Finite Group Databasebeta

← #24913293

Subgroups — #24913293

Order 10624.

472 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#14581784C211yesmaximal, characteristic, complemented
2#19127634C214yesmaximal, complemented
3#19127624C214yesmaximal
4#19127599C212yesmaximal, complemented
5#19127571C211yesmaximal, characteristic, complemented
6#19127561C212yesmaximal
7C2×#117×C83C211yesmaximal, characteristic
8#14581784—24no—
9C2×C4⋊Dic83C2212yes—
10C2×C4⋊Dic83C2212yes—
11C2×C4⋊Dic83C2214yes—
12C2×Dic83⋊C4C2214yes—
13C2×Dic83⋊C4C2214yes—
14C2×C22⋊Dic83C2214yes—
15C83⋊#95C2214yes—
16C83⋊#95C2214yes—
17C23×C4×C83C2211yescharacteristic
18#117×C83—24no—
19C2×C4⋊C4×C83C2212yes—
20C2×C22⋊C4×C83C2212yes—
21C2×C42×C83C2211yescharacteristic
22C2×C42×C83C2211yescharacteristic
23C22×Dic83C2314yes—
24C22×Dic83C2314yes—
25C4⋊Dic83—24no—
26C4⋊Dic83—24no—
27C4⋊Dic83—44no—
28Dic83⋊C4—28no—
29Dic83⋊C4—44no—
30C22⋊Dic83—44no—
31C24×C83C2311yescharacteristic
32C22×C4×C83—22no—
33C22×C4×C83—22no—
34C22×C4×C83Q814yes—
35C22×C4×C83C2312yes—
36C22×C4×C83C2312yes—
37C22×C4×C83C2311yescharacteristic
38C22×C4×C83C2311yescharacteristic
39C4⋊C4×C83—24no—
40C22⋊C4×C83—24no—
41C42×C83—22no—
42C42×C83D414yes—
43C23×C83—21no—
44C23×C83—21no—
45C23×C83—22no—
46C23×C83—22no—
47C23×C83C2×Q812yes—
48C23×C83C2411yescharacteristic
49C2×C4×C83—21no—
50C2×C4×C83—21no—
51C2×C4×C83—22no—
52C2×C4×C83—22no—
53C2×C4×C83—28no—
54C2×C4×C83—22no—
55C2×C4×C83—22no—
56C2×C4×C83—22no—
57C2×C4×C83C2×D414yes—
58C2×C4×C83C2×D412yes—
59C2×C4×C83C2×Q812yes—
60C2×C4×C83C2×Q812yes—
61C2×C4×C83#4112yes—
62C2×Dic83—24no—
63C2×Dic83—24no—
64C2×Dic83—24no—
65C2×Dic83—24no—
66C2×Dic83—24no—
67C2×Dic83—24no—
68C22×C83—22no—
69C22×C83—24no—
70C22×C83—42no—
71C22×C83—41no—
72C22×C83—41no—
73C22×C83C22×D411yescharacteristic
74C22×C83C22×Q811yescharacteristic
75C22×C83C2×#4111yescharacteristic
76C22×C83H(5,𝔽2)12yes—
77C22×C832−1+412yes—
78C4×C83—22no—
79C4×C83—24no—
80C4×C83—42no—
81C4×C83C22⋊Q814yes—
82Dic83—44no—
83Dic83—44no—
84C2×C83—42no—
85C2×C83C2×C22⋊Q811yescharacteristic
86C2×C83#53712yes—
87C2×C83#54011yescharacteristic
88C2×C83#54111yescharacteristic
89C2×C83#54412yes—
90#2629—831nomaximal, Sylow
91C83#262911yescharacteristic, complemented, Sylow
92C2×#125—831no—
93C2×#117D8311yescharacteristic
94#398—834no—
95#396—834no—
96#389—832no—
97#384—831no—
98#380—832no—
99C23×C4C2×D8311yescharacteristic
100#125—1664no—
101#117—24no—
102C2×C4⋊C4—834no—
103C2×C4⋊C4—834no—
104C2×C4⋊C4—832no—
105C2×C4⋊C4—834no—
106C2×C4⋊C4—832no—
107C2×C4⋊C4C2×D8312yes—
108C2×C22⋊C4—834no—
109C2×C22⋊C4C2×D8312yes—
110C2×C42C2×D8311yescharacteristic
111C2×C42C2×D8311yescharacteristic
112#95—834no—
113#95—834no—
114C24C22×D8311yescharacteristic
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—834no—
118C22×C4—834no—
119C22×C4Dic16614yes—
120C22×C4C22×D8312yes—
121C22×C4C22×D8312yes—
122C22×C4C22×D8311yescharacteristic
123C22×C4C22×D8311yescharacteristic
124C4⋊C4—24no—
125C4⋊C4—3324no—
126C4⋊C4—3324no—
127C4⋊C4—1668no—
128C4⋊C4—1664no—
129C4⋊C4—1664no—
130C22⋊C4—24no—
131C22⋊C4—3324no—
132C42—22no—
133C42C22⋊D8314yes—
134C23—21no—
135C23—21no—
136C23—22no—
137C23—22no—
138C23C2×Dic16612yes—
139C23C23×D8311yescharacteristic
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—28no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—1664no—
149C2×C4—1664no—
150C2×C4—1664no—
151C2×C4—1664no—
152C2×C4—1664no—
153C2×C4—1664no—
154C2×C4C2×C22⋊D8314yes—
155C2×C4C2×C22⋊D8312yes—
156C2×C4C2×Dic16612yes—
157C2×C4C2×Dic16612yes—
158C2×C4#1305059012yes—
159C22—24no—
160C22—22no—
161C22—42no—
162C22—41no—
163C22—41no—
164C22C22×C22⋊D8311yescharacteristic
165C22C22×Dic16611yescharacteristic
166C22C2×#1305059011yescharacteristic
167C22#1458183812yes—
168C22#1458183912yes—
169C4—22no—
170C4—24no—
171C4—42no—
172C4—3324no—
173C4—3324no—
174C4#1458177114yes—
175C2—42no—
176C2C2×#1458177111yescharacteristic
177C2#1912827912yes—
178C2#1912830611yescharacteristic
179C2#1912831311yescharacteristic
180C2#1912832912yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
FittingC2×#117×C83C2
prime radicalC24×C83C23
hypercenterC2×#117D83
hypocenterC83#2629
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#14581784C2semidirect
2. #19127634C2semidirect
4. #19127599C2semidirect
5. #19127571C2semidirect
91. C83#2629semidirect

Maximal subgroups

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

subgroupindex
C2×#145817842
#191276342
#191276242
#191275992
#191275712
#191275612
C2×#117×C832
#262983