Finite Group Databasebeta

← #28405268

Subgroups — #28405268

Order 14464.

958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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#20299348C213yesmaximal, complemented
2#20299317C216yesmaximal, complemented
3#20299279C216yesmaximal, complemented
4#20299212C216yesmaximal, complemented
5#20299183C216yesmaximal, complemented
6#20299127C213yesmaximal, complemented
7H(3,𝔽4)×C113C211yesmaximal, characteristic, complemented
8#16813620C2216yescomplemented
9#16813616C2212yescomplemented
10#16813615C2216yescomplemented
11#16813615C2216yescomplemented
12#16813615C2216yescomplemented
13#16813615C2216yescomplemented
14#16813614C2213yescomplemented
15#16813609C2216yes—
16#16813608C2216yescomplemented
17#16813604C2216yescomplemented
18#16813603C2216yes—
19#16813603C2216yes—
20#16813599C2216yescomplemented
21#16813599C2216yescomplemented
22#16813599C2216yescomplemented
23#16813598C2213yescomplemented
24#16813594C2216yes—
25#16813593C2213yes—
26#16813591C2212yescomplemented
27Q8×Dic113C2213yescomplemented
28C4×Dic226C2216yescomplemented
29D4×Dic113C2213yes—
30D4×Dic113C2216yes—
31#16813582C2216yescomplemented
32#16813578C2216yescomplemented
33#16813578C2216yescomplemented
34C2×C22⋊Dic113C2216yescomplemented
35C42×D113C2211yescharacteristic, complemented
36#124×C113C2216yes—
37#124×C113C2213yes—
38#120×C113C2216yes—
39C2×Dic226C2316yes—
40C2×C22⋊D113C2316yes—
41C22×Dic113C2316yes—
42C22×Dic113C2316yes—
43C2×C4×D113C2313yes—
44C4⋊Dic113C2316yes—
45C4⋊Dic113C2313yes—
46C4⋊Dic113C2313yes—
47#14268626C2316yes—
48#14268626C2316yes—
49#14268626C2316yes—
50#14268626C2316yes—
51#14268626C2316yes—
52C22⋊Dic113C2316yes—
53C22⋊Dic113C2316yes—
54C22⋊Dic113C2316yes—
55C22⋊Dic113C2316yes—
56C22⋊Dic113C2316yes—
57#14268624C2316yes—
58C4×Dic113C2313yes—
59C4×Dic113C2316yes—
60C4×Dic113C2316yes—
61C24×C113C2312yes—
62C2×Q8×C113C2313yes—
63C2×D4×C113C2313yes—
64C2×D4×C113C2316yes—
65C22⋊C4×C113C2316yes—
66C22⋊C4×C113C2316yes—
67C22⋊C4×C113C2316yes—
68C42×C113C2311yescharacteristic
69C42×C113C2312yes—
70C23×C113—46no—
71C23×C113C2416yes—
72C22×D113C2411yescharacteristic
73Q8×C113—43no—
74D4×C113—46no—
75D4×C113—43no—
76C2×C4×C113C2416yes—
77C2×C4×C113C2413yes—
78C22⋊D113—46no—
79C2×Dic113—46no—
80C2×Dic113—46no—
81C2×Dic113C2413yes—
82C2×Dic113C2416yes—
83C2×Dic113C2416yes—
84C4×D113—43no—
85Dic226—46no—
86C22×C113—26no—
87C22×C113—26no—
88C22×C113—26no—
89C22×C113—84no—
90C22×C113C2511yescharacteristic
91C2×D113—23no—
92C4×C113—26no—
93C4×C113—23no—
94Dic113—26no—
95Dic113—26no—
96Dic113—23no—
97C2×C113—46no—
98C2×C113#58513yes—
99D113—41no—
100#3568—1131nomaximal, Sylow
101C113#356811yescharacteristic, complemented, Sylow
102#563—1133no—
103H(3,𝔽4)D11311yescharacteristic, complemented
104#556—1136no—
105#551—1136no—
