Finite Group Databasebeta

← #27194275

Subgroups — #27194275

Order 13184.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268502C211yesmaximal, characteristic
2#20268083C211yesmaximal, characteristic, complemented
3#20268078C211yesmaximal, characteristic
4#20267540C211yesmaximal, characteristic, complemented
5#20267523C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic
7#494×C103C211yesmaximal, characteristic, complemented
8#15693012—21no—
9#15693001—21no—
10#15692997—22no—
11C4×Dic206C2211yescharacteristic
12C4×D412C2211yescharacteristic
13#15692983—21no—
14C4⋊C4×D103—21no—
15#15692954—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692944—21no—
20#15692941—21no—
21C2×Q16×C103—22no—
22C4⋊Q8×C103C2211yescharacteristic
23C4⋊Q8×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25C2×Dic206D411yescharacteristic
26C2×D412D411yescharacteristic
27C2×C4×D103—21no—
28C2×C4×D103—22no—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C4⋊Dic103—22no—
32C4⋊Dic103D411yescharacteristic
33C4⋊Dic103D411yescharacteristic
34Dic103⋊C4—22no—
35Dic103⋊C4—21no—
36(C2×D103)⋊C4—22no—
37(C2×D103)⋊C4—21no—
38C4×Dic103—21no—
39C2×Q8×C103—21no—
40C2×Q8×C103D412yes—
41Q16×C103—44no—
42C2×C8×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C42×C103C2311yescharacteristic
48C22×D103—21no—
49Q8×C103—42no—
50Q8×C103—42no—
51C2×C4×C103—22no—
52C2×C4×C103—41no—
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103C2×D411yescharacteristic
55C2×C4×C103C2×D411yescharacteristic
56C2×Dic103—21no—
57C2×Dic103—21no—
58C2×Dic103—21no—
59D412—21no—
60D412Q1612yescomplemented
61C4×D103—41no—
62C4×D103—41no—
63C4×D103—82no—
64Dic206—21no—
65Dic206—21no—
66C8×C103—22no—
67C103⋊C8—41no—
68C103⋊C8—41no—
69C22×C103#12011yescharacteristic
70C2×D103—22no—
71C2×D103—41no—
72C2×D103—41no—
73C4×C103—21no—
74C4×C103—42no—
75C4×C103—81no—
76C4×C103C2×Q1611yescharacteristic
77C4×C103#13511yescharacteristic
78C4×C103#13711yescharacteristic
79C4×C103#13711yescharacteristic
80Dic103—41no—
81Dic103—41no—
82Dic103—41no—
83C2×C103#45111yescharacteristic
84C2×C103#45211yescharacteristic
85C2×C103#45311yescharacteristic
86D103—42no—
87#1632—1031nomaximal, Sylow
88C103#163211yescharacteristic, complemented, Sylow
89#554—1031no—
90#494D10311yescharacteristic, complemented
91#477—1031no—
92#476—1031no—
93#333—1031no—
94Q8⋊C8—1031no—
95D4⋊C8—1031no—
96C2×Q16—22no—
97C4⋊Q8C2×D10311yescharacteristic
98C4⋊Q8C2×D10311yescharacteristic
99#125—2061no—
100C22⋊Q8—2061no—
101C22⋊Q8—2062no—
102C4×Q8—1031no—
103C4×D4—1031no—
104C4×D4—2061no—
105C2×C4⋊C4—2061no—
106#107—2061no—
107#106—2061no—
108C4⋊C8—1031no—
109C4⋊C8—1031no—
110#103—2061no—
111#102—2061no—
112C4×C8C2×D10311yescharacteristic
113C2×Q8—21no—
114C2×Q8—1031no—
115C2×Q8C22⋊D10312yes—
116C2×D4—1031no—
117C22×C4—2062no—
118C22×C4—2061no—
119Q16—44no—
120C2×C8—21no—
121C2×C8—2061no—
122C2×C8—2061no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1031no—
128C4⋊C4—1031no—
129C4⋊C4—2062no—
130C4⋊C4—2062no—
131C4⋊C4—2061no—
132C22⋊C4—2062no—
133C22⋊C4—2061no—
134C42—2061no—
135C42C22×D10311yescharacteristic
136C23—2061no—
137Q8—42no—
138Q8—42no—
139Q8—2061no—
140Q8—2061no—
141D4—1032no—
142D4—2061no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—8242no—
146C2×C4—4121no—
147C2×C4—4121no—
148C2×C4—2061no—
149C2×C4—2061no—
150C2×C4—2061no—
151C2×C4D4×D10311yescharacteristic
152C2×C4D4×D10311yescharacteristic
153C2×C4C2×C22⋊D10311yescharacteristic
154C8—22no—
155C8—4121no—
156C8—4121no—
157C22—4121no—
158C22—4121no—
159C22—2062no—
160C22#1569298911yescharacteristic
161C4—21no—
162C4—42no—
163C4—81no—
164C4—4121no—
165C4—4121no—
166C4—4121no—
167C4Q16×D10311yescharacteristic
168C4#1569304411yescharacteristic
169C4#1569305311yescharacteristic
170C4#1569305311yescharacteristic
171C2—4122no—
172C2#2026794511yescharacteristic
173C2#2026795211yescharacteristic
174C2#2026795811yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#494×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#494D103
hypocenterC103#1632
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #20268083C2semidirect
4. #20267540C2semidirect
5. #20267523C2semidirect
7. #494×C103C2semidirect
60. D412Q16semidirect
88. C103#1632semidirect
90. #494D103semidirect

Maximal subgroups

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

subgroupindex
#202685022
#202680832
#202680782
#202675402
#202675232
#202675202
#494×C1032
#1632103