Finite Group Databasebeta

← #28404714

Subgroups — #28404714

Order 14464.

1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 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#20299342C216yesmaximal, complemented
3#20299337C216yesmaximal, complemented
4#20299147C213yesmaximal, complemented
5#20299127C216yesmaximal, complemented
6#20299104C216yesmaximal, complemented
7H(3,𝔽4)×C113C211yesmaximal, characteristic, complemented
8C2×#14268648C2211yescharacteristic, complemented
9C2×#14268646C2213yes—
10C23×Dic113C2212yescomplemented
11#16813620C2213yescomplemented
12#16813618C2213yes—
13#16813615C22112yescomplemented
14#16813614C2216yescomplemented
15#16813610C2213yescomplemented
16#16813606C2216yescomplemented
17#16813604C22112yescomplemented
18#16813603C2216yes—
19#16813599C22112yescomplemented
20#16813598C2216yescomplemented
21#16813595C22112yescomplemented
22#16813594C22112yes—
23#16813593C2216yes—
24#16813591C2216yescomplemented
25Q8×Dic113C2212yescomplemented
26D4×Dic113C2216yes—
27#16813582C22112yescomplemented
28#16813578C2216yescomplemented
29C42×D113C2213yescomplemented
30#124×C113C2216yes—
31#124×C113C2213yes—
32#120×C113C2216yes—
33#14268648—42no—
34#14268646—46no—
35C2×Dic226C2313yes—
36C2×D452C2313yes—
37C2×C22⋊D113C23112yes—
38C2×C22⋊D113C2316yes—
39C22×Dic113—44no—
40C22×Dic113C2316yes—
41C22×Dic113C2316yes—
42C2×C4×D113C2313yes—
43C2×C4×D113C2316yes—
44C4⋊Dic113C2316yes—
45C4⋊Dic113C2316yes—
46#14268626C23112yes—
47#14268626C23112yes—
48C22⋊Dic113C2316yes—
49C22⋊Dic113C23112yes—
50#14268624C23112yes—
51C4×Dic113C2316yes—
52C4×Dic113C2313yes—
53C24×C113C2312yes—
54C2×Q8×C113C2312yes—
55C2×Q8×C113C2311yescharacteristic
56C2×D4×C113C2316yes—
57C2×D4×C113C2313yes—
58C22⋊C4×C113C2316yes—
59C22⋊C4×C113C23112yes—
60C42×C113C2313yes—
61C23×C113—44no—
62C23×C113—42no—
63C23×C113C2416yes—
64C22×D113C2413yes—
65Q8×C113—42no—
66Q8×C113—41no—
67D4×C113—46no—
68D4×C113—43no—
69C2×C4×C113C2416yes—
70C2×C4×C113C2413yes—
71C22⋊D113—412no—
72C22⋊D113—46no—
73C2×Dic113—212no—
74C2×Dic113—46no—
75C2×Dic113C2416yes—
76C2×Dic113C2416yes—
77C2×Dic113C2411yescharacteristic
78D452—43no—
79C4×D113—26no—
80C4×D113—46no—
81Dic226—43no—
82C22×C113—26no—
83C22×C113—212no—
84C22×C113—48no—
85C22×C113C2511yescharacteristic
86C2×D113—23no—
87C2×D113—26no—
88C4×C113—23no—
89C4×C113—26no—
90Dic113—26no—
91Dic113—26no—
92Dic113H(5,𝔽2)12yes—
93C2×C113—46no—
94C2×C113C2×H(5,𝔽2)11yescharacteristic
95C2×C113#58512yes—
96D113—43no—
97#3529—1131nomaximal, Sylow
98C113#352911yescharacteristic, complemented, Sylow
99#563—1133no—
100#562—1136no—
101H(3,𝔽4)D11311yescharacteristic, complemented
102#560—1136no—
103#532—1133no—
104#529—1136no—
105#525—1136no—
106C2×#41—1131no—
107C2×#41—1133no—
108C23×C4—1132no—
109C4⋊Q8—1133no—
110#127—1133no—
111#126—11312no—
112#125—1136no—
113#124—1133no—
114#124C2×D11316yes—
115#124C2×D11313yes—
116#123—1136no—
117#123—1136no—
118#123—11312no—
119C22⋊Q8—1136no—
120C22⋊Q8—11312no—
121#121—11312no—
122#121—1136no—
123#121—11312no—
124#120—1136no—
125#120C2×D11316yes—
126C4×Q8—1132no—
127C4×D4—1136no—
128C4×D4—11312no—
129#117—1136no—
130C2×C42—1133no—
131C24C22×D11312yes—
132#41—4526no—
133#41—4522no—
134C2×Q8—1133no—
135C2×Q8C22×D11312yes—
136C2×Q8C22×D11311yescharacteristic
137C2×D4—11312no—
138C2×D4—1136no—
139C2×D4—1133no—
140C2×D4C22×D11316yes—
141C2×D4C22×D11313yes—
142C22×C4—1136no—
143C22×C4—1136no—
144C22×C4—1136no—
145C22×C4—1133no—
146C22×C4—4524no—
147C4⋊C4—11312no—
148C4⋊C4—11312no—
149C4⋊C4—1136no—
150C4⋊C4—1136no—
151C22⋊C4—1136no—
152C22⋊C4—11312no—
153C22⋊C4—11312no—
154C22⋊C4C22×D11316yes—
155C22⋊C4C22×D113112yes—
156C42—1136no—
157C42—1133no—
158C42C22×D11313yes—
159C23—42no—
160C23—44no—
161C23—1133no—
162C23C23×D11316yes—
163Q8—41no—
164Q8—42no—
165Q8—4523no—
166D4—43no—
167D4—46no—
168D4—4523no—
169D4—4526no—
170D4—45212no—
171C2×C4—1131no—
172C2×C4—1136no—
173C2×C4—1136no—
174C2×C4—4526no—
175C2×C4—4526no—
176C2×C4—2266no—
177C2×C4—22612no—
178C2×C4C23×D11316yes—
179C2×C4C23×D11313yes—
180C22—26no—
181C22—212no—
182C22—48no—
183C22—2263no—
184C22—2266no—
185C22C24×D11311yescharacteristic
186C4—23no—
187C4—26no—
188C4—1132no—
189C4—2266no—
190C4—2266no—
191C2—46no—
192C2—4523no—
193C2H(5,𝔽2)×D11311yescharacteristic
194C2#2029943312yes—
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
FittingH(3,𝔽4)×C113C2
hypercenterH(3,𝔽4)D113
hypocenterC113#3529
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. #20299342C2semidirect
3. #20299337C2semidirect
4. #20299147C2semidirect
5. #20299127C2semidirect
6. #20299104C2semidirect
7. H(3,𝔽4)×C113C2semidirect
8. C2×#14268648C22semidirect
10. C23×Dic113C22semidirect
11. #16813620C22semidirect
13. #16813615C22semidirect
14. #16813614C22semidirect
15. #16813610C22semidirect
16. #16813606C22semidirect
17. #16813604C22semidirect
19. #16813599C22semidirect
20. #16813598C22semidirect
21. #16813595C22semidirect
24. #16813591C22semidirect
25. Q8×Dic113C22semidirect
27. #16813582C22semidirect
28. #16813578C22semidirect
29. C42×D113C22semidirect
98. C113#3529semidirect
101. 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
#202993422
#202993372
#202991472
#202991272
#202991042
H(3,𝔽4)×C1132
#3529113