Finite Group Databasebeta

← #27193140

Subgroups — #27193140

Order 13184.

222 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 35 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#20267700C211yesmaximal, characteristic
2#20267515C211yesmaximal, characteristic, complemented
3#342×C103C211yesmaximal, characteristic, complemented
4C22×D412C411yescharacteristic, complemented
5C22×C22⋊D103—21no—
6C2×(C2×D103)⋊C4—21no—
7C22⋊(C103⋊C8)—21no—
8C103⋊#95C411yescharacteristic, complemented
9C2×C22⋊C4×C103—21no—
10C2×C22⋊C4×C103C2211yescharacteristic
11C23×D103—21no—
12C2×D412—41no—
13C2×D412—42no—
14C2×C22⋊D103—42no—
15C2×C22⋊D103—42no—
16C2×C22⋊D103—41no—
17C2×C22⋊D103—41no—
18C22×Dic103—21no—
19C2×C103⋊C8—41no—
20(C2×D103)⋊C4—42no—
21C24×C103D411yescharacteristic
22C22×C4×C103—41no—
23C22×C4×C103C2×C411yescharacteristic
24C22×C4×C103D411yescharacteristic
25C22⋊C4×C103—22no—
26C22⋊C4×C103—41no—
27C22⋊C4×C103—41no—
28C23×C103—21no—
29C23×C103—21no—
30C23×C103—41no—
31C23×C103—41no—
32C23×C103C22⋊C411yescharacteristic
33C23×C103D811yescharacteristic
34C23×C103SD1611yescharacteristic
35C22×D103—22no—
36C22×D103—41no—
37C22×D103—41no—
38C22×D103—41no—
39C22×D103—41no—
40C22×D103—41no—
41C22×D103—41no—
42C2×C4×C103—21no—
43C2×C4×C103—21no—
44C2×C4×C103—41no—
45C2×C4×C103—41no—
46C2×C4×C103—42no—
47C2×C4×C103—81no—
48C2×C4×C103—81no—
49C22⋊D103—44no—
50C22⋊D103—44no—
51C2×Dic103—22no—
52C2×Dic103—41no—
53C2×Dic103—41no—
54D412—42no—
55D412—42no—
56C103⋊C8—81no—
57C22×C103—21no—
58C22×C103—21no—
59C22×C103—21no—
60C22×C103—21no—
61C22×C103—41no—
62C22×C103—41no—
63C22×C103—41no—
64C22×C103—41no—
65C22×C103—81no—
66C22×C103#9911yescharacteristic
67C22×C103#10211yescharacteristic
68C22×C103#10411yescharacteristic
69C2×D103—42no—
70C2×D103—42no—
71C2×D103—42no—
72C2×D103—81no—
73C2×D103—81no—
74C2×D103—81no—
75C2×D103—81no—
76C4×C103—41no—
77C4×C103—41no—
78C4×C103—82no—
79Dic103—42no—
80C2×C103—21no—
81C2×C103—21no—
82C2×C103—41no—
83C2×C103—41no—
84C2×C103#32711yescharacteristic
85C2×C103AΣL(1,𝔽16)11yescharacteristic
86C2×C103#35311yescharacteristic
87D103—82no—
88#1343—1031nomaximal, Sylow
89C103#134311yescharacteristic, complemented, Sylow
90#392—1031no—
91#342D10311yescharacteristic, complemented
92#323—1031no—
93C22×D4—1031no—
94C22×D4—2061no—
95C2×C22⋊C4—21no—
96C2×C22⋊C4—2061no—
97C2×C22⋊C4C2×D10311yescharacteristic
98C22⋊C8—2061no—
99#95—1031no—
100C24—2061no—
101C24C22⋊D10311yescharacteristic
102C2×D4—4121no—
103C2×D4—4122no—
104C2×D4—4122no—
105C2×D4—4121no—
106C2×D4—4121no—
107C2×D4—4122no—
108C22×C4—41no—
109C22×C4—2061no—
110C22×C4C4×D10311yescharacteristic
111C22×C4D41211yescharacteristic
112C2×C8—4121no—
113C22⋊C4—22no—
114C22⋊C4—41no—
115C22⋊C4—41no—
116C22⋊C4—4122no—
117C23—21no—
118C23—21no—
119C23—41no—
120C23—41no—
121C23—4121no—
122C23—4121no—
123C23—4121no—
124C23—4121no—
125C23—4121no—
126C23—4121no—
127C23—2062no—
128C23(C2×D103)⋊C411yescharacteristic
129C23#1311009011yescharacteristic
130C23#1311009211yescharacteristic
131D4—4122no—
132D4—4122no—
133D4—4124no—
134D4—4124no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—81no—
141C2×C4—81no—
142C2×C4—4121no—
143C2×C4—4121no—
144C2×C4—2062no—
145C8—8241no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22—21no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—41no—
154C22—81no—
155C22—8241no—
156C22—8241no—
157C22—8241no—
158C22—8241no—
159C22—4122no—
160C22—4122no—
161C22—4122no—
162C22#1569293511yescharacteristic
163C22#1569294111yescharacteristic
164C22#1569294911yescharacteristic
165C4—41no—
166C4—41no—
167C4—82no—
168C4—4122no—
169C2—21no—
170C2—21no—
171C2—41no—
172C2—41no—
173C2—8242no—
174C2#2026752411yescharacteristic
175C2#2026757711yescharacteristic
176C2#2026758311yescharacteristic
subgroupG/H
centerC22#15692935
commutatorC22×C4×C103C2×C4
FrattiniC2×C22⋊C4C2×D103
Fitting#342×C103C2
socleC22×C103#99
prime radical#20267700C2
cosocleC2×C22⋊C4×C103C22
hypercenter#342D103
hypocenterC103#1343
LCSG ▷ C22×C4×C103 ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #20267515C2semidirect
3. #342×C103C2semidirect
4. C22×D412C4semidirect
8. C103⋊#95C4semidirect
89. C103#1343semidirect
91. #342D103semidirect

Maximal subgroups

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

subgroupindex
#202677002
#202675152
#342×C1032
#1343103