Finite Group Databasebeta

← #27194231

Subgroups — #27194231

Order 13184.

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

normal subgroups only

This group has 256 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#20268445C211yesmaximal, characteristic, complemented
2#20268137C211yesmaximal, characteristic, complemented
3#20267983C211yesmaximal, characteristic, complemented
4#20267538C211yesmaximal, characteristic, complemented
5D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic, complemented
7#459×C103C211yesmaximal, characteristic, complemented
8C2×#13110104—21no—
9C2×#13110090—21no—
10#15693021C2211yescharacteristic
11#15693005—22no—
12#15693001—21no—
13#15692995—21no—
14C4×D412C2211yescharacteristic
15C2×C4⋊Dic103—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692942—22no—
18#15692942—21no—
19C4×C103⋊C8C2211yescharacteristic
20C2×D8×C103—21no—
21#127×C103C2211yescharacteristic
22C4×D4×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25#13110104—42no—
26#13110104—42no—
27C2×Dic206—21no—
28C2×D412D411yescharacteristic
29C2×C22⋊D103—22no—
30C22×Dic103—22no—
31C2×C4×D103—21no—
32#13110090—42no—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103—22no—
36C4⋊Dic103—21no—
37C4⋊Dic103D411yescharacteristic
38C4⋊Dic103D412yes—
39(C2×D103)⋊C4—22no—
40(C2×D103)⋊C4—21no—
41C2×D4×C103—21no—
42C2×D4×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103D411yescharacteristic
45C22×C4×C103—21no—
46D8×C103—42no—
47C2×C8×C103—21no—
48C4⋊C4×C103D411yescharacteristic
49C22⋊C4×C103—21no—
50C42×C103C2311yescharacteristic
51C23×C103—21no—
52C23×C103—41no—
53C22×D103—21no—
54D4×C103—21no—
55D4×C103—42no—
56D4×C103—41no—
57D4×C103—41no—
58D4×C103—41no—
59D4×C103—41no—
60D4×C103D812yescomplemented
61C2×C4×C103—21no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×C4×C103C2×D411yescharacteristic
67C22⋊D103—44no—
68C2×Dic103—21no—
69C2×Dic103—22no—
70C2×Dic103—44no—
71D412—21no—
72D412—21no—
73C4×D103—41no—
74C4×D103—41no—
75Dic206—41no—
76Dic206—41no—
77C8×C103—41no—
78C103⋊C8—41no—
79C103⋊C8—41no—
80C22×C103—22no—
81C22×C103—41no—
82C22×C103—41no—
83C22×C103—81no—
84C22×C103—81no—
85C22×C103—81no—
86C22×C103#12011yescharacteristic
87C2×D103—41no—
88C2×D103—41no—
89C2×D103—41no—
90C4×C103—21no—
91C4×C103—41no—
92C4×C103C2×D811yescharacteristic
93C4×C103#13511yescharacteristic
94C4×C103AGL(1,ℤ/8)11yescharacteristic
95C4×C103AGL(1,ℤ/8)11yescharacteristic
96Dic103—42no—
97Dic103—41no—
98C2×C103—42no—
99C2×C103—161no—
100C2×C103#44711yescharacteristic
101C2×C103#44911yescharacteristic
102C2×C103#45411yescharacteristic
103D103—81no—
104#1625—1031nomaximal, Sylow
105C103#162511yescharacteristic, complemented, Sylow
106#547—1031no—
107#486—1031no—
108#459—1031no—
109#459D10311yescharacteristic, complemented
110#332—1031no—
111D4⋊C8—1031no—
112D4⋊C8—1031no—
113C2×#41—2061no—
114C2×D8—21no—
115C2×D8—2061no—
116C4⋊Q8—1031no—
117#127C2×D10311yescharacteristic
118#123—2062no—
119C22⋊Q8—2061no—
120#121—2061no—
121C4×D4—1031no—
122C4×D4C2×D10311yescharacteristic
123C2×C4⋊C4—2061no—
124C4⋊C8—1031no—
125C4⋊C8C2×D10311yescharacteristic
126#102—21no—
127#102—2061no—
128#102—2062no—
129C4×C8—1031no—
130#41—4122no—
131#41—4122no—
132C2×Q8—2061no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—1031no—
137C2×D4—2062no—
138C2×D4C22⋊D10311yescharacteristic
139C22×C4—21no—
140C22×C4—2062no—
141C22×C4—2061no—
142D8—42no—
143D8—4122no—
144C2×C8—21no—
145C2×C8—2061no—
146C2×C8—2061no—
147C4⋊C4—1031no—
148C4⋊C4—1032no—
149C4⋊C4—2062no—
150C4⋊C4—2061no—
151C4⋊C4C22⋊D10311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2062no—
154C22⋊C4—2061no—
155C42C22×D10311yescharacteristic
156C23—21no—
157C23—41no—
158C23—2061no—
159Q8—4121no—
160Q8—4121no—
161D4—21no—
162D4—42no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—4124no—
168D4—2061no—
169D4—2061no—
170D4#1311009012yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—4124no—
175C2×C4—4121no—
176C2×C4—4121no—
177C2×C4—2061no—
178C2×C4—2062no—
179C2×C4D4×D10311yescharacteristic
180C2×C4D4×D10311yescharacteristic
181C2×C4C2×C22⋊D10311yescharacteristic
182C8—41no—
183C8—4121no—
184C8—4121no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—4121no—
192C22—4121no—
193C22—4121no—
194C22#1569298911yescharacteristic
195C4—21no—
196C4—41no—
197C4—4121no—
198C4—4122no—
199C4C2×#1311009011yescharacteristic
200C4#1569304011yescharacteristic
201C4#1569304511yescharacteristic
202C4#1569304611yescharacteristic
203C2—42no—
204C2—161no—
205C2—8241no—
206C2#2026792411yescharacteristic
207C2#2026793311yescharacteristic
208C2#2026796211yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#459×C103C2
socleC22×C103#120
hypercenter#459D103
hypocenterC103#1625
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20268445C2semidirect
2. #20268137C2semidirect
3. #20267983C2semidirect
4. #20267538C2semidirect
5. D4⋊(C103⋊C8)C2semidirect
6. #20267518C2semidirect
7. #459×C103C2semidirect
60. D4×C103D8semidirect
105. C103#1625semidirect
109. #459D103semidirect
170. D4#13110090semidirect

Maximal subgroups

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

subgroupindex
#202684452
#202681372
#202679832
#202675382
D4⋊(C103⋊C8)2
#202675182
#459×C1032
#1625103