Finite Group Databasebeta

← #27208556

Subgroups — #27208556

Order 13184.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#20268390C216yesmaximal, complemented
2#20268381C216yesmaximal, complemented
3#20268353C213yesmaximal, complemented
4#20268327C216yesmaximal, complemented
5#20268304C216yesmaximal, complemented
6C2×(C22⋊D103)⋊C4C213yesmaximal, complemented
7#543×C103C211yesmaximal, characteristic, complemented
8C2×#13110106C2212yescomplemented
9C22×C22⋊D103C2213yes—
10C23×Dic103C2211yescharacteristic
11C22×C4×D103C2213yescomplemented
12#15693016C22112yescomplemented
13#15693012C2216yescomplemented
14#15693010C2216yescomplemented
15#15693006C22112yescomplemented
16#15693005C22112yescomplemented
17#15692997C2216yescomplemented
18#15692996C2216yescomplemented
19#15692995C2216yes—
20#15692995C2216yes—
21#15692991C22112yescomplemented
22Q8×Dic103C2212yescomplemented
23#15692983C2216yescomplemented
24(C22⋊D103)⋊C4C22112yescomplemented
25(C22⋊D103)⋊C4C22112yescomplemented
26#15692979C2216yescomplemented
27C2×Dic103⋊C4C2213yescomplemented
28C2×(C2×D103)⋊C4C2213yescomplemented
29C2×C4×Dic103C2213yescomplemented
30C22⋊Q8×C103C2216yescomplemented
31C22⋊Q8×C103C2216yescomplemented
32C2×C22⋊C4×C103C2213yes—
33C23×D103C2313yes—
34#13110106—44no—
35C2×D412C2316yes—
36C2×D412C2316yes—
37C2×C22⋊D103—212no—
38C2×C22⋊D103C23112yes—
39C22×Dic103—42no—
40C22×Dic103C2313yes—
41C22×Dic103C2313yes—
42C22×Dic103C2313yes—
43C2×C4×D103—46no—
44C2×C4×D103C2316yes—
45C2×C4×D103C2316yes—
46C4⋊Dic103C2316yes—
47C4⋊Dic103C2316yes—
48Dic103⋊C4C23112yes—
49(C2×D103)⋊C4C23112yes—
50(C2×D103)⋊C4C23112yes—
51(C2×D103)⋊C4C23112yes—
52C4×Dic103C2316yes—
53C4×Dic103C2316yes—
54C24×C103C2311yescharacteristic
55C2×Q8×C103C2312yes—
56C2×Q8×C103C2312yes—
57C22×C4×C103C2313yes—
58C22×C4×C103C2313yes—
59C4⋊C4×C103C2316yes—
60C4⋊C4×C103C2316yes—
61C22⋊C4×C103C23112yes—
62C23×C103—41no—
63C23×C103—41no—
64C23×C103#4114yescomplemented
65C23×C103C2413yes—
66C22×D103—26no—
67C22×D103—43no—
68C22×D103—43no—
69C22×D103C2416yes—
70Q8×C103—42no—
71Q8×C103—42no—
72C2×C4×C103—43no—
73C2×C4×C103—43no—
74C2×C4×C103C2416yes—
75C2×C4×C103C2416yes—
76C22⋊D103—224no—
77C2×Dic103—26no—
78C2×Dic103—26no—
79C2×Dic103—43no—
80C2×Dic103C2413yes—
81C2×Dic103C2416yes—
82C2×Dic103C2411yescharacteristic
83D412—46no—
84D412—46no—
85C4×D103—212no—
86C4×D103—46no—
87C22×C103—23no—
88C22×C103—23no—
89C22×C103—44no—
90C22×C103C2×#4116yes—
91C22×C103C2511yescharacteristic
92C2×D103—26no—
93C2×D103—26no—
94C2×D103—26no—
95C2×D103—412no—
96C4×C103—26no—
97C4×C103—26no—
98Dic103—26no—
99Dic103—23no—
100Dic103H(5,𝔽2)12yes—
101C2×C103—26no—
102C2×C103C22×#4111yescharacteristic
103C2×C103C2×H(5,𝔽2)11yescharacteristic
104C2×C103#58511yescharacteristic
105D103—46no—
106#3459—1031nomaximal, Sylow
107C103#345911yescharacteristic, complemented, Sylow
108#543D10311yescharacteristic, complemented
109#539—1036no—
110#538—1036no—
111#534—1033no—
112#529—1036no—
113#525—1036no—
114C2×C4×D4—1033no—
115C2×#41—1032no—
116C22×D4—1033no—
117C23×C4—1031no—
