Finite Group Databasebeta

← #27193412

Subgroups — #27193412

Order 13184.

520 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 197 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×C103⋊#95C211yesmaximal, characteristic
2C2×C103⋊#95C214yesmaximal
3C2×C103⋊#95C211yesmaximal, characteristic
4C22×C4⋊C4×C103C211yesmaximal, characteristic
5C23×Dic103C2212yes—
6C23×Dic103C2212yes—
7C103⋊#95—28no—
8C103⋊#95—22no—
9C103⋊#95—22no—
10C23×C4×C103C2212yes—
11C23×C4×C103C2211yescharacteristic
12C2×C4⋊C4×C103—22no—
13C2×C4⋊C4×C103—22no—
14C2×C4⋊C4×C103C414yescomplemented
15C22×Dic103—24no—
16C22×Dic103—22no—
17C22×Dic103—22no—
18C22×Dic103—22no—
19C22×Dic103—24no—
20C22×Dic103—24no—
21C22×Dic103—22no—
22C22×Dic103—24no—
23C22×Dic103D414yes—
24C22×Dic103Q814yes—
25C24×C103C2311yescharacteristic
26C22×C4×C103—24no—
27C22×C4×C103—22no—
28C22×C4×C103—22no—
29C22×C4×C103—24no—
30C22×C4×C103—24no—
31C22×C4×C103C2×C414yes—
32C22×C4×C103C2×C412yes—
33C22×C4×C103D412yes—
34C22×C4×C103D412yes—
35C4⋊C4×C103—28no—
36C23×C103C22×C411yescharacteristic
37C23×C103C2×D412yes—
38C23×C103C2×D411yescharacteristic
39C23×C103C2×D411yescharacteristic
40C23×C103C2×Q812yes—
41C23×C103#4112yes—
42C23×C103#4114yes—
43C23×C103#4112yes—
44C2×C4×C103—24no—
45C2×C4×C103—24no—
46C2×C4×C103—24no—
47C2×C4×C103—24no—
48C2×C4×C103—28no—
49C2×C4×C103—44no—
50C2×C4×C103—42no—
51C2×C4×C103—42no—
52C2×C4×C103C22⋊C414yes—
53C2×Dic103—24no—
54C2×Dic103—24no—
55C2×Dic103—28no—
56C2×Dic103—28no—
57C2×Dic103—42no—
58C2×Dic103—42no—
59C2×Dic103—44no—
60C2×Dic103—42no—
61C2×Dic103—44no—
62C2×Dic103—42no—
63C22×C103C2×C22⋊C411yescharacteristic
64C22×C103#11712yes—
65C22×C103C4×D412yes—
66C22×C103C4×Q812yes—
67C22×C103#12112yes—
68C22×C103C22⋊Q812yes—
69C22×C103C22⋊Q814yes—
70C22×C103#12312yes—
71C22×C103#12312yes—
72C22×C103#12314yes—
73C22×C103#12411yescharacteristic
74C22×C103#12411yescharacteristic
75C22×C103#12514yes—
76C22×C103#12614yes—
77C22×C103#12711yescharacteristic
78C22×C103C4⋊Q811yescharacteristic
79C4×C103—24no—
80C4×C103—44no—
81Dic103—44no—
82Dic103—44no—
83C2×C103#38111yescharacteristic
84C2×C103#38714yes—
85C2×C103#39011yescharacteristic
86C2×C103#39111yescharacteristic
87C2×C103#39712yes—
88C2×C103#39812yes—
89C2×C103#39912yes—
90C2×C103#40012yes—
91#1445—1031nomaximal, Sylow
92C103#144511yescharacteristic, complemented, Sylow
93C22×C4⋊C4D10311yescharacteristic
94C2×#95—1034no—
95C2×#95—1031no—
96C2×#95—1031no—
97C23×C4—1032no—
98C23×C4—1032no—
99C23×C4C2×D10312yes—
100C23×C4C2×D10311yescharacteristic
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4Dic10314yescomplemented
104#95—2068no—
105#95—2062no—
106#95—2062no—
107C24C22×D10311yescharacteristic
108C22×C4—24no—
109C22×C4—24no—
110C22×C4—22no—
111C22×C4—22no—
112C22×C4—24no—
113C22×C4—1034no—
114C22×C4—1034no—
115C22×C4—2064no—
116C22×C4—2062no—
117C22×C4—2062no—
118C22×C4—2062no—
119C22×C4—2064no—
120C22×C4—2064no—
121C22×C4—2062no—
122C22×C4—2064no—
123C22×C4C2×Dic10314yes—
124C22×C4C2×Dic10312yes—
125C22×C4C22⋊D10312yes—
126C22×C4C22⋊D10312yes—
127C4⋊C4—28no—
128C23C22×Dic10311yescharacteristic
129C23D4×D10312yes—
130C23C2×C22⋊D10311yescharacteristic
131C23C2×C22⋊D10311yescharacteristic
132C23Q8×D10312yes—
133C23#1311010412yes—
134C23#1311010514yes—
135C23#1311010612yes—
136C2×C4—24no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—28no—
141C2×C4—44no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—4122no—
145C2×C4—4122no—
146C2×C4—4124no—
147C2×C4—4122no—
148C2×C4—4124no—
149C2×C4—4122no—
150C2×C4—2064no—
151C2×C4—2064no—
152C2×C4—2068no—
153C2×C4—2068no—
154C2×C4C22⋊Dic10314yes—
155C22C2×C22⋊Dic10311yescharacteristic
156C22#1569298012yes—
157C22D4×Dic10312yes—
158C22Q8×Dic10312yes—
159C22#1569299212yes—
160C22#1569299712yes—
161C22#1569299914yes—
162C22#1569300412yes—
163C22#1569300412yes—
164C22#1569300614yes—
165C22#1569300811yescharacteristic
166C22#1569301011yescharacteristic
167C22#1569301114yes—
168C22#1569301614yes—
169C22#1569301711yescharacteristic
170C22#1569301911yescharacteristic
171C4—24no—
172C4—44no—
173C4—4124no—
174C4—4124no—
175C2#2026765411yescharacteristic
176C2#2026767714yes—
177C2#2026769411yescharacteristic
178C2#2026769811yescharacteristic
179C2#2026771712yes—
180C2#2026772212yes—
181C2#2026772612yes—
182C2#2026772912yes—
subgroupG/H
center, FrattiniC24C22×D103
commutatorC23×C103C22×C4
FittingC22×C4⋊C4×C103C2
socle, prime radical, cosocleC24×C103C23
hypercenterC22×C4⋊C4D103
hypocenterC103#1445
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. C2×C4⋊C4×C103C4semidirect
92. C103#1445semidirect
103. C2×C4⋊C4Dic103semidirect

Maximal subgroups

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

subgroupindex
C2×C103⋊#952
C22×C4⋊C4×C1032
#1445103