Finite Group Databasebeta

← #27195589

Subgroups — #27195589

Order 13184.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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×#15692978C211yesmaximal, 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×D103C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15693002—21no—
11#15692997C412yescomplemented
12#15692992C412yescomplemented
13#15692989—21no—
14C4×C22⋊D103—22no—
15#15692980C2211yescharacteristic
16#15692978—22no—
17#15692978—22no—
18C2×Dic103⋊C4—21no—
19C2×(C2×D103)⋊C4—21no—
20C2×C4×Dic103C2211yescharacteristic
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—21no—
32C2×C4×D103—21no—
33C2×C4×D103—21no—
34C2×C4×D103—21no—
35C2×C4×D103C2×C412yes—
36C2×C4×D103D412yes—
37#13110089—21no—
38#13110089—21no—
39C2×C103⋊C8—21no—
40C4⋊Dic103C2×C412yes—
41Dic103⋊C4—24no—
42Dic103⋊C4—22no—
43C22⋊Dic103—21no—
44C22⋊Dic103—22no—
45(C2×D103)⋊C4—24no—
46(C2×D103)⋊C4—22no—
47C4×Dic103—21no—
48C4×Dic103—21no—
49C4×Dic103D412yescomplemented
50#41×C103—21no—
51#41×C103—21no—
52#41×C103—21no—
53#41×C103—21no—
54C2×Q8×C103C2×C411yescharacteristic
55C2×D4×C103—21no—
56C2×D4×C103C2×C411yescharacteristic
57C22×C4×C103—21no—
58C22×C4×C103—21no—
59C22×C4×C103C2311yescharacteristic
60M16×C103—21no—
61M16×C103—21no—
62C2×C8×C103—21no—
63C42×C103—21no—
64C42×C103D412yescomplemented
65C23×C103—21no—
66C23×C103C2×D411yescharacteristic
67C22×D103—21no—
68C22×D103—21no—
69C22×D103—42no—
70C22×D103C22⋊C412yes—
71Q8×C103—21no—
72Q8×C103—21no—
73D4×C103—21no—
74D4×C103—21no—
75D4×C103—41no—
76D4×C103—41no—
77C2×C4×C103—21no—
78C2×C4×C103—22no—
79C2×C4×C103—42no—
80C2×C4×C103—41no—
81C2×C4×C103—41no—
82C2×C4×C103C22×C411yescharacteristic
83C2×C4×C103C2×D411yescharacteristic
84C2×C4×C103C2×D411yescharacteristic
85C2×C4×C103C2×D411yescharacteristic
86C2×C4×C103#4111yescharacteristic
87C2×C4×C103#4111yescharacteristic
88C22⋊D103—44no—
89C2×Dic103—21no—
90C2×Dic103—21no—
91C2×Dic103—22no—
92C2×Dic103—22no—
93C2×Dic103—42no—
94C2×Dic103C22⋊C412yes—
95C4×D103—22no—
96C4×D103—22no—
97C4×D103—22no—
98C4×D103—22no—
99C8×C103—41no—
100C103⋊C8—41no—
101C22×C103—22no—
102C22×C103—41no—
103C22×C103—42no—
104C22×C103C2×C22⋊C411yescharacteristic
105C22×C103#12011yescharacteristic
106C22×C103#12311yescharacteristic
107C2×D103—22no—
108C2×D103—22no—
109C2×D103—22no—
110C2×D103—42no—
111C2×D103—42no—
112C4×C103—42no—
113C4×C103—41no—
114C4×C103C4×D411yescharacteristic
115C4×C103C4×D411yescharacteristic
116C4×C103#12111yescharacteristic
117C4×C103#12111yescharacteristic
118Dic103—22no—
119Dic103—42no—
120Dic103—42no—
121C2×C103—21no—
122C2×C103—21no—
123C2×C103—81no—
124C2×C103#38611yescharacteristic
125C2×C103#42112yes—
126D103—42no—
127#1897—1031nomaximal, Sylow
128C103#189711yescharacteristic, complemented, Sylow
129#525—1031no—
130C2×#117—1031no—
131C2×#104—1031no—
