Finite Group Databasebeta

← #27193774

Subgroups — #27193774

Order 13184.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#20267846C211yesmaximal, characteristic, complemented
3#20267846C211yesmaximal, characteristic, complemented
4#20267533C211yesmaximal, characteristic, complemented
5#20267530C211yesmaximal, characteristic, complemented
6#20267530C211yesmaximal, characteristic, complemented
7#330×C103C211yesmaximal, characteristic, complemented
8#15693016—21no—
9#15693009C2211yescharacteristic
10#15693006—21no—
11#15693001C411yescharacteristic
12#15692996C411yescharacteristic
13#15692986C411yescharacteristic
14#15692983—21no—
15#15692983C411yescharacteristic
16#15692979—21no—
17C42×D103C2211yescharacteristic
18Dic103⋊C8—21no—
19Dic103⋊C8—21no—
20(C2×D103)⋊C8—21no—
21(C2×D103)⋊C8—21no—
22#15692932C2211yescharacteristic
23#15692932C2211yescharacteristic
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
34C2×C103⋊C8—21no—
35C2×C103⋊C8—21no—
36C4⋊Dic103—21no—
37Dic103⋊C4—21no—
38(C2×D103)⋊C4—21no—
39(C2×D103)⋊C4—21no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42(C2×D103)⋊C4—21no—
43C4×Dic103—21no—
44C4×Dic103C2×C411yescharacteristic
45C4×Dic103D411yescharacteristic
46C4×Dic103D411yescharacteristic
47C2×C8×C103—21no—
48C2×C8×C103—21no—
49C4⋊C4×C103—21no—
50C4⋊C4×C103—21no—
51C4⋊C4×C103C2×C411yescharacteristic
52C4⋊C4×C103C2×C411yescharacteristic
53C42×C103C2311yescharacteristic
54C22×D103—21no—
55C22×D103C22⋊C411yescharacteristic
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103C22×C411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×Dic103—21no—
62C2×Dic103C22⋊C411yescharacteristic
63C2×Dic103C22⋊C411yescharacteristic
64C2×Dic103C22⋊C411yescharacteristic
65D412—41no—
66D412—42no—
67C4×D103—41no—
68C4×D103—41no—
69C4×D103—41no—
70C4×D103—42no—
71Dic206—41no—
72C8×C103—41no—
73C8×C103—41no—
74C103⋊C8—41no—
75C103⋊C8—41no—
76C22×C103C2×C22⋊C411yescharacteristic
77C2×D103—21no—
78C2×D103—21no—
79C2×D103—21no—
80C2×D103—41no—
81C2×D103—41no—
82C2×D103—41no—
83C4×C103—21no—
84C4×C103—21no—
85C4×C103—21no—
86C4×C103—41no—
87C4×C103—41no—
88Dic103—21no—
89Dic103—21no—
90Dic103—21no—
91Dic103—41no—
92C2×C103#41311yescharacteristic
93C2×C103#42111yescharacteristic
94C2×C103#42111yescharacteristic
95D103—41no—
96D103—81no—
97#1535—1031nomaximal, Sylow
98C103#153511yescharacteristic, complemented, Sylow
99#529—1031no—
100#432—1031no—
101#432—1031no—
102#330—1031no—
103#330D10311yescharacteristic, complemented
104#329—1031no—
105#329—1031no—
106#126—2061no—
107#125C2×D10311yescharacteristic
108#124—1031no—
109#123—2061no—
110C22⋊Q8—1031no—
111#121—1031no—
112C4×Q8—1031no—
113C4×D4—1031no—
114C4×D4—2061no—
115#117—2061no—
116C2×C42—1031no—
117C4⋊C8—2061no—
118C4⋊C8—2061no—
119C22⋊C8—2061no—
120C22⋊C8—2061no—
121#97—1031no—
122#97—1031no—
123#97C2×D10311yescharacteristic
124#97C2×D10311yescharacteristic
125C2×Q8—1031no—
126C2×D4—1031no—
127C2×D4—2061no—
128C22×C4—1031no—
129C22×C4—1031no—
130C22×C4—1031no—
131C22×C4—2061no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—2061no—
135C2×C8—2061no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2061no—
139C4⋊C4—2061no—
140C4⋊C4C4×D10311yescharacteristic
141C4⋊C4C4×D10311yescharacteristic
142C22⋊C4—2061no—
143C22⋊C4—2061no—
144C22⋊C4—2061no—
145C22⋊C4—2061no—
146C22⋊C4—2061no—
147C42—1031no—
148C42—1031no—
149C42—1031no—
150C42—2061no—
151C42C22×D10311yescharacteristic
152C23—1031no—
153C23—2061no—
154Q8—4121no—
155D4—4121no—
156D4—4122no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—1031no—
160C2×C4—1031no—
161C2×C4—1031no—
162C2×C4—4121no—
163C2×C4—4121no—
164C2×C4—4121no—
165C2×C4—4122no—
166C2×C4—2061no—
167C2×C4C2×C4×D10311yescharacteristic
168C2×C4D4×D10311yescharacteristic
169C2×C4D4×D10311yescharacteristic
170C8—41no—
171C8—41no—
172C8—4121no—
173C8—4121no—
174C22—4121no—
175C22—4121no—
176C22—4121no—
177C22—2061no—
178C22—2061no—
179C22—2061no—
180C22C22⋊C4×D10311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—4121no—
187C4—2061no—
188C4—2061no—
189C4—2061no—
190C2—8241no—
191C2—4121no—
192C2#2026777411yescharacteristic
193C2#2026780611yescharacteristic
194C2#2026780611yescharacteristic
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#1535
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. #20267846C2semidirect
3. #20267846C2semidirect
4. #20267533C2semidirect
5. #20267530C2semidirect
6. #20267530C2semidirect
7. #330×C103C2semidirect
98. C103#1535semidirect
103. #330D103semidirect

Maximal subgroups

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

subgroupindex
#202683262
#202678462
#202675332
#202675302
#330×C1032
#1535103