Finite Group Databasebeta

← #27194213

Subgroups — #27194213

Order 13184.

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

normal subgroups only

This group has 236 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, complemented
2#20267988C211yesmaximal, characteristic, complemented
3#20267983C211yesmaximal, characteristic
4#20267540C211yesmaximal, characteristic, complemented
5#20267523C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic, complemented
7#492×C103C211yesmaximal, characteristic, complemented
8C2×#13110093—21no—
9C2×#13110090—21no—
10#15693012—21no—
11#15693001—21no—
12#15692997—22no—
13C4×Dic206C2211yescharacteristic
14C4×D412C2211yescharacteristic
15#15692983—21no—
16C4⋊C4×D103—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692942—21no—
20#15692942—21no—
21C2×SD16×C103—22no—
22C4⋊Q8×C103C2211yescharacteristic
23#127×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25C2×Dic206D411yescharacteristic
26C2×D412D411yescharacteristic
27C2×C4×D103—21no—
28C2×C4×D103—22no—
29#13110093—42no—
30#13110090—42no—
31C2×C103⋊C8—21no—
32C2×C103⋊C8—21no—
33C4⋊Dic103—22no—
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×C103D412yes—
42C2×D4×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103—21no—
45SD16×C103—44no—
46C2×C8×C103—21no—
47C4⋊C4×C103—21no—
48C4⋊C4×C103—21no—
49C42×C103C2311yescharacteristic
50C23×C103—41no—
51C22×D103—21no—
52Q8×C103—42no—
53D4×C103—42no—
54D4×C103—41no—
55D4×C103—41no—
56D4×C103—41no—
57D4×C103—41no—
58C2×C4×C103—22no—
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C2×Dic103—21no—
63C2×Dic103—21no—
64C2×Dic103—21no—
65D412—21no—
66D412SD1612yescomplemented
67C4×D103—41no—
68C4×D103—41no—
69C4×D103—82no—
70Dic206—21no—
71Dic206—21no—
72C8×C103—22no—
73C103⋊C8—41no—
74C103⋊C8—41no—
75C22×C103—81no—
76C22×C103—81no—
77C22×C103—81no—
78C22×C103#12011yescharacteristic
79C2×D103—22no—
80C2×D103—41no—
81C2×D103—41no—
82C4×C103—21no—
83C4×C103—42no—
84C4×C103C2×SD1611yescharacteristic
85C4×C103#13511yescharacteristic
86C4×C103AGL(1,ℤ/8)11yescharacteristic
87C4×C103#13711yescharacteristic
88Dic103—41no—
89Dic103—41no—
90Dic103—41no—
91C2×C103—161no—
92C2×C103#44811yescharacteristic
93C2×C103#44911yescharacteristic
94C2×C103#45311yescharacteristic
95D103—42no—
96#1622—1031nomaximal, Sylow
97C103#162211yescharacteristic, complemented, Sylow
98#554—1031no—
99#492D10311yescharacteristic, complemented
100#460—1031no—
101#459—1031no—
102#333—1031no—
103Q8⋊C8—1031no—
104D4⋊C8—1031no—
105C2×SD16—22no—
106C2×SD16—2061no—
107C2×D8—2061no—
108C4⋊Q8C2×D10311yescharacteristic
109#127C2×D10311yescharacteristic
110#125—2061no—
111C22⋊Q8—2061no—
112C22⋊Q8—2062no—
113C4×Q8—1031no—
114C4×D4—1031no—
115C4×D4—2061no—
116C2×C4⋊C4—2061no—
117C4⋊C8—1031no—
118C4⋊C8—1031no—
119#102—2061no—
120#102—2061no—
121C4×C8C2×D10311yescharacteristic
122C2×Q8—1031no—
123C2×Q8C22⋊D10312yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—1031no—
128C22×C4—2062no—
129C22×C4—2061no—
130SD16—44no—
131SD16—4122no—
132D8—4122no—
133C2×C8—21no—
134C2×C8—2061no—
135C2×C8—2061no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—1031no—
139C4⋊C4—1031no—
140C4⋊C4—2062no—
141C4⋊C4—2062no—
142C4⋊C4—2061no—
143C22⋊C4—2062no—
144C22⋊C4—2061no—
145C42—2061no—
146C42C22×D10311yescharacteristic
147C23—41no—
148C23—2061no—
149Q8—42no—
150Q8—2061no—
151Q8—2061no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—1032no—
158D4—2061no—
159C2×C4—22no—
160C2×C4—8242no—
161C2×C4—4121no—
162C2×C4—4121no—
163C2×C4—2061no—
164C2×C4—2061no—
165C2×C4—2061no—
166C2×C4D4×D10311yescharacteristic
167C2×C4D4×D10311yescharacteristic
168C2×C4C2×C22⋊D10311yescharacteristic
169C8—22no—
170C8—4121no—
171C8—4121no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—4121no—
176C22—4121no—
177C22—2062no—
178C22#1569298911yescharacteristic
179C4—21no—
180C4—42no—
181C4—4121no—
182C4—4121no—
183C4—4121no—
184C4SD16×D10311yescharacteristic
185C4#1569304211yescharacteristic
186C4#1569304811yescharacteristic
187C4#1569305011yescharacteristic
188C2—161no—
189C2—4122no—
190C2#2026792811yescharacteristic
191C2#2026793511yescharacteristic
192C2#2026795811yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#492×C103C2
socleC22×C103#120
prime radical#20267983C2
hypercenter#492D103
hypocenterC103#1622
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #20268502C2semidirect
2. #20267988C2semidirect
4. #20267540C2semidirect
5. #20267523C2semidirect
6. #20267520C2semidirect
7. #492×C103C2semidirect
66. D412SD16semidirect
97. C103#1622semidirect
99. #492D103semidirect

Maximal subgroups

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

subgroupindex
#202685022
#202679882
#202679832
#202675402
#202675232
#202675202
#492×C1032
#1622103