Finite Group Databasebeta

← #27193601

Subgroups — #27193601

Order 13184.

230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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#20268323C211yesmaximal, characteristic
2#20267847C211yesmaximal, characteristic, complemented
3C4×C8×D103C211yesmaximal, characteristic, complemented
4#20267523C211yesmaximal, characteristic, complemented
5#20267521C211yesmaximal, characteristic, complemented
6D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
7D4⋊C8×C103C211yesmaximal, characteristic, complemented
8C2×C8×D103—21no—
9#15693014—21no—
10#15693012C411yescharacteristic
11#15693008C411yescharacteristic
12#15693003—21no—
13#15693001C411yescharacteristic
14#15692992C411yescharacteristic
15C4×Dic206C2211yescharacteristic
16C4×C22⋊D103—21no—
17#15692980—21no—
18C42×D103C2211yescharacteristic
19C4⋊(C103⋊C8)C2211yescharacteristic
20(C2×D103)⋊C8—21no—
21#15692931—21no—
22C4×C103⋊C8C2211yescharacteristic
23C8×Dic103—21no—
24C4×D4×C103C2211yescharacteristic
25C4⋊C8×C103C2211yescharacteristic
26C4×C8×C103C2211yescharacteristic
27C2×Dic206C2×C411yescharacteristic
28C2×C22⋊D103—21no—
29C2×C4×D103C2×C411yescharacteristic
30C2×C4×D103D411yescharacteristic
31C2×C4×D103D411yescharacteristic
32C2×C103⋊C8—21no—
33C2×C103⋊C8—21no—
34C8×D103—24no—
35C4⋊Dic103—21no—
36C4⋊Dic103—21no—
37C4⋊Dic103C2×C411yescharacteristic
38Dic103⋊C4—21no—
39Dic103⋊C4—21no—
40C22⋊Dic103—21no—
41C22⋊Dic103—21no—
42C22⋊Dic103—21no—
43(C2×D103)⋊C4—21no—
44C4×Dic103—21no—
45C4×Dic103C2×C411yescharacteristic
46C4×Dic103D411yescharacteristic
47C4×Dic103D411yescharacteristic
48C2×D4×C103C2×C411yescharacteristic
49C22×C4×C103—21no—
50C2×C8×C103—21no—
51C2×C8×C103—21no—
52C4⋊C4×C103C2×C411yescharacteristic
53C22⋊C4×C103—21no—
54C42×C103C2311yescharacteristic
55C23×C103—21no—
56C22×D103C22⋊C411yescharacteristic
57D4×C103—21no—
58D4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—41no—
61C2×C4×C103—41no—
62C2×C4×C103C22×C411yescharacteristic
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C22⋊D103—42no—
66C2×Dic103—21no—
67C2×Dic103—21no—
68C2×Dic103C22⋊C411yescharacteristic
69C2×Dic103C22⋊C411yescharacteristic
70C2×Dic103C22⋊C411yescharacteristic
71C4×D103—22no—
72C4×D103—21no—
73C4×D103—21no—
74C4×D103—21no—
75C4×D103—21no—
76Dic206—21no—
77Dic206—21no—
78C8×C103—22no—
79C8×C103—41no—
80C103⋊C8—22no—
81C103⋊C8—41no—
82C22×C103—41no—
83C22×C103—41no—
84C22×C103—41no—
85C22×C103C2×C22⋊C411yescharacteristic
86C2×D103—21no—
87C2×D103—21no—
88C2×D103#10412yes—
89C4×C103—21no—
90C4×C103—41no—
91C4×C103#13111yescharacteristic
92C4×C103#13111yescharacteristic
93C4×C103#13511yescharacteristic
94C4×C103#13511yescharacteristic
95Dic103—21no—
96Dic103—21no—
97Dic103—21no—
98Dic103—41no—
99Dic103—41no—
100C2×C103—81no—
101C2×C103#40811yescharacteristic
102C2×C103#41611yescharacteristic
103C2×C103C2×#10411yescharacteristic
104D103—22no—
105#1494—1031nomaximal, Sylow
106C103#149411yescharacteristic, complemented, Sylow
107#529—1031no—
108#432—1031no—
109C2×C4×C8—1031no—
110Q8⋊C8—1031no—
111Q8⋊C8—1031no—
112D4⋊C8—1031no—
113D4⋊C8D10311yescharacteristic, complemented
114C22×C8—2061no—
115#126—2061no—
116#125—1031no—
117#124—1031no—
118#123—2061no—
119C22⋊Q8—1031no—
120#121—1031no—
121C4×Q8—1031no—
122C4×D4—2061no—
123C4×D4C2×D10311yescharacteristic
124#117—2061no—
125C2×C42—1031no—
126C4⋊C8—1031no—
127C4⋊C8C2×D10311yescharacteristic
128C22⋊C8—2061no—
129#97—2061no—
130C4×C8—1031no—
131C4×C8—2061no—
132C4×C8C2×D10311yescharacteristic
133C2×Q8—1031no—
134C2×D4—2061no—
135C2×D4C4×D10311yescharacteristic
136C22×C4—21no—
137C22×C4—1031no—
138C22×C4—1031no—
139C22×C4—1031no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—2064no—
143C2×C8—2061no—
144C2×C8—2061no—
145C4⋊C4—1031no—
146C4⋊C4—2061no—
147C4⋊C4—2061no—
148C4⋊C4—2061no—
149C4⋊C4—2061no—
150C4⋊C4C4×D10311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2061no—
153C22⋊C4—2061no—
154C22⋊C4—2061no—
155C22⋊C4—2061no—
156C42—1031no—
157C42—1031no—
158C42—1031no—
159C42—2061no—
160C42C22×D10311yescharacteristic
161C23—21no—
162C23—1031no—
163Q8—2061no—
164Q8—2061no—
165D4—21no—
166D4—21no—
167D4—4122no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1031no—
172C2×C4—1031no—
173C2×C4—1031no—
174C2×C4—2062no—
175C2×C4—2061no—
176C2×C4—2061no—
177C2×C4—2061no—
178C2×C4—2061no—
179C2×C4—2061no—
180C2×C4—2061no—
181C2×C4C2×C4×D10311yescharacteristic
182C2×C4D4×D10311yescharacteristic
183C2×C4D4×D10311yescharacteristic
184C8—22no—
185C8—41no—
186C8—4121no—
187C8—2062no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—1032no—
192C22—2061no—
193C22—2061no—
194C22C22⋊C4×D10311yescharacteristic
195C4—21no—
196C4—41no—
197C4—4121no—
198C4—4121no—
199C4—2061no—
200C4—2061no—
201C4—2061no—
202C4#1569302711yescharacteristic
203C4#1569302911yescharacteristic
204C4#1569304011yescharacteristic
205C4#1569304211yescharacteristic
206C2—81no—
207C2—2062no—
208C2#2026775611yescharacteristic
209C2#2026778411yescharacteristic
210C2#104×D10311yescharacteristic
subgroupG/H
centerC2×C4D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
FittingD4⋊C8×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692992C4
cosocleC42×C103C23
hypercenterD4⋊C8D103
hypocenterC103#1494
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20267847C2semidirect
3. C4×C8×D103C2semidirect
4. #20267523C2semidirect
5. #20267521C2semidirect
6. D4⋊(C103⋊C8)C2semidirect
7. D4⋊C8×C103C2semidirect
106. C103#1494semidirect
113. D4⋊C8D103semidirect

Maximal subgroups

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

subgroupindex
#202683232
#202678472
C4×C8×D1032
#202675232
#202675212
D4⋊(C103⋊C8)2
D4⋊C8×C1032
#1494103