Finite Group Databasebeta

← #27193554

Subgroups — #27193554

Order 13184.

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

normal subgroups only

This group has 234 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
2C4⋊C8×D103C211yesmaximal, characteristic, complemented
3C4×#13110088C211yesmaximal, characteristic, complemented
4#20267523C211yesmaximal, characteristic, complemented
5#20267521C211yesmaximal, characteristic, complemented
6D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
7D4⋊C8×C103C211yesmaximal, characteristic, complemented
8C2×#13110088—21no—
9C2×C8×D103—21no—
10#15693014—21no—
11#15693012C411yescharacteristic
12#15693008C411yescharacteristic
13#15693003—21no—
14#15693001C411yescharacteristic
15#15692992C411yescharacteristic
16C4×Dic206C2211yescharacteristic
17C4×C22⋊D103—21no—
18#15692980—21no—
19C42×D103C2211yescharacteristic
20C4⋊(C103⋊C8)C2211yescharacteristic
21Dic103⋊C8—21no—
22#15692931—21no—
23C4×C103⋊C8C2211yescharacteristic
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
32#13110088—24no—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C8×D103—42no—
36C4⋊Dic103—21no—
37C4⋊Dic103—21no—
38C4⋊Dic103C2×C411yescharacteristic
39Dic103⋊C4—21no—
40Dic103⋊C4—21no—
41C22⋊Dic103—21no—
42C22⋊Dic103—21no—
43C22⋊Dic103—21no—
44(C2×D103)⋊C4—21no—
45C4×Dic103—21no—
46C4×Dic103C2×C411yescharacteristic
47C4×Dic103D411yescharacteristic
48C4×Dic103D411yescharacteristic
49C2×D4×C103C2×C411yescharacteristic
50C22×C4×C103—21no—
51C2×C8×C103—21no—
52C2×C8×C103—21no—
53C4⋊C4×C103C2×C411yescharacteristic
54C22⋊C4×C103—21no—
55C42×C103C2311yescharacteristic
56C23×C103—21no—
57C22×D103C22⋊C411yescharacteristic
58D4×C103—21no—
59D4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103C22×C411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C22⋊D103—42no—
67C2×Dic103—21no—
68C2×Dic103—21no—
69C2×Dic103C22⋊C411yescharacteristic
70C2×Dic103C22⋊C411yescharacteristic
71C2×Dic103C22⋊C411yescharacteristic
72C4×D103—22no—
73C4×D103—21no—
74C4×D103—21no—
75C4×D103—21no—
76C4×D103—21no—
77Dic206—21no—
78Dic206—21no—
79C8×C103—22no—
80C8×C103—41no—
81C103⋊C8—22no—
82C103⋊C8—41no—
83C22×C103—41no—
84C22×C103—41no—
85C22×C103—41no—
86C22×C103C2×C22⋊C411yescharacteristic
87C2×D103—21no—
88C2×D103—21no—
89C2×D103#10412yes—
90C4×C103—21no—
91C4×C103—41no—
92C4×C103#13111yescharacteristic
93C4×C103#13111yescharacteristic
94C4×C103AGL(1,ℤ/8)11yescharacteristic
95C4×C103#13711yescharacteristic
96Dic103—21no—
97Dic103—21no—
98Dic103—21no—
99Dic103—41no—
100Dic103—41no—
101C2×C103—81no—
102C2×C103#40811yescharacteristic
103C2×C103#41711yescharacteristic
104C2×C103C2×#10411yescharacteristic
105D103—22no—
106#1483—1031nomaximal, Sylow
107C103#148311yescharacteristic, complemented, Sylow
108#529—1031no—
109C2×C4⋊C8—1031no—
110C4×M16—1031no—
111Q8⋊C8—1031no—
112Q8⋊C8—1031no—
113D4⋊C8—1031no—
114D4⋊C8D10311yescharacteristic, complemented
115C2×M16—2061no—
116C22×C8—2061no—
117#126—2061no—
118#125—1031no—
119#124—1031no—
120#123—2061no—
121C22⋊Q8—1031no—
122#121—1031no—
123C4×Q8—1031no—
124C4×D4—2061no—
125C4×D4C2×D10311yescharacteristic
126#117—2061no—
127C2×C42—1031no—
128C4⋊C8—1031no—
129C4⋊C8—2061no—
130C4⋊C8C2×D10311yescharacteristic
131#97—2061no—
132C4×C8—1031no—
133C4×C8C2×D10311yescharacteristic
134C2×Q8—1031no—
135C2×D4—2061no—
136C2×D4C4×D10311yescharacteristic
137C22×C4—21no—
138C22×C4—1031no—
139C22×C4—1031no—
140C22×C4—1031no—
141M16—2064no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—4122no—
145C2×C8—2061no—
146C2×C8—2061no—
147C4⋊C4—1031no—
148C4⋊C4—2061no—
149C4⋊C4—2061no—
150C4⋊C4—2061no—
151C4⋊C4—2061no—
152C4⋊C4C4×D10311yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2061no—
155C22⋊C4—2061no—
156C22⋊C4—2061no—
157C22⋊C4—2061no—
158C42—1031no—
159C42—1031no—
160C42—1031no—
161C42—2061no—
162C42C22×D10311yescharacteristic
163C23—21no—
164C23—1031no—
165Q8—2061no—
166Q8—2061no—
167D4—21no—
168D4—21no—
169D4—4122no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1031no—
174C2×C4—1031no—
175C2×C4—1031no—
176C2×C4—2062no—
177C2×C4—2061no—
178C2×C4—2061no—
179C2×C4—2061no—
180C2×C4—2061no—
181C2×C4—2061no—
182C2×C4—2061no—
183C2×C4C2×C4×D10311yescharacteristic
184C2×C4D4×D10311yescharacteristic
185C2×C4D4×D10311yescharacteristic
186C8—22no—
187C8—41no—
188C8—4121no—
189C8—2062no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—1032no—
194C22—2061no—
195C22—2061no—
196C22C22⋊C4×D10311yescharacteristic
197C4—21no—
198C4—41no—
199C4—4121no—
200C4—4121no—
201C4—2061no—
202C4—2061no—
203C4—2061no—
204C4#1569302711yescharacteristic
205C4#1569302911yescharacteristic
206C4#1569304511yescharacteristic
207C4#1569305011yescharacteristic
208C2—81no—
209C2—2062no—
210C2#2026775611yescharacteristic
211C2#2026778911yescharacteristic
212C2#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#1483
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. C4⋊C8×D103C2semidirect
3. C4×#13110088C2semidirect
4. #20267523C2semidirect
5. #20267521C2semidirect
6. D4⋊(C103⋊C8)C2semidirect
7. D4⋊C8×C103C2semidirect
107. C103#1483semidirect
114. D4⋊C8D103semidirect

Maximal subgroups

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

subgroupindex
#202683232
C4⋊C8×D1032
C4×#131100882
#202675232
#202675212
D4⋊(C103⋊C8)2
D4⋊C8×C1032
#1483103