Finite Group Databasebeta

← #27196812

Subgroups — #27196812

Order 13184.

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

normal subgroups only

This group has 286 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#20268359C211yesmaximal, characteristic
2#99×D103C212yesmaximal, complemented
3#20267586C211yesmaximal, characteristic, complemented
4#20267583C212yesmaximal, complemented
5#354×C103C211yesmaximal, characteristic, complemented
6C2×#13110106C411yescharacteristic, complemented
7C2×D4×D103C2211yescharacteristic
8#15693018C411yescharacteristic, complemented
9#15693017C2211yescharacteristic
10#15693010C411yescharacteristic, complemented
11#15692994—22no—
12#15692991—22no—
13#15692978C411yescharacteristic, complemented
14C22⋊C4×D103—22no—
15#15692936C2212yes—
16#15692935—22no—
17#124×C103C2211yescharacteristic
18#99×C103C2212yes—
19C23×D103D412yes—
20#13110106—42no—
21C2×D412—21no—
22C2×D412—22no—
23C2×D412C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic, complemented
25C2×C22⋊D103—22no—
26C2×C22⋊D103D412yes—
27D4×D103—42no—
28C2×C4×D103—21no—
29C2×C4×D103—42no—
30C2×C4×D103C2×C411yescharacteristic
31Dic103⋊C4—21no—
32C22⋊Dic103—22no—
33(C2×D103)⋊C4—21no—
34(C2×D103)⋊C4—22no—
35(C2×D103)⋊C4—42no—
36C4×Dic103C2×C411yescharacteristic, complemented
37C2×Q8×C103C2×C411yescharacteristic, complemented
38C2×D4×C103C2311yescharacteristic
39C22⋊C4×C103—22no—
40C22⋊C4×C103—22no—
41C42×C103C2×C411yescharacteristic, complemented
42C23×C103C2×D412yes—
43C22×D103—22no—
44C22×D103—22no—
45C22×D103—21no—
46C22×D103—82no—
47C22×D103C22⋊C412yes—
48C22×D103C22⋊C411yescharacteristic
49Q8×C103—41no—
50D4×C103—41no—
51C2×C4×C103—21no—
52C2×C4×C103—21no—
53C2×C4×C103—42no—
54C2×C4×C103C22×C411yescharacteristic
55C22⋊D103—42no—
56C22⋊D103—82no—
57C2×Dic103—21no—
58C2×Dic103—42no—
59C2×Dic103C22⋊C411yescharacteristic
60D412—41no—
61D412—41no—
62D412—42no—
63D412—82no—
64C4×D103—22no—
65C4×D103—42no—
66C4×D103—84no—
67C22×C103—22no—
68C22×C103—42no—
69C22×C103C2×C22⋊C411yescharacteristic
70C2×D103—22no—
71C2×D103—41no—
72C2×D103—44no—
73C2×D103—42no—
74C2×D103—42no—
75C2×D103—41no—
76C2×D103—82no—
77C2×D103#9912yes—
78C4×C103—21no—
79C4×C103—41no—
80C4×C103—41no—
81C4×C103—82no—
82Dic103—21no—
83Dic103—41no—
84Dic103—82no—
85C2×C103—21no—
86C2×C103—42no—
87C2×C103C2×#9911yescharacteristic
88D103—22no—
89D103—42no—
90D103—81no—
91#2127—1031nomaximal, Sylow
92C103#212711yescharacteristic, complemented, Sylow
93#535—1031no—
94C2×#99—1032no—
95#354—1031no—
96#354D10311yescharacteristic, complemented
97#353—1032no—
98C2×#41—1031no—
99C22×D4—1031no—
100#127—1031no—
101#127—1031no—
102#124—1031no—
103#124C2×D10311yescharacteristic
104#121—2062no—
105#120—2062no—
106#117—1031no—
107C2×C22⋊C4—2062no—
108#99—1032no—
109#99—2062no—
110#99C2×D10312yes—
111C24—1032no—
112#41—4122no—
113C2×Q8C4×D10311yescharacteristic, complemented
114C2×D4—1032no—
115C2×D4—1031no—
116C2×D4—1031no—
117C2×D4—4122no—
118C2×D4—2062no—
119C2×D4—2061no—
120C2×D4—2062no—
121C2×D4C22×D10311yescharacteristic
122C22×C4—1031no—
123C22×C4—4122no—
124C22×C4—2061no—
125C4⋊C4—2061no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—4122no—
129C22⋊C4—2061no—
130C22⋊C4—2062no—
131C22⋊C4—2062no—
132C42—1031no—
133C42C4×D10311yescharacteristic, complemented
134C23—8242no—
135C23—1031no—
136C23—1032no—
137C23—2062no—
138C23—2062no—
139C23—2061no—
140C23D4×D10312yes—
141Q8—41no—
142D4—41no—
143D4—8242no—
144D4—8242no—
145D4—4121no—
146D4—4121no—
147D4—4122no—
148D4—4122no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—8244no—
153C2×C4—1031no—
154C2×C4—4122no—
155C2×C4—4122no—
156C2×C4—2062no—
157C2×C4—2061no—
158C2×C4C2×C4×D10311yescharacteristic
159C22—22no—
160C22—42no—
161C22—8242no—
162C22—1032no—
163C22—4122no—
164C22—4122no—
165C22—4121no—
166C22—4124no—
167C22—4121no—
168C22—2062no—
169C22C22⋊C4×D10311yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—8242no—
175C4—4121no—
176C4—2061no—
177C2—21no—
178C2—42no—
179C2—8241no—
180C2—4122no—
181C2—2062no—
182C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC2×C4×C103C22×C4
FrattiniC2×D4C22×D103
Fitting#354×C103C2
socleC2×C103C2×#99
prime radical#20268359C2
cosocleC2×D4×C103C23
hypercenter#354D103
hypocenterC103#2127
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D103C2semidirect
3. #20267586C2semidirect
4. #20267583C2semidirect
5. #354×C103C2semidirect
6. C2×#13110106C4semidirect
8. #15693018C4semidirect
10. #15693010C4semidirect
13. #15692978C4semidirect
24. C2×D412C2×C4semidirect
36. C4×Dic103C2×C4semidirect
37. C2×Q8×C103C2×C4semidirect
41. C42×C103C2×C4semidirect
92. C103#2127semidirect
96. #354D103semidirect
113. C2×Q8C4×D103semidirect
133. C42C4×D103semidirect

Maximal subgroups

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

subgroupindex
#202683592
#99×D1032
#202675862
#202675832
#354×C1032
#2127103