Finite Group Databasebeta

← #27205075

Subgroups — #27205075

Order 13184.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#20268302C211yesmaximal, characteristic
2#20268132C214yesmaximal, complemented
3#20268115C214yesmaximal, complemented
4#20267831C212yesmaximal, complemented
5#20267790C212yesmaximal, complemented
6#20267755C211yesmaximal, characteristic, complemented
7C2×#117×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9C2×#13110089C2212yes—
10#15693004—21no—
11#15693000C2212yes—
12#15692995C2212yes—
13#15692990—21no—
14C4×C22⋊D103—22no—
15#15692980C2211yescharacteristic
16#15692954C2214yescomplemented
17#15692952C2214yescomplemented
18#15692944C2214yescomplemented
19#15692941C2214yescomplemented
20C22⋊(C103⋊C8)C2214yes—
21C23×C4×C103C2211yescharacteristic
22#117×C103—22no—
23#117×C103C2214yes—
24C2×C4⋊C4×C103C2212yes—
25C2×C22⋊C4×C103—21no—
26C2×C42×C103—21no—
27#13110105—24no—
28C2×Dic206C2311yescharacteristic
29C2×D412C2311yescharacteristic
30C2×C22⋊D103—21no—
31C2×C22⋊D103—22no—
32C2×C4×D103—21no—
33#13110089—24no—
34C2×C103⋊C8C2314yes—
35C4⋊Dic103C2312yes—
36Dic103⋊C4—22no—
37C22⋊Dic103—21no—
38C22⋊Dic103—22no—
39(C2×D103)⋊C4—22no—
40C4×Dic103—21no—
41C24×C103D411yescharacteristic
42C22×C4×C103—24no—
43C22×C4×C103—22no—
44C22×C4×C103D411yescharacteristic
45C22×C4×C103D412yes—
46C22×C4×C103C2312yes—
47C22×C4×C103C2311yescharacteristic
48C4⋊C4×C103—22no—
49C4⋊C4×C103C2314yes—
50C22⋊C4×C103—24no—
51C42×C103—24no—
52C23×C103—22no—
53C23×C103—42no—
54C23×C103C2×D412yes—
55C23×C103C2×D411yescharacteristic
56C22×D103—21no—
57C2×C4×C103—22no—
58C2×C4×C103—24no—
59C2×C4×C103—24no—
60C2×C4×C103—24no—
61C2×C4×C103—44no—
62C2×C4×C103C2×D412yes—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103#4114yes—
65C2×C4×C103C2411yescharacteristic
66C22⋊D103—44no—
67C22⋊D103—42no—
68C2×Dic103—22no—
69C2×Dic103—21no—
70D412—22no—
71C4×D103—42no—
72Dic206—22no—
73C103⋊C8—24no—
74C22×C103—22no—
75C22×C103—22no—
76C22×C103—22no—
77C22×C103—22no—
78C22×C103—44no—
79C22×C103#12312yes—
80C22×C103C22×D411yescharacteristic
81C2×D103—41no—
82C2×D103—42no—
83C4×C103—22no—
84C4×C103—44no—
85C4×C103#12312yes—
86C4×C103C2×#4112yes—
87Dic103—41no—
88Dic103—42no—
89C2×C103—22no—
90C2×C103—42no—
91C2×C103C2×#12311yescharacteristic
92C2×C103#57512yes—
93D103—81no—
94#3093—1031nomaximal, Sylow
95C103#309311yescharacteristic, complemented, Sylow
96#525—1031no—
97C2×#117D10311yescharacteristic, complemented
98#485—1034no—
99#482—1034no—
100#428—1032no—
101#417—1032no—
102#407—1031no—
103C2×#41—1031no—
104C23×C4C2×D10311yescharacteristic
105C2×M16—1032no—
106#123—2061no—
107C22⋊Q8—1032no—
108#121—1032no—
109#120—2061no—
110C4×D4—2062no—
111#117—22no—
112#117—1031no—
113#117C2×D10314yes—
114C2×C4⋊C4C2×D10312yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—1034no—
118#106—1034no—
119#103—1034no—
120#102—1034no—
121C22⋊C8—1034no—
122C24C22⋊D10311yescharacteristic
123#41—2064no—
124C2×Q8—1031no—
125C2×D4—1031no—
126C2×D4—2062no—
127C2×D4—2061no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—2061no—
131C22×C4C22⋊D10311yescharacteristic
132C22×C4C22⋊D10312yes—
133C22×C4C22×D10312yes—
134C22×C4C22×D10311yescharacteristic
135M16—2064no—
136C2×C8—1034no—
137C4⋊C4—22no—
138C4⋊C4—1032no—
139C4⋊C4—2062no—
140C4⋊C4C22×D10314yes—
141C22⋊C4—24no—
142C22⋊C4—2061no—
143C22⋊C4—2062no—
144C22⋊C4—2062no—
145C42—24no—
146C42—2061no—
147C23—22no—
148C23—42no—
149C23—2061no—
150C23C2×C22⋊D10312yes—
151C23C2×C22⋊D10311yescharacteristic
152Q8—2062no—
153D4—4124no—
154D4—4122no—
155D4—2062no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—4122no—
162C2×C4—2062no—
163C2×C4—2061no—
164C2×C4C2×C22⋊D10312yes—
165C2×C4C2×C22⋊D10311yescharacteristic
166C2×C4#1311010514yes—
167C2×C4C23×D10311yescharacteristic
168C8—2064no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—4121no—
175C22—4122no—
176C22#1569300412yes—
177C22C22×C22⋊D10311yescharacteristic
178C4—22no—
179C4—44no—
180C4—4121no—
181C4—4122no—
182C4#1569300412yes—
183C4C2×#1311010512yes—
184C2—22no—
185C2—42no—
186C2—8241no—
187C2C2×#1569300411yescharacteristic
188C2#2026858912yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#117×C103C2
socleC22×C103C22×D4
prime radical#20268302C2
hypercenterC2×#117D103
hypocenterC103#3093
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20268132C2semidirect
3. #20268115C2semidirect
4. #20267831C2semidirect
5. #20267790C2semidirect
6. #20267755C2semidirect
7. C2×#117×C103C2semidirect
16. #15692954C22semidirect
17. #15692952C22semidirect
18. #15692944C22semidirect
19. #15692941C22semidirect
95. C103#3093semidirect
97. C2×#117D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
#202681322
#202681152
#202678312
#202677902
#202677552
C2×#117×C1032
#3093103