Finite Group Databasebeta

← #27194135

Subgroups — #27194135

Order 13184.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#20268119C212yesmaximal, complemented
2#20267716C211yesmaximal, characteristic
3#20267528C212yesmaximal, complemented
4#20267515C211yesmaximal, characteristic
5#543×C103C211yesmaximal, characteristic
6C2×C4⋊Dic103C2211yescharacteristic
7C2×C22⋊Dic103—21no—
8#15692952—22no—
9#15692945—22no—
10C22⋊(C103⋊C8)C2212yes—
11C103⋊#95—21no—
12C103⋊#95C2211yescharacteristic
13C22⋊Q8×C103—22no—
14C22⋊Q8×C103—21no—
15C22⋊Q8×C103—22no—
16C22⋊Q8×C103C2212yes—
17C2×C22⋊C4×C103—21no—
18C2×C22⋊C4×C103C2211yescharacteristic
19C22×Dic103—21no—
20C22×Dic103—21no—
21C2×C103⋊C8—22no—
22C4⋊Dic103—22no—
23C22⋊Dic103—42no—
24C24×C103D411yescharacteristic
25C2×Q8×C103—21no—
26C2×Q8×C103D412yes—
27C22×C4×C103—21no—
28C22×C4×C103—21no—
29C22×C4×C103D411yescharacteristic
30C22×C4×C103C2311yescharacteristic
31C4⋊C4×C103—21no—
32C4⋊C4×C103—22no—
33C4⋊C4×C103—22no—
34C4⋊C4×C103D412yes—
35C22⋊C4×C103—22no—
36C22⋊C4×C103—22no—
37C22⋊C4×C103—22no—
38C23×C103—21no—
39C23×C103—21no—
40C23×C103—41no—
41C23×C103—41no—
42C23×C103SD1612yes—
43C23×C103C2×D411yescharacteristic
44Q8×C103—42no—
45Q8×C103—81no—
46C2×C4×C103—22no—
47C2×C4×C103—21no—
48C2×C4×C103—22no—
49C2×C4×C103—41no—
50C2×C4×C103—41no—
51C2×C4×C103—81no—
52C2×C4×C103—81no—
53C2×C4×C103C2×D412yes—
54C2×Dic103—41no—
55C2×Dic103—41no—
56C2×Dic103—41no—
57C2×Dic103—41no—
58C2×Dic103—41no—
59C2×Dic103—41no—
60C103⋊C8—42no—
61C22×C103—21no—
62C22×C103—21no—
63C22×C103—22no—
64C22×C103—42no—
65C22×C103—41no—
66C22×C103—41no—
67C22×C103—81no—
68C22×C103#12011yescharacteristic
69C22×C103C2×SD1611yescharacteristic
70C22×C103#13711yescharacteristic
71C4×C103—22no—
72C4×C103—41no—
73C4×C103—42no—
74C4×C103—42no—
75Dic103—81no—
76Dic103—81no—
77C2×C103—21no—
78C2×C103—21no—
79C2×C103—42no—
80C2×C103#44811yescharacteristic
81C2×C103#45511yescharacteristic
82C2×C103#45811yescharacteristic
83#1608—1031nomaximal, Sylow
84C103#160811yescharacteristic, complemented, Sylow
85#543D10311yescharacteristic
86#483—1032no—
87#397—1031no—
88#328—1032no—
89#323—1031no—
90C22⋊Q8—22no—
91C22⋊Q8—21no—
92C22⋊Q8—22no—
93C22⋊Q8C2×D10312yes—
94C2×C4⋊C4—1031no—
95C2×C22⋊C4—21no—
96C2×C22⋊C4—2061no—
97C2×C22⋊C4C2×D10311yescharacteristic
98#106—2062no—
99#103—2062no—
100C22⋊C8—1032no—
101#95—1031no—
102#95—2061no—
103C24C22⋊D10311yescharacteristic
104C2×Q8—21no—
105C2×Q8C22⋊D10312yes—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—2061no—
109C22×C4—2061no—
110C22×C4C22⋊D10311yescharacteristic
111C22×C4C22×D10311yescharacteristic
112C2×C8—2062no—
113C4⋊C4—21no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—2062no—
117C4⋊C4C22⋊D10312yes—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C22⋊C4—4122no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1311009212yes—
127C23C2×C22⋊D10311yescharacteristic
128Q8—42no—
129Q8—81no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—81no—
136C2×C4—81no—
137C2×C4—4121no—
138C2×C4—4121no—
139C2×C4—4121no—
140C2×C4—4121no—
141C2×C4—4121no—
142C2×C4—4121no—
143C2×C4C2×C22⋊D10312yes—
144C8—4122no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1569299011yescharacteristic
153C22C2×#1311009211yescharacteristic
154C22#1569305211yescharacteristic
155C4—22no—
156C4—41no—
157C4—42no—
158C4—42no—
159C4—8241no—
160C4—8241no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#2026793011yescharacteristic
165C2#2026796911yescharacteristic
166C2#2026798111yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#543×C103C2
socleC22×C103#120
prime radicalC24×C103D4
hypercenter#543D103
hypocenterC103#1608
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #20268119C2semidirect
3. #20267528C2semidirect
84. C103#1608semidirect

Maximal subgroups

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

subgroupindex
#202681192
#202677162
#202675282
#202675152
#543×C1032
#1608103