Finite Group Databasebeta

← #27197219

Subgroups — #27197219

Order 13184.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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#20268229C211yesmaximal, characteristic, complemented
2#20268227C211yesmaximal, characteristic, complemented
3#20268166C211yesmaximal, characteristic, complemented
4#20267907C211yesmaximal, characteristic, complemented
5#20267611C211yesmaximal, characteristic, complemented
6#20267603C211yesmaximal, characteristic, complemented
7#361×C103C211yesmaximal, characteristic, complemented
8#15693043C2211yescharacteristic
9C2×D824C2211yescharacteristic
10C2×#13110090—21no—
11#15693029—21no—
12#15693017—21no—
13#15692966—21no—
14#15692965—21no—
15D1648—21no—
16#15692962—21no—
17#15692961C2211yescharacteristic
18#15692947—21no—
19C8×Dic103C2211yescharacteristic
20C2×D8×C103C2211yescharacteristic
21M32×C103C2211yescharacteristic
22#108×C103C2211yescharacteristic
23#13110105—21no—
24C2×D412—21no—
25C2×C22⋊D103—42no—
26Dic412D411yescharacteristic, complemented
27#13110094—21no—
28D824—21no—
29D824—21no—
30D824D411yescharacteristic, complemented
31#13110090—41no—
32#13110090—41no—
33#13110088—41no—
34C2×C103⋊C8D411yescharacteristic
35C8×D103—41no—
36C4×Dic103D411yescharacteristic
37C103⋊C16—21no—
38C2×D4×C103—21no—
39D8×C103—21no—
40D8×C103—21no—
41M16×C103—21no—
42C2×C8×C103C2311yescharacteristic
43C16×C103—21no—
44C23×C103—41no—
45C22×D103—41no—
46D4×C103—41no—
47D4×C103—41no—
48C2×C4×C103C2×D411yescharacteristic
49C22⋊D103—41no—
50C22⋊D103—84no—
51C2×Dic103—21no—
52D412—21no—
53D412—41no—
54D412—41no—
55C4×D103—41no—
56Dic206—21no—
57C8×C103—41no—
58C8×C103C2×D411yescharacteristic
59C8×C103#4111yescharacteristic
60C103⋊C8D811yescharacteristic
61C103⋊C8D811yescharacteristic
62C22×C103—82no—
63C22×C103—81no—
64C22×C103AGL(1,ℤ/8)11yescharacteristic
65C2×D103—41no—
66C2×D103—82no—
67C2×D103—81no—
68C4×C103#12111yescharacteristic
69C4×C103C2×D811yescharacteristic
70Dic103—22no—
71Dic103—41no—
72C2×C103—21no—
73C2×C103—161no—
74C2×C103#45911yescharacteristic
75D103—81no—
76D103—161no—
77#2213—1031nomaximal, Sylow
78C103#221311yescharacteristic, complemented, Sylow
79#509—1031no—
80#509—1031no—
81#493—1031no—
82#443—1031no—
83#364—1031no—
84#361—1031no—
85#361D10311yescharacteristic, complemented
86#135—1031no—
87C2×D8—1031no—
88C2×D8—2061no—
89C2×D8C2×D10311yescharacteristic
90#131—2061no—
91#127—2061no—
92SD32—2061no—
93SD32—2061no—
94D16—2061no—
95D16—2061no—
96M32—1031no—
97M32C2×D10311yescharacteristic
98#108C2×D10311yescharacteristic
99#104—2061no—
100C4×C8—1031no—
101#41—2061no—
102C2×D4—21no—
103C2×D4—4122no—
104C2×D4—2061no—
105Q16—1031no—
106SD16—2061no—
107D8—21no—
108D8—21no—
109D8—1031no—
110D8—4121no—
111D8—4121no—
112D8—2061no—
113D8—2061no—
114M16—21no—
115M16—4121no—
116C2×C8—1031no—
117C2×C8—4121no—
118C2×C8C22×D10311yescharacteristic
119C42—1031no—
120C16—21no—
121C16—2061no—
122C23—41no—
123C23—4121no—
124Q8—2061no—
125D4—41no—
126D4—41no—
127D4—8244no—
128D4—4121no—
129D4—4121no—
130D4—4121no—
131D4—2061no—
132C2×C4—4121no—
133C2×C4—2061no—
134C2×C4D4×D10311yescharacteristic
135C8—41no—
136C8—1031no—
137C8—1031no—
138C8D4×D10311yescharacteristic
139C8#1311010511yescharacteristic
140C22—82no—
141C22—81no—
142C22—8242no—
143C22—8241no—
144C22—4121no—
145C22#1569304811yescharacteristic
146C4—4121no—
147C4—2062no—
148C4#1569299411yescharacteristic
149C4D8×D10311yescharacteristic
150C2—21no—
151C2—161no—
152C2—8241no—
153C2—16481no—
154C2#2026798511yescharacteristic
subgroupG/H
centerC2#20267985
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
Fitting#361×C103C2
socleC2×C103#459
hypercenter#361D103
hypocenterC103#2213
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #20268229C2semidirect
2. #20268227C2semidirect
3. #20268166C2semidirect
4. #20267907C2semidirect
5. #20267611C2semidirect
6. #20267603C2semidirect
7. #361×C103C2semidirect
26. Dic412D4semidirect
30. D824D4semidirect
78. C103#2213semidirect
85. #361D103semidirect

Maximal subgroups

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

subgroupindex
#202682292
#202682272
#202681662
#202679072
#202676112
#202676032
#361×C1032
#2213103