Finite Group Databasebeta

← #27205897

Subgroups — #27205897

Order 13184.

468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692995C211yesmaximal, characteristic
2#20268119C212yesmaximal, complemented
3#20268109C212yesmaximal, complemented
4#20268022C214yesmaximal, complemented
5#20267941C212yesmaximal, complemented
6#20267930C212yesmaximal, complemented
7C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C103C211yesmaximal, characteristic, complemented
9C22×D412C2211yescharacteristic
10C22×C22⋊D103—21no—
11C2×#13110092C2214yescomplemented
12C22×C103⋊C8C2212yescomplemented
13#15692995—21no—
14#15692995—21no—
15#15692995C2212yes—
16#15692995C2212yes—
17C2×C4⋊Dic103C2211yescharacteristic
18C2×(C2×D103)⋊C4—21no—
19#15692952C2214yescomplemented
20#15692945C2214yescomplemented
21#15692941C2214yescomplemented
22C22⋊(C103⋊C8)C2212yes—
23C22⋊(C103⋊C8)C2212yescomplemented
24C22×Q8×C103C2211yescharacteristic, complemented
25C23×C4×C103C2211yescharacteristic
26C22⋊Q8×C103—21no—
27C22⋊Q8×C103—21no—
28C22⋊Q8×C103C2212yes—
29C22⋊Q8×C103C2212yescomplemented
30C2×C4⋊C4×C103—21no—
31C2×C4⋊C4×C103C2211yescharacteristic, complemented
32C2×C22⋊C4×C103—21no—
33C23×D103—21no—
34C2×D412—21no—
35C2×D412—42no—
36C2×D412C2312yes—
37C2×C22⋊D103—22no—
38C2×C22⋊D103—22no—
39C2×C22⋊D103—44no—
40C22×Dic103—21no—
41#13110092—44no—
42C2×C103⋊C8—42no—
43C2×C103⋊C8C2314yes—
44C4⋊Dic103—21no—
45C4⋊Dic103C2312yes—
46(C2×D103)⋊C4—22no—
47(C2×D103)⋊C4—22no—
48C24×C103D411yescharacteristic
49C2×Q8×C103—21no—
50C2×Q8×C103—42no—
51C2×Q8×C103C2312yes—
52C22×C4×C103—21no—
53C22×C4×C103—21no—
54C22×C4×C103—42no—
55C22×C4×C103D411yescharacteristic
56C22×C4×C103D411yescharacteristic
57C22×C4×C103D411yescharacteristic
58C22×C4×C103C2311yescharacteristic
59C22×C4×C103C2311yescharacteristic
60C22×C4×C103C2311yescharacteristic
61C4⋊C4×C103—22no—
62C4⋊C4×C103—22no—
63C4⋊C4×C103—21no—
64C4⋊C4×C103C2312yes—
65C22⋊C4×C103—22no—
66C22⋊C4×C103—22no—
67C23×C103—41no—
68C23×C103—41no—
69C23×C103SD1614yescomplemented
70C23×C103C2×D411yescharacteristic
71C23×C103C2×D411yescharacteristic
72C23×C103C2×D411yescharacteristic
73C22×D103—22no—
74C22×D103—42no—
75C22×D103—42no—
76C22×D103—42no—
77Q8×C103—24no—
78Q8×C103—42no—
79C2×C4×C103—22no—
80C2×C4×C103—22no—
81C2×C4×C103—22no—
82C2×C4×C103—22no—
83C2×C4×C103—22no—
84C2×C4×C103—41no—
85C2×C4×C103—41no—
86C2×C4×C103—41no—
87C2×C4×C103—42no—
88C2×C4×C103—42no—
89C2×C4×C103C2×D411yescharacteristic
90C2×C4×C103C2×D411yescharacteristic
91C2×C4×C103C2×D411yescharacteristic
92C2×C4×C103C2411yescharacteristic
93C22⋊D103—44no—
94C22⋊D103—44no—
95C2×Dic103—22no—
96C2×Dic103—42no—
97D412—24no—
98D412—42no—
99C103⋊C8—24no—
100C22×C103—21no—
101C22×C103—21no—
102C22×C103—21no—
103C22×C103—21no—
104C22×C103—21no—
105C22×C103—21no—
106C22×C103—44no—
107C22×C103C2×SD1612yes—
108C22×C103C2×SD1612yes—
109C22×C103C2×SD1612yes—
110C22×C103C22×D411yescharacteristic
111C2×D103—42no—
112C2×D103—42no—
113C2×D103—42no—
114C2×D103—84no—
115C4×C103—21no—
116C4×C103—21no—
117C4×C103—21no—
118C4×C103—42no—
119C4×C103—42no—
120C4×C103H(5,𝔽2)12yes—
121Dic103—42no—
122C2×C103—22no—
123C2×C103—22no—
124C2×C103—22no—
125C2×C103#53411yescharacteristic
126C2×C103C22×SD1611yescharacteristic
127C2×C103#57511yescharacteristic
128D103—82no—
129#3187—1031nomaximal, Sylow
130C103#318711yescharacteristic, complemented, Sylow
131C2×C22⋊Q8D10311yescharacteristic, complemented
132C2×#121—1031no—
133#483—1032no—
