Finite Group Databasebeta

← #27193628

Subgroups — #27193628

Order 13184.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#20267844C211yesmaximal, characteristic, complemented
3#20267527C212yesmaximal, complemented
4#20267524C212yesmaximal
5#376×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—
16C4⋊(C103⋊C8)—21no—
17C22⋊(C103⋊C8)C2212yes—
18C4×C103⋊C8—21no—
19C2×C42×C103—21no—
20C2×C42×C103C2211yescharacteristic
21#95×C103—21no—
22#95×C103C2212yes—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26C2×C4×D103—21no—
27C2×C103⋊C8—22no—
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×C103—22no—
41C22×C4×C103D411yescharacteristic
42C22×C4×C103D411yescharacteristic
43C22×C4×C103C2311yescharacteristic
44C42×C103—24no—
45C42×C103C2×C411yescharacteristic
46C42×C103C2×C411yescharacteristic
47C42×C103D411yescharacteristic
48C42×C103D411yescharacteristic
49C23×C103C2×D411yescharacteristic
50C22×D103—21no—
51C2×C4×C103—22no—
52C2×C4×C103—22no—
53C2×C4×C103—24no—
54C2×C4×C103—41no—
55C2×C4×C103—42no—
56C2×C4×C103—42no—
57C2×C4×C103C22⋊C411yescharacteristic
58C2×C4×C103C22⋊C411yescharacteristic
59C2×C4×C103C22⋊C411yescharacteristic
60C2×C4×C103C22⋊C411yescharacteristic
61C2×C4×C103C22×C411yescharacteristic
62C2×C4×C103C2×D411yescharacteristic
63C22⋊D103—42no—
64C2×Dic103—21no—
65C2×Dic103—21no—
66C2×Dic103—21no—
67D412—41no—
68C4×D103—42no—
69Dic206—41no—
70C103⋊C8—42no—
71C22×C103—21no—
72C22×C103—21no—
73C22×C103C2×C22⋊C411yescharacteristic
74C22×C103#13512yes—
75C2×D103—41no—
76C2×D103—41no—
77C2×D103—41no—
78C4×C103—21no—
79C4×C103—21no—
80C4×C103—21no—
81C4×C103—21no—
82C4×C103—21no—
83C4×C103—44no—
84C4×C103#10412yes—
85Dic103—41no—
86Dic103—41no—
87Dic103—41no—
88C2×C103—22no—
89C2×C103#41011yescharacteristic
90C2×C103#41611yescharacteristic
91C2×C103C2×#10411yescharacteristic
92D103—81no—
93#1500—1031nomaximal, Sylow
94C103#150011yescharacteristic, complemented, Sylow
95#529—1031no—
96#431—1031no—
97#376D10311yescharacteristic, complemented
98#328—1032no—
99#327—1032no—
100#126—2061no—
101#125—1031no—
102#124—1031no—
103#123—2061no—
104C22⋊Q8—1031no—
105#121—1031no—
106C4×Q8—1031no—
107C4×D4—1031no—
108C4×D4—2061no—
109#117—2061no—
110C2×C42—21no—
111C2×C42C2×D10311yescharacteristic
112C4⋊C8—2061no—
113C22⋊C8—1032no—
114C4×C8—2061no—
115#95—21no—
116#95C2×D10312yes—
117C2×Q8—1031no—
118C2×D4—1031no—
119C2×D4—2061no—
120C22×C4—22no—
121C22×C4—2061no—
122C22×C4C22⋊D10311yescharacteristic
123C22×C4C22⋊D10311yescharacteristic
124C22×C4C22×D10311yescharacteristic
125C2×C8—2062no—
126C4⋊C4—1031no—
127C4⋊C4—1031no—
128C4⋊C4—2061no—
129C4⋊C4—2061no—
130C4⋊C4—2061no—
131C4⋊C4—2061no—
132C22⋊C4—2061no—
133C22⋊C4—2061no—
134C22⋊C4—2061no—
135C22⋊C4—2061no—
136C22⋊C4—2061no—
137C42—24no—
138C42—2061no—
139C42C4×D10311yescharacteristic
140C42C4×D10311yescharacteristic
141C42D41211yescharacteristic
142C42D41211yescharacteristic
143C23—2061no—
144C23C2×C22⋊D10311yescharacteristic
145Q8—4121no—
146D4—4121no—
147D4—4122no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—4122no—
155C2×C4—2061no—
156C2×C4—2061no—
157C2×C4—2061no—
158C2×C4(C2×D103)⋊C411yescharacteristic
159C2×C4(C2×D103)⋊C411yescharacteristic
160C2×C4(C2×D103)⋊C411yescharacteristic
161C2×C4(C2×D103)⋊C411yescharacteristic
162C2×C4C2×C4×D10311yescharacteristic
163C2×C4C2×D41211yescharacteristic
164C8—4122no—
165C22—21no—
166C22—21no—
167C22—4121no—
168C22—4121no—
169C22—4121no—
170C22C2×(C2×D103)⋊C411yescharacteristic
171C22#1569304112yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—44no—
178C4—4121no—
179C4—4121no—
180C4—4121no—
181C4#1569294912yes—
182C2—22no—
183C2—8241no—
184C2#2026776411yescharacteristic
185C2#2026778511yescharacteristic
186C2C2×#1569294911yescharacteristic
subgroupG/H
centerC2×C4(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#376×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692995C22
cosocleC22×C4×C103C23
hypercenter#376D103
hypocenterC103#1500
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #20267844C2semidirect
3. #20267527C2semidirect
5. #376×C103C2semidirect
7. #15693013C4semidirect
8. #15693009C4semidirect
12. C4×Dic206C4semidirect
13. C4×D412C4semidirect
94. C103#1500semidirect
97. #376D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
#202678442
#202675272
#202675242
#376×C1032
#1500103