Finite Group Databasebeta

← #27194226

Subgroups — #27194226

Order 13184.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268506C211yesmaximal, characteristic, complemented
2#20268163C211yesmaximal, characteristic, complemented
3#20267983C211yesmaximal, characteristic, complemented
4#20267539C211yesmaximal, characteristic, complemented
5D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic, complemented
7#459×C103C211yesmaximal, characteristic, complemented
8C2×#13110093—22no—
9C2×#13110090—21no—
10#15693021C2211yescharacteristic
11#15693007—22no—
12#15692995—21no—
13#15692992—21no—
14C4×D412C2211yescharacteristic
15#15692980—21no—
16#15692979—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18#15692942—21no—
19C4×C103⋊C8C2211yescharacteristic
20C2×D8×C103—21no—
21#127×C103C2211yescharacteristic
22C4×D4×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25C2×Dic206D412yes—
26C2×D412D411yescharacteristic
27C2×C22⋊D103—22no—
28C2×C4×D103—21no—
29#13110093—44no—
30#13110090—42no—
31C2×C103⋊C8—21no—
32C2×C103⋊C8—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103D411yescharacteristic
36C22⋊Dic103—22no—
37(C2×D103)⋊C4—22no—
38(C2×D103)⋊C4—21no—
39C4×Dic103—22no—
40C2×D4×C103—21no—
41C2×D4×C103—21no—
42C2×D4×C103—21no—
43C2×D4×C103D411yescharacteristic
44C22×C4×C103—21no—
45D8×C103—42no—
46C2×C8×C103—21no—
47C4⋊C4×C103D411yescharacteristic
48C22⋊C4×C103—21no—
49C42×C103C2311yescharacteristic
50C23×C103—21no—
51C23×C103—41no—
52C22×D103—21no—
53D4×C103—21no—
54D4×C103—21no—
55D4×C103—42no—
56D4×C103—41no—
57D4×C103—41no—
58D4×C103—41no—
59D4×C103—41no—
60C2×C4×C103—21no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C22⋊D103—82no—
67C2×Dic103—21no—
68C2×Dic103—22no—
69D412—21no—
70D412—21no—
71C4×D103—41no—
72C4×D103—41no—
73Dic206—42no—
74C8×C103—41no—
75C103⋊C8—22no—
76C103⋊C8—41no—
77C22×C103—41no—
78C22×C103—41no—
79C22×C103—41no—
80C22×C103—81no—
81C22×C103—81no—
82C22×C103—81no—
83C22×C103#12011yescharacteristic
84C2×D103—41no—
85C2×D103—41no—
86C2×D103—41no—
87C4×C103—21no—
88C4×C103—41no—
89C4×C103#13511yescharacteristic
90C4×C103#13511yescharacteristic
91C4×C103AGL(1,ℤ/8)11yescharacteristic
92C4×C103AGL(1,ℤ/8)11yescharacteristic
93Dic103—41no—
94Dic103—42no—
95C2×C103—81no—
96C2×C103—161no—
97C2×C103#44911yescharacteristic
98C2×C103#44911yescharacteristic
99C2×C103#45311yescharacteristic
100D103—81no—
101#1624—1031nomaximal, Sylow
102C103#162411yescharacteristic, complemented, Sylow
103#555—1031no—
104#492—1031no—
105#459—1031no—
106#459D10311yescharacteristic, complemented
107#333—1031no—
108D4⋊C8—1031no—
109D4⋊C8—1031no—
110C2×SD16—2062no—
111C2×D8—21no—
112C2×D8—2061no—
113C4⋊Q8—1031no—
114#127C2×D10311yescharacteristic
115#124—2062no—
116#121—2061no—
117#121—2061no—
118C4×D4—1031no—
119C4×D4C2×D10311yescharacteristic
120#117—2061no—
121#117—2061no—
122C4⋊C8—1031no—
123C4⋊C8C2×D10311yescharacteristic
124#102—21no—
125#102—2061no—
126C4×C8—1031no—
127C2×Q8—1032no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—1031no—
132C2×D4—2062no—
133C2×D4C22⋊D10311yescharacteristic
134C22×C4—21no—
135C22×C4—2061no—
136SD16—4124no—
137D8—42no—
138D8—4122no—
139C2×C8—21no—
140C2×C8—2061no—
141C2×C8—2061no—
142C4⋊C4—1031no—
143C4⋊C4—2061no—
144C4⋊C4—2061no—
145C4⋊C4C22⋊D10311yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—2062no—
148C22⋊C4—2062no—
149C22⋊C4—2061no—
150C42—2062no—
151C42C22×D10311yescharacteristic
152C23—21no—
153C23—41no—
154C23—2061no—
155Q8—4122no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—8242no—
164D4—2061no—
165D4—2061no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—4121no—
170C2×C4—4121no—
171C2×C4—2061no—
172C2×C4—2062no—
173C2×C4D4×D10311yescharacteristic
174C2×C4D4×D10311yescharacteristic
175C2×C4C2×C22⋊D10311yescharacteristic
176C8—41no—
177C8—4121no—
178C8—2062no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—4121no—
186C22—4121no—
187C22—4121no—
188C22#1569298911yescharacteristic
189C4—21no—
190C4—41no—
191C4—4121no—
192C4—4122no—
193C4#1569304011yescharacteristic
194C4#1569304111yescharacteristic
195C4#1569304511yescharacteristic
196C4#1569304711yescharacteristic
197C2—81no—
198C2—161no—
199C2—8241no—
200C2#2026793311yescharacteristic
201C2#2026793411yescharacteristic
202C2#2026795711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#459×C103C2
socleC22×C103#120
hypercenter#459D103
hypocenterC103#1624
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. #20268506C2semidirect
2. #20268163C2semidirect
3. #20267983C2semidirect
4. #20267539C2semidirect
5. D4⋊(C103⋊C8)C2semidirect
6. #20267518C2semidirect
7. #459×C103C2semidirect
102. C103#1624semidirect
106. #459D103semidirect

Maximal subgroups

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

subgroupindex
#202685062
#202681632
#202679832
#202675392
D4⋊(C103⋊C8)2
#202675182
#459×C1032
#1624103