Finite Group Databasebeta

← #27193722

Subgroups — #27193722

Order 13184.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#20268325C211yesmaximal, characteristic
2#20267659C211yesmaximal, characteristic, complemented
3#20267529C212yesmaximal, complemented
4#20267526C212yesmaximal
5#431×C103C211yesmaximal, characteristic, complemented
6#15693015—21no—
7#15693013C411yescharacteristic, complemented
8#15693009C411yescharacteristic, complemented
9#15693004—21no—
10#15693000C2211yescharacteristic
11#15692995C2211yescharacteristic
12C4×Dic206C411yescharacteristic, complemented
13C4×D412C411yescharacteristic, complemented
14C4×C22⋊D103—21no—
15#15692978—21no—
16C103⋊#95—21no—
17C103⋊#95—21no—
18C103⋊#95C2212yes—
19C2×C42×C103C2211yescharacteristic
20C4⋊C8×C103—21no—
21C22⋊C8×C103C2212yes—
22C4×C8×C103—21no—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26C22×Dic103—22no—
27C2×C4×D103—21no—
28C4⋊Dic103C2×C411yescharacteristic
29C4⋊Dic103C2×C411yescharacteristic
30Dic103⋊C4—21no—
31Dic103⋊C4—21no—
32Dic103⋊C4—21no—
33Dic103⋊C4—21no—
34C22⋊Dic103—21no—
35(C2×D103)⋊C4—21no—
36(C2×D103)⋊C4—21no—
37(C2×D103)⋊C4—21no—
38(C2×D103)⋊C4—21no—
39C4×Dic103—21no—
40C22×C4×C103D411yescharacteristic
41C22×C4×C103D411yescharacteristic
42C22×C4×C103C2311yescharacteristic
43C2×C8×C103—22no—
44C42×C103C2×C411yescharacteristic
45C42×C103C2×C411yescharacteristic
46C42×C103D411yescharacteristic
47C42×C103D411yescharacteristic
48C23×C103C2×D411yescharacteristic
49C22×D103—21no—
50C2×C4×C103—22no—
51C2×C4×C103—41no—
52C2×C4×C103—41no—
53C2×C4×C103C22⋊C411yescharacteristic
54C2×C4×C103C22⋊C411yescharacteristic
55C2×C4×C103C22⋊C411yescharacteristic
56C2×C4×C103C22⋊C411yescharacteristic
57C2×C4×C103C22×C411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C22⋊D103—42no—
60C2×Dic103—21no—
61C2×Dic103—21no—
62C2×Dic103—21no—
63C2×Dic103—42no—
64C2×Dic103—42no—
65C2×Dic103—42no—
66D412—41no—
67C4×D103—42no—
68Dic206—41no—
69C8×C103—42no—
70C22×C103—21no—
71C22×C103—21no—
72C22×C103C2×C22⋊C411yescharacteristic
73C22×C103#13512yes—
74C2×D103—41no—
75C2×D103—41no—
76C2×D103—41no—
77C4×C103—21no—
78C4×C103—21no—
79C4×C103—21no—
80C4×C103—21no—
81C4×C103—21no—
82C4×C103—21no—
83Dic103—41no—
84Dic103—41no—
85Dic103—41no—
86Dic103—82no—
87C2×C103—22no—
88C2×C103#41011yescharacteristic
89C2×C103#41611yescharacteristic
90C2×C103#42111yescharacteristic
91D103—81no—
92#1521—1031nomaximal, Sylow
93C103#152111yescharacteristic, complemented, Sylow
94#529—1031no—
95#431D10311yescharacteristic, complemented
96#383—1031no—
97#328—1032no—
98#327—1032no—
99#126—2061no—
100#125—1031no—
101#124—1031no—
102#123—2061no—
103C22⋊Q8—1031no—
104#121—1031no—
105C4×Q8—1031no—
106C4×D4—1031no—
107C4×D4—2061no—
108#117—2061no—
109C2×C42C2×D10311yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C2×D10312yes—
112C4×C8—21no—
113#95—1032no—
114#95—2061no—
115#95—2061no—
116C2×Q8—1031no—
117C2×D4—1031no—
118C2×D4—2061no—
119C22×C4—2062no—
120C22×C4—2061no—
121C22×C4D41211yescharacteristic
122C22×C4D41211yescharacteristic
123C22×C4C22×D10311yescharacteristic
124C2×C8—22no—
125C4⋊C4—1031no—
126C4⋊C4—1031no—
127C4⋊C4—2061no—
128C4⋊C4—2061no—
129C4⋊C4—2061no—
130C4⋊C4—2061no—
131C22⋊C4—2061no—
132C22⋊C4—2061no—
133C22⋊C4—2061no—
134C22⋊C4—2061no—
135C22⋊C4—2061no—
136C42—2061no—
137C42C4×D10311yescharacteristic
138C42C4×D10311yescharacteristic
139C42C22⋊D10311yescharacteristic
140C42C22⋊D10311yescharacteristic
141C23—2061no—
142C23C2×D41211yescharacteristic
143Q8—4121no—
144D4—4121no—
145D4—4122no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—4122no—
150C2×C4—4122no—
151C2×C4—4122no—
152C2×C4—4122no—
153C2×C4—2061no—
154C2×C4—2061no—
155C2×C4—2061no—
156C2×C4(C2×D103)⋊C411yescharacteristic
157C2×C4(C2×D103)⋊C411yescharacteristic
158C2×C4(C2×D103)⋊C411yescharacteristic
159C2×C4(C2×D103)⋊C411yescharacteristic
160C2×C4C2×C4×D10311yescharacteristic
161C2×C4C2×C22⋊D10311yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—4121no—
166C22—4121no—
167C22—4121no—
168C22C2×(C2×D103)⋊C411yescharacteristic
169C22#1569304312yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—8242no—
177C4—4121no—
178C4—4121no—
179C4—4121no—
180C2—22no—
181C2—8241no—
182C2#2026776411yescharacteristic
183C2#2026778811yescharacteristic
184C2#2026780711yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#431×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692995C22
cosocleC22×C4×C103C23
hypercenter#431D103
hypocenterC103#1521
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #20267659C2semidirect
3. #20267529C2semidirect
5. #431×C103C2semidirect
7. #15693013C4semidirect
8. #15693009C4semidirect
12. C4×Dic206C4semidirect
13. C4×D412C4semidirect
93. C103#1521semidirect
95. #431D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
#202676592
#202675292
#202675262
#431×C1032
#1521103