Finite Group Databasebeta

← #27194067

Subgroups — #27194067

Order 13184.

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

normal subgroups only

This group has 316 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, complemented
2#20267700C211yesmaximal, characteristic
3#20267528C212yesmaximal, complemented
4#20267515C211yesmaximal, characteristic, complemented
5#543×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7C22×C22⋊D103—21no—
8C2×#13110092—22no—
9C2×(C2×D103)⋊C4—21no—
10#15692941—22no—
11C22⋊(C103⋊C8)C2212yes—
12C103⋊#95C2211yescharacteristic
13C22⋊Q8×C103—22no—
14C22⋊Q8×C103—21no—
15C22⋊Q8×C103—22no—
16C22⋊Q8×C103C2212yes—
17C2×C22⋊C4×C103—21no—
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#13110092—44no—
27C2×C103⋊C8—22no—
28(C2×D103)⋊C4—42no—
29C24×C103D411yescharacteristic
30C2×Q8×C103—21no—
31C2×Q8×C103D412yescomplemented
32C22×C4×C103—21no—
33C22×C4×C103—21no—
34C22×C4×C103D411yescharacteristic
35C22×C4×C103C2311yescharacteristic
36C4⋊C4×C103—21no—
37C4⋊C4×C103—22no—
38C4⋊C4×C103—22no—
39C4⋊C4×C103D412yescomplemented
40C22⋊C4×C103—22no—
41C22⋊C4×C103—22no—
42C22⋊C4×C103—22no—
43C23×C103—21no—
44C23×C103—21no—
45C23×C103—41no—
46C23×C103—41no—
47C23×C103SD1612yescomplemented
48C23×C103C2×D411yescharacteristic
49C22×D103—22no—
50C22×D103—41no—
51C22×D103—41no—
52C22×D103—41no—
53C22×D103—41no—
54C22×D103—41no—
55C22×D103—41no—
56Q8×C103—42no—
57Q8×C103—81no—
58C2×C4×C103—22no—
59C2×C4×C103—21no—
60C2×C4×C103—22no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103—81no—
64C2×C4×C103—81no—
65C2×C4×C103C2×D412yes—
66C22⋊D103—48no—
67C2×Dic103—22no—
68C2×Dic103—41no—
69C2×Dic103—41no—
70D412—24no—
71D412—42no—
72C103⋊C8—42no—
73C22×C103—21no—
74C22×C103—21no—
75C22×C103—22no—
76C22×C103—42no—
77C22×C103—41no—
78C22×C103—41no—
79C22×C103—81no—
80C22×C103#12011yescharacteristic
81C22×C103C2×SD1611yescharacteristic
82C22×C103#13711yescharacteristic
83C2×D103—42no—
84C2×D103—42no—
85C2×D103—42no—
86C2×D103—81no—
87C2×D103—81no—
88C2×D103—81no—
89C2×D103—81no—
90C4×C103—22no—
91C4×C103—41no—
92C4×C103—42no—
93C4×C103—42no—
94Dic103—42no—
95C2×C103—21no—
96C2×C103—21no—
97C2×C103—42no—
98C2×C103#44811yescharacteristic
99C2×C103#45311yescharacteristic
100C2×C103B(4,𝔽2)11yescharacteristic
101D103—82no—
102#1596—1031nomaximal, Sylow
103C103#159611yescharacteristic, complemented, Sylow
104#543D10311yescharacteristic, complemented
105#450—1032no—
106#392—1031no—
107#328—1032no—
108#323—1031no—
109C22×D4—1031no—
110C22×D4—2061no—
111C2×SD16—2062no—
112C22⋊Q8—22no—
113C22⋊Q8—21no—
114C22⋊Q8—22no—
115C22⋊Q8C2×D10312yes—
116C2×C22⋊C4—21no—
117C2×C22⋊C4—2061no—
118C2×C22⋊C4C2×D10311yescharacteristic
119#102—2062no—
120C22⋊C8—1032no—
121#95—1031no—
122C24—2061no—
123C24C22⋊D10311yescharacteristic
124C2×Q8—21no—
125C2×Q8C22⋊D10312yescomplemented
126C2×D4—4122no—
127C2×D4—4122no—
128C2×D4—4122no—
129C2×D4—4122no—
130C2×D4—2062no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—2061no—
134C22×C4C22⋊D10311yescharacteristic
135C22×C4C22×D10311yescharacteristic
136SD16—4124no—
137C2×C8—2062no—
138C4⋊C4—21no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4C22⋊D10312yescomplemented
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C22⋊C4—4122no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—4121no—
151C23—4121no—
152C23—4121no—
153C23—4121no—
154C23—4121no—
155C23—4121no—
156C23—2062no—
157C23#1311009212yescomplemented
158C23C2×C22⋊D10311yescharacteristic
159Q8—42no—
160Q8—81no—
161D4—4122no—
162D4—4128no—
163D4—2064no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—4121no—
172C2×C4—4121no—
173C2×C4—2062no—
174C2×C4C2×C22⋊D10312yes—
175C8—4122no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—8241no—
184C22—8241no—
185C22—8241no—
186C22—8241no—
187C22—4122no—
188C22—4122no—
189C22—4122no—
190C22#1569299011yescharacteristic
191C22C2×#1311009211yescharacteristic
192C22#1569305211yescharacteristic
193C4—22no—
194C4—41no—
195C4—42no—
196C4—42no—
197C4—4122no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—8242no—
202C2#2026793011yescharacteristic
203C2#2026795911yescharacteristic
204C2#2026797811yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#543×C103C2
socleC22×C103#120
prime radical#20267700C2
hypercenter#543D103
hypocenterC103#1596
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #20267941C2semidirect
3. #20267528C2semidirect
4. #20267515C2semidirect
5. #543×C103C2semidirect
31. C2×Q8×C103D4semidirect
39. C4⋊C4×C103D4semidirect
47. C23×C103SD16semidirect
103. C103#1596semidirect
104. #543D103semidirect
125. C2×Q8C22⋊D103semidirect
141. C4⋊C4C22⋊D103semidirect
157. C23#13110092semidirect

Maximal subgroups

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

subgroupindex
#202679412
#202677002
#202675282
#202675152
#543×C1032
#1596103