118C23×C4—1033no—
119#126—10312no—
120#125—1036no—
121#124—1036no—
122#123—10312no—
123#123—10312no—
124C22⋊Q8—1036no—
125C22⋊Q8C2×D10316yescomplemented
126C22⋊Q8C2×D10316yescomplemented
127#121—1036no—
128#121—1036no—
129#121—1036no—
130#120—10312no—
131C4×Q8—1032no—
132C4×D4—1036no—
133C4×D4—10312no—
134C4×D4—10312no—
135#117—1036no—
136C2×C4⋊C4—1033no—
137C2×C22⋊C4—1033no—
138C2×C22⋊C4C2×D10313yes—
139C2×C42—1033no—
140C24—1033no—
141C24C22×D10311yescharacteristic
142#41—4124no—
143C2×Q8C22×D10312yes—
144C2×Q8C22×D10312yes—
145C2×D4—10312no—
146C2×D4—1036no—
147C2×D4—1036no—
148C2×D4—20612no—
149C22×C4—1033no—
150C22×C4—1033no—
151C22×C4—1033no—
152C22×C4—1036no—
153C22×C4—1036no—
154C22×C4—4126no—
155C22×C4—4122no—
156C22×C4C22×D10313yes—
157C22×C4C22×D10313yes—
158C4⋊C4—10312no—
159C4⋊C4—1036no—
160C4⋊C4—1036no—
161C4⋊C4C22×D10316yes—
162C4⋊C4C22×D10316yes—
163C22⋊C4—10312no—
164C22⋊C4—10312no—
165C22⋊C4—10312no—
166C22⋊C4C22×D103112yes—
167C42—1036no—
168C42—1036no—
169C23—41no—
170C23—41no—
171C23—1036no—
172C23—4123no—
173C23—4123no—
174C23—2066no—
175C23#1311010614yescomplemented
176C23C23×D10313yes—
177Q8—42no—
178Q8—42no—
179D4—4126no—
180D4—4126no—
181D4—20624no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—1031no—
185C2×C4—1036no—
186C2×C4—1033no—
187C2×C4—4126no—
188C2×C4—4123no—
189C2×C4—20612no—
190C2×C4—2066no—
191C2×C4—2066no—
192C2×C4C23×D10316yes—
193C2×C4C23×D10316yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—41212no—
198C22—2066no—
199C22—2066no—
200C22—2066no—
201C22C2×#1311010616yes—
202C22C24×D10311yescharacteristic
203C4—26no—
204C4—26no—
205C4—1032no—
206C4—2066no—
207C4—2063no—
208C2—26no—
209C2—4126no—
210C2C22×#1311010611yescharacteristic
211C2H(5,𝔽2)×D10311yescharacteristic
212C2#2026862611yescharacteristic
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
Fitting#543×C103C2
hypercenter#543D103
hypocenterC103#3459
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #20268390C2semidirect
2. #20268381C2semidirect
3. #20268353C2semidirect
4. #20268327C2semidirect
5. #20268304C2semidirect
6. C2×(C22⋊D103)⋊C4C2semidirect
7. #543×C103C2semidirect
8. C2×#13110106C22semidirect
11. C22×C4×D103C22semidirect
12. #15693016C22semidirect
13. #15693012C22semidirect
14. #15693010C22semidirect
15. #15693006C22semidirect
16. #15693005C22semidirect
17. #15692997C22semidirect
18. #15692996C22semidirect
21. #15692991C22semidirect
22. Q8×Dic103C22semidirect
23. #15692983C22semidirect
24. (C22⋊D103)⋊C4C22semidirect
25. (C22⋊D103)⋊C4C22semidirect
26. #15692979C22semidirect
27. C2×Dic103⋊C4C22semidirect
28. C2×(C2×D103)⋊C4C22semidirect
29. C2×C4×Dic103C22semidirect
30. C22⋊Q8×C103C22semidirect
31. C22⋊Q8×C103C22semidirect
64. C23×C103#41semidirect
107. C103#3459semidirect
108. #543D103semidirect
125. C22⋊Q8C2×D103semidirect
126. C22⋊Q8C2×D103semidirect
175. C23#13110106semidirect

Maximal subgroups

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

subgroupindex
#202683902
#202683812
#202683532
#202683272
#202683042
C2×(C22⋊D103)⋊C42
#543×C1032
#3459103