Finite Group Databasebeta

← C103×#1468 #27190834

Subgroups — C103×#1468 #27190834

Order 13184.

280 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 92 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×#123×C103C211yesmaximal, characteristic
2#407×C103C211yesmaximal, characteristic, complemented
3C2×C22⋊C8×C103C211yesmaximal, characteristic, complemented
4#324×C103C212yesmaximal, complemented
5#323×C103C212yesmaximal, complemented
6C22×D4×C103C411yescharacteristic
7C23×C4×C103C2211yescharacteristic
8C2×M16×C103—21no—
9C22×C8×C103—21no—
10#123×C103—21no—
11#123×C103—21no—
12#123×C103—21no—
13#123×C103—21no—
14C2×C4⋊C4×C103C411yescharacteristic
15C2×C4⋊C4×C103C2211yescharacteristic
16C2×C22⋊C4×C103C411yescharacteristic
17C2×C22⋊C4×C103C411yescharacteristic
18C2×C22⋊C4×C103C2211yescharacteristic
19C22⋊C8×C103—21no—
20C22⋊C8×C103—21no—
21C22⋊C8×C103C2212yes—
22C22⋊C8×C103C2212yes—
23C24×C103C2×C411yescharacteristic
24C24×C103C2×C411yescharacteristic
25C2×D4×C103—21no—
26C2×D4×C103—21no—
27C2×D4×C103—42no—
28C22×C4×C103—42no—
29C22×C4×C103C2×C411yescharacteristic
30C22×C4×C103C2×C411yescharacteristic
31C22×C4×C103C2×C411yescharacteristic
32C22×C4×C103C2×C411yescharacteristic
33C22×C4×C103D411yescharacteristic
34C22×C4×C103D411yescharacteristic
35C22×C4×C103D411yescharacteristic
36C22×C4×C103D411yescharacteristic
37C22×C4×C103C2311yescharacteristic
38M16×C103—42no—
39C2×C8×C103—22no—
40C2×C8×C103—22no—
41C2×C8×C103—42no—
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C22⋊C4×C103—21no—
47C22⋊C4×C103—21no—
48C22⋊C4×C103—21no—
49C22⋊C4×C103—21no—
50C22⋊C4×C103—21no—
51C22⋊C4×C103—21no—
52C23×C103—22no—
53C23×C103—22no—
54C23×C103—21no—
55C23×C103—22no—
56C23×C103—41no—
57C23×C103—41no—
58C23×C103—41no—
59C23×C103C22⋊C411yescharacteristic
60C23×C103C22⋊C411yescharacteristic
61C23×C103C22×C411yescharacteristic
62D4×C103—42no—
63D4×C103—42no—
64C2×C4×C103—22no—
65C2×C4×C103—22no—
66C2×C4×C103—21no—
67C2×C4×C103—21no—
68C2×C4×C103—21no—
69C2×C4×C103—22no—
70C2×C4×C103—41no—
71C2×C4×C103—41no—
72C2×C4×C103—41no—
73C2×C4×C103—41no—
74C2×C4×C103—41no—
75C2×C4×C103—41no—
76C2×C4×C103C22⋊C411yescharacteristic
77C2×C4×C103C22⋊C411yescharacteristic
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2×D411yescharacteristic
80C8×C103—42no—
81C8×C103—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—41no—
91C22×C103—41no—
92C22×C103—41no—
93C22×C103—82no—
94C22×C103#9912yes—
95C22×C103C2×C22⋊C411yescharacteristic
96C22×C103#13112yes—
97C4×C103—21no—
98C4×C103—21no—
99C4×C103—21no—
100C4×C103—21no—
101C4×C103—41no—
102C4×C103—41no—
103C4×C103—41no—
104C2×C103—22no—
105C2×C103—22no—
106C2×C103—41no—
107C2×C103—81no—
108C2×C103#40811yescharacteristic
109C2×C103C2×#9911yescharacteristic
110C2×C103#41311yescharacteristic
111#1468C10311yesmaximal, characteristic, direct product factor, Sylow
112C103#146811yescharacteristic, direct product factor, Sylow
113C2×#123C2×C10311yescharacteristic
114#407C2×C10311yescharacteristic, complemented
115C2×C22⋊C8C2×C10311yescharacteristic, complemented
116#324C2×C10312yescomplemented
117#323C2×C10312yescomplemented
118C22×D4C4×C10311yescharacteristic
119C23×C4C22×C10311yescharacteristic
120C2×M16—21no—
121C22×C8—21no—
122#123—21no—
123#123—21no—
124#123—21no—
125#123—21no—
126C2×C4⋊C4C4×C10311yescharacteristic
127C2×C4⋊C4C22×C10311yescharacteristic
128C2×C22⋊C4C4×C10311yescharacteristic
129C2×C22⋊C4C4×C10311yescharacteristic
130C2×C22⋊C4C22×C10311yescharacteristic
131C22⋊C8—21no—
132C22⋊C8—21no—
133C22⋊C8C22×C10312yes—
134C22⋊C8C22×C10312yes—
135C24C2×C4×C10311yescharacteristic
136C24C2×C4×C10311yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—42no—
140C22×C4—42no—
141C22×C4C2×C4×C10311yescharacteristic
142C22×C4C2×C4×C10311yescharacteristic
143C22×C4C2×C4×C10311yescharacteristic
144C22×C4C2×C4×C10311yescharacteristic
145C22×C4D4×C10311yescharacteristic
146C22×C4D4×C10311yescharacteristic
147C22×C4D4×C10311yescharacteristic
148C22×C4D4×C10311yescharacteristic
149C22×C4C23×C10311yescharacteristic
150M16—42no—
151C2×C8—22no—
152C2×C8—22no—
153C2×C8—42no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C23—22no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23C22⋊C4×C10311yescharacteristic
172C23C22⋊C4×C10311yescharacteristic
173C23C22×C4×C10311yescharacteristic
174D4—42no—
175D4—42no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4C22⋊C4×C10311yescharacteristic
189C2×C4C22⋊C4×C10311yescharacteristic
190C2×C4C2×D4×C10311yescharacteristic
191C2×C4C2×D4×C10311yescharacteristic
192C8—42no—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—82no—
206C22#99×C10312yes—
207C22C2×C22⋊C4×C10311yescharacteristic
208C22#131×C10312yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—41no—
215C4—41no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—81no—
220C2#408×C10311yescharacteristic
221C2C2×#99×C10311yescharacteristic
222C2#413×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×C22⋊C4
commutatorC23C22×C4×C103
Frattini, cosocleC22×C4C23×C103
prime radicalC22×D4×C103C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. #407×C103C2semidirect
3. C2×C22⋊C8×C103C2semidirect
4. #324×C103C2semidirect
5. #323×C103C2semidirect
111. #1468C103direct (N × H)
112. C103#1468direct (N × H)
114. #407C2×C103semidirect
115. C2×C22⋊C8C2×C103semidirect
116. #324C2×C103semidirect
117. #323C2×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#123×C1032
#407×C1032
C2×C22⋊C8×C1032
#324×C1032
#323×C1032
#1468103