Finite Group Databasebeta

← #27207793

Subgroups — #27207793

Order 13184.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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#20268514C211yesmaximal, characteristic, complemented
2#20268148C212yesmaximal, complemented
3#20268143C211yesmaximal, characteristic, complemented
4#20268095C212yesmaximal, complemented
5#20268078C211yesmaximal, characteristic, complemented
6#20268006C212yesmaximal
7#20267996C211yesmaximal, characteristic, complemented
8Q8×C103⋊C8C211yesmaximal, characteristic, complemented
9C4×#13110093C212yesmaximal, complemented
10C4×#13110090C211yesmaximal, characteristic
11#554×C103C211yesmaximal, characteristic, complemented
12C2×#13110093C2212yes—
13C2×#13110090C2211yescharacteristic
14#15693021C2211yescharacteristic
15#15693016—22no—
16#15693009C2212yes—
17#15692997—21no—
18C4×Dic206C2212yes—
19C4×D412C2211yescharacteristic
20#15692979—21no—
21#15692954C2211yescharacteristic
22#15692952C2212yes—
23C4⋊(C103⋊C8)C2211yescharacteristic
24C4⋊(C103⋊C8)C2212yes—
25#15692944C2212yes—
26#15692944C2212yes—
27#15692944C2212yes—
28#15692942C2211yescharacteristic
29#15692941C2212yes—
30#15692941C2211yescharacteristic
31C4×C103⋊C8C2211yescharacteristic
32C4×C103⋊C8C2212yes—
33C4⋊Q8×C103C2211yescharacteristic
34#125×C103C2212yes—
35C22⋊Q8×C103—21no—
36C22⋊Q8×C103—22no—
37C4×Q8×C103C2211yescharacteristic
38C4×D4×C103C2211yescharacteristic
39C4×D4×C103C2212yes—
40C2×C4⋊C4×C103—21no—
41C2×Dic206C2312yes—
42C2×D412C2311yescharacteristic
43C2×C4×D103—21no—
44#13110093—24no—
45#13110090—22no—
46C2×C103⋊C8C2311yescharacteristic
47C2×C103⋊C8C2312yes—
48C2×C103⋊C8C2311yescharacteristic
49C4⋊Dic103—21no—
50C4⋊Dic103—21no—
51C4⋊Dic103C2311yescharacteristic
52Dic103⋊C4—22no—
53(C2×D103)⋊C4—22no—
54(C2×D103)⋊C4—21no—
55(C2×D103)⋊C4—22no—
56C4×Dic103—22no—
57C2×Q8×C103—21no—
58C2×Q8×C103D411yescharacteristic
59C2×D4×C103C2311yescharacteristic
60C22×C4×C103—21no—
61C22×C4×C103—22no—
62C4⋊C4×C103—22no—
63C4⋊C4×C103—21no—
64C4⋊C4×C103—22no—
65C4⋊C4×C103D411yescharacteristic
66C4⋊C4×C103D412yes—
67C4⋊C4×C103C2311yescharacteristic
68C4⋊C4×C103C2312yes—
69C22⋊C4×C103—21no—
70C22⋊C4×C103—22no—
71C42×C103C2312yes—
72C42×C103C2311yescharacteristic
73C23×C103—21no—
74C22×D103—21no—
75Q8×C103—22no—
76Q8×C103—81no—
77D4×C103—21no—
78D4×C103#4112yes—
79C2×C4×C103—21no—
80C2×C4×C103—22no—
81C2×C4×C103—42no—
82C2×C4×C103—82no—
83C2×C4×C103C2×D412yes—
84C2×C4×C103C2×D411yescharacteristic
85C2×C4×C103C2×D412yes—
86C2×C4×C103C2×D411yescharacteristic
87C2×C4×C103C2411yescharacteristic
88C2×Dic103—21no—
89C2×Dic103—22no—
90D412—21no—
91D412—21no—
92C4×D103—42no—
93Dic206—22no—
94Dic206—22no—
95C103⋊C8—21no—
96C103⋊C8—22no—
97C103⋊C8—21no—
98C22×C103—22no—
99C22×C103—41no—
100C22×C103—41no—
101C22×C103C22×D411yescharacteristic
102C2×D103—41no—
103C2×D103—41no—
104C2×D103—41no—
105C4×C103—22no—
106C4×C103—22no—
107C4×C103—21no—
108C4×C103—41no—
109C4×C103—42no—
110C4×C103#13512yes—
111C4×C103C2×#4111yescharacteristic
112C4×C1032−1+411yescharacteristic
113Dic103—42no—
114Dic103—41no—