106#542—1136no—
107#538—1136no—
108#529—1133no—
109C4⋊Q8—1136no—
110#126—1136no—
111#126—1136no—
112#126—1136no—
113#126—1136no—
114#126—1132no—
115#125—1133no—
116#124—1136no—
117#124—1136no—
118#124C2×D11313yes—
119#124C2×D11316yes—
120#123—1136no—
121#123—1136no—
122#123—1136no—
123C22⋊Q8—1133no—
124C22⋊Q8—1136no—
125C22⋊Q8—1136no—
126C22⋊Q8—1136no—
127#121—1133no—
128#121—1136no—
129#120—1132no—
130#120C2×D11316yes—
131C4×Q8—1133no—
132C4×Q8—1136no—
133C4×D4—1133no—
134C4×D4—1136no—
135C4×D4—1136no—
136#117—1136no—
137#117—1136no—
138C2×C22⋊C4—1136no—
139C2×C42—1131no—
140C24C22×D11312yes—
141C2×Q8—1136no—
142C2×Q8C22×D11313yes—
143C2×D4—1136no—
144C2×D4C22×D11313yes—
145C2×D4C22×D11316yes—
146C22×C4—1136no—
147C22×C4—1136no—
148C22×C4—1133no—
149C4⋊C4—1136no—
150C4⋊C4—1136no—
151C4⋊C4—1136no—
152C4⋊C4—1136no—
153C4⋊C4—1133no—
154C4⋊C4—1136no—
155C4⋊C4—1133no—
156C4⋊C4—1136no—
157C22⋊C4—1136no—
158C22⋊C4—1136no—
159C22⋊C4—1136no—
160C22⋊C4—1136no—
161C22⋊C4—1136no—
162C22⋊C4—1136no—
163C22⋊C4C22×D11316yes—
164C22⋊C4C22×D11316yes—
165C22⋊C4C22×D11316yes—
166C42—1133no—
167C42—1136no—
168C42—1136no—
169C42C22×D11311yescharacteristic
170C42C22×D11312yes—
171C23—46no—
172C23—1131no—
173C23C23×D11316yes—
174Q8—43no—
175Q8—4526no—
176D4—43no—
177D4—46no—
178D4—4526no—
179C2×C4—1133no—
180C2×C4—1136no—
181C2×C4—1136no—
182C2×C4—4523no—
183C2×C4—4526no—
184C2×C4—4526no—
185C2×C4C23×D11316yes—
186C2×C4C23×D11313yes—
187C22—26no—
188C22—26no—
189C22—26no—
190C22—84no—
191C22—2263no—
192C22C24×D11311yescharacteristic
193C4—23no—
194C4—26no—
195C4—2263no—
196C4—2266no—
197C4—2266no—
198C2—46no—
199C2—4521no—
200C2#2029943313yes—
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
FittingH(3,𝔽4)×C113C2
hypercenterH(3,𝔽4)D113
hypocenterC113#3568
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #20299348C2semidirect
2. #20299317C2semidirect
3. #20299279C2semidirect
4. #20299212C2semidirect
5. #20299183C2semidirect
6. #20299127C2semidirect
7. H(3,𝔽4)×C113C2semidirect
8. #16813620C22semidirect
9. #16813616C22semidirect
10. #16813615C22semidirect
11. #16813615C22semidirect
12. #16813615C22semidirect
13. #16813615C22semidirect
14. #16813614C22semidirect
16. #16813608C22semidirect
17. #16813604C22semidirect
20. #16813599C22semidirect
21. #16813599C22semidirect
22. #16813599C22semidirect
23. #16813598C22semidirect
26. #16813591C22semidirect
27. Q8×Dic113C22semidirect
28. C4×Dic226C22semidirect
31. #16813582C22semidirect
32. #16813578C22semidirect
33. #16813578C22semidirect
34. C2×C22⋊Dic113C22semidirect
35. C42×D113C22semidirect
101. C113#3568semidirect
103. H(3,𝔽4)D113semidirect

Maximal subgroups

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

subgroupindex
#202993482
#202993172
#202992792
#202992122
#202991832
#202991272
H(3,𝔽4)×C1132
#3568113