134#481—1032no—
135#465—1034no—
136#450—1032no—
137#448—1032no—
138C2×C22⋊C8—1031no—
139C22×Q8C2×D10311yescharacteristic, complemented
140C22×D4—1031no—
141C22×D4—2061no—
142C23×C4C2×D10311yescharacteristic
143C2×SD16—1034no—
144C22×C8—1032no—
145C22⋊Q8—21no—
146C22⋊Q8—21no—
147C22⋊Q8C2×D10312yes—
148C22⋊Q8C2×D10312yescomplemented
149#121—1032no—
150#121—1032no—
151#121—2061no—
152#121—2061no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—1031no—
155C2×C4⋊C4C2×D10311yescharacteristic, complemented
156C2×C22⋊C4—21no—
157C2×C22⋊C4—2061no—
158#106—1034no—
159#103—1034no—
160#102—1034no—
161C22⋊C8—1032no—
162C22⋊C8—1032no—
163C24—2061no—
164C24C22⋊D10311yescharacteristic
165C2×Q8—21no—
166C2×Q8—42no—
167C2×Q8C22×D10312yes—
168C2×D4—1032no—
169C2×D4—4122no—
170C2×D4—4124no—
171C2×D4—2062no—
172C2×D4—2062no—
173C2×D4—2061no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—42no—
177C22×C4—2061no—
178C22×C4C22⋊D10311yescharacteristic
179C22×C4C22⋊D10311yescharacteristic
180C22×C4C22⋊D10311yescharacteristic
181C22×C4C22×D10311yescharacteristic
182C22×C4C22×D10311yescharacteristic
183C22×C4C22×D10311yescharacteristic
184SD16—4124no—
185C2×C8—1034no—
186C2×C8—4122no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—1032no—
191C4⋊C4—2061no—
192C4⋊C4C22×D10312yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—2062no—
196C22⋊C4—2062no—
197C23—41no—
198C23—41no—
199C23—4122no—
200C23—4122no—
201C23—4122no—
202C23—2062no—
203C23#1311009214yescomplemented
204C23C2×C22⋊D10311yescharacteristic
205C23C2×C22⋊D10311yescharacteristic
206C23C2×C22⋊D10311yescharacteristic
207Q8—24no—
208Q8—42no—
209D4—4122no—
210D4—4124no—
211D4—4124no—
212D4—2064no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—4122no—
224C2×C4—2062no—
225C2×C4C2×C22⋊D10311yescharacteristic
226C2×C4C2×C22⋊D10311yescharacteristic
227C2×C4C2×C22⋊D10311yescharacteristic
228C2×C4C23×D10311yescharacteristic
229C8—2064no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—44no—
237C22—8244no—
238C22—4122no—
239C22—4122no—
240C22—4122no—
241C22C2×#1311009212yes—
242C22C2×#1311009212yes—
243C22C2×#1311009212yes—
244C22C22×C22⋊D10311yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—42no—
250C4—4122no—
251C4#1569306612yes—
252C2—22no—
253C2—22no—
254C2—22no—
255C2—8242no—
256C2#2026835011yescharacteristic
257C2C22×#1311009211yescharacteristic
258C2#2026858911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C22⋊Q8×C103C2
socleC22×C103C22×D4
prime radicalC2×#15692995C2
hypercenterC2×C22⋊Q8D103
hypocenterC103#3187
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20268119C2semidirect
3. #20268109C2semidirect
4. #20268022C2semidirect
5. #20267941C2semidirect
6. #20267930C2semidirect
7. C2×C22⋊(C103⋊C8)C2semidirect
8. C2×C22⋊Q8×C103C2semidirect
11. C2×#13110092C22semidirect
12. C22×C103⋊C8C22semidirect
19. #15692952C22semidirect
20. #15692945C22semidirect
21. #15692941C22semidirect
23. C22⋊(C103⋊C8)C22semidirect
24. C22×Q8×C103C22semidirect
29. C22⋊Q8×C103C22semidirect
31. C2×C4⋊C4×C103C22semidirect
69. C23×C103SD16semidirect
130. C103#3187semidirect
131. C2×C22⋊Q8D103semidirect
139. C22×Q8C2×D103semidirect
148. C22⋊Q8C2×D103semidirect
155. C2×C4⋊C4C2×D103semidirect
203. C23#13110092semidirect

Maximal subgroups

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

subgroupindex
C2×#156929952
#202681192
#202681092
#202680222
#202679412
#202679302
C2×C22⋊(C103⋊C8)2
C2×C22⋊Q8×C1032
#3187103