Finite Group Databasebeta

← #46825579

Subgroups — #46825579

Order 34432.

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#31771355C213yesmaximal, complemented
2#31771324C216yesmaximal, complemented
3#31771286C216yesmaximal, complemented
4#31771219C216yesmaximal, complemented
5#31771190C216yesmaximal, complemented
6#31771134C213yesmaximal, complemented
7H(3,𝔽4)×C269C211yesmaximal, characteristic, complemented
8#22575451C2216yescomplemented
9#22575447C2212yescomplemented
10#22575446C2216yescomplemented
11#22575446C2216yescomplemented
12#22575446C2216yescomplemented
13#22575446C2216yescomplemented
14#22575445C2213yescomplemented
15#22575440C2216yes—
16#22575439C2216yescomplemented
17#22575435C2216yescomplemented
18#22575434C2216yes—
19#22575434C2216yes—
20#22575430C2216yescomplemented
21#22575430C2216yescomplemented
22#22575430C2216yescomplemented
23#22575429C2213yescomplemented
24#22575425C2216yes—
25#22575424C2213yes—
26#22575422C2212yescomplemented
27Q8×Dic269C2213yescomplemented
28C4×Dic538C2216yescomplemented
29D4×Dic269C2216yes—
30D4×Dic269C2213yes—
31#22575413C2216yescomplemented
32#22575409C2216yescomplemented
33#22575409C2216yescomplemented
34C2×C22⋊Dic269C2216yescomplemented
35C42×D269C2211yescharacteristic, complemented
36#124×C269C2216yes—
37#124×C269C2213yes—
38#120×C269C2216yes—
39C2×Dic538C2316yes—
40C2×C22⋊D269C2316yes—
41C22×Dic269C2316yes—
42C22×Dic269C2316yes—
43C2×C4×D269C2313yes—
44C4⋊Dic269C2316yes—
45C4⋊Dic269C2313yes—
46C4⋊Dic269C2313yes—
47#16864381C2316yes—
48#16864381C2316yes—
49#16864381C2316yes—
50#16864381C2316yes—
51#16864381C2316yes—
52C22⋊Dic269C2316yes—
53C22⋊Dic269C2316yes—
54C22⋊Dic269C2316yes—
55C22⋊Dic269C2316yes—
56C22⋊Dic269C2316yes—
57#16864379C2316yes—
58C4×Dic269C2313yes—
59C4×Dic269C2316yes—
60C4×Dic269C2316yes—
61C24×C269C2312yes—
62C2×Q8×C269C2313yes—
63C2×D4×C269C2313yes—
64C2×D4×C269C2316yes—
65C22⋊C4×C269C2316yes—
66C22⋊C4×C269C2316yes—
67C22⋊C4×C269C2316yes—
68C42×C269C2311yescharacteristic
69C42×C269C2312yes—
70C22×D269C2411yescharacteristic
71Dic538—46no—
72C22⋊D269—46no—
73C2×Dic269—46no—
74C2×Dic269—46no—
75C2×Dic269C2413yes—
76C2×Dic269C2416yes—
77C2×Dic269C2416yes—
78C4×D269—43no—
79C23×C269—46no—
80C23×C269C2416yes—
81Q8×C269—43no—
82D4×C269—43no—
83D4×C269—46no—
84C2×C4×C269C2416yes—
85C2×C4×C269C2413yes—
86C22×C269—26no—
87C22×C269—26no—
88C22×C269—26no—
89C22×C269—84no—
90C22×C269C2511yescharacteristic
91C2×D269—23no—
92C4×C269—23no—
93C4×C269—26no—
94Dic269—23no—
95Dic269—26no—
96Dic269—26no—
97C2×C269—46no—
98C2×C269#58513yes—
99D269—41no—
100C269#356811yescharacteristic, complemented, Sylow
101#3568—2691nomaximal, Sylow
102#563—2693no—
103H(3,𝔽4)D26911yescharacteristic, complemented
104#556—2696no—
105#551—2696no—
106#542—2696no—
107#538—2696no—
108#529—2693no—
