Finite Group Databasebeta

← #27205865

Subgroups — #27205865

Order 13184.

402 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 121 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#20268346C211yesmaximal, characteristic, complemented
2#20268342C211yesmaximal, characteristic
3#20268194C211yesmaximal, characteristic, complemented
4#20268165C211yesmaximal, characteristic, complemented
5#20268138C211yesmaximal, characteristic, complemented
6#20268040C214yesmaximal, complemented
7#20267894C214yesmaximal, complemented
8C4×#13110088C211yesmaximal, characteristic, complemented
9#487×C103C211yesmaximal, characteristic, complemented
10C2×#13110106—21no—
11C2×#13110092C2214yes—
12C2×#13110088C2212yes—
13#15693021C2211yescharacteristic
14#15693018C2211yescharacteristic
15#15693012—21no—
16#15693010—21no—
17#15693001—21no—
18#15692997C2212yes—
19#15692996—21no—
20#15692996C2212yes—
21Q8×Dic103C2212yes—
22#15692986—21no—
23#15692983—21no—
24#15692983C2212yes—
25#15692979—21no—
26C42×D103C2211yescharacteristic
27#15692954C2214yes—
28#15692943C2214yes—
29#15692931C2212yes—
30C4×C103⋊C8C2211yescharacteristic
31C4⋊Q8×C103C2211yescharacteristic
32C4⋊Q8×C103C2211yescharacteristic
33#103×C103C2214yes—
34C4×C8×C103C2211yescharacteristic
35#13110106—44no—
36C2×Dic206—21no—
37C2×D412—22no—
38C2×D412—21no—
39C2×D412—21no—
40C2×D412C2312yes—
41C2×C4×D103—22no—
42C2×C4×D103D411yescharacteristic
43C2×C4×D103D411yescharacteristic
44C2×C4×D103C2311yescharacteristic
45#13110092—28no—
46#13110088—24no—
47C2×C103⋊C8C2312yes—
48C4⋊Dic103—21no—
49C4⋊Dic103—22no—
50C4⋊Dic103C2312yes—
51Dic103⋊C4—22no—
52(C2×D103)⋊C4—22no—
53(C2×D103)⋊C4—22no—
54(C2×D103)⋊C4—22no—
55C4×Dic103—22no—
56C4×Dic103D411yescharacteristic
57C4×Dic103D411yescharacteristic
58C4×Dic103C2311yescharacteristic
59C2×Q8×C103—21no—
60C2×Q8×C103C2312yes—
61C2×C8×C103C2312yes—
62C4⋊C4×C103—21no—
63C4⋊C4×C103—21no—
64C4⋊C4×C103—21no—
65C4⋊C4×C103C2312yes—
66C42×C103C2311yescharacteristic
67C22×D103—22no—
68C22×D103C2×D411yescharacteristic
69Q8×C103—24no—
70Q8×C103—42no—
71C2×C4×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103C2411yescharacteristic
76C2×Dic103—22no—
77C2×Dic103C2×D411yescharacteristic
78C2×Dic103C2×D411yescharacteristic
79C2×Dic103C2×D411yescharacteristic
80D412—24no—
81D412—44no—
82D412—42no—
83D412—42no—
84C4×D103—22no—
85C4×D103—22no—
86C4×D103—22no—
87C4×D103—44no—
88Dic206—42no—
89C8×C103—22no—
90C103⋊C8#4114yescomplemented
91C22×C103C22×D411yescharacteristic
92C2×D103—21no—
93C2×D103—21no—
94C2×D103—21no—
95C2×D103—42no—
96C2×D103—42no—
97C2×D103—42no—
98C4×C103—42no—
99C4×C103—42no—
100C4×C103AGL(1,ℤ/8)12yes—
101C4×C103#13712yes—
102C4×C103C2×#4112yes—
103Dic103—21no—
104Dic103—21no—
105Dic103—21no—
106Dic103—42no—
107C2×C103#53211yescharacteristic
108C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C103C2×#13711yescharacteristic
