Finite Group Databasebeta

← #27194306

Subgroups — #27194306

Order 13184.

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

normal subgroups only

This group has 228 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#20268456C211yesmaximal, characteristic
2#20268083C211yesmaximal, characteristic, complemented
3#20268078C211yesmaximal, characteristic
4#20267537C211yesmaximal, characteristic, complemented
5#20267523C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic
7#487×C103C211yesmaximal, characteristic, complemented
8C2×Q8×D103—21no—
9#15693020—21no—
10#15692999—22no—
11#15692997—21no—
12C4×Dic206C2211yescharacteristic
13C4×D412C2211yescharacteristic
14#15692983—21no—
15#15692954—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692944—21no—
20#15692941—21no—
21C4⋊Q8×C103C2211yescharacteristic
22C4⋊Q8×C103C2211yescharacteristic
23#103×C103—22no—
24C4×C8×C103C2211yescharacteristic
25C2×Dic206—22no—
26C2×Dic206D411yescharacteristic
27Q8×D103—42no—
28Q8×D103—42no—
29C2×D412D411yescharacteristic
30C2×C4×D103—22no—
31C2×C4×D103—21no—
32C2×C103⋊C8—21no—
33C2×C103⋊C8—21no—
34C4⋊Dic103D411yescharacteristic
35C4⋊Dic103D411yescharacteristic
36Dic103⋊C4—22no—
37Dic103⋊C4—21no—
38(C2×D103)⋊C4—22no—
39(C2×D103)⋊C4—21no—
40C4×Dic103—21no—
41C2×Q8×C103—21no—
42C2×Q8×C103—21no—
43C2×C8×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C4⋊C4×C103D412yes—
48C42×C103C2311yescharacteristic
49C22×D103—21no—
50Q8×C103—42no—
51Q8×C103—41no—
52Q8×C103—41no—
53C2×C4×C103—22no—
54C2×C4×C103—41no—
55C2×C4×C103C2×D411yescharacteristic
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×Dic103—21no—
59C2×Dic103—21no—
60C2×Dic103—21no—
61D412—21no—
62D412Q1612yes—
63C4×D103—44no—
64C4×D103—41no—
65C4×D103—41no—
66Dic206—21no—
67Dic206—44no—
68Dic206SD1612yes—
69C8×C103—41no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103#12011yescharacteristic
73C2×D103—22no—
74C2×D103—41no—
75C2×D103—41no—
76C4×C103—21no—
77C4×C103—42no—
78C4×C103—81no—
79C4×C103C2×SD1611yescharacteristic
80C4×C103C2×Q1611yescharacteristic
81C4×C103AGL(1,ℤ/8)11yescharacteristic
82C4×C103#13711yescharacteristic
83Dic103—22no—
84Dic103—41no—
85Dic103—41no—
86C2×C103#45011yescharacteristic
87C2×C103#45111yescharacteristic
88C2×C103#45411yescharacteristic
89D103—42no—
90#1637—1031nomaximal, Sylow
91C103#163711yescharacteristic, complemented, Sylow
92D4×Q8—1031no—
93#487D10311yescharacteristic, complemented
94#477—1031no—
95#476—1031no—
96#332—1031no—
97Q8⋊C8—1031no—
98D4⋊C8—1031no—
99C22×Q8—2061no—
100C4⋊Q8—2061no—
101C4⋊Q8C2×D10311yescharacteristic
102C4⋊Q8C2×D10311yescharacteristic
103C22⋊Q8—2061no—
104C22⋊Q8—2062no—
105C4×Q8—1031no—
106C4×D4—1031no—
107C4×D4—2061no—
108#107—2061no—
109#106—2061no—
110C4⋊C8—1031no—
111C4⋊C8—1031no—
112#103—22no—
113#103—2061no—
114#102—2061no—
115C4×C8C2×D10311yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—1031no—
119C2×Q8—4122no—
120C2×Q8—4122no—
121C2×Q8—2062no—
122C2×D4—1031no—
123C22×C4—2062no—
124C22×C4—2061no—
125C2×C8—21no—
126C2×C8—2061no—
127C2×C8—2061no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1031no—
132C4⋊C4—1031no—
133C4⋊C4—2062no—
134C4⋊C4—2061no—
135C4⋊C4C22⋊D10312yes—
136C22⋊C4—2062no—
137C22⋊C4—2061no—
138C42—2061no—
139C42C22×D10311yescharacteristic
140C23—2061no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—1032no—
145Q8—4124no—
146Q8—2061no—
147D4—1032no—
148D4—2061no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—4124no—
152C2×C4—4121no—
153C2×C4—4121no—
154C2×C4—2061no—
155C2×C4—2061no—
156C2×C4—2061no—
157C2×C4D4×D10311yescharacteristic
158C2×C4D4×D10311yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C8—41no—
161C8—4121no—
162C8—4121no—
163C22—4121no—
164C22—4121no—
165C22—2062no—
166C22#1569298911yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—4121no—
171C4—4121no—
172C4—2062no—
173C4SD16×D10311yescharacteristic
174C4Q16×D10311yescharacteristic
175C4#1569304811yescharacteristic
176C4#1569305311yescharacteristic
177C2—4122no—
178C2#2026794011yescharacteristic
179C2#2026794511yescharacteristic
180C2#2026796311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#487×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#487D103
hypocenterC103#1637
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #20268083C2semidirect
4. #20267537C2semidirect
5. #20267523C2semidirect
7. #487×C103C2semidirect
91. C103#1637semidirect
93. #487D103semidirect

Maximal subgroups

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

subgroupindex
#202684562
#202680832
#202680782
#202675372
#202675232
#202675202
#487×C1032
#1637103