Finite Group Databasebeta

← #27205938

Subgroups — #27205938

Order 13184.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#20268304C212yesmaximal, complemented
2#20268131C212yesmaximal, complemented
3#20268118C212yesmaximal, complemented
4#20268027C211yesmaximal, characteristic, complemented
5#20268022C212yesmaximal, complemented
6#20267952C212yesmaximal, complemented
7#20267939C212yesmaximal, complemented
8C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
9#467×C103C211yesmaximal, characteristic, complemented
10C2×#13110106C2212yes—
11C22×C4×D103C2211yescharacteristic
12C2×#13110092C2212yescomplemented
13C2×D824C2211yescharacteristic, complemented
14C22×C103⋊C8C2211yescharacteristic
15#15693006—22no—
16#15692997C2212yes—
17#15692996C2212yes—
18#15692995C2212yes—
19#15692991—22no—
20#15692983—22no—
21(C22⋊D103)⋊C4—22no—
22#15692979C2212yes—
23#15692955C2211yescharacteristic, complemented
24#15692952C2212yescomplemented
25#15692945C2212yescomplemented
26#15692943C2212yescomplemented
27#15692941C2212yescomplemented
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×Q16×C103C2211yescharacteristic, complemented
31C22×C8×C103C2211yescharacteristic
32C22⋊Q8×C103C2212yes—
33#107×C103C2211yescharacteristic, complemented
34#103×C103C2212yescomplemented
35C23×D103D411yescharacteristic
36#13110106—42no—
37#13110106—42no—
38C2×D412—22no—
39C2×D412—22no—
40C2×D412C2312yes—
41C2×C22⋊D103—22no—
42C22×Dic103D411yescharacteristic
43C2×C4×D103—22no—
44C2×C4×D103—41no—
45C2×C4×D103—41no—
46C2×C4×D103D412yes—
47C2×C4×D103C2312yes—
48#13110092—42no—
49D824—41no—
50C2×C103⋊C8—41no—
51C2×C103⋊C8C2312yes—
52C4⋊Dic103C2312yes—
53Dic103⋊C4—22no—
54(C2×D103)⋊C4—22no—
55(C2×D103)⋊C4—22no—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—22no—
58C4×Dic103—22no—
59C2×Q8×C103C2312yes—
60C22×C4×C103C2311yescharacteristic
61Q16×C103—41no—
62C2×C8×C103—41no—
63C2×C8×C103C2311yescharacteristic
64C2×C8×C103C2311yescharacteristic
65C4⋊C4×C103—22no—
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C23×C103C2×D411yescharacteristic
69C22×D103—22no—
70C22×D103—22no—
71C22×D103—41no—
72C22×D103—41no—
73C22×D103C2×D412yes—
74Q8×C103—22no—
75Q8×C103—22no—
76C2×C4×C103—21no—
77C2×C4×C103—21no—
78C2×C4×C103—22no—
79C2×C4×C103—22no—
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2411yescharacteristic
82C22⋊D103—44no—
83C2×Dic103—22no—
84C2×Dic103—41no—
85C2×Dic103C2×D412yes—
86D412—22no—
87D412—22no—
88D412—44no—
89D412—44no—
90C4×D103—22no—
91C4×D103—22no—
92C4×D103—42no—
93C4×D103—44no—
94C8×C103—21no—
95C8×C103—21no—
96C103⋊C8—22no—
97C22×C103—21no—
98C22×C103—21no—
99C22×C103#13512yes—
100C22×C103C22×D411yescharacteristic
101C2×D103—22no—
102C2×D103—22no—
103C2×D103—22no—
104C2×D103—44no—
105C2×D103—42no—
106C2×D103—42no—
107C2×D103—42no—
108C4×C103—21no—
109C4×C103—42no—
110C4×C103—42no—
111C4×C103H(5,𝔽2)11yescharacteristic
112C4×C103H(5,𝔽2)11yescharacteristic
113Dic103—22no—
114Dic103—42no—
115C2×C103—22no—
116C2×C103#53411yescharacteristic
117C2×C103C2×#13511yescharacteristic
118C2×C103#57511yescharacteristic
119D103—42no—
120D103—82no—
121#3191—1031nomaximal, Sylow
122C103#319111yescharacteristic, complemented, Sylow
123#525—1032no—
