Finite Group Databasebeta

← #27207792

Subgroups — #27207792

Order 13184.

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

normal subgroups only

This group has 350 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#20268511C211yesmaximal, characteristic, complemented
2#20268502C211yesmaximal, characteristic, complemented
3#20268144C212yesmaximal, complemented
4#20268143C211yesmaximal, characteristic, complemented
5#20268101C212yesmaximal, complemented
6#20268005C212yesmaximal
7#20267997C211yesmaximal, characteristic, complemented
8#20267915C211yesmaximal, characteristic, complemented
9#20267878C212yesmaximal, complemented
10C4×#13110090C211yesmaximal, characteristic
11#476×C103C211yesmaximal, characteristic, complemented
12C2×#13110094C2212yes—
13C2×#13110090C2211yescharacteristic
14#15693021C2211yescharacteristic
15#15693014—22no—
16#15693012C2212yes—
17#15693008C2212yes—
18#15693001—21no—
19#15693000—21no—
20#15692997—22no—
21C4×Dic206C2211yescharacteristic
22#15692986C2212yes—
23C4×D412C2211yescharacteristic
24#15692983C2212yes—
25#15692980—21no—
26C4⋊C4×D103—21no—
27#15692954C2211yescharacteristic
28Dic103⋊C8C2212yes—
29#15692946C2212yes—
30#15692944C2212yes—
31#15692944C2212yes—
32#15692942C2211yescharacteristic
33#15692941C2211yescharacteristic
34C4×C103⋊C8C2211yescharacteristic
35C8×Dic103C2212yes—
36C4⋊Q8×C103C2211yescharacteristic
37C4×D4×C103C2211yescharacteristic
38#106×C103C2212yes—
39C4⋊C8×C103C2211yescharacteristic
40#102×C103C2212yes—
41C2×Dic206D411yescharacteristic
42C2×Dic206C2312yes—
43C2×D412C2311yescharacteristic
44C2×C4×D103—21no—
45C2×C4×D103—22no—
46#13110094—24no—
47#13110090—22no—
48C2×C103⋊C8C2311yescharacteristic
49C2×C103⋊C8C2311yescharacteristic
50C4⋊Dic103—21no—
51C4⋊Dic103—21no—
52C4⋊Dic103—22no—
53C4⋊Dic103D411yescharacteristic
54C4⋊Dic103C2311yescharacteristic
55Dic103⋊C4—22no—
56Dic103⋊C4—22no—
57Dic103⋊C4D412yes—
58C22⋊Dic103—22no—
59C22⋊Dic103—22no—
60(C2×D103)⋊C4—21no—
61(C2×D103)⋊C4—22no—
62C4×Dic103—22no—
63C4×Dic103C2312yes—
64C2×Q8×C103—21no—
65C2×D4×C103C2311yescharacteristic
66C22×C4×C103—21no—
67C2×C8×C103C2312yes—
68C4⋊C4×C103—21no—
69C4⋊C4×C103C2312yes—
70C4⋊C4×C103C2311yescharacteristic
71C22⋊C4×C103—21no—
72C42×C103C2311yescharacteristic
73C23×C103—21no—
74C22×D103—21no—
75Q8×C103—81no—
76D4×C103—21no—
77D4×C103—21no—
78C2×C4×C103—21no—
79C2×C4×C103—22no—
80C2×C4×C103—42no—
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103C2411yescharacteristic
84C2×Dic103—22no—
85C2×Dic103—21no—
86C2×Dic103C2×D412yes—
87C2×Dic103C2×D412yes—
88D412—21no—
89D412#4112yes—
90C4×D103—42no—
91C4×D103—82no—
92Dic206—22no—
93Dic206—22no—
94Dic206—22no—
95C8×C103—22no—
96C103⋊C8—21no—
97C103⋊C8—21no—
98C22×C103—41no—
99C22×C103—41no—
100C22×C103—41no—
101C22×C103C22×D411yescharacteristic
102C2×D103—22no—
103C2×D103—41no—
104C2×D103—41no—
105C4×C103—21no—
106C4×C103—41no—
107C4×C103—42no—
108C4×C103#13512yes—
109C4×C103C2×#4111yescharacteristic
110C4×C1032−1+411yescharacteristic
111Dic103—22no—
112Dic103—22no—
113Dic103—42no—
114Dic103—41no—
115C2×C103—81no—
116C2×C103#54811yescharacteristic
