Finite Group Databasebeta

← #27198307

Subgroups — #27198307

Order 13184.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#15693000C211yesmaximal, characteristic
2#20267695C212yesmaximal, complemented
3#20267686C212yesmaximal, complemented
4#20267685C212yesmaximal
5#20267679C212yesmaximal
6#20267674C212yesmaximal, complemented
7#20267672C212yesmaximal, complemented
8#20267654C211yesmaximal, characteristic
9#380×C103C211yesmaximal, characteristic
10C22×Dic206C2211yescharacteristic
11#15693000C418yescomplemented
12C2×C4⋊Dic103C2211yescharacteristic
13C2×Dic103⋊C4C2212yes—
14C2×Dic103⋊C4C2212yes—
15C2×Dic103⋊C4C2212yes—
16C2×C22⋊Dic103C2212yes—
17C2×C22⋊Dic103C2212yes—
18C2×C4×Dic103C2212yes—
19C2×C4×Dic103C2212yes—
20C103⋊#95C2211yescharacteristic
21C103⋊#95C2212yes—
22C103⋊#95C2211yescharacteristic
23C103⋊#95C2212yes—
24C103⋊#95C2212yes—
25C103⋊#95C2212yes—
26C103⋊#95C2212yes—
27C23×C4×C103C2211yescharacteristic
28C2×C4⋊C4×C103C2212yes—
29C2×C22⋊C4×C103C2211yescharacteristic
30C2×C22⋊C4×C103C2211yescharacteristic
31#95×C103C2212yes—
32C2×Dic206—42no—
33C2×Dic206C2×C414yes—
34C22×Dic103C2312yes—
35C22×Dic103C2312yes—
36C22×Dic103C2312yes—
37C22×Dic103C2312yes—
38C4⋊Dic103C2×C414yes—
39Dic103⋊C4—42no—
40Dic103⋊C4—42no—
41Dic103⋊C4C2×C418yes—
42C22⋊Dic103—42no—
43C22⋊Dic103C2×C418yes—
44C4×Dic103—42no—
45C4×Dic103—42no—
46C24×C103C2311yescharacteristic
47C22×C4×C103—42no—
48C22×C4×C103C2×C414yes—
49C22×C4×C103C2312yes—
50C22×C4×C103C2312yes—
51C22×C4×C103C2311yescharacteristic
52C22×C4×C103C2311yescharacteristic
53C4⋊C4×C103—42no—
54C22⋊C4×C103—41no—
55C22⋊C4×C103—41no—
56C23×C103—21no—
57C23×C103—22no—
58C23×C103—22no—
59C23×C103—21no—
60C23×C103C22×C412yes—
61C23×C103C2411yescharacteristic
62C2×C4×C103—22no—
63C2×C4×C103—22no—
64C2×C4×C103—22no—
65C2×C4×C103—22no—
66C2×C4×C103—22no—
67C2×C4×C103—22no—
68C2×C4×C103—22no—
69C2×C4×C103—22no—
70C2×C4×C103—44no—
71C2×C4×C103C22×C412yes—
72C2×C4×C103C22×C412yes—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103—22no—
78C2×Dic103—22no—
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103—22no—
82C2×Dic103—22no—
83C2×Dic103C22×C414yes—
84C2×Dic103C22×C414yes—
85Dic206—44no—
86C22×C103—22no—
87C22×C103—22no—
88C22×C103—22no—
89C22×C103—42no—
90C22×C103—42no—
91C22×C103C23×C411yescharacteristic
92C22×C103H(5,𝔽2)12yes—
93C22×C103H(5,𝔽2)11yescharacteristic
94C22×C1032−1+412yes—
95C22×C1032−1+411yescharacteristic
96C4×C103—22no—
97C4×C103—22no—
98C4×C103—42no—
99C4×C103—42no—
100Dic103—24no—
101Dic103—24no—
102Dic103—42no—
103Dic103—42no—
104C2×C103—42no—
105C2×C103#51811yescharacteristic
106C2×C103#51911yescharacteristic
107C2×C103#52011yescharacteristic
108C2×C103#56212yes—
109C2×C103#56312yes—
110#2378—1031nomaximal, Sylow
111C103#237811yescharacteristic, complemented, Sylow
112C2×C22⋊Q8—1031no—
113#391—1032no—
114#389—1032no—
115#388—1032no—
116#388—1032no—
117#387—1032no—
118#387—1032no—
119#381—1031no—
120#380D10311yescharacteristic
121C22×Q8—1031no—
122C23×C4C2×D10311yescharacteristic
123C22⋊Q8—1038no—
124C2×C4⋊C4—1031no—
125C2×C4⋊C4—1032no—
126C2×C4⋊C4—1032no—
127C2×C4⋊C4—1032no—
128C2×C4⋊C4C2×D10312yes—
129C2×C22⋊C4—1032no—
130C2×C22⋊C4—1032no—
131C2×C22⋊C4C2×D10311yescharacteristic
132C2×C22⋊C4C2×D10311yescharacteristic
133C2×C42—1032no—
134C2×C42—1032no—
135#95—1031no—
136#95—1032no—
137#95—1031no—
138#95—1032no—
139#95—1032no—
140#95—1032no—
141#95—1032no—
142#95C2×D10312yes—
143C24C22×D10311yescharacteristic
144C2×Q8—1034no—
145C2×Q8—4122no—
146C22×C4—42no—
147C22×C4—1032no—
148C22×C4—1032no—
149C22×C4—1032no—
150C22×C4—1032no—
151C22×C4C4×D10314yes—
152C22×C4C22×D10312yes—
153C22×C4C22×D10312yes—
154C22×C4C22×D10311yescharacteristic
155C22×C4C22×D10311yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—1038no—
158C4⋊C4—1034no—
159C4⋊C4—4122no—
160C4⋊C4—4122no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—1038no—
164C22⋊C4—4122no—
165C42—4122no—
166C42—4122no—
167C23—21no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23C2×C4×D10312yes—
172C23C23×D10311yescharacteristic
173Q8—4124no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—1034no—
184C2×C4—1034no—
185C2×C4—2062no—
186C2×C4—2062no—
187C2×C4—2062no—
188C2×C4—2062no—
189C2×C4—2062no—
190C2×C4—2062no—
191C2×C4—2062no—
192C2×C4—2062no—
193C2×C4—2062no—
194C2×C4—2062no—
195C2×C4C2×C4×D10312yes—
196C2×C4C2×C4×D10312yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D10311yescharacteristic
203C22#1569306612yes—
204C22#1569306611yescharacteristic
205C22#1569306812yes—
206C22#1569306911yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—4122no—
212C4—4122no—
213C4—2064no—
214C4—2064no—
215C2—42no—
216C2#2026826411yescharacteristic
217C2#2026826811yescharacteristic
218C2#2026827211yescharacteristic
219C2#2026853612yes—
220C2#2026854212yes—
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#380×C103C2
socle, cosocleC23×C103C24
prime radicalC24×C103C23
hypercenter#380D103
hypocenterC103#2378
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #20267695C2semidirect
3. #20267686C2semidirect
6. #20267674C2semidirect
7. #20267672C2semidirect
11. #15693000C4semidirect
111. C103#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#156930002
#202676952
#202676862
#202676852
#202676792
#202676742
#202676722
#202676542
#380×C1032
#2378103