Finite Group Databasebeta

← #27196806

Subgroups — #27196806

Order 13184.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268339C211yesmaximal, characteristic
2#20267763C212yesmaximal, complemented
3#20267585C212yesmaximal, complemented
4#20267584C211yesmaximal, characteristic, complemented
5#353×C103C211yesmaximal, characteristic, complemented
6C2×#13110104C411yescharacteristic, complemented
7C2×#13110104C2211yescharacteristic
8#15693021C411yescharacteristic, complemented
9#15693008C411yescharacteristic, complemented
10#15693008C2211yescharacteristic
11#15692992—22no—
12D4×Dic103—22no—
13#15692977—22no—
14C42×D103C411yescharacteristic, complemented
15#15692936C2212yes—
16#15692935—22no—
17#127×C103C2211yescharacteristic
18#99×C103C2212yes—
19#13110104—41no—
20#13110104—41no—
21#13110104—41no—
22#13110104—41no—
23C2×Dic206C2×C411yescharacteristic
24C2×Dic206C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26C2×C22⋊D103D412yes—
27C22×Dic103—21no—
28C22×Dic103D412yes—
29C2×C4×D103—21no—
30C2×C4×D103C2×C411yescharacteristic
31C4⋊Dic103—22no—
32Dic103⋊C4—42no—
33C22⋊Dic103—22no—
34C22⋊Dic103—22no—
35C22⋊Dic103—22no—
36C4×Dic103—21no—
37C4×Dic103—42no—
38C4×Dic103C2×C411yescharacteristic
39C2×D4×C103—22no—
40C2×D4×C103C2×C411yescharacteristic
41C2×D4×C103C2311yescharacteristic
42C22⋊C4×C103—22no—
43C42×C103C2×C411yescharacteristic
44C23×C103—21no—
45C23×C103C2×D412yes—
46C22×D103C22⋊C411yescharacteristic
47D4×C103—41no—
48D4×C103—41no—
49D4×C103—44no—
50C2×C4×C103—21no—
51C2×C4×C103—42no—
52C2×C4×C103C22×C411yescharacteristic
53C22⋊D103—42no—
54C22⋊D103—42no—
55C2×Dic103—22no—
56C2×Dic103—22no—
57C2×Dic103—21no—
58C2×Dic103—21no—
59C2×Dic103—41no—
60C2×Dic103—41no—
61C2×Dic103—42no—
62C2×Dic103C22⋊C412yes—
63C2×Dic103C22⋊C411yescharacteristic
64C4×D103—21no—
65C4×D103—21no—
66C4×D103—42no—
67Dic206—41no—
68Dic206—41no—
69C22×C103—22no—
70C22×C103—42no—
71C22×C103—42no—
72C22×C103—41no—
73C22×C103C2×C22⋊C411yescharacteristic
74C2×D103—21no—
75C2×D103—41no—
76C4×C103—22no—
77C4×C103—21no—
78C4×C103—82no—
79Dic103—22no—
80Dic103—41no—
81Dic103—41no—
82Dic103—82no—
83Dic103#9911yescharacteristic
84Dic103#9911yescharacteristic
85C2×C103—21no—
86C2×C103—42no—
87C2×C103—81no—
88C2×C103C2×#9911yescharacteristic
89D103—41no—
90#2126—1031nomaximal, Sylow
91C103#212611yescharacteristic, complemented, Sylow
92#532—1031no—
93#410—1032no—
94#354—1032no—
95#353—1031no—
96#353D10311yescharacteristic, complemented
97C2×#41—1031no—
98C2×#41—1031no—
99C4⋊Q8—1031no—
100#127C2×D10311yescharacteristic
101#124—1031no—
102#124—1031no—
103#121—2062no—
104C4×D4—2062no—
105#117—2062no—
106C2×C42—1031no—
107#99—1032no—
108#99—2062no—
109#99C2×D10312yes—
110#41—4121no—
111#41—4121no—
112#41—4121no—
113#41—4121no—
114C2×Q8—1031no—
115C2×Q8—1031no—
116C2×D4—22no—
117C2×D4—1032no—
118C2×D4—2061no—
119C2×D4C4×D10311yescharacteristic
120C2×D4C22×D10311yescharacteristic
121C22×C4—1032no—
122C22×C4—1031no—
123C22×C4—2061no—
124C22×C4—2061no—
125C4⋊C4—4122no—
126C4⋊C4—2062no—
127C22⋊C4—22no—
128C22⋊C4—2062no—
129C22⋊C4—2062no—
130C22⋊C4—2062no—
131C42—1031no—
132C42—4122no—
133C42—2061no—
134C42C4×D10311yescharacteristic
135C23—21no—
136C23—1031no—
137C23D4×D10312yes—
138Q8—4121no—
139Q8—4121no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—4122no—
144D4—4122no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—1031no—
148C2×C4—1032no—
149C2×C4—4122no—
150C2×C4—4122no—
151C2×C4—4121no—
152C2×C4—4121no—
153C2×C4—2061no—
154C2×C4—2061no—
155C2×C4—2062no—
156C2×C4—2062no—
157C2×C4—2061no—
158C2×C4—2061no—
159C2×C4C2×C4×D10311yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—4121no—
165C22—2061no—
166C22C22⋊C4×D10311yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—8242no—
171C4—1031no—
172C4—1031no—
173C4—4121no—
174C4—4121no—
175C4—2062no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—4121no—
180C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC2×C4×C103C22×C4
FrattiniC2×D4C22×D103
Fitting#353×C103C2
socleC2×C103C2×#99
prime radical#20268339C2
cosocleC2×D4×C103C23
hypercenter#353D103
hypocenterC103#2126
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #20267763C2semidirect
3. #20267585C2semidirect
4. #20267584C2semidirect
5. #353×C103C2semidirect
6. C2×#13110104C4semidirect
8. #15693021C4semidirect
9. #15693008C4semidirect
14. C42×D103C4semidirect
91. C103#2126semidirect
96. #353D103semidirect

Maximal subgroups

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

subgroupindex
#202683392
#202677632
#202675852
#202675842
#353×C1032
#2126103