110D103—41no—
111D103—82no—
112#3182—1031nomaximal, Sylow
113C103#318211yescharacteristic, complemented, Sylow
114#533—1031no—
115#532—1031no—
116#500—1031no—
117#492—1031no—
118#487D10311yescharacteristic, complemented
119#486—1031no—
120#468—1034no—
121#440—1034no—
122C4×M16—1031no—
123C2×#41—2061no—
124C2×SD16—1034no—
125C2×M16—1032no—
126C4⋊Q8—1031no—
127C4⋊Q8C2×D10311yescharacteristic
128C4⋊Q8C2×D10311yescharacteristic
129#127—1031no—
130#125—2061no—
131#124—2061no—
132C22⋊Q8—1032no—
133C22⋊Q8—2061no—
134#121—1032no—
135#121—2061no—
136C4×Q8—1032no—
137C4×Q8—2061no—
138C4×D4—1032no—
139C4×D4—2061no—
140#117—2061no—
141C2×C42—1031no—
142#107—1034no—
143#103C2×D10314yes—
144#102—1034no—
145#97—1032no—
146C4×C8—1031no—
147C4×C8C2×D10311yescharacteristic
148#41—4124no—
149C2×Q8—21no—
150C2×Q8—2061no—
151C2×Q8C22×D10312yes—
152C2×D4—1032no—
153C2×D4—2062no—
154C2×D4—2061no—
155C2×D4—2061no—
156C22×C4—1031no—
157C22×C4—1031no—
158C22×C4—1031no—
159C22×C4—2062no—
160SD16—2068no—
161M16—2064no—
162C2×C8—1032no—
163C2×C8C22×D10312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—1032no—
168C4⋊C4—2062no—
169C4⋊C4—2062no—
170C4⋊C4—2061no—
171C4⋊C4C22×D10312yes—
172C22⋊C4—2062no—
173C22⋊C4—2062no—
174C22⋊C4—2062no—
175C42—1031no—
176C42—1031no—
177C42—1031no—
178C42—2062no—
179C42C22×D10311yescharacteristic
180C23—1031no—
181C23—2062no—
182Q8—24no—
183Q8—42no—
184Q8—4122no—
185D4—4124no—
186D4—4122no—
187D4—4122no—
188D4—2064no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—1031no—
192C2×C4—1031no—
193C2×C4—1031no—
194C2×C4—4124no—
195C2×C4—2062no—
196C2×C4—2062no—
197C2×C4—2062no—
198C2×C4—2062no—
199C2×C4D4×D10311yescharacteristic
200C2×C4D4×D10311yescharacteristic
201C2×C4C23×D10311yescharacteristic
202C8—22no—
203C8—1034no—
204C22—4122no—
205C22—4122no—
206C22—4122no—
207C22—2061no—
208C22—2061no—
209C22—2061no—
210C22C2×D4×D10311yescharacteristic
211C4—42no—
212C4—42no—
213C4—4122no—
214C4—2061no—
215C4—2061no—
216C4—2061no—
217C4#1569304812yes—
218C4#1569305312yes—
219C4#41×D10312yes—
220C2—8242no—
221C2—4121no—
222C2#2026834011yescharacteristic
223C2C2×#1569304811yescharacteristic
224C2C2×#1569305311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#487×C103C2
socleC22×C103C22×D4
prime radical#20268342C2
hypercenter#487D103
hypocenterC103#3182
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #20268346C2semidirect
3. #20268194C2semidirect
4. #20268165C2semidirect
5. #20268138C2semidirect
6. #20268040C2semidirect
7. #20267894C2semidirect
8. C4×#13110088C2semidirect
9. #487×C103C2semidirect
90. C103⋊C8#41semidirect
113. C103#3182semidirect
118. #487D103semidirect

Maximal subgroups

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

subgroupindex
#202683462
#202683422
#202681942
#202681652
#202681382
#202680402
#202678942
C4×#131100882
#487×C1032
#3182103