic83—21no—
51C22⋊Dic83C2×C411yescharacteristic
52(C2×D83)⋊C4—21no—
53C4×Dic83—21no—
54C4×Dic83—41no—
55C24×C83C2×C411yescharacteristic
56C2×D4×C83—21no—
57C2×D4×C83C2311yescharacteristic
58M16×C83—21no—
59C22⋊C4×C83—21no—
60C22⋊C4×C83—21no—
61C22⋊C4×C83C2×C411yescharacteristic
62C23×C83—21no—
63C23×C83—42no—
64C23×C83—41no—
65C23×C83C22×C411yescharacteristic
66C23×C83C2×D411yescharacteristic
67C22×D83C22⋊C411yescharacteristic
68D4×C83—41no—
69D4×C83—42no—
70C2×C4×C83—21no—
71C2×C4×C83—41no—
72C2×C4×C83C2×D411yescharacteristic
73C22⋊D83—41no—
74C22⋊D83—41no—
75C22⋊D83—42no—
76C2×Dic83—21no—
77C2×Dic83—21no—
78C2×Dic83—21no—
79C2×Dic83—21no—
80C2×Dic83—21no—
81C2×Dic83—21no—
82C2×Dic83—42no—
83C2×Dic83—41no—
84C2×Dic83—41no—
85C2×Dic83—41no—
86C2×Dic83—41no—
87C2×Dic83C22⋊C411yescharacteristic
88C2×Dic83C22⋊C411yescharacteristic
89C2×Dic83C22⋊C411yescharacteristic
90C4×D83—21no—
91C4×D83—21no—
92Dic166—41no—
93C8×C83—41no—
94C83⋊C8—41no—
95C22×C83—22no—
96C22×C83—21no—
97C22×C83—21no—
98C22×C83—41no—
99C22×C83—41no—
100C22×C83—41no—
101C22×C83—42no—
102C22×C83—42no—
103C22×C83—41no—
104C22×C83C2×C22⋊C411yescharacteristic
105C2×D83—21no—
106C2×D83—41no—
107C4×C83—21no—
108C4×C83—41no—
109C4×C83—81no—
110Dic83—21no—
111Dic83—21no—
112Dic83—41no—
113Dic83—41no—
114Dic83—81no—
115Dic83#9911yescharacteristic
116Dic83#9911yescharacteristic
117C2×C83—21no—
118C2×C83—41no—
119C2×C83—42no—
120C2×C83—41no—
121C2×C83C2×#9911yescharacteristic
122D83—41no—
123#2120—831nomaximal, Sylow
124C83#212011yescharacteristic, complemented, Sylow
125#525—831no—
126#413—831no—
127#410—831no—
128#352—831no—
129#352—831no—
130AΣL(1,𝔽16)—831no—
131AΣL(1,𝔽16)D8311yescharacteristic, complemented
132C2×#41—831no—
133C23×C4—831no—
134C2×M16—1661no—
135#123—831no—
136#123—831no—
137C22⋊Q8—1661no—
138#121—1661no—
139#120—831no—
140#120C2×D8311yescharacteristic
141C4×D4—1661no—
142C4×D4—1661no—
143#117—831no—
144#117—1661no—
145#101—1661no—
146#100—831no—
147#100C2×D8311yescharacteristic
148#99—831no—
149#99—1661no—
150#99C2×D8311yescharacteristic
151C24C4×D8311yescharacteristic
152#41—3321no—
153#41—3321no—
154C2×Q8—831no—
155C2×D4—21no—
156C2×D4—831no—
157C2×D4—831no—
158C2×D4—1661no—
159C2×D4C22×D8311yescharacteristic
160C22×C4—3321no—
161C22×C4—3321no—
162C22×C4—831no—
163C22×C4—831no—
164C22×C4—831no—
165C22×C4—831no—
166C22×C4—1661no—
167C22×C4—1661no—
168M16—21no—
169M16—3321no—
170M16—1661no—
171C2×C8—3321no—
172C4⋊C4—3321no—
173C4⋊C4—1661no—
174C4⋊C4—1661no—
175C4⋊C4—1661no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—831no—
179C22⋊C4—1661no—
180C22⋊C4—1661no—
181C22⋊C4—1661no—
182C22⋊C4—1661no—
183C22⋊C4C4×D8311yescharacteristic
184C42—3321no—
185C42—1661no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23—831no—
190C23C2×C4×D8311yescharacteristic
191C23D4×D8311yescharacteristic
192Q8—3321no—
193D4—41no—
194D4—42no—
195D4—3322no—
196D4—3321no—
197D4—3321no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—3321no—
201C2×C4—3321no—
202C2×C4—3322no—
203C2×C4—3321no—
204C2×C4—3321no—
205C2×C4—831no—
206C2×C4—831no—
207C2×C4—831no—
208C2×C4—1661no—
209C2×C4—1661no—
210C2×C4—1661no—
211C2×C4—1661no—
212C2×C4—1661no—
213C2×C4—1661no—
214C2×C4—1661no—
215C2×C4—1661no—
216C2×C4D4×D8311yescharacteristic
217C8—41no—
218C8—3321no—
219C22—22no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—3321no—
229C22—1661no—
230C22C22⋊C4×D8311yescharacteristic
231C4—21no—
232C4—41no—
233C4—81no—
234C4—3321no—
235C4—3321no—
236C4—831no—
237C4—831no—
238C4—6641no—
239C4—1661no—
240C4—1661no—
241C2—21no—
242C2—41no—
243C2—42no—
244C2—41no—
245C2—3321no—
246C2#99×D8311yescharacteristic
subgroupG/H
centerC2#99×D83
commutatorC23×C83C22×C4
FrattiniC2×D4C22×D83
FittingAΣL(1,𝔽16)×C83C2
socleC2×C83C2×#99
prime radical#19128207C2
cosocleC2×D4×C83C23
hypercenterAΣL(1,𝔽16)D83
hypocenterC83#2120
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #19127682C2semidirect
3. #19127673C2semidirect
4. #19127492C2semidirect
5. #19127490C2semidirect
6. #19127488C2semidirect
7. AΣL(1,𝔽16)×C83C2semidirect
9. C23×Dic83C4semidirect
11. #14581776C4semidirect
15. #14581761C4semidirect
19. #14581748C4semidirect
124. C83#2120semidirect
131. AΣL(1,𝔽16)D83semidirect

Maximal subgroups

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

subgroupindex
#191282072
#191276822
#191276732
#191274922
#191274902
#191274882
AΣL(1,𝔽16)×C832
#212083