Finite Group Databasebeta

← #27193733

Subgroups — #27193733

Order 13184.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#20268325C211yesmaximal, characteristic
2C2×#15692932C211yesmaximal, characteristic, complemented
3#20267532C212yesmaximal, complemented
4#20267530C212yesmaximal, complemented
5C4×M16×C103C211yesmaximal, characteristic, complemented
6C22×C103⋊C8—21no—
7#15693015—21no—
8#15693013C2211yescharacteristic
9#15693009C2211yescharacteristic
10#15693004—21no—
11#15693000C411yescharacteristic
12#15692995C411yescharacteristic
13C4×Dic206C411yescharacteristic
14C4×D412C411yescharacteristic
15C4×C22⋊D103—21no—
16#15692978—21no—
17#15692932—21no—
18#15692932C2212yes—
19C2×M16×C103—21no—
20C2×C42×C103C2211yescharacteristic
21#97×C103C2212yes—
22C4×C8×C103—21no—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26C2×C4×D103—21no—
27C2×C103⋊C8—24no—
28C2×C103⋊C8—22no—
29C4⋊Dic103C2×C411yescharacteristic
30C4⋊Dic103C2×C411yescharacteristic
31Dic103⋊C4—21no—
32Dic103⋊C4—21no—
33Dic103⋊C4—21no—
34Dic103⋊C4—21no—
35C22⋊Dic103—21no—
36(C2×D103)⋊C4—21no—
37(C2×D103)⋊C4—21no—
38(C2×D103)⋊C4—21no—
39(C2×D103)⋊C4—21no—
40C4×Dic103—21no—
41C22×C4×C103C2×C411yescharacteristic
42C22×C4×C103D411yescharacteristic
43C22×C4×C103D411yescharacteristic
44M16×C103—24no—
45C2×C8×C103—22no—
46C42×C103C2×C411yescharacteristic
47C42×C103D411yescharacteristic
48C42×C103D411yescharacteristic
49C42×C103C2311yescharacteristic
50C23×C103C22⋊C411yescharacteristic
51C22×D103—21no—
52C2×C4×C103—22no—
53C2×C4×C103—22no—
54C2×C4×C103—41no—
55C2×C4×C103C22⋊C411yescharacteristic
56C2×C4×C103C22⋊C411yescharacteristic
57C2×C4×C103C22⋊C411yescharacteristic
58C2×C4×C103C22×C411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C22⋊D103—42no—
62C2×Dic103—21no—
63C2×Dic103—21no—
64C2×Dic103—21no—
65D412—41no—
66C4×D103—42no—
67Dic206—41no—
68C8×C103—24no—
69C103⋊C8—24no—
70C22×C103—21no—
71C22×C103—21no—
72C22×C103#10412yes—
73C22×C103C2×C22⋊C411yescharacteristic
74C2×D103—41no—
75C2×D103—41no—
76C2×D103—41no—
77C4×C103—21no—
78C4×C103—21no—
79C4×C103—21no—
80C4×C103—21no—
81C4×C103—21no—
82C4×C103#10412yes—
83Dic103—41no—
84Dic103—41no—
85Dic103—41no—
86C2×C103—22no—
87C2×C103#41311yescharacteristic
88C2×C103C2×#10411yescharacteristic
89C2×C103C2×#10411yescharacteristic
90D103—81no—
91#1524—1031nomaximal, Sylow
92C103#152411yescharacteristic, complemented, Sylow
93#529—1031no—
94C4×M16D10311yescharacteristic, complemented
95C2×#97—1031no—
96#330—1032no—
97#329—1032no—
98C2×M16—21no—
99C22×C8—2061no—
100#126—2061no—
101#125—1031no—
102#124—1031no—
103#123—2061no—
104C22⋊Q8—1031no—
105#121—1031no—
106C4×Q8—1031no—
107C4×D4—1031no—
108C4×D4—2061no—
109#117—2061no—
110C2×C42C2×D10311yescharacteristic
111#97—1032no—
112#97—2061no—
113#97C2×D10312yes—
114C4×C8—21no—
115C2×Q8—1031no—
116C2×D4—1031no—
117C2×D4—2061no—
118C22×C4—2061no—
119C22×C4C4×D10311yescharacteristic
120C22×C4D41211yescharacteristic
121C22×C4C22⋊D10311yescharacteristic
122M16—24no—
123C2×C8—22no—
124C2×C8—2064no—
125C2×C8—2062no—
126C4⋊C4—1031no—
127C4⋊C4—1031no—
128C4⋊C4—2061no—
129C4⋊C4—2061no—
130C4⋊C4—2061no—
131C4⋊C4—2061no—
132C22⋊C4—2061no—
133C22⋊C4—2061no—
134C22⋊C4—2061no—
135C22⋊C4—2061no—
136C22⋊C4—2061no—
137C42—2061no—
138C42C4×D10311yescharacteristic
139C42D41211yescharacteristic
140C42C22⋊D10311yescharacteristic
141C42C22×D10311yescharacteristic
142C23—2061no—
143C23(C2×D103)⋊C411yescharacteristic
144Q8—4121no—
145D4—4121no—
146D4—4122no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—4122no—
151C2×C4—2061no—
152C2×C4—2061no—
153C2×C4—2061no—
154C2×C4(C2×D103)⋊C411yescharacteristic
155C2×C4(C2×D103)⋊C411yescharacteristic
156C2×C4(C2×D103)⋊C411yescharacteristic
157C2×C4C2×C4×D10311yescharacteristic
158C2×C4C2×C22⋊D10311yescharacteristic
159C2×C4C2×D41211yescharacteristic
160C8—24no—
161C8—2064no—
162C22—21no—
163C22—21no—
164C22—4121no—
165C22—4121no—
166C22—4121no—
167C22#1569294912yes—
168C22C2×(C2×D103)⋊C411yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—4121no—
175C4—4121no—
176C4—4121no—
177C4#1569294712yes—
178C2—22no—
179C2—8241no—
180C2#2026777311yescharacteristic
181C2C2×#1569294711yescharacteristic
182C2C2×#1569294911yescharacteristic
subgroupG/H
centerC2×C4(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
FittingC4×M16×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692995C4
cosocleC42×C103C23
hypercenterC4×M16D103
hypocenterC103#1524
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#15692932C2semidirect
3. #20267532C2semidirect
4. #20267530C2semidirect
5. C4×M16×C103C2semidirect
92. C103#1524semidirect
94. C4×M16D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
C2×#156929322
#202675322
#202675302
C4×M16×C1032
#1524103