109C4⋊Q8—2696no—
110#126—2696no—
111#126—2696no—
112#126—2696no—
113#126—2696no—
114#126—2692no—
115#125—2693no—
116#124—2696no—
117#124—2696no—
118#124C2×D26913yes—
119#124C2×D26916yes—
120#123—2696no—
121#123—2696no—
122#123—2696no—
123C22⋊Q8—2693no—
124C22⋊Q8—2696no—
125C22⋊Q8—2696no—
126C22⋊Q8—2696no—
127#121—2693no—
128#121—2696no—
129#120—2692no—
130#120C2×D26916yes—
131C4×Q8—2693no—
132C4×Q8—2696no—
133C4×D4—2693no—
134C4×D4—2696no—
135C4×D4—2696no—
136#117—2696no—
137#117—2696no—
138C2×C22⋊C4—2696no—
139C2×C42—2691no—
140C24C22×D26912yes—
141C2×Q8—2696no—
142C2×Q8C22×D26913yes—
143C2×D4—2696no—
144C2×D4C22×D26913yes—
145C2×D4C22×D26916yes—
146C22×C4—2696no—
147C22×C4—2696no—
148C22×C4—2693no—
149C4⋊C4—2696no—
150C4⋊C4—2696no—
151C4⋊C4—2696no—
152C4⋊C4—2696no—
153C4⋊C4—2693no—
154C4⋊C4—2696no—
155C4⋊C4—2693no—
156C4⋊C4—2696no—
157C22⋊C4—2696no—
158C22⋊C4—2696no—
159C22⋊C4—2696no—
160C22⋊C4—2696no—
161C22⋊C4—2696no—
162C22⋊C4—2696no—
163C22⋊C4C22×D26916yes—
164C22⋊C4C22×D26916yes—
165C22⋊C4C22×D26916yes—
166C42—2693no—
167C42—2696no—
168C42—2696no—
169C42C22×D26911yescharacteristic
170C42C22×D26912yes—
171C23—46no—
172C23—2691no—
173C23C23×D26916yes—
174Q8—43no—
175Q8—10766no—
176D4—43no—
177D4—46no—
178D4—10766no—
179C2×C4—2693no—
180C2×C4—2696no—
181C2×C4—2696no—
182C2×C4—10763no—
183C2×C4—10766no—
184C2×C4—10766no—
185C2×C4C23×D26916yes—
186C2×C4C23×D26913yes—
187C22—26no—
188C22—26no—
189C22—26no—
190C22—84no—
191C22—5383no—
192C22C24×D26911yescharacteristic
193C4—23no—
194C4—26no—
195C4—5383no—
196C4—5386no—
197C4—5386no—
198C2—46no—
199C2—10761no—
200C2#3177144013yes—
subgroupG/H
center, FrattiniC22C24×D269
commutator, socle, cosocleC22×C269C25
FittingH(3,𝔽4)×C269C2
hypercenterH(3,𝔽4)D269
hypocenterC269#3568
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #31771355C2semidirect
2. #31771324C2semidirect
3. #31771286C2semidirect
4. #31771219C2semidirect
5. #31771190C2semidirect
6. #31771134C2semidirect
7. H(3,𝔽4)×C269C2semidirect
8. #22575451C22semidirect
9. #22575447C22semidirect
10. #22575446C22semidirect
11. #22575446C22semidirect
12. #22575446C22semidirect
13. #22575446C22semidirect
14. #22575445C22semidirect
16. #22575439C22semidirect
17. #22575435C22semidirect
20. #22575430C22semidirect
21. #22575430C22semidirect
22. #22575430C22semidirect
23. #22575429C22semidirect
26. #22575422C22semidirect
27. Q8×Dic269C22semidirect
28. C4×Dic538C22semidirect
31. #22575413C22semidirect
32. #22575409C22semidirect
33. #22575409C22semidirect
34. C2×C22⋊Dic269C22semidirect
35. C42×D269C22semidirect
100. C269#3568semidirect
103. H(3,𝔽4)D269semidirect

Maximal subgroups

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

subgroupindex
#317713552
#317713242
#317712862
#317712192
#317711902
#317711342
H(3,𝔽4)×C2692
#3568269