Finite Group Databasebeta

← #27193731

Subgroups — #27193731

Order 13184.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#20268326C211yesmaximal, characteristic
2#20267743C211yesmaximal, characteristic, complemented
3#97×D103C211yesmaximal, characteristic, complemented
4#20267533C211yesmaximal, characteristic, complemented
5#20267530C211yesmaximal, characteristic, complemented
6#20267530C211yesmaximal, characteristic, complemented
7#330×C103C211yesmaximal, characteristic, complemented
8C2×#13110088—21no—
9C2×C8×D103—21no—
10#15693016—21no—
11#15693009C2211yescharacteristic
12#15693006—21no—
13#15693001C411yescharacteristic
14#15692996C411yescharacteristic
15#15692986C411yescharacteristic
16#15692983—21no—
17#15692983C411yescharacteristic
18#15692979—21no—
19C42×D103C2211yescharacteristic
20#15692932C2211yescharacteristic
21#15692932C2211yescharacteristic
22#15692931—21no—
23C8×Dic103—21no—
24#125×C103C2211yescharacteristic
25#97×C103C2211yescharacteristic
26#97×C103C2211yescharacteristic
27C2×Dic206C2×C411yescharacteristic
28C2×D412—21no—
29C2×D412C2×C411yescharacteristic
30C2×C4×D103—21no—
31C2×C4×D103C2×C411yescharacteristic
32C2×C4×D103D411yescharacteristic
33C2×C4×D103D411yescharacteristic
34#13110088—24no—
35C2×C103⋊C8—21no—
36C2×C103⋊C8—21no—
37C8×D103—24no—
38C4⋊Dic103—21no—
39Dic103⋊C4—21no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42(C2×D103)⋊C4—21no—
43(C2×D103)⋊C4—21no—
44(C2×D103)⋊C4—21no—
45C4×Dic103—21no—
46C4×Dic103C2×C411yescharacteristic
47C4×Dic103D411yescharacteristic
48C4×Dic103D411yescharacteristic
49C2×C8×C103—21no—
50C2×C8×C103—21no—
51C4⋊C4×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103C2×C411yescharacteristic
54C4⋊C4×C103C2×C411yescharacteristic
55C42×C103C2311yescharacteristic
56C22×D103—21no—
57C22×D103C22⋊C411yescharacteristic
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103C22×C411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C2×C4×C103C2×D411yescharacteristic
63C2×Dic103—21no—
64C2×Dic103C22⋊C411yescharacteristic
65C2×Dic103C22⋊C411yescharacteristic
66C2×Dic103C22⋊C411yescharacteristic
67D412—41no—
68D412—42no—
69C4×D103—22no—
70C4×D103—22no—
71C4×D103—41no—
72C4×D103—42no—
73Dic206—41no—
74C8×C103—22no—
75C8×C103—22no—
76C103⋊C8—22no—
77C103⋊C8—22no—
78C22×C103C2×C22⋊C411yescharacteristic
79C2×D103—21no—
80C2×D103—21no—
81C2×D103—41no—
82C2×D103—41no—
83C2×D103—41no—
84C2×D103#10412yes—
85C4×C103—21no—
86C4×C103—21no—
87C4×C103—21no—
88C4×C103—41no—
89C4×C103—41no—
90Dic103—21no—
91Dic103—21no—
92Dic103—41no—
93Dic103#10412yes—
94C2×C103#41311yescharacteristic
95C2×C103C2×#10411yescharacteristic
96C2×C103C2×#10411yescharacteristic
97D103—22no—
98D103—81no—
99#1524—1031nomaximal, Sylow
100C103#152411yescharacteristic, complemented, Sylow
101#529—1031no—
102C4×M16—1031no—
103C2×#97—1031no—
104#330—1031no—
105#330D10311yescharacteristic, complemented
106#329—1031no—
107#329—1031no—
108C2×M16—2061no—
109C22×C8—2061no—
110#126—2061no—
111#125C2×D10311yescharacteristic
112#124—1031no—
113#123—2061no—
114C22⋊Q8—1031no—
115#121—1031no—
116C4×Q8—1031no—
117C4×D4—1031no—
118C4×D4—2061no—
119#117—2061no—
120C2×C42—1031no—
121#97—1031no—
122#97—1031no—
123#97—2061no—
124#97C2×D10311yescharacteristic
125#97C2×D10311yescharacteristic
126C4×C8—2061no—
127C2×Q8—1031no—
128C2×D4—1031no—
129C2×D4—2061no—
130C22×C4—1031no—
131C22×C4—1031no—
132C22×C4—1031no—
133C22×C4—2061no—
134M16—2064no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—2064no—
138C2×C8—2061no—
139C2×C8—2061no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—2061no—
143C4⋊C4—2061no—
144C4⋊C4C4×D10311yescharacteristic
145C4⋊C4C4×D10311yescharacteristic
146C22⋊C4—2061no—
147C22⋊C4—2061no—
148C22⋊C4—2061no—
149C22⋊C4—2061no—
150C22⋊C4—2061no—
151C42—1031no—
152C42—1031no—
153C42—1031no—
154C42—2061no—
155C42C22×D10311yescharacteristic
156C23—1031no—
157C23—2061no—
158Q8—4121no—
159D4—4121no—
160D4—4122no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—1031no—
164C2×C4—1031no—
165C2×C4—1031no—
166C2×C4—4121no—
167C2×C4—4122no—
168C2×C4—2062no—
169C2×C4—2062no—
170C2×C4—2061no—
171C2×C4C2×C4×D10311yescharacteristic
172C2×C4D4×D10311yescharacteristic
173C2×C4D4×D10311yescharacteristic
174C8—22no—
175C8—22no—
176C8—2062no—
177C8—2062no—
178C22—1032no—
179C22—4121no—
180C22—4121no—
181C22—4121no—
182C22—2061no—
183C22—2061no—
184C22C22⋊C4×D10311yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—41no—
190C4—1032no—
191C4—4121no—
192C4—2061no—
193C4—2061no—
194C2—8241no—
195C2—2062no—
196C2#2026777411yescharacteristic
197C2#104×D10311yescharacteristic
198C2#104×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#330×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692996C4
cosocleC42×C103C23
hypercenter#330D103
hypocenterC103#1524
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #20267743C2semidirect
3. #97×D103C2semidirect
4. #20267533C2semidirect
5. #20267530C2semidirect
6. #20267530C2semidirect
7. #330×C103C2semidirect
100. C103#1524semidirect
105. #330D103semidirect

Maximal subgroups

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

subgroupindex
#202683262
#202677432
#97×D1032
#202675332
#202675302
#330×C1032
#1524103