Finite Group Databasebeta

← #27193493

Subgroups — #27193493

Order 13184.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#15693004C211yesmaximal, characteristic
2C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
3#20267516C212yesmaximal, complemented
4#20267514C212yesmaximal, complemented
5#407×C103C211yesmaximal, characteristic, complemented
6C22×C22⋊D103C411yescharacteristic
7C22×C103⋊C8—21no—
8#15693004—21no—
9#15693004—21no—
10#15693004—21no—
11#15693004—21no—
12C2×Dic103⋊C4C411yescharacteristic
13C2×Dic103⋊C4C2211yescharacteristic
14C2×C22⋊Dic103C411yescharacteristic
15C2×(C2×D103)⋊C4C411yescharacteristic
16C2×(C2×D103)⋊C4C2211yescharacteristic
17C22⋊(C103⋊C8)—21no—
18C22⋊(C103⋊C8)C2212yes—
19C23×C4×C103C2211yescharacteristic
20C2×M16×C103—21no—
21C22⋊C8×C103—21no—
22C22⋊C8×C103C2212yes—
23C23×D103C2×C411yescharacteristic
24C2×C22⋊D103—21no—
25C2×C22⋊D103—21no—
26C2×C22⋊D103—42no—
27C22×Dic103C2×C411yescharacteristic
28C22×Dic103C2×C411yescharacteristic
29C22×Dic103C2×C411yescharacteristic
30C2×C103⋊C8—22no—
31C2×C103⋊C8—42no—
32Dic103⋊C4—21no—
33Dic103⋊C4—21no—
34Dic103⋊C4—21no—
35Dic103⋊C4—21no—
36C22⋊Dic103—21no—
37C22⋊Dic103—21no—
38(C2×D103)⋊C4—21no—
39(C2×D103)⋊C4—21no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42C24×C103C2×C411yescharacteristic
43C22×C4×C103—42no—
44C22×C4×C103C2×C411yescharacteristic
45C22×C4×C103D411yescharacteristic
46C22×C4×C103D411yescharacteristic
47C22×C4×C103D411yescharacteristic
48C22×C4×C103D411yescharacteristic
49C22×C4×C103C2311yescharacteristic
50M16×C103—42no—
51C2×C8×C103—22no—
52C23×C103—22no—
53C23×C103—22no—
54C23×C103—41no—
55C23×C103C22⋊C411yescharacteristic
56C23×C103C22⋊C411yescharacteristic
57C23×C103C22×C411yescharacteristic
58C22×D103—21no—
59C22×D103—22no—
60C22×D103—41no—
61C22×D103—41no—
62C2×C4×C103—22no—
63C2×C4×C103—22no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103—41no—
68C2×C4×C103C22⋊C411yescharacteristic
69C2×C4×C103C22⋊C411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2×D411yescharacteristic
72C22⋊D103—42no—
73C22⋊D103—42no—
74C2×Dic103—21no—
75C2×Dic103—21no—
76C2×Dic103—21no—
77C2×Dic103—22no—
78C2×Dic103—41no—
79C2×Dic103—41no—
80C8×C103—42no—
81C103⋊C8—42no—
82C22×C103—21no—
83C22×C103—21no—
84C22×C103—21no—
85C22×C103—21no—
86C22×C103—21no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—44no—
90C22×C103#9912yes—
91C22×C103C2×C22⋊C411yescharacteristic
92C22×C103#13112yes—
93C2×D103—41no—
94C2×D103—41no—
95C2×D103—41no—
96C2×D103—82no—
97C4×C103—21no—
98C4×C103—21no—
99C4×C103—21no—
100C4×C103—21no—
101Dic103—41no—
102Dic103—41no—
103Dic103—41no—
104C2×C103—22no—
105C2×C103—22no—
106C2×C103—41no—
107C2×C103#40811yescharacteristic
108C2×C103C2×#9911yescharacteristic
109C2×C103#41311yescharacteristic
110D103—81no—
111#1468—1031nomaximal, Sylow
112C103#146811yescharacteristic, complemented, Sylow
113C2×#123—1031no—
114#407D10311yescharacteristic, complemented
115C2×C22⋊C8—1031no—
116#324—1032no—
117#323—1032no—
118C22×D4—1031no—
119C23×C4C2×D10311yescharacteristic
120C2×M16—21no—
121C22×C8—2061no—
122#123—2061no—
123#123—2061no—
124#123—2061no—
125#123—2061no—
126C2×C4⋊C4—1031no—
127C2×C4⋊C4—1031no—
128C2×C22⋊C4—1031no—
129C2×C22⋊C4—1031no—
130C2×C22⋊C4—1031no—
131C22⋊C8—21no—
132C22⋊C8—1032no—
133C22⋊C8—2061no—
134C22⋊C8C2×D10312yes—
135C24—1031no—
136C24C4×D10311yescharacteristic
137C2×D4—4122no—
138C2×D4—2061no—
139C2×D4—2061no—
140C22×C4—42no—
141C22×C4—1031no—
142C22×C4—1031no—
143C22×C4—1031no—
144C22×C4C4×D10311yescharacteristic
145C22×C4D41211yescharacteristic
146C22×C4D41211yescharacteristic
147C22×C4C22⋊D10311yescharacteristic
148C22×C4C22⋊D10311yescharacteristic
149C22×C4C22×D10311yescharacteristic
150M16—42no—
151C2×C8—22no—
152C2×C8—4122no—
153C2×C8—2062no—
154C4⋊C4—2061no—
155C4⋊C4—2061no—
156C4⋊C4—2061no—
157C4⋊C4—2061no—
158C22⋊C4—2061no—
159C22⋊C4—2061no—
160C22⋊C4—2061no—
161C22⋊C4—2061no—
162C22⋊C4—2061no—
163C22⋊C4—2061no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—4121no—
168C23—4121no—
169C23—2062no—
170C23—2061no—
171C23(C2×D103)⋊C411yescharacteristic
172C23(C2×D103)⋊C411yescharacteristic
173C23C2×C4×D10311yescharacteristic
174D4—4122no—
175D4—4122no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—4121no—
183C2×C4—4121no—
184C2×C4—2061no—
185C2×C4—2061no—
186C2×C4—2061no—
187C2×C4—2062no—
188C2×C4(C2×D103)⋊C411yescharacteristic
189C2×C4(C2×D103)⋊C411yescharacteristic
190C2×C4C2×C22⋊D10311yescharacteristic
191C2×C4C2×D41211yescharacteristic
192C8—42no—
193C8—4122no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—8242no—
203C22—4121no—
204C22—4121no—
205C22—4121no—
206C22#1569293512yes—
207C22C2×(C2×D103)⋊C411yescharacteristic
208C22#1569302912yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—4121no—
214C4—4121no—
215C4—4121no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—8241no—
220C2#2026775911yescharacteristic
221C2C2×#1569293511yescharacteristic
222C2#2026777311yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#407×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC22×C22⋊D103C4
cosocleC22×C4×C103C23
hypercenter#407D103
hypocenterC103#1468
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C103⋊C8)C2semidirect
3. #20267516C2semidirect
4. #20267514C2semidirect
5. #407×C103C2semidirect
112. C103#1468semidirect
114. #407D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930042
C2×C22⋊(C103⋊C8)2
#202675162
#202675142
#407×C1032
#1468103