Finite Group Databasebeta

← #27194084

Subgroups — #27194084

Order 13184.

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

normal subgroups only

This group has 266 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#20267941C212yesmaximal
2#20267708C211yesmaximal, characteristic
3#20267528C212yesmaximal, complemented
4#20267517C211yesmaximal, characteristic, complemented
5#544×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7C2×#13110092—22no—
8C2×(C2×D103)⋊C4—21no—
9C2×(C2×D103)⋊C4—21no—
10#15692941—22no—
11C22⋊(C103⋊C8)C2212yes—
12C103⋊#95C2211yescharacteristic
13C4⋊Q8×C103—22no—
14#125×C103—22no—
15C22⋊Q8×C103—21no—
16C22⋊Q8×C103C2212yes—
17#117×C103—21no—
18C2×C4⋊C4×C103C2211yescharacteristic
19C23×D103—21no—
20C2×D412—22no—
21C2×D412—42no—
22C22×Dic103—21no—
23#13110092—44no—
24C2×C103⋊C8—22no—
25(C2×D103)⋊C4—42no—
26(C2×D103)⋊C4—42no—
27C2×Q8×C103—21no—
28C2×Q8×C103D412yes—
29C22×C4×C103D411yescharacteristic
30C22×C4×C103D411yescharacteristic
31C22×C4×C103C2311yescharacteristic
32C4⋊C4×C103—21no—
33C4⋊C4×C103—21no—
34C4⋊C4×C103—21no—
35C4⋊C4×C103—22no—
36C4⋊C4×C103—22no—
37C4⋊C4×C103—22no—
38C4⋊C4×C103D412yes—
39C22⋊C4×C103—22no—
40C42×C103—22no—
41C23×C103C2×D411yescharacteristic
42C22×D103—22no—
43C22×D103—41no—
44C22×D103—41no—
45C22×D103—41no—
46C22×D103—41no—
47C22×D103—41no—
48C22×D103—41no—
49Q8×C103—42no—
50Q8×C103—81no—
51C2×C4×C103—21no—
52C2×C4×C103—21no—
53C2×C4×C103—22no—
54C2×C4×C103—22no—
55C2×C4×C103—21no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103SD1612yescomplemented
59C2×C4×C103C2×D412yes—
60C2×Dic103—41no—
61C2×Dic103—41no—
62C2×Dic103—41no—
63D412—24no—
64D412—42no—
65C103⋊C8—42no—
66C22×C103—21no—
67C22×C103—21no—
68C22×C103#12011yescharacteristic
69C22×C103C2×SD1611yescharacteristic
70C22×C103#13711yescharacteristic
71C2×D103—42no—
72C2×D103—42no—
73C2×D103—42no—
74C2×D103—81no—
75C2×D103—81no—
76C2×D103—81no—
77C2×D103—81no—
78C4×C103—22no—
79C4×C103—22no—
80C4×C103—42no—
81C4×C103—41no—
82C4×C103—42no—
83Dic103—81no—
84C2×C103—21no—
85C2×C103—21no—
86C2×C103#44811yescharacteristic
87C2×C103#45411yescharacteristic
88C2×C103B(4,𝔽2)11yescharacteristic
89D103—82no—
90#1599—1031nomaximal, Sylow
91C103#159911yescharacteristic, complemented, Sylow
92#544D10311yescharacteristic, complemented
93#450—1032no—
94#394—1031no—
95#328—1032no—
96#324—1031no—
97C22×D4—1031no—
98C2×SD16—2062no—
99C4⋊Q8—22no—
100#125—22no—
101C22⋊Q8—21no—
102C22⋊Q8C2×D10312yes—
103#117—21no—
104C2×C4⋊C4C2×D10311yescharacteristic
105C2×C22⋊C4—2061no—
106C2×C22⋊C4—2061no—
107#102—2062no—
108C22⋊C8—1032no—
109#95—1031no—
110C24—2061no—
111C2×Q8—21no—
112C2×Q8C22⋊D10312yes—
113C2×D4—4122no—
114C2×D4—2062no—
115C22×C4—2061no—
116C22×C4C22⋊D10311yescharacteristic
117C22×C4C22⋊D10311yescharacteristic
118C22×C4C22×D10311yescharacteristic
119SD16—4124no—
120C2×C8—2062no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—22no—
127C4⋊C4C22⋊D10312yes—
128C22⋊C4—22no—
129C22⋊C4—4122no—
130C22⋊C4—4122no—
131C42—22no—
132C23—4121no—
133C23—4121no—
134C23—4121no—
135C23—4121no—
136C23—4121no—
137C23—4121no—
138C23—2062no—
139C23C2×C22⋊D10311yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—4122no—
143D4—2064no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—4121no—
152C2×C4—4121no—
153C2×C4—4121no—
154C2×C4#1311009212yescomplemented
155C2×C4C2×C22⋊D10312yes—
156C8—4122no—
157C22—21no—
158C22—21no—
159C22—8241no—
160C22—8241no—
161C22—8241no—
162C22—8241no—
163C22—4122no—
164C22—4122no—
165C22—4122no—
166C22#1569299011yescharacteristic
167C22C2×#1311009211yescharacteristic
168C22#1569305211yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—8241no—
175C2—21no—
176C2—21no—
177C2—8242no—
178C2#2026793011yescharacteristic
179C2#2026796411yescharacteristic
180C2#2026797811yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#544×C103C2
socleC22×C103#120
prime radicalC22×D412C22
hypercenter#544D103
hypocenterC103#1599
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #20267528C2semidirect
4. #20267517C2semidirect
5. #544×C103C2semidirect
58. C2×C4×C103SD16semidirect
91. C103#1599semidirect
92. #544D103semidirect
154. C2×C4#13110092semidirect

Maximal subgroups

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

subgroupindex
#202679412
#202677082
#202675282
#202675172
#544×C1032
#1599103