Finite Group Databasebeta

← #27194062

Subgroups — #27194062

Order 13184.

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

normal subgroups only

This group has 368 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#20267924C212yesmaximal, complemented
2#20267700C211yesmaximal, characteristic, complemented
3#20267525C212yesmaximal, complemented
4#20267515C211yesmaximal, characteristic, complemented
5#534×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic, complemented
7C22×C22⋊D103—21no—
8C2×#13110090—22no—
9C2×(C2×D103)⋊C4—21no—
10#15692941—22no—
11C22⋊(C103⋊C8)C2212yescomplemented
12C103⋊#95C2211yescharacteristic, complemented
13C22×D4×C103—21no—
14#123×C103—22no—
15#121×C103—21no—
16#121×C103C2212yes—
17#120×C103—22no—
18C2×C22⋊C4×C103C2211yescharacteristic
19C23×D103—21no—
20C2×D412—22no—
21C2×D412—42no—
22C2×C22⋊D103—42no—
23C2×C22⋊D103—42no—
24C2×C22⋊D103—42no—
25C22×Dic103—21no—
26#13110090—44no—
27C2×C103⋊C8—22no—
28(C2×D103)⋊C4—42no—
29C24×C103—21no—
30C24×C103D411yescharacteristic
31C2×D4×C103—22no—
32C2×D4×C103—22no—
33C2×D4×C103—21no—
34C2×D4×C103—42no—
35C2×D4×C103—42no—
36C2×D4×C103D412yescomplemented
37C22×C4×C103—21no—
38C22×C4×C103D411yescharacteristic
39C22×C4×C103C2311yescharacteristic
40C4⋊C4×C103—21no—
41C4⋊C4×C103D412yescomplemented
42C22⋊C4×C103—22no—
43C22⋊C4×C103—22no—
44C22⋊C4×C103—22no—
45C23×C103—21no—
46C23×C103—21no—
47C23×C103—22no—
48C23×C103—41no—
49C23×C103—41no—
50C23×C103—42no—
51C23×C103—81no—
52C23×C103—81no—
53C23×C103D812yescomplemented
54C23×C103C2×D411yescharacteristic
55C22×D103—22no—
56C22×D103—41no—
57C22×D103—41no—
58C22×D103—41no—
59C22×D103—41no—
60C22×D103—41no—
61C22×D103—41no—
62D4×C103—42no—
63D4×C103—44no—
64D4×C103—42no—
65D4×C103—42no—
66D4×C103—81no—
67C2×C4×C103—21no—
68C2×C4×C103—22no—
69C2×C4×C103—41no—
70C2×C4×C103—42no—
71C2×C4×C103—41no—
72C2×C4×C103C2×D412yes—
73C22⋊D103—48no—
74C2×Dic103—22no—
75C2×Dic103—41no—
76C2×Dic103—41no—
77D412—24no—
78D412—42no—
79C103⋊C8—42no—
80C22×C103—21no—
81C22×C103—21no—
82C22×C103—22no—
83C22×C103—42no—
84C22×C103—41no—
85C22×C103—41no—
86C22×C103—42no—
87C22×C103—42no—
88C22×C103—42no—
89C22×C103—81no—
90C22×C103—84no—
91C22×C103#12011yescharacteristic
92C22×C103C2×D811yescharacteristic
93C22×C103AGL(1,ℤ/8)11yescharacteristic
94C2×D103—42no—
95C2×D103—42no—
96C2×D103—42no—
97C2×D103—81no—
98C2×D103—81no—
99C2×D103—81no—
100C2×D103—81no—
101C4×C103—22no—
102C4×C103—42no—
103C4×C103—41no—
104Dic103—42no—
105C2×C103—21no—
106C2×C103—21no—
107C2×C103—42no—
108C2×C103—82no—
109C2×C103#44711yescharacteristic
110C2×C103#45311yescharacteristic
111C2×C103B(4,𝔽2)11yescharacteristic
112D103—82no—
113#1595—1031nomaximal, Sylow
114C103#159511yescharacteristic, complemented, Sylow
115#534D10311yescharacteristic, complemented
116#447—1032no—
117#392—1031no—
118#327—1032no—
119#323—1031no—
120C22×D4—21no—
121C22×D4—1031no—
122C22×D4—2061no—
123C2×D8—2062no—
124#123—22no—
125#121—21no—
126#121C2×D10312yes—
127#120—22no—
128C2×C22⋊C4—2061no—
129C2×C22⋊C4C2×D10311yescharacteristic
130#102—2062no—
131C22⋊C8—1032no—
132#95—1031no—
133C24—21no—
134C24—2061no—
135C24C22⋊D10311yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—42no—
140C2×D4—42no—
141C2×D4—4122no—
142C2×D4—4122no—
143C2×D4—4122no—
144C2×D4—4122no—
145C2×D4—2062no—
146C2×D4C22⋊D10312yescomplemented
147C22×C4—21no—
148C22×C4—2061no—
149C22×C4C22⋊D10311yescharacteristic
150C22×C4C22×D10311yescharacteristic
151D8—4124no—
152C2×C8—2062no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D10312yescomplemented
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—4122no—
159C23—21no—
160C23—21no—
161C23—22no—
162C23—41no—
163C23—41no—
164C23—42no—
165C23—81no—
166C23—81no—
167C23—4121no—
168C23—4121no—
169C23—4121no—
170C23—4121no—
171C23—4121no—
172C23—4121no—
173C23—2062no—
174C23#1311009012yescomplemented
175C23C2×C22⋊D10311yescharacteristic
176D4—42no—
177D4—44no—
178D4—42no—
179D4—42no—
180D4—81no—
181D4—4122no—
182D4—4128no—
183D4—2064no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—41no—
189C2×C4—4121no—
190C2×C4—4121no—
191C2×C4—2062no—
192C2×C4C2×C22⋊D10312yes—
193C8—4122no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—84no—
205C22—8241no—
206C22—8241no—
207C22—8241no—
208C22—8241no—
209C22—4122no—
210C22—4122no—
211C22—4122no—
212C22#1569299011yescharacteristic
213C22C2×#1311009011yescharacteristic
214C22#1569304711yescharacteristic
215C4—22no—
216C4—42no—
217C4—41no—
218C4—4122no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—82no—
223C2—8242no—
224C2#2026792511yescharacteristic
225C2#2026795911yescharacteristic
226C2#2026797811yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#534×C103C2
socleC22×C103#120
hypercenter#534D103
hypocenterC103#1595
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #20267924C2semidirect
2. #20267700C2semidirect
3. #20267525C2semidirect
4. #20267515C2semidirect
5. #534×C103C2semidirect
6. C22×D412C22semidirect
11. C22⋊(C103⋊C8)C22semidirect
12. C103⋊#95C22semidirect
36. C2×D4×C103D4semidirect
41. C4⋊C4×C103D4semidirect
53. C23×C103D8semidirect
114. C103#1595semidirect
115. #534D103semidirect
146. C2×D4C22⋊D103semidirect
154. C4⋊C4C22⋊D103semidirect
174. C23#13110090semidirect

Maximal subgroups

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

subgroupindex
#202679242
#202677002
#202675252
#202675152
#534×C1032
#1595103