132C2×#104D10311yescharacteristic, complemented
133#407—1031no—
134#339—1031no—
135#339—1031no—
136C2×#41C2×D10311yescharacteristic
137C23×C4—1031no—
138C2×M16—1031no—
139C2×M16C2×D10311yescharacteristic
140#123—2061no—
141C22⋊Q8—1032no—
142#121—1032no—
143#120—2061no—
144C4×D4—2062no—
145#117—1031no—
146#117—2062no—
147#117—2062no—
148C2×C4⋊C4—2061no—
149C2×C22⋊C4—2061no—
150C2×C42—1031no—
151C2×C42C2×D10311yescharacteristic
152#104—22no—
153#104—2062no—
154C22⋊C8—2062no—
155C24—1031no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D10311yescharacteristic
161C2×D4—21no—
162C2×D4—2062no—
163C2×D4C4×D10311yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—1031no—
167C22×C4—1032no—
168C22×C4—1032no—
169C22×C4—2061no—
170C22×C4—2061no—
171C22×C4—2061no—
172C22×C4—2061no—
173C22×C4—2061no—
174C22×C4C22×D10311yescharacteristic
175M16—21no—
176M16—21no—
177M16—2061no—
178M16—2061no—
179C2×C8—21no—
180C2×C8—2061no—
181C4⋊C4—1032no—
182C4⋊C4—2062no—
183C4⋊C4—2064no—
184C22⋊C4—2062no—
185C22⋊C4—2064no—
186C22⋊C4—2062no—
187C22⋊C4—2061no—
188C42—21no—
189C42—1032no—
190C42—2061no—
191C42—2061no—
192C42C22⋊D10312yescomplemented
193C23—21no—
194C23—1032no—
195C23—4122no—
196C23—2061no—
197C23—2061no—
198C23D4×D10311yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—4124no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—1032no—
212C2×C4—4122no—
213C2×C4—2062no—
214C2×C4—2062no—
215C2×C4—2061no—
216C2×C4—2061no—
217C2×C4—2062no—
218C2×C4—2062no—
219C2×C4—2062no—
220C2×C4—2062no—
221C2×C4C2×C4×D10311yescharacteristic
222C2×C4D4×D10311yescharacteristic
223C2×C4D4×D10311yescharacteristic
224C2×C4C2×C22⋊D10311yescharacteristic
225C2×C4#1311010411yescharacteristic
226C2×C4#1311010511yescharacteristic
227C8—41no—
228C8—4121no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—4122no—
233C22—4122no—
234C22—2062no—
235C22—2062no—
236C22—2062no—
237C22C22⋊C4×D10311yescharacteristic
238C22#1569298911yescharacteristic
239C22#1569300311yescharacteristic
240C4—42no—
241C4—41no—
242C4—4122no—
243C4—4122no—
244C4—2062no—
245C4(C22⋊D103)⋊C411yescharacteristic
246C4C4×C22⋊D10311yescharacteristic
247C4#1569299211yescharacteristic
248C4#1569299411yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—4122no—
253C2#2026766711yescharacteristic
254C2#2026780612yes—
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#1897
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×#15692978C2semidirect
3. C2×#15692948C2semidirect
4. #20267754C2semidirect
5. #20267552C2semidirect
6. #20267551C2semidirect
7. C2×#104×C103C2semidirect
11. #15692997C4semidirect
12. #15692992C4semidirect
49. C4×Dic103D4semidirect
64. C42×C103D4semidirect
128. C103#1897semidirect
132. C2×#104D103semidirect
192. C42C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202682982
C2×#156929782
C2×#156929482
#202677542
#202675522
#202675512
C2×#104×C1032
#1897103