Finite Group Databasebeta

← #27205858

Subgroups — #27205858

Order 13184.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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#20268348C211yesmaximal, characteristic, complemented
2#20268194C211yesmaximal, characteristic, complemented
3#20268163C211yesmaximal, characteristic, complemented
4#20268143C211yesmaximal, characteristic, complemented
5#20268137C211yesmaximal, characteristic, complemented
6#20268035C214yesmaximal, complemented
7#20267891C214yesmaximal, complemented
8C4×#13110089C211yesmaximal, characteristic, complemented
9#532×C103C211yesmaximal, characteristic
10C2×#13110093C2214yes—
11C2×#13110089C2212yes—
12#15693021C2211yescharacteristic
13#15693021C2211yescharacteristic
14#15693013—21no—
15#15693000—21no—
16#15693000C2212yes—
17C4×Dic206—21no—
18C4×Dic206C2212yes—
19#15692980—21no—
20#15692954C2214yes—
21#15692944C2214yes—
22#15692942C2214yes—
23#15692932C2212yes—
24C4×C103⋊C8C2211yescharacteristic
25C4×C103⋊C8C2211yescharacteristic
26C2×#41×C103—21no—
27C4⋊Q8×C103C2211yescharacteristic
28#127×C103C2211yescharacteristic
29#124×C103—21no—
30#121×C103—21no—
31#121×C103C2212yes—
32C4×D4×C103—21no—
33C4×D4×C103C2212yes—
34C2×C42×C103C2211yescharacteristic
35C2×Dic206—21no—
36C2×Dic206C2312yes—
37#13110093—28no—
38#13110089—24no—
39C2×C103⋊C8C2312yes—
40C2×C103⋊C8C2312yes—
41C4⋊Dic103—21no—
42C4⋊Dic103—21no—
43C4⋊Dic103—21no—
44C4⋊Dic103C2312yes—
45Dic103⋊C4—22no—
46Dic103⋊C4—22no—
47C22⋊Dic103—22no—
48C4×Dic103—22no—
49#41×C103—44no—
50C2×Q8×C103—21no—
51C2×D4×C103—22no—
52C2×D4×C103—21no—
53C2×D4×C103—21no—
54C2×D4×C103C2312yes—
55C22×C4×C103—22no—
56C22×C4×C103D411yescharacteristic
57C22×C4×C103D411yescharacteristic
58C22×C4×C103C2311yescharacteristic
59C4⋊C4×C103—21no—
60C4⋊C4×C103C2312yes—
61C22⋊C4×C103—22no—
62C22⋊C4×C103—22no—
63C42×C103D411yescharacteristic
64C42×C103D411yescharacteristic
65C42×C103C2311yescharacteristic
66C42×C103C2311yescharacteristic
67C23×C103—22no—
68C23×C103C2×D411yescharacteristic
69Q8×C103—42no—
70D4×C103—24no—
71D4×C103—44no—
72D4×C103—42no—
73D4×C103—42no—
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103—22no—
77C2×C4×C103—22no—
78C2×C4×C103—44no—
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103C2×D411yescharacteristic
84C2×C4×C103C2411yescharacteristic
85C2×Dic103—22no—
86C2×Dic103—22no—
87Dic206—24no—
88Dic206—42no—
89C103⋊C8—22no—
90C103⋊C8#4114yescomplemented
91C22×C103—21no—
92C22×C103—21no—
93C22×C103—21no—
94C22×C103—42no—
95C22×C103—42no—
96C22×C103—42no—
97C22×C103C22×D411yescharacteristic
98C4×C103—21no—
99C4×C103—21no—
100C4×C103—21no—
101C4×C103—42no—
102C4×C103AGL(1,ℤ/8)12yes—
103C4×C103#13712yes—
104C4×C103C2×#4112yes—
105Dic103—42no—
106Dic103—42no—
107C2×C103—41no—
108C2×C103—82no—
109C2×C103#53211yescharacteristic
110C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C103C2×#13711yescharacteristic