117C2×C103C2×#13511yescharacteristic
118C2×C103#57711yescharacteristic
119D103—42no—
120#3360—1031nomaximal, Sylow
121C103#336011yescharacteristic, complemented, Sylow
122#556—1031no—
123#554—1031no—
124#488—1032no—
125#487—1031no—
126#479—1032no—
127#476D10311yescharacteristic, complemented
128#463—1032no—
129#461—1031no—
130C8×Q8—1031no—
131C4×SD16—1032no—
132C4×D8—1031no—
133C2×SD16—1032no—
134C2×D8—1031no—
135C4⋊Q8—1031no—
136C4⋊Q8C2×D10311yescharacteristic
137#126—2062no—
138#125—1032no—
139#124—1032no—
140C22⋊Q8—2061no—
141C22⋊Q8—2062no—
142C22⋊Q8—2061no—
143C4×Q8—1031no—
144C4×Q8—1032no—
145C4×D4—1032no—
146C4×D4—1031no—
147C4×D4C2×D10311yescharacteristic
148#117—2061no—
149C2×C4⋊C4—2061no—
150#107—1031no—
151#106C2×D10312yes—
152C4⋊C8—1032no—
153C4⋊C8C2×D10311yescharacteristic
154#103—1032no—
155#103—1032no—
156#103—1032no—
157#102—1031no—
158#102—1031no—
159#102C2×D10312yes—
160C4×C8—1032no—
161C4×C8—1031no—
162C2×Q8—21no—
163C2×Q8—1031no—
164C2×Q8—1032no—
165C2×D4—1031no—
166C2×D4C22×D10311yescharacteristic
167C22×C4—21no—
168C22×C4—2062no—
169C22×C4—2061no—
170SD16—2064no—
171D8—2062no—
172C2×C8—1031no—
173C2×C8—1031no—
174C2×C8C22×D10312yes—
175C4⋊C4—21no—
176C4⋊C4—1032no—
177C4⋊C4—1031no—
178C4⋊C4—1031no—
179C4⋊C4—2062no—
180C4⋊C4—2062no—
181C4⋊C4—2062no—
182C4⋊C4—2061no—
183C4⋊C4—2061no—
184C4⋊C4C22×D10311yescharacteristic
185C4⋊C4C22×D10312yes—
186C22⋊C4—21no—
187C22⋊C4—2062no—
188C22⋊C4—2062no—
189C22⋊C4—2062no—
190C22⋊C4—2061no—
191C42—1032no—
192C42—2062no—
193C42C22×D10311yescharacteristic
194C23—21no—
195C23—2061no—
196Q8—81no—
197Q8—2062no—
198Q8—2062no—
199Q8—2062no—
200D4—21no—
201D4—21no—
202D4—1032no—
203D4—2061no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—8242no—
208C2×C4—1032no—
209C2×C4—1032no—
210C2×C4—4122no—
211C2×C4—2062no—
212C2×C4—2061no—
213C2×C4D4×D10311yescharacteristic
214C2×C4D4×D10311yescharacteristic
215C2×C4C23×D10311yescharacteristic
216C8—22no—
217C8—2061no—
218C8—2061no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—4121no—
223C22—4121no—
224C22—2062no—
225C22C2×D4×D10311yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—4121no—
230C4—4122no—
231C4—2062no—
232C4—2062no—
233C4#1569304212yes—
234C4#41×D10311yescharacteristic
235C4#1569306911yescharacteristic
236C2—81no—
237C2—4122no—
238C2#2026845111yescharacteristic
239C2C2×#1569304211yescharacteristic
240C2#2026860111yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#476×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110090C22
hypercenter#476D103
hypocenterC103#3360
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #20268511C2semidirect
2. #20268502C2semidirect
3. #20268144C2semidirect
4. #20268143C2semidirect
5. #20268101C2semidirect
7. #20267997C2semidirect
8. #20267915C2semidirect
9. #20267878C2semidirect
11. #476×C103C2semidirect
121. C103#3360semidirect
127. #476D103semidirect

Maximal subgroups

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

subgroupindex
#202685112
#202685022
#202681442
#202681432
#202681012
#202680052
#202679972
#202679152
#202678782
C4×#131100902
#476×C1032
#3360103