Finite Group Databasebeta

← #27169401

Subgroups — #27169401

Order 12928.

520 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 193 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
1C22×C4⋊Dic101C211yesmaximal, characteristic
2C2×#15692162C214yesmaximal
3C2×#15692162C211yesmaximal, characteristic
4C2×#95×C101C211yesmaximal, characteristic
5C23×Dic101C2212yes—
6C23×Dic101C2212yes—
7C2×C4⋊Dic101—22no—
8C2×C4⋊Dic101—22no—
9C2×C4⋊Dic101C414yescomplemented
10#15692162—28no—
11#15692162—22no—
12C23×C4×C101C2212yes—
13C23×C4×C101C2211yescharacteristic
14#95×C101—22no—
15C22×Dic101—24no—
16C22×Dic101—22no—
17C22×Dic101—22no—
18C22×Dic101—22no—
19C22×Dic101—24no—
20C22×Dic101—24no—
21C22×Dic101—24no—
22C22×Dic101—22no—
23C22×Dic101C2×C414yes—
24C22×Dic101D414yes—
25C4⋊Dic101—28no—
26C24×C101C2311yescharacteristic
27C22×C4×C101—24no—
28C22×C4×C101—22no—
29C22×C4×C101—24no—
30C22×C4×C101—24no—
31C22×C4×C101—22no—
32C22×C4×C101C2×C412yes—
33C22×C4×C101D412yes—
34C22×C4×C101D412yes—
35C22×C4×C101Q814yes—
36C23×C101C22×C411yescharacteristic
37C23×C101C2×D412yes—
38C23×C101C2×D411yescharacteristic
39C23×C101C2×D411yescharacteristic
40C23×C101C2×Q812yes—
41C23×C101#4114yes—
42C23×C101#4112yes—
43C23×C101#4112yes—
44C2×C4×C101—24no—
45C2×C4×C101—24no—
46C2×C4×C101—24no—
47C2×C4×C101—28no—
48C2×C4×C101—24no—
49C2×C4×C101—42no—
50C2×C4×C101—44no—
51C2×C4×C101—42no—
52C2×C4×C101C22⋊C414yes—
53C2×Dic101—24no—
54C2×Dic101—28no—
55C2×Dic101—24no—
56C2×Dic101—28no—
57C2×Dic101—44no—
58C2×Dic101—42no—
59C2×Dic101—42no—
60C2×Dic101—42no—
61C2×Dic101—44no—
62C2×Dic101—42no—
63C22×C101C2×C22⋊C411yescharacteristic
64C22×C101#11712yes—
65C22×C101C4×D412yes—
66C22×C101C4×Q812yes—
67C22×C101#12112yes—
68C22×C101C22⋊Q814yes—
69C22×C101C22⋊Q812yes—
70C22×C101#12312yes—
71C22×C101#12314yes—
72C22×C101#12312yes—
73C22×C101#12411yescharacteristic
74C22×C101#12411yescharacteristic
75C22×C101#12514yes—
76C22×C101#12614yes—
77C22×C101#12711yescharacteristic
78C22×C101C4⋊Q811yescharacteristic
79C4×C101—24no—
80C4×C101—44no—
81Dic101—44no—
82Dic101—44no—
83C2×C101#38111yescharacteristic
84C2×C101#38714yes—
85C2×C101#39011yescharacteristic
86C2×C101#39111yescharacteristic
87C2×C101#39712yes—
88C2×C101#39812yes—
89C2×C101#39912yes—
90C2×C101#40012yes—
91#1445—1011nomaximal, Sylow
92C101#144511yescharacteristic, complemented, Sylow
93C22×C4⋊C4—1011no—
94C2×#95—1014no—
95C2×#95—1011no—
96C2×#95D10111yescharacteristic
97C23×C4—1012no—
98C23×C4—1012no—
99C23×C4C2×D10112yes—
100C23×C4C2×D10111yescharacteristic
101C2×C4⋊C4—1014no—
102C2×C4⋊C4—2022no—
103C2×C4⋊C4—2022no—
104#95—22no—
105#95—2028no—
106#95—2022no—
107C24C22×D10111yescharacteristic
108C22×C4—24no—
109C22×C4—24no—
110C22×C4—22no—
111C22×C4—24no—
112C22×C4—22no—
113C22×C4—1014no—
114C22×C4—1014no—
115C22×C4—2024no—
116C22×C4—2022no—
117C22×C4—2022no—
118C22×C4—2022no—
119C22×C4—2024no—
120C22×C4—2024no—
121C22×C4—2024no—
122C22×C4—2022no—
123C22×C4Dic20214yes—
124C22×C4C4×D10112yes—
125C22×C4D40412yes—
126C22×C4C22⋊D10112yes—
127C4⋊C4—2028no—
128C23C2×C4×D10111yescharacteristic
129C23D4×D10112yes—
130C23C2×C22⋊D10111yescharacteristic
131C23C2×D40411yescharacteristic
132C23C2×Dic20212yes—
133C23#1310807314yes—
134C23#1310807412yes—
135C23#1310807512yes—
136C2×C4—24no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—28no—
140C2×C4—24no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4—42no—
144C2×C4—4044no—
145C2×C4—4042no—
146C2×C4—4042no—
147C2×C4—4042no—
148C2×C4—4044no—
149C2×C4—4042no—
150C2×C4—2024no—
151C2×C4—2028no—
152C2×C4—2024no—
153C2×C4—2028no—
154C2×C4#1310805114yes—
155C22C2×#1310805111yescharacteristic
156C22#1569221112yes—
157C22#1569221712yes—
158C22C4×Dic20212yes—
159C22#1569223012yes—
160C22#1569223214yes—
161C22#1569223412yes—
162C22#1569223612yes—
163C22#1569223714yes—
164C22#1569223912yes—
165C22#1569224311yescharacteristic
166C22#1569224411yescharacteristic
167C22#1569224614yes—
168C22#1569225014yes—
169C22#1569225111yescharacteristic
170C22#1569225511yescharacteristic
171C4—24no—
172C4—44no—
173C4—4044no—
174C4—4044no—
175C2#2026503811yescharacteristic
176C2#2026506014yes—
177C2#2026507811yescharacteristic
178C2#2026508311yescharacteristic
179C2#2026510412yes—
180C2#2026510912yes—
181C2#2026511312yes—
182C2#2026511612yes—
subgroupG/H
center, FrattiniC24C22×D101
commutatorC23×C101C22×C4
FittingC2×#95×C101C2
socle, prime radical, cosocleC24×C101C23
hypercenterC2×#95D101
hypocenterC101#1445
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
9. C2×C4⋊Dic101C4semidirect
92. C101#1445semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1012
C2×#156921622
C2×#95×C1012
#1445101