Finite Group Databasebeta

← #27194295

Subgroups — #27194295

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#20268143C211yesmaximal, characteristic, complemented
2#20268081C211yesmaximal, characteristic, complemented
3#20268081C211yesmaximal, characteristic, complemented
4#20267537C211yesmaximal, characteristic, complemented
5D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
7#547×C103C211yesmaximal, characteristic
8#15693021C2211yescharacteristic
9#15692952—21no—
10#15692952—21no—
11C4⋊(C103⋊C8)C2211yescharacteristic
12C4⋊(C103⋊C8)C2211yescharacteristic
13#15692944—22no—
14#15692942—21no—
15#15692942—21no—
16C4×C103⋊C8C2211yescharacteristic
17C2×#41×C103—21no—
18C4⋊Q8×C103C2211yescharacteristic
19#123×C103—22no—
20C22⋊Q8×C103—21no—
21#121×C103—21no—
22C4×D4×C103C2211yescharacteristic
23C4×D4×C103C2211yescharacteristic
24C2×C4⋊C4×C103—21no—
25C2×Dic206—21no—
26C2×C103⋊C8—21no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C4⋊Dic103—21no—
30C4⋊Dic103—21no—
31#41×C103—42no—
32#41×C103—42no—
33C2×Q8×C103—21no—
34C2×D4×C103—22no—
35C2×D4×C103D411yescharacteristic
36C2×D4×C103D411yescharacteristic
37C22×C4×C103—22no—
38C22×C4×C103—21no—
39C22×C4×C103—21no—
40C4⋊C4×C103—22no—
41C4⋊C4×C103—21no—
42C4⋊C4×C103D411yescharacteristic
43C4⋊C4×C103D411yescharacteristic
44C4⋊C4×C103D412yes—
45C22⋊C4×C103—22no—
46C22⋊C4×C103—21no—
47C22⋊C4×C103—21no—
48C42×C103C2311yescharacteristic
49C23×C103—21no—
50C23×C103—21no—
51Q8×C103—41no—
52Q8×C103—41no—
53D4×C103—21no—
54D4×C103—21no—
55D4×C103—21no—
56D4×C103—44no—
57D4×C103SD1612yes—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—22no—
61C2×C4×C103—44no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103C2×D411yescharacteristic
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103C2×D411yescharacteristic
69C2×Dic103—41no—
70Dic206—42no—
71C103⋊C8—41no—
72C103⋊C8—41no—
73C103⋊C8—41no—
74C22×C103—22no—
75C22×C103—41no—
76C22×C103—41no—
77C22×C103—41no—
78C22×C103—41no—
79C22×C103—41no—
80C22×C103#12011yescharacteristic
81C4×C103—21no—
82C4×C103—41no—
83C4×C103—42no—
84C4×C103—41no—
85C4×C103C2×SD1611yescharacteristic
86C4×C103#13511yescharacteristic
87C4×C103AGL(1,ℤ/8)11yescharacteristic
88C4×C103#13711yescharacteristic
89Dic103—81no—
90C2×C103—42no—
91C2×C103—81no—
92C2×C103#45011yescharacteristic
93C2×C103#45211yescharacteristic
94C2×C103#45411yescharacteristic
95#1635—1031nomaximal, Sylow
96C103#163511yescharacteristic, complemented, Sylow
97#547D10311yescharacteristic
98#487—1031no—
99#476—1031no—
100#476—1031no—
101#332—1031no—
102D4⋊C8—1031no—
103D4⋊C8—1031no—
104C2×#41—21no—
105C4⋊Q8—1031no—
106C4⋊Q8C2×D10311yescharacteristic
107#123—22no—
108C22⋊Q8—21no—
109#121—21no—
110C4×D4C2×D10311yescharacteristic
111C4×D4C2×D10311yescharacteristic
112C2×C4⋊C4—21no—
113#106—2061no—
114#106—2061no—
115C4⋊C8—1031no—
116C4⋊C8—1031no—
117#103—2062no—
118#102—2061no—
119#102—2061no—
120C4×C8—1031no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×Q8—2061no—
125C2×D4—22no—
126C2×D4C22⋊D10311yescharacteristic
127C2×D4C22⋊D10311yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C2×C8—2061no—
132C2×C8—2061no—
133C2×C8—2061no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—2061no—
137C4⋊C4—2061no—
138C4⋊C4C22⋊D10312yes—
139C4⋊C4C22⋊D10311yescharacteristic
140C4⋊C4C22⋊D10311yescharacteristic
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C42C22×D10311yescharacteristic
145C23—21no—
146C23—21no—
147Q8—41no—
148Q8—41no—
149Q8—4122no—
150D4—21no—
151D4—21no—
152D4—21no—
153D4—44no—
154D4#1311009312yes—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—4121no—
164C2×C4C2×C22⋊D10311yescharacteristic
165C2×C4C2×C22⋊D10311yescharacteristic
166C2×C4C2×C22⋊D10311yescharacteristic
167C8—4121no—
168C8—4121no—
169C8—4121no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#1569299011yescharacteristic
177C4—21no—
178C4—41no—
179C4—42no—
180C4—41no—
181C4—8241no—
182C4C2×#1311009311yescharacteristic
183C4#1569304111yescharacteristic
184C4#1569304711yescharacteristic
185C4#1569305111yescharacteristic
186C2—42no—
187C2—81no—
188C2#2026794211yescharacteristic
189C2#2026795311yescharacteristic
190C2#2026796411yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting, prime radical#547×C103C2
socleC22×C103#120
hypercenter#547D103
hypocenterC103#1635
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #20268143C2semidirect
2. #20268081C2semidirect
3. #20268081C2semidirect
4. #20267537C2semidirect
5. D4⋊(C103⋊C8)C2semidirect
6. D4⋊(C103⋊C8)C2semidirect
96. C103#1635semidirect

Maximal subgroups

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

subgroupindex
#202681432
#202680812
#202675372
D4⋊(C103⋊C8)2
#547×C1032
#1635103