124#485—1032no—
125#482—1032no—
126#467D10311yescharacteristic, complemented
127#466—1031no—
128#465—1032no—
129#452—1032no—
130#449—1032no—
131C2×C22⋊C8—1031no—
132C2×#41—1032no—
133C23×C4—1031no—
134C2×Q16C2×D10311yescharacteristic, complemented
135C2×SD16—1032no—
136C2×D8—1031no—
137C22×C8—1031no—
138C22×C8C2×D10311yescharacteristic
139#123—2062no—
140C22⋊Q8—1032no—
141C22⋊Q8C2×D10312yes—
142#121—1032no—
143#121—1032no—
144#120—2062no—
145C4×D4—2062no—
146C4×D4—2062no—
147#117—1032no—
148#107—1031no—
149#107C2×D10311yescharacteristic, complemented
150#106—1032no—
151#103—1032no—
152#103C2×D10312yescomplemented
153#102—1032no—
154#102—1032no—
155C22⋊C8—1032no—
156C22⋊C8—1032no—
157C24—1031no—
158#41—4122no—
159#41—4122no—
160C2×Q8C22×D10312yes—
161C2×D4—1032no—
162C2×D4—2062no—
163C2×D4—2062no—
164C2×D4—2062no—
165C22×C4—1031no—
166C22×C4—1032no—
167C22×C4—1032no—
168C22×C4—4121no—
169C22×C4—4121no—
170C22×C4—2062no—
171C22×C4C22×D10311yescharacteristic
172Q16—41no—
173SD16—4122no—
174D8—4121no—
175C2×C8—41no—
176C2×C8—1032no—
177C2×C8—4121no—
178C2×C8C22×D10311yescharacteristic
179C2×C8C22×D10311yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—1032no—
182C4⋊C4—2062no—
183C4⋊C4C22×D10312yes—
184C22⋊C4—22no—
185C22⋊C4—2062no—
186C22⋊C4—2062no—
187C22⋊C4—2062no—
188C22⋊C4—2062no—
189C42—2062no—
190C23—1032no—
191C23—4121no—
192C23—4121no—
193C23—2062no—
194C23—2062no—
195C23D4×D10311yescharacteristic
196Q8—22no—
197Q8—22no—
198D4—4124no—
199D4—4124no—
200D4—4124no—
201D4—2062no—
202D4—2062no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—1032no—
208C2×C4—4122no—
209C2×C4—4124no—
210C2×C4—4121no—
211C2×C4—2062no—
212C2×C4—2062no—
213C2×C4—2062no—
214C2×C4D4×D10311yescharacteristic
215C2×C4C23×D10311yescharacteristic
216C8—21no—
217C8—21no—
218C8—2062no—
219C22—21no—
220C22—21no—
221C22—4124no—
222C22—4122no—
223C22—4122no—
224C22—4122no—
225C22—2062no—
226C22—2062no—
227C22—2062no—
228C22#1569304412yes—
229C22C2×D4×D10311yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—4122no—
234C4—2062no—
235C4#1569306611yescharacteristic
236C4#1569306711yescharacteristic
237C2—22no—
238C2—8242no—
239C2—4122no—
240C2#2026834911yescharacteristic
241C2C2×#1569304411yescharacteristic
242C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#467×C103C2
socleC22×C103C22×D4
hypercenter#467D103
hypocenterC103#3191
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #20268304C2semidirect
2. #20268131C2semidirect
3. #20268118C2semidirect
4. #20268027C2semidirect
5. #20268022C2semidirect
6. #20267952C2semidirect
7. #20267939C2semidirect
8. C2×(C2×D103)⋊C8C2semidirect
9. #467×C103C2semidirect
12. C2×#13110092C22semidirect
13. C2×D824C22semidirect
23. #15692955C22semidirect
24. #15692952C22semidirect
25. #15692945C22semidirect
26. #15692943C22semidirect
27. #15692941C22semidirect
30. C2×Q16×C103C22semidirect
33. #107×C103C22semidirect
34. #103×C103C22semidirect
122. C103#3191semidirect
126. #467D103semidirect
134. C2×Q16C2×D103semidirect
149. #107C2×D103semidirect
152. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683042
#202681312
#202681182
#202680272
#202680222
#202679522
#202679392
C2×(C2×D103)⋊C82
#467×C1032
#3191103