Finite Group Databasebeta

← #27196817

Subgroups — #27196817

Order 13184.

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

normal subgroups only

This group has 238 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#20268361C211yesmaximal, characteristic
2#20267763C212yesmaximal
3#20267586C211yesmaximal, characteristic, complemented
4#20267585C212yesmaximal, complemented
5#354×C103C211yesmaximal, characteristic, complemented
6C2×#13110104C2211yescharacteristic
7C2×Q8×D103C411yescharacteristic, complemented
8#15693021C411yescharacteristic, complemented
9#15693019C411yescharacteristic, complemented
10#15693008C2211yescharacteristic
11#15693003—22no—
12#15692998—22no—
13#15692978C411yescharacteristic, complemented
14#15692977—22no—
15#15692936C2212yes—
16#15692935—22no—
17#124×C103C2211yescharacteristic
18#99×C103C2212yes—
19#13110104—42no—
20C2×Dic206—21no—
21C2×Dic206C2×C411yescharacteristic
22C2×Dic206C2×C411yescharacteristic
23Q8×D103—42no—
24C2×C22⋊D103D412yes—
25C22×Dic103D412yes—
26C2×C4×D103—21no—
27C2×C4×D103C2×C411yescharacteristic
28C4⋊Dic103—22no—
29Dic103⋊C4—21no—
30Dic103⋊C4—22no—
31Dic103⋊C4—42no—
32C22⋊Dic103—22no—
33C22⋊Dic103—22no—
34(C2×D103)⋊C4—21no—
35C4×Dic103—42no—
36C4×Dic103C2×C411yescharacteristic
37C2×Q8×C103C2×C411yescharacteristic
38C2×D4×C103C2311yescharacteristic
39C22⋊C4×C103—22no—
40C22⋊C4×C103—22no—
41C42×C103C2×C411yescharacteristic
42C23×C103C2×D412yes—
43C22×D103C22⋊C411yescharacteristic
44Q8×C103—41no—
45D4×C103—41no—
46C2×C4×C103—21no—
47C2×C4×C103—21no—
48C2×C4×C103—42no—
49C2×C4×C103C22×C411yescharacteristic
50C22⋊D103—42no—
51C2×Dic103—22no—
52C2×Dic103—22no—
53C2×Dic103—21no—
54C2×Dic103—21no—
55C2×Dic103—42no—
56C2×Dic103C22⋊C412yes—
57C2×Dic103C22⋊C411yescharacteristic
58C4×D103—22no—
59C4×D103—42no—
60Dic206—41no—
61Dic206—42no—
62Dic206—41no—
63C22×C103—22no—
64C22×C103—42no—
65C22×C103C2×C22⋊C411yescharacteristic
66C2×D103—21no—
67C2×D103—41no—
68C4×C103—21no—
69C4×C103—41no—
70C4×C103—41no—
71C4×C103—82no—
72Dic103—22no—
73Dic103—41no—
74Dic103—41no—
75Dic103—82no—
76Dic103#9912yes—
77C2×C103—21no—
78C2×C103—42no—
79C2×C103C2×#9911yescharacteristic
80D103—41no—
81#2129—1031nomaximal, Sylow
82C103#212911yescharacteristic, complemented, Sylow
83#536—1031no—
84#410—1032no—
85#354—1031no—
86#354—1032no—
87#354D10311yescharacteristic, complemented
88C2×#41—1031no—
89C22×Q8—1031no—
90C4⋊Q8—1031no—
91C4⋊Q8—1031no—
92#124—1031no—
93#124C2×D10311yescharacteristic
94#123—2062no—
95C22⋊Q8—2062no—
96#117—1031no—
97#117—2062no—
98#99—1032no—
99#99—2062no—
100#99C2×D10312yes—
101#41—4122no—
102C2×Q8—1031no—
103C2×Q8—1031no—
104C2×Q8—4122no—
105C2×Q8—2061no—
106C2×Q8C4×D10311yescharacteristic
107C2×D4—1032no—
108C2×D4C22×D10311yescharacteristic
109C22×C4—1032no—
110C22×C4—1031no—
111C22×C4—2061no—
112C4⋊C4—4122no—
113C4⋊C4—2061no—
114C4⋊C4—2062no—
115C4⋊C4—2062no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—2061no—
119C22⋊C4—2062no—
120C22⋊C4—2062no—
121C42—1031no—
122C42—4122no—
123C42C4×D10311yescharacteristic
124C23—1031no—
125C23D4×D10312yes—
126Q8—41no—
127Q8—4121no—
128Q8—4121no—
129Q8—4122no—
130D4—41no—
131D4—4122no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—1031no—
136C2×C4—1032no—
137C2×C4—4122no—
138C2×C4—4122no—
139C2×C4—2062no—
140C2×C4—2062no—
141C2×C4—2062no—
142C2×C4—2061no—
143C2×C4—2061no—
144C2×C4C2×C4×D10311yescharacteristic
145C22—22no—
146C22—42no—
147C22—4121no—
148C22—2061no—
149C22C22⋊C4×D10311yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—8242no—
155C4—1032no—
156C4—4121no—
157C4—4121no—
158C4—2062no—
159C2—21no—
160C2—42no—
161C2—4121no—
162C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC2×C4×C103C22×C4
FrattiniC2×D4C22×D103
Fitting#354×C103C2
socleC2×C103C2×#99
prime radicalC2×#13110104C22
cosocleC2×D4×C103C23
hypercenter#354D103
hypocenterC103#2129
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #20267586C2semidirect
4. #20267585C2semidirect
5. #354×C103C2semidirect
7. C2×Q8×D103C4semidirect
8. #15693021C4semidirect
9. #15693019C4semidirect
13. #15692978C4semidirect
82. C103#2129semidirect
87. #354D103semidirect

Maximal subgroups

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

subgroupindex
#202683612
#202677632
#202675862
#202675852
#354×C1032
#2129103