Finite Group Databasebeta

← #24915729

Subgroups — #24915729

Order 10624.

348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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#19127642C212yesmaximal
2#19127640C211yesmaximal, characteristic
3#19127635C212yesmaximal
4#19127634C212yesmaximal
5#19127632C212yesmaximal
6#19127620C212yesmaximal
7#19127570C211yesmaximal, characteristic
8#19127568C212yesmaximal
9#395×C83C211yesmaximal, characteristic
10C2×C4⋊Dic83C2211yescharacteristic
11C2×C4⋊Dic83C2211yescharacteristic
12C2×Dic83⋊C4C2212yes—
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×C4×Dic83C2211yescharacteristic
18C83⋊#95C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2211yescharacteristic
25C83⋊#95C2212yes—
26C22×Q8×C83C2211yescharacteristic
27C2×C4⋊C4×C83C2211yescharacteristic
28C2×C4⋊C4×C83C2212yes—
29#95×C83C2212yes—
30#95×C83C2211yescharacteristic
31C22×Dic83C2312yes—
32C22×Dic83C2312yes—
33C22×Dic83C2312yes—
34C22×Dic83C2312yes—
35C4⋊Dic83—41no—
36C4⋊Dic83—41no—
37Dic83⋊C4—42no—
38Dic83⋊C4—42no—
39Dic83⋊C4—42no—
40Dic83⋊C4—42no—
41Dic83⋊C4—42no—
42C4×Dic83Q814yescomplemented
43C2×Q8×C83—42no—
44C2×Q8×C83—41no—
45C22×C4×C83C2312yes—
46C22×C4×C83C2312yes—
47C22×C4×C83C2311yescharacteristic
48C22×C4×C83C2311yescharacteristic
49C22×C4×C83C2311yescharacteristic
50C4⋊C4×C83—41no—
51C4⋊C4×C83—42no—
52C23×C83C2411yescharacteristic
53Q8×C83—44no—
54C2×C4×C83—21no—
55C2×C4×C83—21no—
56C2×C4×C83—22no—
57C2×C4×C83—21no—
58C2×C4×C83—22no—
59C2×C4×C83—22no—
60C2×C4×C83—21no—
61C2×C4×C83—22no—
62C2×C4×C83—22no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83C2×Q812yes—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—22no—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—24no—
77C2×Dic83C2×Q814yes—
78C22×C83C22×Q811yescharacteristic
79C22×C83H(5,𝔽2)12yes—
80C22×C83H(5,𝔽2)11yescharacteristic
81C22×C832−1+411yescharacteristic
82C22×C832−1+412yes—
83C4×C83—22no—
84C4×C83—41no—
85C4×C83—42no—
86C4×C83—41no—
87C4×C83—42no—
88Dic83—24no—
89Dic83—42no—
90Dic83—42no—
91Dic83—42no—
92C2×C83#54412yes—
93C2×C83#54411yescharacteristic
94C2×C83#56011yescharacteristic
95C2×C83#56311yescharacteristic
96C2×C83#56312yes—
97#2843—831nomaximal, Sylow
98C83#284311yescharacteristic, complemented, Sylow
99#400—831no—
100#400—832no—
101#398—832no—
102#398—832no—
103#398—832no—
104#395—832no—
105#395D8311yescharacteristic
106#384—831no—
107#383—832no—
108C22×Q8C2×D8311yescharacteristic
109C2×C4⋊C4—832no—
110C2×C4⋊C4—832no—
111C2×C4⋊C4—831no—
112C2×C4⋊C4—832no—
113C2×C4⋊C4—832no—
114C2×C4⋊C4—832no—
115C2×C4⋊C4—831no—
116C2×C4⋊C4C2×D8311yescharacteristic
117C2×C4⋊C4C2×D8312yes—
118C2×C42—831no—
119#95—832no—
120#95—832no—
121#95—832no—
122#95—832no—
123#95—832no—
124#95—832no—
125#95—831no—
126#95—832no—
127#95C2×D8312yes—
128#95C2×D8311yescharacteristic
129C2×Q8—42no—
130C2×Q8—41no—
131C22×C4—832no—
132C22×C4—832no—
133C22×C4—832no—
134C22×C4—832no—
135C22×C4C22×D8312yes—
136C22×C4C22×D8312yes—
137C22×C4C22×D8311yescharacteristic
138C22×C4C22×D8311yescharacteristic
139C22×C4C22×D8311yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—3322no—
143C4⋊C4—3322no—
144C4⋊C4—3322no—
145C4⋊C4—3322no—
146C4⋊C4—3322no—
147C4⋊C4—3321no—
148C4⋊C4—3321no—
149C42—834no—
150C23C23×D8311yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—834no—
165C2×C4—1662no—
166C2×C4—1662no—
167C2×C4—1662no—
168C2×C4—1662no—
169C2×C4—1662no—
170C2×C4—1662no—
171C2×C4—1664no—
172C2×C4—1662no—
173C2×C4—1662no—
174C2×C4—1662no—
175C2×C4Q8×D8312yes—
176C22C2×Q8×D8311yescharacteristic
177C22#1458183712yes—
178C22#1458183711yescharacteristic
179C22#1458183911yescharacteristic
180C22#1458184012yes—
181C4—22no—
182C4—42no—
183C4—41no—
184C4—41no—
185C4—42no—
186C4—3322no—
187C4—3322no—
188C4—3322no—
189C4—1664no—
190C2#1912832812yes—
191C2#1912833011yescharacteristic
192C2#1912844011yescharacteristic
193C2#1912845011yescharacteristic
194C2#1912845212yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#395×C83C2
hypercenter#395D83
hypocenterC83#2843
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
42. C4×Dic83Q8semidirect
98. C83#2843semidirect

Maximal subgroups

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

subgroupindex
#191276422
#191276402
#191276352
#191276342
#191276322
#191276202
#191275702
#191275682
#395×C832
#284383