Finite Group Databasebeta

← #27195584

Subgroups — #27195584

Order 13184.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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#20268298C211yesmaximal, characteristic
2C2×C42×D103C211yesmaximal, characteristic, complemented
3C2×#15692948C211yesmaximal, characteristic, complemented
4#20267754C211yesmaximal, characteristic, complemented
5#20267552C211yesmaximal, characteristic, complemented
6#20267551C211yesmaximal, characteristic, complemented
7C2×#104×C103C211yesmaximal, characteristic, complemented
8C22×C4×D103—21no—
9C22×C4×D103C2211yescharacteristic
10C2×#13110089C2211yescharacteristic
11#15693002—21no—
12#15692997C412yescomplemented
13#15692992C412yescomplemented
14#15692989—21no—
15C4×C22⋊D103—22no—
16#15692980C2211yescharacteristic
17C2×C4×Dic103—21no—
18C2×C4×Dic103C2211yescharacteristic
19C42×D103—22no—
20C42×D103—22no—
21#15692948—22no—
22(C2×D103)⋊C8—22no—
23C2×#41×C103C2211yescharacteristic
24C2×M16×C103C2211yescharacteristic
25C2×C42×C103C2211yescharacteristic
26#104×C103—22no—
27C23×D103D411yescharacteristic
28C2×C22⋊D103—22no—
29C22×Dic103—21no—
30C22×Dic103D411yescharacteristic
31C2×C4×D103—24no—
32C2×C4×D103—28no—
33C2×C4×D103—21no—
34C2×C4×D103—21no—
35C2×C4×D103—21no—
36C2×C4×D103—21no—
37C2×C4×D103C2×C412yes—
38C2×C4×D103D412yes—
39#13110089—21no—
40#13110089—21no—
41C2×C103⋊C8—21no—
42C4⋊Dic103C2×C412yescomplemented
43Dic103⋊C4—22no—
44C22⋊Dic103—21no—
45C22⋊Dic103—22no—
46(C2×D103)⋊C4—22no—
47C4×Dic103—24no—
48C4×Dic103—21no—
49C4×Dic103—21no—
50C4×Dic103D412yescomplemented
51#41×C103—21no—
52#41×C103—21no—
53#41×C103—21no—
54#41×C103—21no—
55C2×Q8×C103C2×C411yescharacteristic, complemented
56C2×D4×C103—21no—
57C2×D4×C103C2×C411yescharacteristic, complemented
58C22×C4×C103—21no—
59C22×C4×C103—21no—
60C22×C4×C103C2311yescharacteristic
61M16×C103—21no—
62M16×C103—21no—
63C2×C8×C103—21no—
64C42×C103—21no—
65C42×C103D412yescomplemented
66C23×C103—21no—
67C23×C103C2×D411yescharacteristic
68C22×D103—21no—
69C22×D103—21no—
70C22×D103—24no—
71C22×D103C22⋊C412yes—
72Q8×C103—21no—
73Q8×C103—21no—
74D4×C103—21no—
75D4×C103—21no—
76D4×C103—41no—
77D4×C103—41no—
78C2×C4×C103—24no—
79C2×C4×C103—22no—
80C2×C4×C103—21no—
81C2×C4×C103—41no—
82C2×C4×C103—41no—
83C2×C4×C103C22×C411yescharacteristic
84C2×C4×C103C2×D411yescharacteristic
85C2×C4×C103C2×D411yescharacteristic
86C2×C4×C103C2×D411yescharacteristic
87C2×C4×C103#4111yescharacteristic
88C2×C4×C103#4111yescharacteristic
89C22⋊D103—44no—
90C2×Dic103—24no—
91C2×Dic103—21no—
92C2×Dic103—22no—
93C2×Dic103—21no—
94C2×Dic103—22no—
95C2×Dic103C22⋊C412yes—
96C4×D103—216no—
97C4×D103—22no—
98C4×D103—22no—
99C4×D103—22no—
100C4×D103—22no—
101C8×C103—41no—
102C103⋊C8—41no—
103C22×C103—22no—
104C22×C103—41no—
105C22×C103—42no—
106C22×C103C2×C22⋊C411yescharacteristic
107C22×C103#12011yescharacteristic
108C22×C103#12311yescharacteristic
109C2×D103—24no—
110C2×D103—24no—
111C2×D103—22no—
112C2×D103—22no—
113C2×D103#10414yescomplemented
114C4×C103—24no—
115C4×C103—41no—
116C4×C103C4×D411yescharacteristic
117C4×C103C4×D411yescharacteristic
118C4×C103#12111yescharacteristic
119C4×C103#12111yescharacteristic
120Dic103—24no—
121Dic103—22no—
122Dic103—42no—
123C2×C103—21no—
124C2×C103—21no—
125C2×C103—81no—
126C2×C103#38611yescharacteristic
127C2×C103C2×#10412yes—
128D103—24no—
129#1896—1031nomaximal, Sylow