112#3182—1031nomaximal, Sylow
113C103#318211yescharacteristic, complemented, Sylow
114#533—1031no—
115#532D10311yescharacteristic
116#500—1031no—
117#492—1031no—
118#487—1031no—
119#486—1031no—
120#468—1034no—
121#440—1034no—
122C4×M16—1031no—
123C2×#41—21no—
124C2×SD16—1034no—
125C2×M16—1032no—
126C4⋊Q8—1031no—
127C4⋊Q8—1031no—
128C4⋊Q8C2×D10311yescharacteristic
129#127C2×D10311yescharacteristic
130#125—2061no—
131#124—21no—
132C22⋊Q8—1032no—
133C22⋊Q8—2061no—
134#121—21no—
135#121C2×D10312yes—
136C4×Q8—1032no—
137C4×Q8—2061no—
138C4×D4—21no—
139C4×D4C2×D10312yes—
140#117—2061no—
141C2×C42C2×D10311yescharacteristic
142#107—1034no—
143#103—1034no—
144#102—1034no—
145#97—1032no—
146C4×C8—1031no—
147C4×C8—1031no—
148#41—44no—
149C2×Q8—21no—
150C2×Q8—1032no—
151C2×Q8—2061no—
152C2×D4—22no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4C22×D10312yes—
156C22×C4—22no—
157C22×C4C22⋊D10311yescharacteristic
158C22×C4C22⋊D10311yescharacteristic
159C22×C4C22×D10311yescharacteristic
160SD16—2068no—
161M16—2064no—
162C2×C8—1032no—
163C2×C8—1032no—
164C4⋊C4—21no—
165C4⋊C4—1032no—
166C4⋊C4—2062no—
167C4⋊C4—2062no—
168C4⋊C4—2061no—
169C4⋊C4—2061no—
170C4⋊C4—2061no—
171C4⋊C4C22×D10312yes—
172C22⋊C4—22no—
173C22⋊C4—22no—
174C22⋊C4—2062no—
175C42—2062no—
176C42C22⋊D10311yescharacteristic
177C42C22⋊D10311yescharacteristic
178C42C22×D10311yescharacteristic
179C42C22×D10311yescharacteristic
180C23—22no—
181C23C2×C22⋊D10311yescharacteristic
182Q8—42no—
183Q8—4122no—
184Q8—2064no—
185D4—24no—
186D4—44no—
187D4—42no—
188D4—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—2062no—
195C2×C4—2062no—
196C2×C4C2×C22⋊D10311yescharacteristic
197C2×C4C2×C22⋊D10311yescharacteristic
198C2×C4C2×C22⋊D10311yescharacteristic
199C2×C4C2×C22⋊D10311yescharacteristic
200C2×C4C2×C22⋊D10311yescharacteristic
201C2×C4C23×D10311yescharacteristic
202C8—1034no—
203C8—2062no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C22×C22⋊D10311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—4122no—
216C4—4122no—
217C4#1569304712yes—
218C4#1569305112yes—
219C4#41×D10312yes—
220C2—41no—
221C2—82no—
222C2#2026833711yescharacteristic
223C2C2×#1569304711yescharacteristic
224C2C2×#1569305111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#532×C103C2
socleC22×C103C22×D4
hypercenter#532D103
hypocenterC103#3182
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #20268348C2semidirect
2. #20268194C2semidirect
3. #20268163C2semidirect
4. #20268143C2semidirect
5. #20268137C2semidirect
6. #20268035C2semidirect
7. #20267891C2semidirect
8. C4×#13110089C2semidirect
90. C103⋊C8#41semidirect
113. C103#3182semidirect

Maximal subgroups

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

subgroupindex
#202683482
#202681942
#202681632
#202681432
#202681372
#202680352
#202678912
C4×#131100892
#532×C1032
#3182103