Finite Group Databasebeta

← #27194294

Subgroups — #27194294

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#20268141C211yesmaximal, characteristic, complemented
3#20268078C211yesmaximal, characteristic, complemented
4#20267536C211yesmaximal, characteristic, complemented
5D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic, complemented
7#476×C103C211yesmaximal, characteristic, complemented
8C2×#13110105—21no—
9#15693021C2211yescharacteristic
10#15693003—22no—
11#15693000—21no—
12#15692992—21no—
13C4×D412C2211yescharacteristic
14C4⋊C4×D103—21no—
15#15692952—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692945—22no—
18#15692941—21no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×D4×C103C2211yescharacteristic
22#106×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25#13110105—42no—
26#13110105—42no—
27C2×Dic206—21no—
28C2×D412D411yescharacteristic
29C2×C22⋊D103—22no—
30C2×C4×D103—22no—
31C2×C4×D103—21no—
32C2×C103⋊C8—21no—
33C2×C103⋊C8—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103D412yes—
36C4⋊Dic103D411yescharacteristic
37Dic103⋊C4—22no—
38C22⋊Dic103—22no—
39(C2×D103)⋊C4—21no—
40C2×Q8×C103—21no—
41C2×D4×C103D411yescharacteristic
42C22×C4×C103—21no—
43C2×C8×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103D411yescharacteristic
47C22⋊C4×C103—21no—
48C42×C103C2311yescharacteristic
49C23×C103—21no—
50C22×D103—21no—
51Q8×C103—42no—
52D4×C103—21no—
53D4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C22⋊D103—44no—
62C2×Dic103—21no—
63C2×Dic103—22no—
64D412—21no—
65D412SD1612yes—
66C4×D103—44no—
67C4×D103—41no—
68C4×D103—41no—
69Dic206—41no—
70Dic206—41no—
71C8×C103—41no—
72C103⋊C8—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×C103—81no—
84C4×C103C2×SD1611yescharacteristic
85C4×C103#13511yescharacteristic
86C4×C103AGL(1,ℤ/8)11yescharacteristic
87C4×C103#13711yescharacteristic
88Dic103—42no—
89Dic103—41no—
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#476D10311yescharacteristic, complemented
101#332—1031no—
102D4⋊C8—1031no—
103D4⋊C8—1031no—
104C2×#41—2061no—
105C4⋊Q8—1031no—
106C4⋊Q8C2×D10311yescharacteristic
107#123—2062no—
108C22⋊Q8—2061no—
109#121—2061no—
110C4×D4—1031no—
111C4×D4C2×D10311yescharacteristic
112C2×C4⋊C4—2061no—
113#106—21no—
114#106—2061no—
115C4⋊C8—1031no—
116C4⋊C8C2×D10311yescharacteristic
117#103—2062no—
118#102—21no—
119#102—2061no—
120C4×C8—1031no—
121#41—4122no—
122#41—4122no—
123C2×Q8—21no—
124C2×Q8—2061no—
125C2×D4—1031no—
126C2×D4—2062no—
127C2×D4C22⋊D10311yescharacteristic
128C22×C4—21no—
129C22×C4—2062no—
130C22×C4—2061no—
131C2×C8—21no—
132C2×C8—2061no—
133C2×C8—2061no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—1032no—
137C4⋊C4—1031no—
138C4⋊C4—2062no—
139C4⋊C4—2061no—
140C4⋊C4C22⋊D10311yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—2062no—
143C22⋊C4—2061no—
144C42C22×D10311yescharacteristic
145C23—21no—
146C23—2061no—
147Q8—42no—
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—41no—
159C2×C4—4124no—
160C2×C4—4121no—
161C2×C4—4121no—
162C2×C4—2061no—
163C2×C4—2062no—
164C2×C4D4×D10311yescharacteristic
165C2×C4D4×D10311yescharacteristic
166C2×C4C2×C22⋊D10311yescharacteristic
167C8—41no—
168C8—4121no—
169C8—4121no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—4121no—
174C22—4121no—
175C22—2062no—
176C22#1569298911yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—4122no—
181C4—4121no—
182C4SD16×D10311yescharacteristic
183C4#1569304111yescharacteristic
184C4#1569304811yescharacteristic
185C4#1569305211yescharacteristic
186C2—81no—
187C2—4122no—
188C2#2026794011yescharacteristic
189C2#2026795111yescharacteristic
190C2#2026796211yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#476×C103C2
socleC22×C103#120
prime radical#20268446C2
hypercenter#476D103
hypocenterC103#1635
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #20268141C2semidirect
3. #20268078C2semidirect
4. #20267536C2semidirect
5. D4⋊(C103⋊C8)C2semidirect
6. #20267518C2semidirect
7. #476×C103C2semidirect
96. C103#1635semidirect
100. #476D103semidirect

Maximal subgroups

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

subgroupindex
#202684462
#202681412
#202680782
#202675362
D4⋊(C103⋊C8)2
#202675182
#476×C1032
#1635103