Finite Group Databasebeta

← #27196684

Subgroups — #27196684

Order 13184.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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×#15692952C211yesmaximal, characteristic
2C2×#15692946C211yesmaximal, characteristic
3C2×#15692944C211yesmaximal, characteristic
4#20267696C211yesmaximal, characteristic
5#20267660C211yesmaximal, characteristic
6#20267545C211yesmaximal, characteristic
7C2×#106×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10C2×C4⋊Dic103C2211yescharacteristic
11C2×Dic103⋊C4—22no—
12C2×C4×Dic103C2211yescharacteristic
13#15692952—22no—
14#15692946—22no—
15#15692944—22no—
16C103⋊#95—22no—
17C22×C8×C103C2211yescharacteristic
18C2×C4⋊C4×C103C2211yescharacteristic
19C2×C4⋊C4×C103C2211yescharacteristic
20#106×C103—22no—
21C2×Dic206—21no—
22C2×Dic206—21no—
23C2×Dic206—21no—
24C2×Dic206—21no—
25C2×Dic206—21no—
26C2×Dic206Q812yes—
27C22×Dic103—21no—
28C22×Dic103—21no—
29C22×Dic103D412yes—
30C2×C103⋊C8—21no—
31C2×C103⋊C8—21no—
32C2×C103⋊C8D412yes—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35Dic103⋊C4—44no—
36C4×Dic103—21no—
37C4×Dic103—21no—
38C22×C4×C103—21no—
39C22×C4×C103—21no—
40C22×C4×C103C2311yescharacteristic
41C2×C8×C103—21no—
42C2×C8×C103—21no—
43C2×C8×C103D412yes—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C4⋊C4×C103—21no—
48C23×C103C2×D411yescharacteristic
49C2×C4×C103—41no—
50C2×C4×C103—41no—
51C2×C4×C103—42no—
52C2×C4×C103—42no—
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103C2×D411yescharacteristic
55C2×C4×C103C2×Q811yescharacteristic
56C2×C4×C103#4111yescharacteristic
57C2×C4×C103#4111yescharacteristic
58C2×C4×C103#4111yescharacteristic
59C2×Dic103—22no—
60C2×Dic103—22no—
61C2×Dic103—22no—
62C2×Dic103—41no—
63C2×Dic103—41no—
64C2×Dic103—41no—
65C2×Dic103—42no—
66C2×Dic103SD1614yes—
67Dic206—22no—
68Dic206—22no—
69Dic206—41no—
70Dic206—41no—
71C8×C103—22no—
72C103⋊C8—22no—
73C22×C103C22⋊Q811yescharacteristic
74C22×C103#12311yescharacteristic
75C22×C103#12711yescharacteristic
76C22×C103C2×SD1612yes—
77C22×C103#13712yes—
78C4×C103—81no—
79C4×C103—81no—
80C4×C103C22⋊Q811yescharacteristic
81C4×C103C22⋊Q811yescharacteristic
82C4×C103#12311yescharacteristic
83C4×C103#12311yescharacteristic
84Dic103—24no—
85Dic103—42no—
86Dic103—81no—
87C2×C103#39911yescharacteristic
88C2×C103#47512yes—
89C2×C103#48312yes—
90C2×C103#49211yescharacteristic
91C2×C103#49711yescharacteristic
92#2096—1031nomaximal, Sylow
93C103#209611yescharacteristic, complemented, Sylow
94C2×#106—1031no—
95C2×#106D10311yescharacteristic
96C2×#103—1031no—
97C2×#103—1031no—
98#391—1031no—
99#384—1031no—
100#336—1031no—
101C22×Q8—1031no—
102C22×C8—1031no—
103C22×C8C2×D10311yescharacteristic
104C2×C4⋊C4—1031no—
105C2×C4⋊C4—2062no—
106C2×C4⋊C4C2×D10311yescharacteristic
107C2×C4⋊C4C2×D10311yescharacteristic
108C2×C42—1031no—
109#106—22no—
110#106—2062no—
111#103—2062no—
112#103—2062no—
113#95—2062no—
114C2×Q8—1032no—
115C2×Q8—2061no—
116C2×Q8—2061no—
117C2×Q8—2061no—
118C2×Q8—2061no—
119C2×Q8—2061no—
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—21no—
135C4⋊C4—21no—
136C4⋊C4—4124no—
137C4⋊C4—2061no—
138C4⋊C4—2061no—
139C42—2061no—
140C42—2061no—
141C23D4×D10311yescharacteristic
142Q8—4121no—
143Q8—4121no—
144Q8—2062no—
145Q8—2062no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—1034no—
151C2×C4—4121no—
152C2×C4—4122no—
153C2×C4—4121no—
154C2×C4—4121no—
155C2×C4—2062no—
156C2×C4—2062no—
157C2×C4—2062no—
158C2×C4D4×D10311yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C2×C4Q8×D10311yescharacteristic
161C2×C4#1311010511yescharacteristic
162C2×C4#1311010511yescharacteristic
163C2×C4#1311010611yescharacteristic
164C8—22no—
165C8—2062no—
166C22#1569299911yescharacteristic
167C22#1569300611yescharacteristic
168C22#1569301711yescharacteristic
169C22SD16×D10312yes—
170C22#1569305012yes—
171C4—81no—
172C4—81no—
173C4—8241no—
174C4—4122no—
175C4—2064no—
176C4#1569299711yescharacteristic
177C4#1569299911yescharacteristic
178C4#1569300411yescharacteristic
179C4#1569300611yescharacteristic
180C2#2026772611yescharacteristic
181C2#2026807512yes—
182C2#2026812312yes—
183C2#2026816211yescharacteristic
184C2#2026818211yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#106×C103C2
socle, prime radicalC23×C103C2×D4
hypercenterC2×#106D103
hypocenterC103#2096
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
93. C103#2096semidirect

Maximal subgroups

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

subgroupindex
C2×#156929522
C2×#156929462
C2×#156929442
#202676962
#202676602
#202675452
C2×#106×C1032
#2096103