Finite Group Databasebeta

← #27193683

Subgroups — #27193683

Order 13184.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#20267657C211yesmaximal, characteristic, complemented
3#20267529C212yesmaximal, complemented
4#20267526C212yesmaximal
5#432×C103C211yesmaximal, characteristic, complemented
6#15693015—21no—
7#15693013C411yescharacteristic, complemented
8#15693009C411yescharacteristic, complemented
9#15693004—21no—
10#15693000C2211yescharacteristic
11#15692995C2211yescharacteristic
12C4×Dic206C411yescharacteristic, complemented
13C4×D412C411yescharacteristic, complemented
14C4×C22⋊D103—21no—
15#15692978—21no—
16C2×C4⋊Dic103—21no—
17C103⋊#95—21no—
18C103⋊#95C2212yes—
19C2×C42×C103C2211yescharacteristic
20C4⋊C8×C103—21no—
21C22⋊C8×C103C2212yes—
22#97×C103—21no—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26C22×Dic103—22no—
27C2×C4×D103—21no—
28C4⋊Dic103—42no—
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×C103D411yescharacteristic
42C22×C4×C103D411yescharacteristic
43C22×C4×C103C2311yescharacteristic
44C2×C8×C103—22no—
45C42×C103C2×C411yescharacteristic
46C42×C103C2×C411yescharacteristic
47C42×C103D411yescharacteristic
48C42×C103D411yescharacteristic
49C23×C103C2×D411yescharacteristic
50C22×D103—21no—
51C2×C4×C103—21no—
52C2×C4×C103—21no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103C22⋊C411yescharacteristic
56C2×C4×C103C22⋊C411yescharacteristic
57C2×C4×C103C22⋊C411yescharacteristic
58C2×C4×C103C22⋊C411yescharacteristic
59C2×C4×C103C22×C411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C22⋊D103—41no—
62C22⋊D103—41no—
63C2×Dic103—21no—
64C2×Dic103—21no—
65C2×Dic103—21no—
66C2×Dic103—42no—
67C2×Dic103—42no—
68C2×Dic103—42no—
69D412—41no—
70C4×D103—42no—
71Dic206—41no—
72C8×C103—42no—
73C22×C103—21no—
74C22×C103—21no—
75C22×C103C2×C22⋊C411yescharacteristic
76C22×C103AGL(1,ℤ/8)11yescharacteristic
77C22×C103#13711yescharacteristic
78C2×D103—41no—
79C2×D103—41no—
80C2×D103—41no—
81C4×C103—21no—
82C4×C103—21no—
83C4×C103—21no—
84C4×C103—21no—
85C4×C103—21no—
86C4×C103—21no—
87Dic103—41no—
88Dic103—41no—
89Dic103—41no—
90Dic103—82no—
91C2×C103—21no—
92C2×C103—21no—
93C2×C103#41011yescharacteristic
94C2×C103#41711yescharacteristic
95C2×C103#42111yescharacteristic
96D103—81no—
97#1512—1031nomaximal, Sylow
98C103#151211yescharacteristic, complemented, Sylow
99#529—1031no—
100#432D10311yescharacteristic, complemented
101#382—1031no—
102#328—1032no—
103#327—1032no—
104#126—2061no—
105#125—1031no—
106#124—1031no—
107#123—2061no—
108C22⋊Q8—1031no—
109#121—1031no—
110C4×Q8—1031no—
111C4×D4—1031no—
112C4×D4—2061no—
113#117—2061no—
114C2×C4⋊C4—2061no—
115C2×C42C2×D10311yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C2×D10312yes—
118#97—21no—
119#95—1032no—
120#95—2061no—
121C2×Q8—1031no—
122C2×D4—1031no—
123C2×D4—2061no—
124C22×C4—2062no—
125C22×C4—2061no—
126C22×C4D41211yescharacteristic
127C22×C4D41211yescharacteristic
128C22×C4C22×D10311yescharacteristic
129C2×C8—22no—
130C4⋊C4—1031no—
131C4⋊C4—1031no—
132C4⋊C4—4122no—
133C4⋊C4—2061no—
134C4⋊C4—2061no—
135C4⋊C4—2061no—
136C4⋊C4—2061no—
137C22⋊C4—2061no—
138C22⋊C4—2061no—
139C22⋊C4—2061no—
140C22⋊C4—2061no—
141C22⋊C4—2061no—
142C42—2061no—
143C42C4×D10311yescharacteristic
144C42C4×D10311yescharacteristic
145C42C22⋊D10311yescharacteristic
146C42C22⋊D10311yescharacteristic
147C23—2061no—
148C23C2×D41211yescharacteristic
149Q8—4121no—
150D4—4121no—
151D4—4121no—
152D4—4121no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—4122no—
158C2×C4—4122no—
159C2×C4—4122no—
160C2×C4—4122no—
161C2×C4—2061no—
162C2×C4—2061no—
163C2×C4—2061no—
164C2×C4(C2×D103)⋊C411yescharacteristic
165C2×C4(C2×D103)⋊C411yescharacteristic
166C2×C4(C2×D103)⋊C411yescharacteristic
167C2×C4(C2×D103)⋊C411yescharacteristic
168C2×C4C2×C4×D10311yescharacteristic
169C2×C4C2×C22⋊D10311yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—4121no—
174C22—4121no—
175C22—4121no—
176C22C2×(C2×D103)⋊C411yescharacteristic
177C22#1569304911yescharacteristic
178C22#1569305411yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—8242no—
186C4—4121no—
187C4—4121no—
188C4—4121no—
189C2—21no—
190C2—21no—
191C2—8241no—
192C2#2026776411yescharacteristic
193C2#2026779311yescharacteristic
194C2#2026780711yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#432×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692995C22
cosocleC22×C4×C103C23
hypercenter#432D103
hypocenterC103#1512
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #20267657C2semidirect
3. #20267529C2semidirect
5. #432×C103C2semidirect
7. #15693013C4semidirect
8. #15693009C4semidirect
12. C4×Dic206C4semidirect
13. C4×D412C4semidirect
98. C103#1512semidirect
100. #432D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
#202676572
#202675292
#202675262
#432×C1032
#1512103