Finite Group Databasebeta

← #27195590

Subgroups — #27195590

Order 13184.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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
2C2×#15692980C211yesmaximal, characteristic, complemented
3C2×#15692947C212yesmaximal, complemented
4#20267552C212yesmaximal, complemented
5#407×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C2211yescharacteristic
7#15693004—21no—
8#15693000C412yescomplemented
9#15692995C412yescomplemented
10#15692990—21no—
11C4×C22⋊D103—22no—
12#15692980—24no—
13#15692980C2211yescharacteristic
14C2×C4⋊Dic103—21no—
15C2×C22⋊Dic103—21no—
16C2×C4×Dic103C2212yes—
17#15692947—24no—
18C23×C4×C103C2211yescharacteristic
19C2×M16×C103C2212yes—
20C22⋊C8×C103—22no—
21#13110105—22no—
22#13110105—22no—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—22no—
26C2×C22⋊D103—21no—
27C22×Dic103—22no—
28C2×C4×D103—21no—
29C4⋊Dic103—24no—
30C4⋊Dic103C2×C412yes—
31Dic103⋊C4—22no—
32C22⋊Dic103—24no—
33C22⋊Dic103—22no—
34C22⋊Dic103—21no—
35(C2×D103)⋊C4—22no—
36C4×Dic103—22no—
37C4×Dic103—21no—
38C4×Dic103D414yescomplemented
39C24×C103D411yescharacteristic
40C22×C4×C103—22no—
41C22×C4×C103—22no—
42C22×C4×C103C2×C412yes—
43C22×C4×C103D411yescharacteristic
44C22×C4×C103D412yes—
45C22×C4×C103C2311yescharacteristic
46M16×C103—22no—
47M16×C103—22no—
48C2×C8×C103—22no—
49C23×C103—21no—
50C23×C103—21no—
51C23×C103—42no—
52C23×C103C22⋊C412yes—
53C23×C103C2×D411yescharacteristic
54C22×D103—21no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—24no—
58C2×C4×C103—24no—
59C2×C4×C103C22⋊C412yes—
60C2×C4×C103C22×C411yescharacteristic
61C2×C4×C103C2×D412yes—
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103#4112yes—
64C22⋊D103—44no—
65C22⋊D103—41no—
66C22⋊D103—41no—
67C2×Dic103—22no—
68C2×Dic103—21no—
69C2×Dic103—24no—
70C2×Dic103—44no—
71D412—22no—
72C4×D103—42no—
73Dic206—22no—
74C8×C103—42no—
75C22×C103—22no—
76C22×C103—22no—
77C22×C103—22no—
78C22×C103—22no—
79C22×C103—42no—
80C22×C103—42no—
81C22×C103C2×C22⋊C411yescharacteristic
82C22×C103#12011yescharacteristic
83C22×C103#12311yescharacteristic
84C2×D103—41no—
85C2×D103—42no—
86C4×C103—22no—
87C4×C103C4×D412yes—
88C4×C103#12112yes—
89Dic103—44no—
90Dic103—41no—
91Dic103—42no—
92C2×C103—21no—
93C2×C103—21no—
94C2×C103—42no—
95C2×C103#38611yescharacteristic
96C2×C103#42112yes—
97D103—81no—
98#1897—1031nomaximal, Sylow
99C103#189711yescharacteristic, complemented, Sylow
100#525—1031no—
101C2×#117—1031no—
102C2×#104—1032no—
103#407D10311yescharacteristic, complemented
104#339—1032no—
105C2×#41—1031no—
106C23×C4C2×D10311yescharacteristic
107C2×M16C2×D10312yes—
108#123—2061no—
109C22⋊Q8—1032no—
110#121—1032no—
111#120—2061no—
112C4×D4—2062no—
113#117—1031no—
114#117—2064no—
115C2×C4⋊C4—2061no—
116C2×C22⋊C4—2061no—
117C2×C42—1032no—
118#104—2064no—
119C22⋊C8—22no—
120C24D41211yescharacteristic
121#41—2062no—
122#41—2062no—
123C2×Q8—1031no—
124C2×D4—1031no—
125C2×D4—2062no—
126C2×D4—2061no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—2062no—
130C22×C4—2061no—
131C22×C4C4×D10312yes—
132C22×C4D41211yescharacteristic
133C22×C4C22⋊D10312yes—
134C22×C4C22×D10311yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—1032no—
139C4⋊C4—2064no—
140C4⋊C4—2062no—
141C22⋊C4—2064no—
142C22⋊C4—2062no—
143C22⋊C4—2061no—
144C22⋊C4—2062no—
145C42—1034no—
146C42—2062no—
147C42—2061no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—2061no—
152C23(C2×D103)⋊C412yes—
153C23C2×D41211yescharacteristic
154Q8—2062no—
155D4—4124no—
156D4—4121no—
157D4—4121no—
158D4—2062no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—4124no—
164C2×C4—4122no—
165C2×C4—2062no—
166C2×C4—2061no—
167C2×C4—2064no—
168C2×C4(C2×D103)⋊C412yes—
169C2×C4C2×C4×D10311yescharacteristic
170C2×C4D4×D10312yes—
171C2×C4C2×C22⋊D10311yescharacteristic
172C2×C4#1311010412yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—4122no—
181C22—4121no—
182C22C2×(C2×D103)⋊C411yescharacteristic
183C22#1569299111yescharacteristic
184C22#1569300511yescharacteristic
185C4—22no—
186C4—4124no—
187C4—4122no—
188C4—4121no—
189C4(C22⋊D103)⋊C412yes—
190C4#1569299312yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—8241no—
195C2#2026766811yescharacteristic
196C2#2026780712yes—
subgroupG/H
centerC2×C4C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#407×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268302C2
cosocleC22×C4×C103C23
hypercenter#407D103
hypocenterC103#1897
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#15692980C2semidirect
3. C2×#15692947C2semidirect
4. #20267552C2semidirect
5. #407×C103C2semidirect
8. #15693000C4semidirect
9. #15692995C4semidirect
38. C4×Dic103D4semidirect
99. C103#1897semidirect
103. #407D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
C2×#156929802
C2×#156929472
#202675522
#407×C1032
#1897103