Finite Group Databasebeta

← #27196680

Subgroups — #27196680

Order 13184.

254 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 89 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×#15692955C211yesmaximal, characteristic
2C2×#15692954C211yesmaximal, characteristic
3C2×#15692945C211yesmaximal, characteristic
4#20267698C211yesmaximal, characteristic
5#20267660C211yesmaximal, characteristic
6#20267545C211yesmaximal, characteristic
7C2×#103×C103C211yesmaximal, characteristic
8C22×C103⋊C8C2211yescharacteristic
9C2×C4⋊Dic103C2211yescharacteristic
10C2×C4⋊Dic103C2211yescharacteristic
11C2×Dic103⋊C4—22no—
12C2×C4×Dic103C2211yescharacteristic
13#15692955—22no—
14#15692954—22no—
15#15692945—22no—
16C103⋊#95—22no—
17C22×Q8×C103C2211yescharacteristic
18C22×C8×C103C2211yescharacteristic
19C2×C4⋊C4×C103C2211yescharacteristic
20#103×C103—22no—
21C22×Dic103—21no—
22C22×Dic103—21no—
23C22×Dic103D412yes—
24C2×C103⋊C8—21no—
25C2×C103⋊C8—21no—
26C2×C103⋊C8D412yes—
27C4⋊Dic103—21no—
28C4⋊Dic103—21no—
29C4⋊Dic103—21no—
30C4⋊Dic103—21no—
31Dic103⋊C4—44no—
32C4×Dic103—21no—
33C4×Dic103—21no—
34C2×Q8×C103—21no—
35C2×Q8×C103—21no—
36C2×Q8×C103—21no—
37C2×Q8×C103—21no—
38C2×Q8×C103—21no—
39C2×Q8×C103Q812yes—
40C22×C4×C103—21no—
41C22×C4×C103—21no—
42C22×C4×C103C2311yescharacteristic
43C2×C8×C103—21no—
44C2×C8×C103—21no—
45C2×C8×C103D412yes—
46C4⋊C4×C103—21no—
47C4⋊C4×C103—21no—
48C23×C103C2×D411yescharacteristic
49Q8×C103—22no—
50Q8×C103—22no—
51Q8×C103—41no—
52Q8×C103—41no—
53C2×C4×C103—22no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—42no—
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×Q811yescharacteristic
61C2×C4×C103#4111yescharacteristic
62C2×C4×C103#4111yescharacteristic
63C2×C4×C103#4111yescharacteristic
64C2×Dic103—22no—
65C2×Dic103—22no—
66C2×Dic103—41no—
67C2×Dic103—41no—
68C2×Dic103—42no—
69C2×Dic103—42no—
70C2×Dic103Q1614yes—
71C8×C103—22no—
72C103⋊C8—22no—
73C22×C103C22⋊Q811yescharacteristic
74C22×C103#12311yescharacteristic
75C22×C103#12711yescharacteristic
76C22×C103C2×Q1612yes—
77C22×C103AGL(1,ℤ/8)12yes—
78C4×C103—42no—
79C4×C103—81no—
80C4×C103C22⋊Q811yescharacteristic
81C4×C103C22⋊Q811yescharacteristic
82C4×C103#12311yescharacteristic
83C4×C103#12311yescharacteristic
84Dic103—24no—
85Dic103—81no—
86Dic103—81no—
87C2×C103#39911yescharacteristic
88C2×C103#47712yes—
89C2×C103#48412yes—
90C2×C103#49411yescharacteristic
91C2×C103#49611yescharacteristic
92#2095—1031nomaximal, Sylow
93C103#209511yescharacteristic, complemented, Sylow
94C2×#107—1031no—
95C2×#107—1031no—
96C2×#103—1031no—
97C2×#103D10311yescharacteristic
98#391—1031no—
99#384—1031no—
100#336—1031no—
101C22×Q8C2×D10311yescharacteristic
102C22×C8—1031no—
103C22×C8C2×D10311yescharacteristic
104C2×C4⋊C4—1031no—
105C2×C4⋊C4—1031no—
106C2×C4⋊C4—2062no—
107C2×C4⋊C4C2×D10311yescharacteristic
108C2×C42—1031no—
109#107—2062no—
110#107—2062no—
111#103—22no—
112#103—2062no—
113#95—2062no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Dic20612yes—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—1032no—
123C22×C4—2061no—
124C22×C4—2061no—
125C22×C4C22×D10311yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—1032no—
129C2×C8—2061no—
130C2×C8—2061no—
131C2×C8C22⋊D10312yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—4124no—
135C4⋊C4—2061no—
136C4⋊C4—2061no—
137C4⋊C4—2061no—
138C4⋊C4—2061no—
139C42—2061no—
140C42—2061no—
141C23D4×D10311yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—42no—
151C2×C4—1034no—
152C2×C4—4121no—
153C2×C4—4121no—
154C2×C4—4122no—
155C2×C4—4122no—
156C2×C4—2062no—
157C2×C4—2062no—
158C2×C4D4×D10311yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C2×C4C2×Dic20611yescharacteristic
161C2×C4#1311010411yescharacteristic
162C2×C4#1311010411yescharacteristic
163C2×C4#1311010511yescharacteristic
164C8—22no—
165C8—2062no—
166C22#1569299811yescharacteristic
167C22#1569300311yescharacteristic
168C22#1569301711yescharacteristic
169C22Q16×D10312yes—
170C22#1569304812yes—
171C4—42no—
172C4—81no—
173C4—8241no—
174C4—8241no—
175C4—2064no—
176C4#1569299811yescharacteristic
177C4#1569300011yescharacteristic
178C4#1569300211yescharacteristic
179C4#1569300311yescharacteristic
180C2#2026772711yescharacteristic
181C2#2026808412yes—
182C2#2026812512yes—
183C2#2026816911yescharacteristic
184C2#2026817711yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#103×C103C2
socle, prime radicalC23×C103C2×D4
hypercenterC2×#103D103
hypocenterC103#2095
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
93. C103#2095semidirect

Maximal subgroups

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

subgroupindex
C2×#156929552
C2×#156929542
C2×#156929452
#202676982
#202676602
#202675452
C2×#103×C1032
#2095103