Finite Group Databasebeta

← #24912852

Subgroups — #24912852

Order 10624.

468 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 169 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×C4×Dic166C211yesmaximal, characteristic
2#19127631C212yesmaximal
3#19127621C212yesmaximal
4#19127597C212yesmaximal
5#19127597C212yesmaximal
6#19127596C214yesmaximal
7C4×C4⋊Dic83C211yesmaximal, characteristic
8C2×#125×C83C211yesmaximal, characteristic
9C22×Dic166C2211yescharacteristic
10C4×Dic166—24no—
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2212yes—
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2214yes—
15C2×Dic83⋊C4C2214yes—
16C2×C4×Dic83C2212yes—
17C2×C4×Dic83C2212yes—
18C83⋊#95C2212yes—
19C83⋊#95C2214yes—
20C83⋊#95C2214yes—
21#125×C83—24no—
22C2×C4⋊C4×C83C2212yes—
23C2×C4⋊C4×C83C2211yescharacteristic
24C2×C4⋊C4×C83C2211yescharacteristic
25C2×C4⋊C4×C83C2212yes—
26C2×C42×C83C2211yescharacteristic
27C2×Dic166—22no—
28C2×Dic166—24no—
29C22×Dic83C2312yes—
30C22×Dic83C2314yes—
31C22×Dic83C2312yes—
32C4⋊Dic83—22no—
33C4⋊Dic83Q818yescomplemented
34Dic83⋊C4—24no—
35Dic83⋊C4—28no—
36Dic83⋊C4—44no—
37C4×Dic83—24no—
38C4×Dic83—42no—
39C22×C4×C83C2312yes—
40C22×C4×C83C2312yes—
41C22×C4×C83C2311yescharacteristic
42C22×C4×C83C2311yescharacteristic
43C22×C4×C83C2311yescharacteristic
44C4⋊C4×C83—24no—
45C4⋊C4×C83—24no—
46C4⋊C4×C83—22no—
47C4⋊C4×C83—22no—
48C42×C83D414yes—
49C23×C83C2411yescharacteristic
50C2×C4×C83—22no—
51C2×C4×C83—21no—
52C2×C4×C83—21no—
53C2×C4×C83—22no—
54C2×C4×C83—22no—
55C2×C4×C83—24no—
56C2×C4×C83—22no—
57C2×C4×C83—22no—
58C2×C4×C83C2×D412yes—
59C2×C4×C83C2×D412yes—
60C2×C4×C83C2×D412yes—
61C2×C4×C83C2×Q814yes—
62C2×Dic83—22no—
63C2×Dic83—24no—
64C2×Dic83—22no—
65C2×Dic83—24no—
66C2×Dic83—22no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83C2×Q818yes—
70C2×Dic83#4114yes—
71Dic166—28no—
72C22×C83C22×D411yescharacteristic
73C22×C83C22×Q812yes—
74C22×C83C2×#4112yes—
75C22×C83H(5,𝔽2)11yescharacteristic
76C22×C832−1+411yescharacteristic
77C4×C83—22no—
78C4×C83—22no—
79C4×C83—42no—
80C4×C83—42no—
81C4×C83C4⋊Q814yes—
82Dic83—24no—
83Dic83—28no—
84Dic83—42no—
85C2×C83#52511yescharacteristic
86C2×C83C2×C4⋊Q811yescharacteristic
87C2×C83#53711yescharacteristic
88C2×C83#55412yes—
89C2×C83#55712yes—
90#2584—831nomaximal, Sylow
91C83#258411yescharacteristic, complemented, Sylow
92C2×#125D8311yescharacteristic
93C2×C4×Q8—831no—
94#398—832no—
95#395—832no—
96#389—834no—
97#389—832no—
98#389—832no—
99C4×C4⋊C4—831no—
100C22×Q8—831no—
101#125—24no—
102C4×Q8—1664no—
103C2×C4⋊C4—834no—
104C2×C4⋊C4—832no—
105C2×C4⋊C4—832no—
106C2×C4⋊C4—831no—
107C2×C4⋊C4—834no—
108C2×C4⋊C4C2×D8312yes—
109C2×C4⋊C4C2×D8311yescharacteristic
110C2×C4⋊C4C2×D8311yescharacteristic
111C2×C4⋊C4C2×D8312yes—
112C2×C42—832no—
113C2×C42—832no—
114C2×C42C2×D8311yescharacteristic
115#95—832no—
116#95—834no—
117#95—834no—
118C2×Q8—1664no—
119C2×Q8—1662no—
120C22×C4—834no—
121C22×C4—832no—
122C22×C4—832no—
123C22×C4C22×D8312yes—
124C22×C4C22×D8312yes—
125C22×C4C22×D8311yescharacteristic
126C22×C4C22×D8311yescharacteristic
127C22×C4C22×D8311yescharacteristic
128C4⋊C4—24no—
129C4⋊C4—24no—
130C4⋊C4—22no—
131C4⋊C4—22no—
132C4⋊C4—3324no—
133C4⋊C4—838no—
134C4⋊C4—1668no—
135C4⋊C4—1664no—
136C4⋊C4—1662no—
137C42—3322no—
138C42—1664no—
139C42C22⋊D8314yes—
140C23C23×D8311yescharacteristic
141Q8—1668no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—24no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—838no—
151C2×C4—834no—
152C2×C4—1662no—
153C2×C4—1662no—
154C2×C4—1662no—
155C2×C4—1662no—
156C2×C4—1664no—
157C2×C4—1662no—
158C2×C4—1664no—
159C2×C4C2×C22⋊D8312yes—
160C2×C4C2×C22⋊D8312yes—
161C2×C4C2×C22⋊D8312yes—
162C2×C4Q8×D8314yes—
163C22C22×C22⋊D8311yescharacteristic
164C22C2×Q8×D8312yes—
165C22#41×D8312yes—
166C22#1458183811yescharacteristic
167C22#1458183911yescharacteristic
168C4—22no—
169C4—22no—
170C4—42no—
171C4—42no—
172C4—3322no—
173C4—1668no—
174C4—1664no—
175C4#1458179014yes—
176C2#1912820811yescharacteristic
177C2C2×#1458179011yescharacteristic
178C2#1912827911yescharacteristic
179C2#1912840712yes—
180C2#1912842812yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
FittingC2×#125×C83C2
hypercenterC2×#125D83
hypocenterC83#2584
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
33. C4⋊Dic83Q8semidirect
91. C83#2584semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic1662
#191276312
#191276212
#191275972
#191275962
C4×C4⋊Dic832
C2×#125×C832
#258483