Finite Group Databasebeta

← #27193717

Subgroups — #27193717

Order 13184.

288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#15693000C211yesmaximal, characteristic
2#20267651C211yesmaximal, characteristic
3#20267529C214yesmaximal, complemented
4C2×C22⋊C8×C103C211yesmaximal, characteristic
5C22×Dic206C411yescharacteristic, complemented
6#15693000—21no—
7#15693000—21no—
8#15693000C412yescomplemented
9#15693000C2212yes—
10C2×C4⋊Dic103—21no—
11C2×C4⋊Dic103C411yescharacteristic, complemented
12C2×Dic103⋊C4—21no—
13C2×C22⋊Dic103—21no—
14C2×C22⋊Dic103—21no—
15C103⋊#95C2212yes—
16C23×C4×C103C2211yescharacteristic
17C22×C8×C103—21no—
18C22⋊C8×C103—21no—
19C22⋊C8×C103C2212yes—
20C2×Dic206—21no—
21C2×Dic206—42no—
22C2×Dic206C2×C412yes—
23C22×Dic103—21no—
24C22×Dic103—21no—
25C22×Dic103—22no—
26C4⋊Dic103—21no—
27C4⋊Dic103—42no—
28C4⋊Dic103C2×C412yes—
29Dic103⋊C4—22no—
30Dic103⋊C4—22no—
31C22⋊Dic103—22no—
32C22⋊Dic103—22no—
33C22⋊Dic103—42no—
34C24×C103D411yescharacteristic
35C22×C4×C103—42no—
36C22×C4×C103C2×C411yescharacteristic
37C22×C4×C103C2×C411yescharacteristic
38C22×C4×C103D411yescharacteristic
39C22×C4×C103D411yescharacteristic
40C22×C4×C103D411yescharacteristic
41C22×C4×C103C2311yescharacteristic
42C2×C8×C103—22no—
43C2×C8×C103—42no—
44C23×C103—41no—
45C23×C103—41no—
46C23×C103C22⋊C411yescharacteristic
47C23×C103C22⋊C411yescharacteristic
48C23×C103SD1612yes—
49C23×C103Q1612yes—
50C23×C103C2×D411yescharacteristic
51C2×C4×C103—22no—
52C2×C4×C103—22no—
53C2×C4×C103—22no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103C22⋊C411yescharacteristic
58C2×C4×C103C22⋊C411yescharacteristic
59C2×C4×C103C22×C411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×Dic103—22no—
62C2×Dic103—22no—
63C2×Dic103—42no—
64C2×Dic103—42no—
65C2×Dic103—42no—
66C2×Dic103—42no—
67C2×Dic103—42no—
68Dic206—42no—
69Dic206—42no—
70C8×C103—42no—
71C22×C103—21no—
72C22×C103—21no—
73C22×C103—21no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103—21no—
77C22×C103—42no—
78C22×C103—42no—
79C22×C103#10312yes—
80C22×C103#10312yes—
81C22×C103C2×C22⋊C411yescharacteristic
82C22×C103C2×SD1611yescharacteristic
83C22×C103C2×Q1611yescharacteristic
84C4×C103—21no—
85C4×C103—21no—
86C4×C103—21no—
87C4×C103#9912yes—
88Dic103—42no—
89Dic103—42no—
90Dic103—82no—
91C2×C103—21no—
92C2×C103—22no—
93C2×C103—22no—
94C2×C103—21no—
95C2×C103C2×#9911yescharacteristic
96C2×C103C2×#10311yescharacteristic
97C2×C103#42111yescharacteristic
98#1520—1031nomaximal, Sylow
99C103#152011yescharacteristic, complemented, Sylow
100C2×C22⋊Q8—1031no—
101C2×C22⋊C8D10311yescharacteristic
102#380—1031no—
103#328—1034no—
104C22×Q8—1031no—
105C23×C4C2×D10311yescharacteristic
106C22×C8—21no—
107C22⋊Q8—1032no—
108C22⋊Q8—1032no—
109C22⋊Q8—2061no—
110C22⋊Q8—2061no—
111C2×C4⋊C4—1031no—
112C2×C4⋊C4—2061no—
113C2×C4⋊C4—2061no—
114C2×C22⋊C4—2061no—
115C2×C22⋊C4—2061no—
116C22⋊C8—21no—
117C22⋊C8C2×D10312yes—
118#95—1032no—
119C24D41211yescharacteristic
120C2×Q8—1032no—
121C2×Q8—4122no—
122C2×Q8—2061no—
123C22×C4—42no—
124C22×C4—2062no—
125C22×C4—2061no—
126C22×C4—2061no—
127C22×C4C4×D10311yescharacteristic
128C22×C4C4×D10311yescharacteristic
129C22×C4D41211yescharacteristic
130C22×C4C22⋊D10311yescharacteristic
131C22×C4C22⋊D10311yescharacteristic
132C22×C4C22×D10311yescharacteristic
133C2×C8—22no—
134C2×C8—42no—
135C4⋊C4—1032no—
136C4⋊C4—4122no—
137C4⋊C4—2062no—
138C4⋊C4—2061no—
139C4⋊C4—2062no—
140C22⋊C4—4122no—
141C22⋊C4—2062no—
142C22⋊C4—2062no—
143C23—41no—
144C23—41no—
145C23(C2×D103)⋊C411yescharacteristic
146C23(C2×D103)⋊C411yescharacteristic
147C23#1311009412yes—
148C23Dic41212yes—
149C23C2×D41211yescharacteristic
150Q8—4122no—
151Q8—4122no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—4122no—
159C2×C4—4122no—
160C2×C4—4122no—
161C2×C4—4122no—
162C2×C4—4122no—
163C2×C4—2062no—
164C2×C4—2062no—
165C2×C4(C2×D103)⋊C411yescharacteristic
166C2×C4(C2×D103)⋊C411yescharacteristic
167C2×C4C2×C4×D10311yescharacteristic
168C2×C4C2×C22⋊D10311yescharacteristic
169C8—42no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22#1569294612yes—
179C22#1569294612yes—
180C22C2×(C2×D103)⋊C411yescharacteristic
181C22C2×#1311009411yescharacteristic
182C22C2×Dic41211yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—8242no—
187C4—4122no—
188C4—4122no—
189C4#1569293512yes—
190C2—21no—
191C2—22no—
192C2—22no—
193C2—21no—
194C2C2×#1569293511yescharacteristic
195C2C2×#1569294611yescharacteristic
196C2#2026780711yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×C22⋊C8×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC24×C103D4
cosocleC22×C4×C103C23
hypercenterC2×C22⋊C8D103
hypocenterC103#1520
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #20267529C2semidirect
5. C22×Dic206C4semidirect
8. #15693000C4semidirect
11. C2×C4⋊Dic103C4semidirect
99. C103#1520semidirect

Maximal subgroups

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

subgroupindex
C2×#156930002
#202676512
#202675292
C2×C22⋊C8×C1032
#1520103