Finite Group Databasebeta

← #27195245

Subgroups — #27195245

Order 13184.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic103C211yesmaximal, characteristic
2#20267775C211yesmaximal, characteristic
3#20267550C212yesmaximal, complemented
4#20267547C212yesmaximal, complemented
5#410×C103C211yesmaximal, characteristic
6C2×#13110089C2212yes—
7Q8×Dic103—21no—
8D4×Dic103—21no—
9D4×Dic103—22no—
10#15692980C412yescomplemented
11#15692980C2211yescharacteristic
12C2×C4×Dic103C412yescomplemented
13C2×C4×Dic103C2211yescharacteristic
14#15692940—21no—
15#15692938—21no—
16C2×#41×C103C2211yescharacteristic
17#117×C103C2212yes—
18#99×C103—22no—
19C22×Dic103—22no—
20C22×Dic103—21no—
21#13110089—22no—
22#13110089—22no—
23C2×C103⋊C8—22no—
24C4⋊Dic103—22no—
25C4⋊Dic103—21no—
26C22⋊Dic103—22no—
27C22⋊Dic103—21no—
28C4×Dic103—22no—
29C4×Dic103—21no—
30C4×Dic103C2×C411yescharacteristic
31C4×Dic103C2×C412yes—
32C4×Dic103C2×C411yescharacteristic
33#41×C103—22no—
34#41×C103—22no—
35C2×Q8×C103D411yescharacteristic
36C2×D4×C103D411yescharacteristic
37C2×D4×C103D412yes—
38C22×C4×C103C2×C412yes—
39C22×C4×C103C2311yescharacteristic
40C4⋊C4×C103—22no—
41C22⋊C4×C103—22no—
42C42×C103—22no—
43C23×C103C22⋊C412yes—
44C23×C103C2×D411yescharacteristic
45Q8×C103—22no—
46D4×C103—24no—
47D4×C103—22no—
48C2×C4×C103—22no—
49C2×C4×C103—22no—
50C2×C4×C103—42no—
51C2×C4×C103C22⋊C412yes—
52C2×C4×C103C22×C411yescharacteristic
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103#4112yes—
55C2×C4×C103#4112yes—
56C2×Dic103—21no—
57C2×Dic103—22no—
58C2×Dic103—21no—
59C2×Dic103—42no—
60C2×Dic103—44no—
61C103⋊C8—42no—
62C22×C103—22no—
63C22×C103—41no—
64C22×C103—42no—
65C22×C103C2×C22⋊C411yescharacteristic
66C22×C103#12312yes—
67C4×C103—22no—
68C4×C103—82no—
69C4×C103#11711yescharacteristic
70C4×C103#11711yescharacteristic
71C4×C103#12312yes—
72Dic103—22no—
73Dic103—42no—
74Dic103—41no—
75C2×C103—21no—
76C2×C103—22no—
77C2×C103—42no—
78C2×C103#38111yescharacteristic
79#1827—1031nomaximal, Sylow
80C103#182711yescharacteristic, complemented, Sylow
81C4×#41—1031no—
82#413—1031no—
83#410D10311yescharacteristic
84#339—1032no—
85H(3,ℤ/4)—1032no—
86C2×#41C2×D10311yescharacteristic
87C2×M16—1032no—
88C4×Q8—2061no—
89C4×D4—2061no—
90C4×D4—2062no—
91#117—1032no—
92#117—1031no—
93#117C2×D10312yes—
94C2×C42—1032no—
95C2×C42—1031no—
96#101—2061no—
97#100—2061no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D41211yescharacteristic
102C2×D4D41211yescharacteristic
103C2×D4C22⋊D10312yes—
104C22×C4—2062no—
105C22×C4—2061no—
106C22×C4C4×D10312yes—
107C22×C4C22×D10311yescharacteristic
108M16—2062no—
109M16—2062no—
110C2×C8—2062no—
111C4⋊C4—22no—
112C4⋊C4—2062no—
113C4⋊C4—2061no—
114C22⋊C4—22no—
115C22⋊C4—2062no—
116C22⋊C4—2061no—
117C42—22no—
118C42—1031no—
119C42—1032no—
120C42—1031no—
121C42—2062no—
122C42—2061no—
123C23(C2×D103)⋊C412yes—
124C23C2×C22⋊D10311yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—4122no—
132C2×C4—4124no—
133C2×C4—2062no—
134C2×C4—2061no—
135C2×C4—2061no—
136C2×C4(C2×D103)⋊C412yes—
137C2×C4C2×C4×D10311yescharacteristic
138C2×C4C2×D41211yescharacteristic
139C2×C4#1311010412yes—
140C2×C4#1311010412yes—
141C8—4122no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×(C2×D103)⋊C411yescharacteristic
146C22#1569300212yes—
147C4—22no—
148C4—82no—
149C4—4121no—
150C4—4122no—
151C4—2062no—
152C4#1569297711yescharacteristic
153C4#1569297711yescharacteristic
154C4#1569300512yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#2026765211yescharacteristic
subgroupG/H
centerC4#15692977
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#410×C103C2
socleC2×C103#381
prime radicalC2×#41×C103C22
cosocleC22×C4×C103C23
hypercenter#410D103
hypocenterC103#1827
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #20267550C2semidirect
4. #20267547C2semidirect
10. #15692980C4semidirect
12. C2×C4×Dic103C4semidirect
80. C103#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1032
#202677752
#202675502
#202675472
#410×C1032
#1827103