Finite Group Databasebeta

← #27205868

Subgroups — #27205868

Order 13184.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268322C212yesmaximal, complemented
2#20268191C211yesmaximal, characteristic, complemented
3#20268174C211yesmaximal, characteristic, complemented
4#20268144C212yesmaximal, complemented
5#20268049C211yesmaximal, characteristic, complemented
6#20268035C212yesmaximal, complemented
7#20267903C211yesmaximal, characteristic, complemented
8#20267897C211yesmaximal, characteristic, complemented
9#20267888C212yesmaximal, complemented
10M16×Dic103C211yesmaximal, characteristic, complemented
11#469×C103C211yesmaximal, characteristic
12C2×Dic412C2211yescharacteristic
13C2×#13110093C2212yes—
14C2×#13110089C2211yescharacteristic
15#15693014—22no—
16#15693012C2212yes—
17#15693008C2212yes—
18#15693002—22no—
19#15693000C2212yes—
20#15692986C2212yes—
21D4×Dic103—22no—
22D4×Dic103C2212yes—
23#15692977—22no—
24C2×C4×Dic103C2211yescharacteristic
25#15692954C2212yes—
26#15692953C2211yescharacteristic
27#15692946C2212yes—
28#15692944C2212yes—
29#15692942C2212yes—
30#15692931C2211yescharacteristic
31#15692931C2211yescharacteristic
32C8×Dic103C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×D8×C103C2211yescharacteristic
35C2×M16×C103C2211yescharacteristic
36#121×C103C2212yes—
37#106×C103C2211yescharacteristic
38#102×C103C2212yes—
39C2×Dic206C2312yes—
40C22×Dic103—22no—
41C22×Dic103D412yes—
42Dic412—22no—
43#13110093—24no—
44#13110089—22no—
45C2×C103⋊C8C2311yescharacteristic
46C2×C103⋊C8C2311yescharacteristic
47C4⋊Dic103—22no—
48C4⋊Dic103C2312yes—
49Dic103⋊C4—22no—
50Dic103⋊C4—22no—
51Dic103⋊C4—22no—
52C22⋊Dic103—22no—
53C22⋊Dic103—22no—
54C22⋊Dic103—22no—
55C22⋊Dic103—22no—
56C4×Dic103—22no—
57C4×Dic103D412yes—
58C4×Dic103C2311yescharacteristic
59C4×Dic103C2311yescharacteristic
60C2×D4×C103—22no—
61C2×D4×C103C2312yes—
62C22×C4×C103C2311yescharacteristic
63D8×C103—22no—
64M16×C103—22no—
65C2×C8×C103C2311yescharacteristic
66C2×C8×C103C2311yescharacteristic
67C4⋊C4×C103C2312yes—
68C22⋊C4×C103—22no—
69C23×C103—22no—
70C23×C103C2×D411yescharacteristic
71D4×C103—22no—
72D4×C103—22no—
73D4×C103—44no—
74C2×C4×C103—21no—
75C2×C4×C103—21no—
76C2×C4×C103—22no—
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2411yescharacteristic
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103—42no—
82C2×Dic103—44no—
83C2×Dic103C2×D412yes—
84C2×Dic103C2×D412yes—
85Dic206—22no—
86Dic206—22no—
87C8×C103—21no—
88C8×C103#4112yes—
89C103⋊C8—21no—
90C103⋊C8#4112yes—
91C22×C103—21no—
92C22×C103—22no—
93C22×C103—42no—
94C22×C103—42no—
95C22×C103—42no—
96C22×C103C22×D411yescharacteristic
97C4×C103—21no—
98C4×C103—42no—
99C4×C103C2×#4111yescharacteristic
100C4×C103C2×#4111yescharacteristic
101Dic103—22no—
102Dic103—22no—
103Dic103—42no—
104Dic103—42no—
105C2×C103—41no—
106C2×C103—82no—
107C2×C103#53211yescharacteristic
108C2×C103#57512yes—
109#3183—1031nomaximal, Sylow
110C103#318311yescharacteristic, complemented, Sylow
111#529—1032no—
112#499—1031no—
113#495—1031no—
114#488—1032no—
115#470—1031no—
116#469D10311yescharacteristic
117#468—1032no—
118#442—1031no—
119#441—1031no—
120#440—1032no—
121C4×M16—1031no—
122C2×Q16—1031no—
123C2×SD16—1032no—
124C2×D8C2×D10311yescharacteristic
125C2×M16—1031no—
126C2×M16C2×D10311yescharacteristic
127#126—2062no—
128#125—1032no—
129#124—1032no—
130#123—2062no—
131C22⋊Q8—1032no—
132#121C2×D10312yes—
133C4×Q8—1032no—
134C4×D4—1032no—
135C4×D4—2062no—
136#117—2062no—
137C2×C42—1031no—
138#107—1032no—
139#106—1031no—
140#106C2×D10311yescharacteristic
141#103—1032no—
142#103—1032no—
143#102—1032no—
144#102C2×D10312yes—
145#97—1031no—
146#97—1031no—
147C4×C8—1031no—
148C4×C8—1031no—
149C2×Q8—1032no—
150C2×D4—22no—
151C2×D4C22×D10312yes—
152C22×C4—1032no—
153C22×C4—2062no—
154C22×C4C22×D10311yescharacteristic
155Q16—2062no—
156SD16—2064no—
157D8—22no—
158M16—22no—
159M16—2062no—
160C2×C8—1031no—
161C2×C8—1031no—
162C2×C8C22×D10311yescharacteristic
163C2×C8C22×D10311yescharacteristic
164C4⋊C4—1032no—
165C4⋊C4—2062no—
166C4⋊C4—2062no—
167C4⋊C4—2062no—
168C4⋊C4—2062no—
169C4⋊C4C22×D10312yes—
170C22⋊C4—22no—
171C22⋊C4—2062no—
172C22⋊C4—2062no—
173C22⋊C4—2062no—
174C22⋊C4—2062no—
175C42—1032no—
176C42—1031no—
177C42—1031no—
178C42—2062no—
179C23—22no—
180C23D4×D10311yescharacteristic
181Q8—2062no—
182Q8—2062no—
183D4—22no—
184D4—22no—
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—1032no—
190C2×C4—1032no—
191C2×C4—4124no—
192C2×C4—4122no—
193C2×C4—2062no—
194C2×C4—2062no—
195C2×C4D4×D10311yescharacteristic
196C2×C4C23×D10311yescharacteristic
197C8—21no—
198C8—1032no—
199C8—2061no—
200C8#1311010412yes—
201C22—22no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C2×D4×D10311yescharacteristic
207C4—21no—
208C4—42no—
209C4—4122no—
210C4—4122no—
211C4—2062no—
212C4—2062no—
213C4#41×D10311yescharacteristic
214C4C2×#1311010411yescharacteristic
215C2—41no—
216C2—82no—
217C2#2026833611yescharacteristic
218C2#2026858712yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#469×C103C2
socleC22×C103C22×D4
hypercenter#469D103
hypocenterC103#3183
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20268322C2semidirect
2. #20268191C2semidirect
3. #20268174C2semidirect
4. #20268144C2semidirect
5. #20268049C2semidirect
6. #20268035C2semidirect
7. #20267903C2semidirect
8. #20267897C2semidirect
9. #20267888C2semidirect
10. M16×Dic103C2semidirect
110. C103#3183semidirect

Maximal subgroups

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

subgroupindex
#202683222
#202681912
#202681742
#202681442
#202680492
#202680352
#202679032
#202678972
#202678882
M16×Dic1032
#469×C1032
#3183103