Finite Group Databasebeta

← #27193511

Subgroups — #27193511

Order 13184.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15693015C211yesmaximal, characteristic
2#20267848C211yesmaximal, characteristic, complemented
3#20267516C212yesmaximal, complemented
4#20267514C212yesmaximal
5#431×C103C211yesmaximal, characteristic, complemented
6#15693015—21no—
7#15693015—21no—
8#15693015—21no—
9#15693015—21no—
10C2×Dic103⋊C4C411yescharacteristic
11C2×Dic103⋊C4C411yescharacteristic
12C2×Dic103⋊C4C2211yescharacteristic
13C2×(C2×D103)⋊C4C411yescharacteristic
14C2×(C2×D103)⋊C4C411yescharacteristic
15C2×(C2×D103)⋊C4C2211yescharacteristic
16C4⋊(C103⋊C8)—21no—
17C22⋊(C103⋊C8)C2212yes—
18#15692932—21no—
19C2×C42×C103C2211yescharacteristic
20C4⋊C8×C103—21no—
21C22⋊C8×C103C2212yes—
22C4×C8×C103—21no—
23C23×D103C2×C411yescharacteristic
24C22×Dic103C2×C411yescharacteristic
25C22×Dic103C2×C411yescharacteristic
26C22×Dic103C2×C411yescharacteristic
27C2×C103⋊C8—22no—
28Dic103⋊C4—21no—
29Dic103⋊C4—21no—
30Dic103⋊C4—21no—
31Dic103⋊C4—21no—
32Dic103⋊C4—21no—
33Dic103⋊C4—21no—
34(C2×D103)⋊C4—21no—
35(C2×D103)⋊C4—21no—
36(C2×D103)⋊C4—21no—
37(C2×D103)⋊C4—21no—
38(C2×D103)⋊C4—21no—
39(C2×D103)⋊C4—21no—
40C22×C4×C103C2×C411yescharacteristic
41C22×C4×C103C2×C411yescharacteristic
42C22×C4×C103C2311yescharacteristic
43C2×C8×C103—22no—
44C42×C103D411yescharacteristic
45C42×C103D411yescharacteristic
46C42×C103D411yescharacteristic
47C42×C103D411yescharacteristic
48C23×C103C22×C411yescharacteristic
49C22×D103—21no—
50C22×D103—22no—
51C22×D103—41no—
52C22×D103—41no—
53C2×C4×C103—22no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103C22⋊C411yescharacteristic
57C2×C4×C103C22⋊C411yescharacteristic
58C2×C4×C103C22⋊C411yescharacteristic
59C2×C4×C103C22⋊C411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C2×Dic103—21no—
63C2×Dic103—21no—
64C2×Dic103—21no—
65C2×Dic103—22no—
66C2×Dic103—41no—
67C2×Dic103—41no—
68C8×C103—42no—
69C103⋊C8—42no—
70C22×C103—21no—
71C22×C103—21no—
72C22×C103C2×C22⋊C411yescharacteristic
73C22×C103#13112yes—
74C2×D103—41no—
75C2×D103—41no—
76C2×D103—41no—
77C2×D103—82no—
78C4×C103—21no—
79C4×C103—21no—
80C4×C103—21no—
81C4×C103—21no—
82C4×C103—21no—
83C4×C103—21no—
84Dic103—41no—
85Dic103—41no—
86Dic103—41no—
87C2×C103—22no—
88C2×C103#40811yescharacteristic
89C2×C103#41011yescharacteristic
90C2×C103#41311yescharacteristic
91D103—81no—
92#1473—1031nomaximal, Sylow
93C103#147311yescharacteristic, complemented, Sylow
94C2×#126—1031no—
95#432—1031no—
96#431D10311yescharacteristic, complemented
97#324—1032no—
98#323—1032no—
99#126—2061no—
100#126—2061no—
101#126—2061no—
102#126—2061no—
103C2×C4⋊C4—1031no—
104C2×C4⋊C4—1031no—
105C2×C4⋊C4—1031no—
106C2×C22⋊C4—1031no—
107C2×C22⋊C4—1031no—
108C2×C22⋊C4—1031no—
109C2×C42C2×D10311yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—2061no—
112C22⋊C8—1032no—
113C22⋊C8C2×D10312yes—
114#97—2061no—
115C4×C8—21no—
116C24—1031no—
117C22×C4—1031no—
118C22×C4—1031no—
119C22×C4—1031no—
120C22×C4C4×D10311yescharacteristic
121C22×C4C4×D10311yescharacteristic
122C22×C4C22×D10311yescharacteristic
123C2×C8—22no—
124C2×C8—2062no—
125C4⋊C4—2061no—
126C4⋊C4—2061no—
127C4⋊C4—2061no—
128C4⋊C4—2061no—
129C4⋊C4—2061no—
130C4⋊C4—2061no—
131C22⋊C4—2061no—
132C22⋊C4—2061no—
133C22⋊C4—2061no—
134C22⋊C4—2061no—
135C22⋊C4—2061no—
136C22⋊C4—2061no—
137C42D41211yescharacteristic
138C42D41211yescharacteristic
139C42C22⋊D10311yescharacteristic
140C42C22⋊D10311yescharacteristic
141C23—4121no—
142C23—4121no—
143C23—2062no—
144C23—2061no—
145C23C2×C4×D10311yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—4121no—
150C2×C4—4121no—
151C2×C4—2061no—
152C2×C4—2061no—
153C2×C4—2061no—
154C2×C4—2062no—
155C2×C4(C2×D103)⋊C411yescharacteristic
156C2×C4(C2×D103)⋊C411yescharacteristic
157C2×C4(C2×D103)⋊C411yescharacteristic
158C2×C4(C2×D103)⋊C411yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C2×C4C2×D41211yescharacteristic
161C8—42no—
162C8—4122no—
163C22—21no—
164C22—21no—
165C22—8242no—
166C22—4121no—
167C22—4121no—
168C22—4121no—
169C22C2×(C2×D103)⋊C411yescharacteristic
170C22#1569302712yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—4121no—
178C4—4121no—
179C4—4121no—
180C2—22no—
181C2—8241no—
182C2#2026775711yescharacteristic
183C2#2026776411yescharacteristic
184C2#2026777311yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#431×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×D103C2×C4
cosocleC22×C4×C103C23
hypercenter#431D103
hypocenterC103#1473
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #20267848C2semidirect
3. #20267516C2semidirect
5. #431×C103C2semidirect
93. C103#1473semidirect
96. #431D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930152
#202678482
#202675162
#202675142
#431×C1032
#1473103