Finite Group Databasebeta

← #27194218

Subgroups — #27194218

Order 13184.

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

normal subgroups only

This group has 236 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#20268498C211yesmaximal, characteristic, complemented
2#20268164C211yesmaximal, characteristic, complemented
3#20267992C211yesmaximal, characteristic, complemented
4#20267986C211yesmaximal, characteristic
5#20267539C211yesmaximal, characteristic, complemented
6#20267523C211yesmaximal, characteristic, complemented
7D4⋊C8×C103C211yesmaximal, characteristic, complemented
8C2×#13110094—22no—
9C2×#13110094—21no—
10C2×#13110090—21no—
11#15693021C2211yescharacteristic
12#15693018C2211yescharacteristic
13#15693012—21no—
14#15693000—21no—
15#15692998—22no—
16C4×Dic206C2211yescharacteristic
17D4×Dic103—21no—
18C2×C4⋊Dic103—21no—
19C4⋊(C103⋊C8)C2211yescharacteristic
20#15692943—21no—
21#15692941—21no—
22C4×D4×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25C2×Dic206D411yescharacteristic
26C2×Dic206D412yes—
27C2×D412—21no—
28C2×D412—21no—
29C2×D412—21no—
30C22×Dic103—22no—
31#13110094—44no—
32#13110094—42no—
33#13110090—42no—
34C2×C103⋊C8—21no—
35C4⋊Dic103—22no—
36C4⋊Dic103—21no—
37C4⋊Dic103—21no—
38C4⋊Dic103D411yescharacteristic
39Dic103⋊C4—22no—
40Dic103⋊C4—21no—
41C22⋊Dic103—22no—
42C4×Dic103—21no—
43C2×D4×C103D411yescharacteristic
44C22×C4×C103—21no—
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C4⋊C4×C103D411yescharacteristic
48C22⋊C4×C103—21no—
49C42×C103C2311yescharacteristic
50C23×C103—21no—
51C22×D103—41no—
52D4×C103—21no—
53D4×C103SD1612yescomplemented
54C2×C4×C103—21no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×Dic103—21no—
61C2×Dic103—21no—
62C2×Dic103—22no—
63C2×Dic103—82no—
64D412—42no—
65D412—41no—
66D412—41no—
67D412—41no—
68D412—41no—
69Dic206—21no—
70Dic206—21no—
71Dic206—42no—
72C8×C103—22no—
73C8×C103—41no—
74C103⋊C8—41no—
75C22×C103—22no—
76C22×C103—41no—
77C22×C103—41no—
78C22×C103#12011yescharacteristic
79C2×D103—81no—
80C2×D103—81no—
81C2×D103—81no—
82C4×C103—21no—
83C4×C103—41no—
84C4×C103C2×SD1611yescharacteristic
85C4×C103#13511yescharacteristic
86C4×C103AGL(1,ℤ/8)11yescharacteristic
87C4×C103#13711yescharacteristic
88Dic103—41no—
89Dic103—42no—
90Dic103—41no—
91C2×C103—42no—
92C2×C103#44811yescharacteristic
93C2×C103#44911yescharacteristic
94C2×C103#45311yescharacteristic
95D103—161no—
96#1622—1031nomaximal, Sylow
97C103#162211yescharacteristic, complemented, Sylow
98#554—1031no—
99#492—1031no—
100#460—1031no—
101#459—1031no—
102#333—1031no—
103Q8⋊C8—1031no—
104D4⋊C8D10311yescharacteristic, complemented
105C2×SD16—2061no—
106C2×SD16—2062no—
107C2×D8—2061no—
108C4⋊Q8—1031no—
109#127—1031no—
110#125—2061no—
111C22⋊Q8—2062no—
112C22⋊Q8—2061no—
113C4×Q8—1031no—
114C4×D4—2061no—
115C4×D4C2×D10311yescharacteristic
116C2×C4⋊C4—2061no—
117C4⋊C8—1031no—
118C4⋊C8C2×D10311yescharacteristic
119#102—2061no—
120#102—2061no—
121C4×C8C2×D10311yescharacteristic
122C2×Q8—1032no—
123C2×Q8—1031no—
124C2×D4—2061no—
125C2×D4—2061no—
126C2×D4—2061no—
127C2×D4D41211yescharacteristic
128C22×C4—21no—
129C22×C4—2062no—
130SD16—4124no—
131SD16—4122no—
132D8—4122no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2061no—
136C4⋊C4—1031no—
137C4⋊C4—2062no—
138C4⋊C4—2062no—
139C4⋊C4—2061no—
140C4⋊C4—2061no—
141C4⋊C4—2061no—
142C4⋊C4D41211yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2062no—
145C42—2061no—
146C42C22×D10311yescharacteristic
147C23—21no—
148C23—4121no—
149Q8—4122no—
150Q8—2061no—
151Q8—2061no—
152D4—21no—
153D4—4122no—
154D4—4121no—
155D4—4121no—
156D4—4121no—
157D4—4121no—
158D4#1311009412yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—8242no—
163C2×C4—2061no—
164C2×C4—2061no—
165C2×C4—2062no—
166C2×C4D4×D10311yescharacteristic
167C2×C4D4×D10311yescharacteristic
168C2×C4C2×D41211yescharacteristic
169C8—22no—
170C8—41no—
171C8—4121no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—8241no—
176C22—8241no—
177C22—8241no—
178C22#1569299111yescharacteristic
179C4—21no—
180C4—41no—
181C4—4121no—
182C4—4121no—
183C4—4122no—
184C4C2×#1311009411yescharacteristic
185C4#1569304211yescharacteristic
186C4#1569304511yescharacteristic
187C4#1569305411yescharacteristic
188C2—42no—
189C2—16481no—
190C2#2026793211yescharacteristic
191C2#2026793711yescharacteristic
192C2#2026796011yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
FittingD4⋊C8×C103C2
socleC22×C103#120
prime radical#20267986C2
hypercenterD4⋊C8D103
hypocenterC103#1622
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
1. #20268498C2semidirect
2. #20268164C2semidirect
3. #20267992C2semidirect
5. #20267539C2semidirect
6. #20267523C2semidirect
7. D4⋊C8×C103C2semidirect
53. D4×C103SD16semidirect
97. C103#1622semidirect
104. D4⋊C8D103semidirect
158. D4#13110094semidirect

Maximal subgroups

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

subgroupindex
#202684982
#202681642
#202679922
#202679862
#202675392
#202675232
D4⋊C8×C1032
#1622103