Finite Group Databasebeta

← #27194079

Subgroups — #27194079

Order 13184.

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

normal subgroups only

This group has 310 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#20267708C211yesmaximal, characteristic, complemented
3#20267525C212yesmaximal, complemented
4#20267517C211yesmaximal, characteristic, complemented
5#537×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7C2×#13110090—22no—
8C2×(C2×D103)⋊C4—21no—
9C2×(C2×D103)⋊C4—21no—
10#15692941—22no—
11C22⋊(C103⋊C8)C2212yes—
12C103⋊#95C2211yescharacteristic
13C2×#41×C103—21no—
14C22⋊Q8×C103—22no—
15#121×C103—22no—
16#121×C103—21no—
17#121×C103C2212yes—
18C2×C4⋊C4×C103C2211yescharacteristic
19C23×D103—21no—
20C2×D412—22no—
21C2×D412—42no—
22C22×Dic103—21no—
23#13110090—44no—
24C2×C103⋊C8—22no—
25(C2×D103)⋊C4—42no—
26(C2×D103)⋊C4—42no—
27#41×C103—42no—
28#41×C103—42no—
29C2×Q8×C103—21no—
30C2×D4×C103—21no—
31C2×D4×C103—22no—
32C2×D4×C103—21no—
33C2×D4×C103D412yes—
34C22×C4×C103—22no—
35C22×C4×C103D411yescharacteristic
36C22×C4×C103D411yescharacteristic
37C22×C4×C103C2311yescharacteristic
38C4⋊C4×C103—21no—
39C4⋊C4×C103—22no—
40C4⋊C4×C103D412yes—
41C22⋊C4×C103—22no—
42C22⋊C4×C103—22no—
43C23×C103—22no—
44C23×C103C2×D411yescharacteristic
45C22×D103—22no—
46C22×D103—41no—
47C22×D103—41no—
48C22×D103—41no—
49C22×D103—41no—
50C22×D103—41no—
51C22×D103—41no—
52Q8×C103—42no—
53D4×C103—42no—
54D4×C103—42no—
55D4×C103—42no—
56D4×C103—42no—
57D4×C103—81no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—22no—
62C2×C4×C103—41no—
63C2×C4×C103—44no—
64C2×C4×C103—41no—
65C2×C4×C103D812yescomplemented
66C2×C4×C103C2×D412yes—
67C2×Dic103—41no—
68C2×Dic103—41no—
69C2×Dic103—41no—
70D412—24no—
71D412—42no—
72C103⋊C8—42no—
73C22×C103—21no—
74C22×C103—21no—
75C22×C103—42no—
76C22×C103—42no—
77C22×C103—42no—
78C22×C103#12011yescharacteristic
79C22×C103C2×D811yescharacteristic
80C22×C103AGL(1,ℤ/8)11yescharacteristic
81C2×D103—42no—
82C2×D103—42no—
83C2×D103—42no—
84C2×D103—81no—
85C2×D103—81no—
86C2×D103—81no—
87C2×D103—81no—
88C4×C103—22no—
89C4×C103—22no—
90C4×C103—42no—
91C4×C103—41no—
92Dic103—81no—
93C2×C103—21no—
94C2×C103—21no—
95C2×C103—82no—
96C2×C103#44711yescharacteristic
97C2×C103#45411yescharacteristic
98C2×C103B(4,𝔽2)11yescharacteristic
99D103—82no—
100#1598—1031nomaximal, Sylow
101C103#159811yescharacteristic, complemented, Sylow
102#537D10311yescharacteristic, complemented
103#447—1032no—
104#394—1031no—
105#327—1032no—
106#324—1031no—
107C2×#41—21no—
108C22×D4—1031no—
109C2×D8—2062no—
110C22⋊Q8—22no—
111#121—22no—
112#121—21no—
113#121C2×D10312yes—
114C2×C4⋊C4C2×D10311yescharacteristic
115C2×C22⋊C4—2061no—
116C2×C22⋊C4—2061no—
117#102—2062no—
118C22⋊C8—1032no—
119#95—1031no—
120C24—2061no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×D4—21no—
125C2×D4—22no—
126C2×D4—21no—
127C2×D4—4122no—
128C2×D4—2062no—
129C2×D4C22⋊D10312yes—
130C22×C4—22no—
131C22×C4—2061no—
132C22×C4C22⋊D10311yescharacteristic
133C22×C4C22⋊D10311yescharacteristic
134C22×C4C22×D10311yescharacteristic
135D8—4124no—
136C2×C8—2062no—
137C4⋊C4—21no—
138C4⋊C4—22no—
139C4⋊C4C22⋊D10312yes—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—4122no—
143C22⋊C4—4122no—
144C23—22no—
145C23—4121no—
146C23—4121no—
147C23—4121no—
148C23—4121no—
149C23—4121no—
150C23—4121no—
151C23—2062no—
152C23C2×C22⋊D10311yescharacteristic
153Q8—42no—
154D4—42no—
155D4—42no—
156D4—42no—
157D4—42no—
158D4—81no—
159D4—4122no—
160D4—2064no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—44no—
167C2×C4—41no—
168C2×C4—4121no—
169C2×C4—4121no—
170C2×C4—4121no—
171C2×C4#1311009012yescomplemented
172C2×C4C2×C22⋊D10312yes—
173C8—4122no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—8241no—
180C22—8241no—
181C22—8241no—
182C22—8241no—
183C22—4122no—
184C22—4122no—
185C22—4122no—
186C22#1569299011yescharacteristic
187C22C2×#1311009011yescharacteristic
188C22#1569304711yescharacteristic
189C4—22no—
190C4—22no—
191C4—42no—
192C4—41no—
193C4—8241no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—8242no—
198C2#2026792511yescharacteristic
199C2#2026796411yescharacteristic
200C2#2026797811yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#537×C103C2
socleC22×C103#120
hypercenter#537D103
hypocenterC103#1598
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #20267924C2semidirect
2. #20267708C2semidirect
3. #20267525C2semidirect
4. #20267517C2semidirect
5. #537×C103C2semidirect
65. C2×C4×C103D8semidirect
101. C103#1598semidirect
102. #537D103semidirect
171. C2×C4#13110090semidirect

Maximal subgroups

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

subgroupindex
#202679242
#202677082
#202675252
#202675172
#537×C1032
#1598103