115C2×C103—42no—
116C2×C103#54811yescharacteristic
117C2×C103C2×#13511yescharacteristic
118C2×C103#57711yescharacteristic
119D103—81no—
120#3360—1031nomaximal, Sylow
121C103#336011yescharacteristic, complemented, Sylow
122#556—1031no—
123#554D10311yescharacteristic, complemented
124#488—1032no—
125#487—1031no—
126#479—1032no—
127#476—1031no—
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#125C2×D10312yes—
139#124—1032no—
140C22⋊Q8—21no—
141C22⋊Q8—22no—
142C22⋊Q8—2061no—
143C4×Q8—1032no—
144C4×Q8C2×D10311yescharacteristic
145C4×D4—1031no—
146C4×D4C2×D10311yescharacteristic
147C4×D4C2×D10312yes—
148#117—2061no—
149C2×C4⋊C4—21no—
150#107—1031no—
151#106—1032no—
152C4⋊C8—1031no—
153C4⋊C8—1032no—
154#103—1032no—
155#103—1032no—
156#103—1032no—
157#102—1031no—
158#102—1031no—
159#102—1032no—
160C4×C8—1031no—
161C4×C8—1032no—
162C2×Q8—21no—
163C2×Q8—1032no—
164C2×Q8C22⋊D10311yescharacteristic
165C2×D4—1031no—
166C2×D4C22×D10311yescharacteristic
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—2061no—
170SD16—2064no—
171D8—2062no—
172C2×C8—1031no—
173C2×C8—1032no—
174C2×C8—1031no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—1031no—
179C4⋊C4—2062no—
180C4⋊C4—2061no—
181C4⋊C4—2061no—
182C4⋊C4C22⋊D10311yescharacteristic
183C4⋊C4C22⋊D10312yes—
184C4⋊C4C22×D10312yes—
185C4⋊C4C22×D10311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—22no—
188C22⋊C4—2062no—
189C22⋊C4—2061no—
190C22⋊C4—2062no—
191C42—2062no—
192C42C22×D10311yescharacteristic
193C42C22×D10312yes—
194C23—21no—
195C23—2061no—
196Q8—22no—
197Q8—81no—
198Q8—2062no—
199Q8—2062no—
200D4—21no—
201D4—2061no—
202D4—2061no—
203D4#1311010612yes—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4—4122no—
209C2×C4—2061no—
210C2×C4—2062no—
211C2×C4C2×C22⋊D10312yes—
212C2×C4C2×C22⋊D10312yes—
213C2×C4C2×C22⋊D10311yescharacteristic
214C2×C4C2×C22⋊D10311yescharacteristic
215C2×C4C23×D10311yescharacteristic
216C8—2061no—
217C8—2062no—
218C8—2061no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—4121no—
223C22—4121no—
224C22—4121no—
225C22C22×C22⋊D10311yescharacteristic
226C4—22no—
227C4—22no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—4121no—
232C4—4122no—
233C4#1569304112yes—
234C4C2×#1311010611yescharacteristic
235C4#1569306911yescharacteristic
236C2—42no—
237C2—8241no—
238C2#2026845211yescharacteristic
239C2C2×#1569304111yescharacteristic
240C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#554×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110090C22
hypercenter#554D103
hypocenterC103#3360
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #20268514C2semidirect
2. #20268148C2semidirect
3. #20268143C2semidirect
4. #20268095C2semidirect
5. #20268078C2semidirect
7. #20267996C2semidirect
8. Q8×C103⋊C8C2semidirect
9. C4×#13110093C2semidirect
11. #554×C103C2semidirect
121. C103#3360semidirect
123. #554D103semidirect

Maximal subgroups

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

subgroupindex
#202685142
#202681482
#202681432
#202680952
#202680782
#202680062
#202679962
Q8×C103⋊C82
C4×#131100932
C4×#131100902
#554×C1032
#3360103