130C103#189611yescharacteristic, complemented, Sylow
131#525—1031no—
132C22×C42—1031no—
133C2×#104—1031no—
134C2×#104D10311yescharacteristic, complemented
135#407—1031no—
136#339—1031no—
137#339—1031no—
138C2×#41C2×D10311yescharacteristic
139C23×C4—1031no—
140C23×C4—2061no—
141C2×M16—1031no—
142C2×M16C2×D10311yescharacteristic
143#123—2061no—
144C22⋊Q8—1032no—
145#121—1032no—
146#120—2061no—
147C4×D4—2062no—
148#117—1031no—
149C2×C42—1031no—
150C2×C42—2062no—
151C2×C42—2061no—
152C2×C42—2062no—
153C2×C42C2×D10311yescharacteristic
154#104—22no—
155#104—2062no—
156C22⋊C8—2062no—
157C24—1031no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8C4×D10311yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—2062no—
165C2×D4C4×D10311yescharacteristic, complemented
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—1031no—
169C22×C4—1032no—
170C22×C4—1032no—
171C22×C4—2064no—
172C22×C4—2068no—
173C22×C4—2061no—
174C22×C4—2061no—
175C22×C4—2061no—
176C22×C4—2061no—
177C22×C4—2061no—
178C22×C4C22×D10311yescharacteristic
179M16—21no—
180M16—21no—
181M16—2061no—
182M16—2061no—
183C2×C8—21no—
184C2×C8—2061no—
185C4⋊C4—1032no—
186C4⋊C4—2062no—
187C22⋊C4—2062no—
188C22⋊C4—2062no—
189C22⋊C4—2061no—
190C42—21no—
191C42—1032no—
192C42—2064no—
193C42—2061no—
194C42—2061no—
195C42C22⋊D10312yescomplemented
196C23—21no—
197C23—1032no—
198C23—2064no—
199C23—2061no—
200C23—2061no—
201C23D4×D10311yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—4124no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1032no—
215C2×C4—20616no—
216C2×C4—2062no—
217C2×C4—2064no—
218C2×C4—2062no—
219C2×C4—2061no—
220C2×C4—2061no—
221C2×C4—2062no—
222C2×C4—2062no—
223C2×C4—2062no—
224C2×C4—2062no—
225C2×C4C2×C4×D10311yescharacteristic
226C2×C4D4×D10311yescharacteristic
227C2×C4D4×D10311yescharacteristic
228C2×C4C2×C22⋊D10311yescharacteristic
229C2×C4#1311010411yescharacteristic
230C2×C4#1311010511yescharacteristic
231C8—41no—
232C8—4121no—
233C22—22no—
234C22—42no—
235C22—41no—
236C22—1034no—
237C22—2064no—
238C22—2064no—
239C22—2062no—
240C22—2062no—
241C22C22⋊C4×D10311yescharacteristic
242C22#1569298911yescharacteristic
243C22#1569300311yescharacteristic
244C4—24no—
245C4—41no—
246C4—4122no—
247C4—2064no—
248C4—2062no—
249C4(C22⋊D103)⋊C411yescharacteristic
250C4C4×C22⋊D10311yescharacteristic
251C4#1569299211yescharacteristic
252C4#1569299411yescharacteristic
253C2—21no—
254C2—21no—
255C2—81no—
256C2—2064no—
257C2#2026766711yescharacteristic
258C2#104×D10312yes—
subgroupG/H
centerC2×C4D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#104×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268298C2
cosocleC22×C4×C103C23
hypercenterC2×#104D103
hypocenterC103#1896
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C42×D103C2semidirect
3. C2×#15692948C2semidirect
4. #20267754C2semidirect
5. #20267552C2semidirect
6. #20267551C2semidirect
7. C2×#104×C103C2semidirect
12. #15692997C4semidirect
13. #15692992C4semidirect
42. C4⋊Dic103C2×C4semidirect
50. C4×Dic103D4semidirect
55. C2×Q8×C103C2×C4semidirect
57. C2×D4×C103C2×C4semidirect
65. C42×C103D4semidirect
113. C2×D103#104semidirect
130. C103#1896semidirect
134. C2×#104D103semidirect
162. C2×Q8C4×D103semidirect
165. C2×D4C4×D103semidirect
195. C42C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202682982
C2×C42×D1032
C2×#156929482
#202677542
#202675522
#202675512
C2×#104×C1032
#1896103