Finite Group Databasebeta

← #27194298

Subgroups — #27194298

Order 13184.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268446C211yesmaximal, characteristic
2#20268142C211yesmaximal, characteristic, complemented
3#20268082C211yesmaximal, characteristic, complemented
4#20268081C211yesmaximal, characteristic, complemented
5#20267538C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic, complemented
7D4⋊C8×C103C211yesmaximal, characteristic, complemented
8C2×#13110105—21no—
9#15693021C2211yescharacteristic
10#15693021C2211yescharacteristic
11#15693003—22no—
12#15693000—21no—
13#15692992—21no—
14C4×D412C2211yescharacteristic
15C4⋊C4×D103—21no—
16#15692953—21no—
17#15692952—21no—
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692946—22no—
20#15692943—21no—
21#15692942—21no—
22C4×D4×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25#13110105—42no—
26#13110105—42no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×D412D411yescharacteristic
30C2×C22⋊D103—22no—
31C2×C4×D103—22no—
32C2×C4×D103—21no—
33C2×C103⋊C8—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103—21no—
37C4⋊Dic103D412yes—
38C4⋊Dic103D411yescharacteristic
39Dic103⋊C4—22no—
40C22⋊Dic103—22no—
41(C2×D103)⋊C4—21no—
42C2×D4×C103D411yescharacteristic
43C22×C4×C103—21no—
44C2×C8×C103—21no—
45C2×C8×C103—21no—
46C4⋊C4×C103D411yescharacteristic
47C22⋊C4×C103—21no—
48C42×C103C2311yescharacteristic
49C23×C103—21no—
50C22×D103—21no—
51D4×C103—21no—
52D4×C103—21no—
53C2×C4×C103—21no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C22⋊D103—44no—
60C2×Dic103—21no—
61C2×Dic103—22no—
62C2×Dic103—41no—
63D412—21no—
64D412SD1612yes—
65C4×D103—44no—
66C4×D103—41no—
67C4×D103—41no—
68Dic206—41no—
69Dic206—41no—
70Dic206—42no—
71C8×C103—41no—
72C8×C103—41no—
73C103⋊C8—41no—
74C22×C103—41no—
75C22×C103—41no—
76C22×C103—41no—
77C22×C103#12011yescharacteristic
78C2×D103—22no—
79C2×D103—41no—
80C2×D103—41no—
81C4×C103—21no—
82C4×C103—41no—
83C4×C103C2×SD1611yescharacteristic
84C4×C103#13511yescharacteristic
85C4×C103AGL(1,ℤ/8)11yescharacteristic
86C4×C103#13711yescharacteristic
87Dic103—42no—
88Dic103—41no—
89Dic103—81no—
90C2×C103—81no—
91C2×C103#45011yescharacteristic
92C2×C103#45211yescharacteristic
93C2×C103#45411yescharacteristic
94D103—42no—
95#1635—1031nomaximal, Sylow
96C103#163511yescharacteristic, complemented, Sylow
97#547—1031no—
98#487—1031no—
99#476—1031no—
100#476—1031no—
101#332—1031no—
102D4⋊C8—1031no—
103D4⋊C8D10311yescharacteristic, complemented
104C2×#41—2061no—
105C4⋊Q8—1031no—
106C4⋊Q8—1031no—
107#123—2062no—
108C22⋊Q8—2061no—
109#121—2061no—
110C4×D4—1031no—
111C4×D4C2×D10311yescharacteristic
112C2×C4⋊C4—2061no—
113#106—2061no—
114#106—2061no—
115C4⋊C8—1031no—
116C4⋊C8C2×D10311yescharacteristic
117#103—2062no—
118#102—2061no—
119#102—2061no—
120C4×C8C2×D10311yescharacteristic
121#41—4122no—
122#41—4122no—
123C2×Q8—2061no—
124C2×Q8—2061no—
125C2×D4—1031no—
126C2×D4—2062no—
127C2×D4D41211yescharacteristic
128C22×C4—21no—
129C22×C4—2062no—
130C22×C4—2061no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2061no—
134C4⋊C4—1032no—
135C4⋊C4—1031no—
136C4⋊C4—2062no—
137C4⋊C4—2061no—
138C4⋊C4—2061no—
139C4⋊C4—2061no—
140C4⋊C4D41211yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—2062no—
143C22⋊C4—2061no—
144C42C22×D10311yescharacteristic
145C23—21no—
146C23—2061no—
147Q8—4122no—
148Q8—4121no—
149Q8—4121no—
150D4—21no—
151D4—21no—
152D4—1032no—
153D4—4124no—
154D4—2061no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—4124no—
159C2×C4—4121no—
160C2×C4—4121no—
161C2×C4—4121no—
162C2×C4—2061no—
163C2×C4—2062no—
164C2×C4D4×D10311yescharacteristic
165C2×C4D4×D10311yescharacteristic
166C2×C4C2×D41211yescharacteristic
167C8—41no—
168C8—41no—
169C8—4121no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—4121no—
174C22—4121no—
175C22—2062no—
176C22#1569299111yescharacteristic
177C4—21no—
178C4—41no—
179C4—8241no—
180C4—4122no—
181C4—4121no—
182C4SD16×D10311yescharacteristic
183C4#1569304311yescharacteristic
184C4#1569304511yescharacteristic
185C4#1569305411yescharacteristic
186C2—81no—
187C2—4122no—
188C2#2026794311yescharacteristic
189C2#2026795511yescharacteristic
190C2#2026796511yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
FittingD4⋊C8×C103C2
socleC22×C103#120
prime radical#20268446C2
hypercenterD4⋊C8D103
hypocenterC103#1635
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20268142C2semidirect
3. #20268082C2semidirect
4. #20268081C2semidirect
5. #20267538C2semidirect
6. #20267520C2semidirect
7. D4⋊C8×C103C2semidirect
96. C103#1635semidirect
103. D4⋊C8D103semidirect

Maximal subgroups

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

subgroupindex
#202684462
#202681422
#202680822
#202680812
#202675382
#202675202
D4⋊C8×C1032
#1635103