Finite Group Databasebeta

← #27194302

Subgroups — #27194302

Order 13184.

188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#20268143C211yesmaximal, characteristic
2#20268086C211yesmaximal, characteristic
3#20268086C211yesmaximal, characteristic
4#20267537C211yesmaximal, characteristic
5Q8⋊(C103⋊C8)C211yesmaximal, characteristic
6Q8⋊(C103⋊C8)C211yesmaximal, characteristic
7#557×C103C211yesmaximal, characteristic
8#15693021C2211yescharacteristic
9#15692954—21no—
10#15692954—21no—
11C4⋊(C103⋊C8)C2211yescharacteristic
12C4⋊(C103⋊C8)C2211yescharacteristic
13#15692945—21no—
14#15692945—21no—
15#15692944—22no—
16C4×C103⋊C8C2211yescharacteristic
17C4⋊Q8×C103—21no—
18C4⋊Q8×C103C2211yescharacteristic
19#125×C103—22no—
20#125×C103—21no—
21C4×Q8×C103—21no—
22C4×Q8×C103—21no—
23C4×Q8×C103C2211yescharacteristic
24C4×Q8×C103C2211yescharacteristic
25C2×Dic206—21no—
26C2×C103⋊C8—21no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C4⋊Dic103—21no—
30C4⋊Dic103—21no—
31C2×Q8×C103—21no—
32C2×Q8×C103D411yescharacteristic
33C2×Q8×C103D411yescharacteristic
34C4⋊C4×C103—22no—
35C4⋊C4×C103—22no—
36C4⋊C4×C103—22no—
37C4⋊C4×C103—21no—
38C4⋊C4×C103—21no—
39C4⋊C4×C103—21no—
40C4⋊C4×C103D411yescharacteristic
41C4⋊C4×C103D411yescharacteristic
42C4⋊C4×C103D412yes—
43C42×C103—22no—
44C42×C103—21no—
45C42×C103—21no—
46C42×C103C2311yescharacteristic
47Q8×C103—21no—
48Q8×C103—21no—
49Q8×C103—21no—
50Q8×C103—41no—
51Q8×C103—41no—
52Q8×C103Q1612yes—
53C2×C4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—22no—
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×Dic103—41no—
62Dic206—42no—
63C103⋊C8—41no—
64C103⋊C8—41no—
65C103⋊C8—41no—
66C22×C103#12011yescharacteristic
67C4×C103—22no—
68C4×C103—21no—
69C4×C103—41no—
70C4×C103—42no—
71C4×C103—41no—
72C4×C103—41no—
73C4×C103C2×Q1611yescharacteristic
74C4×C103#13511yescharacteristic
75C4×C103#13711yescharacteristic
76C4×C103#13711yescharacteristic
77Dic103—81no—
78C2×C103#45111yescharacteristic
79C2×C103#45211yescharacteristic
80C2×C103#45411yescharacteristic
81#1636—1031nomaximal, Sylow
82C103#163611yescharacteristic, complemented, Sylow
83#557D10311yescharacteristic
84#487—1031no—
85#477—1031no—
86#477—1031no—
87#332—1031no—
88Q8⋊C8—1031no—
89Q8⋊C8—1031no—
90C4⋊Q8—21no—
91C4⋊Q8—1031no—
92C4⋊Q8C2×D10311yescharacteristic
93#125—22no—
94#125—21no—
95C4×Q8—21no—
96C4×Q8—21no—
97C4×Q8C2×D10311yescharacteristic
98C4×Q8C2×D10311yescharacteristic
99#107—2061no—
100#107—2061no—
101C4⋊C8—1031no—
102C4⋊C8—1031no—
103#103—2061no—
104#103—2061no—
105#103—2062no—
106C4×C8—1031no—
107C2×Q8—21no—
108C2×Q8—2061no—
109C2×Q8C22⋊D10311yescharacteristic
110C2×Q8C22⋊D10311yescharacteristic
111C2×C8—2061no—
112C2×C8—2061no—
113C2×C8—2061no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—2061no—
121C4⋊C4—2061no—
122C4⋊C4C22⋊D10312yes—
123C4⋊C4C22⋊D10311yescharacteristic
124C4⋊C4C22⋊D10311yescharacteristic
125C42—22no—
126C42—21no—
127C42—21no—
128C42C22×D10311yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—21no—
132Q8—41no—
133Q8—41no—
134Q8—4122no—
135Q8#1311009512yes—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—4121no—
142C2×C4C2×C22⋊D10311yescharacteristic
143C2×C4C2×C22⋊D10311yescharacteristic
144C2×C4C2×C22⋊D10311yescharacteristic
145C8—4121no—
146C8—4121no—
147C8—4121no—
148C22#1569299011yescharacteristic
149C4—22no—
150C4—21no—
151C4—41no—
152C4—42no—
153C4—41no—
154C4—41no—
155C4—8241no—
156C4C2×#1311009511yescharacteristic
157C4#1569304111yescharacteristic
158C4#1569305111yescharacteristic
159C4#1569305211yescharacteristic
160C2#2026794711yescharacteristic
161C2#2026795311yescharacteristic
162C2#2026796411yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#557×C103C2
socle, prime radicalC22×C103#120
hypercenter#557D103
hypocenterC103#1636
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #557

Complements

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

NH ≅ G/Ntype
82. C103#1636semidirect

Maximal subgroups

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

subgroupindex
#202681432
#202680862
#202675372
Q8⋊(C103⋊C8)2
#557×C1032
#1636103