Finite Group Databasebeta

← #27206610

Subgroups — #27206610

Order 13184.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#20268414C212yesmaximal, complemented
2#20268080C212yesmaximal, complemented
3#20268074C212yesmaximal, complemented
4#20268044C211yesmaximal, characteristic
5#20268022C212yesmaximal, complemented
6#20268015C212yesmaximal, complemented
7#20268009C212yesmaximal, complemented
8#20267819C211yesmaximal, characteristic, complemented
9#470×C103C211yesmaximal, characteristic, complemented
10C2×#13110092C2212yes—
11C2×D824C2211yescharacteristic
12C22×C103⋊C8C2211yescharacteristic
13#15693020C2212yes—
14#15693016—22no—
15#15693010C2212yes—
16#15693007—22no—
17#15693003—22no—
18#15693001—22no—
19#15692995C2212yes—
20Q8×Dic103C2212yes—
21#15692983C2212yes—
22#15692980C2211yescharacteristic
23#15692953C2211yescharacteristic
24#15692952C2212yes—
25Dic103⋊C8C2212yes—
26Dic103⋊C8C2212yes—
27#15692945C2212yes—
28#15692943C2212yes—
29#15692941C2212yes—
30C2×Q16×C103C2211yescharacteristic
31C2×M16×C103C2211yescharacteristic
32C22⋊Q8×C103C2212yes—
33#106×C103C2211yescharacteristic
34#103×C103C2212yes—
35C2×Dic206—22no—
36C2×D412C2312yes—
37C2×C22⋊D103—22no—
38C2×C4×D103—22no—
39#13110092—42no—
40D824—41no—
41C2×C103⋊C8—41no—
42C2×C103⋊C8C2312yes—
43C4⋊Dic103—22no—
44C4⋊Dic103D412yes—
45C4⋊Dic103C2312yes—
46Dic103⋊C4—22no—
47C22⋊Dic103D411yescharacteristic
48C22⋊Dic103D411yescharacteristic
49(C2×D103)⋊C4—22no—
50(C2×D103)⋊C4—22no—
51(C2×D103)⋊C4—22no—
52(C2×D103)⋊C4—22no—
53C4×Dic103—22no—
54C4×Dic103C2312yes—
55C2×Q8×C103C2312yes—
56C22×C4×C103C2311yescharacteristic
57Q16×C103—41no—
58M16×C103—41no—
59C2×C8×C103C2311yescharacteristic
60C2×C8×C103C2311yescharacteristic
61C4⋊C4×C103—22no—
62C4⋊C4×C103C2312yes—
63C22⋊C4×C103—22no—
64C23×C103C2×D411yescharacteristic
65C22×D103—22no—
66Q8×C103—22no—
67Q8×C103—22no—
68C2×C4×C103—21no—
69C2×C4×C103—21no—
70C2×C4×C103—22no—
71C2×C4×C103—22no—
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2411yescharacteristic
74C22⋊D103—82no—
75C2×Dic103—22no—
76C2×Dic103C2×D412yes—
77C2×Dic103C2×D412yes—
78D412—22no—
79D412—22no—
80C4×D103—82no—
81Dic206—82no—
82C8×C103—21no—
83C8×C103—21no—
84C103⋊C8—22no—
85C22×C103—21no—
86C22×C103—22no—
87C22×C103C22×D411yescharacteristic
88C2×D103—42no—
89C2×D103—42no—
90C2×D103—42no—
91C4×C103—21no—
92C4×C103—42no—
93C4×C103—42no—
94C4×C103H(5,𝔽2)11yescharacteristic
95C4×C1032−1+411yescharacteristic
96Dic103—22no—
97Dic103—22no—
98Dic103—42no—
99C2×C103—41no—
100C2×C103#53711yescharacteristic
101C2×C103#57712yes—
102D103—82no—
103#3263—1031nomaximal, Sylow
104C103#326311yescharacteristic, complemented, Sylow
105#542—1032no—
106#476—1032no—
107#475—1032no—
108#470D10311yescharacteristic, complemented
109#469—1031no—
110#465—1032no—
111#464—1032no—
112#463—1032no—
113#424—1031no—
114C2×Q16C2×D10311yescharacteristic
115C2×SD16—1032no—
116C2×D8—1031no—
117C2×M16C2×D10311yescharacteristic
118C22×C8—1031no—
119C4⋊Q8—1032no—
120#126—2062no—
121#124—1032no—
122#124—2062no—
123#123—2062no—
124C22⋊Q8—2062no—
125C22⋊Q8C2×D10312yes—
126#121—1032no—
127C4×Q8—1032no—
128C4×D4—1032no—
129#117—1031no—
130#106—1031no—
131#106—1032no—
132#106C2×D10311yescharacteristic
133C4⋊C8—1032no—
134C4⋊C8—1032no—
135#103—1032no—
136#103C2×D10312yes—
137#102—1032no—
138#102—1032no—
139C2×Q8—2062no—
140C2×Q8C22×D10312yes—
141C2×D4—1032no—
142C2×D4—2062no—
143C22×C4—2062no—
144C22×C4C22×D10311yescharacteristic
145Q16—41no—
146SD16—4122no—
147D8—4121no—
148M16—41no—
149C2×C8—1032no—
150C2×C8—4121no—
151C2×C8C22×D10311yescharacteristic
152C2×C8C22×D10311yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—1032no—
155C4⋊C4—1032no—
156C4⋊C4—2062no—
157C4⋊C4—2062no—
158C4⋊C4C22×D10312yes—
159C22⋊C4—22no—
160C22⋊C4—1031no—
161C22⋊C4—1031no—
162C22⋊C4—2062no—
163C22⋊C4—2062no—
164C22⋊C4—2062no—
165C22⋊C4—2062no—
166C42—1032no—
167C42—2062no—
168C23—2062no—
169C23D4×D10311yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—8242no—
173D4—8242no—
174D4—2062no—
175D4—2062no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—8242no—
181C2×C4—1032no—
182C2×C4—1032no—
183C2×C4—2062no—
184C2×C4D4×D10311yescharacteristic
185C2×C4C23×D10311yescharacteristic
186C8—21no—
187C8—21no—
188C8—2062no—
189C22—22no—
190C22—21no—
191C22—4122no—
192C22—4122no—
193C22—4122no—
194C22C2×D4×D10311yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—4122no—
199C4—2062no—
200C4—2062no—
201C4#1569306611yescharacteristic
202C4#1569306811yescharacteristic
203C2—41no—
204C2—8242no—
205C2#2026836811yescharacteristic
206C2#2026860012yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#470×C103C2
socleC22×C103C22×D4
prime radical#20268044C2
hypercenter#470D103
hypocenterC103#3263
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20268414C2semidirect
2. #20268080C2semidirect
3. #20268074C2semidirect
5. #20268022C2semidirect
6. #20268015C2semidirect
7. #20268009C2semidirect
8. #20267819C2semidirect
9. #470×C103C2semidirect
104. C103#3263semidirect
108. #470D103semidirect

Maximal subgroups

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

subgroupindex
#202684142
#202680802
#202680742
#202680442
#202680222
#202680152
#202680092
#202678192
#470×C1032
#3263103