Finite Group Databasebeta

← C2×#34036872 #49172906

Subgroups — C2×#34036872 #49172906

Order 37504.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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#34036872C2116yesmaximal, direct product factor
2C2×#22627611C213yesmaximal, complemented
3C2×#22627610C216yesmaximal, complemented
4C2×#22627593C212yesmaximal, complemented
5C2×#22627592C213yesmaximal, complemented
6C2×#120×C293C211yesmaximal, characteristic, complemented
7C24×D293C2211yescharacteristic, complemented
8C22×Dic586C2213yescomplemented
9C22×C22⋊D293C2216yes—
10#22627611C22124yescomplemented
11#22627610C22148yescomplemented
12#22627593C22116yescomplemented
13#22627592C22124yescomplemented
14C2×C22⋊Dic293C2213yescomplemented
15C2×C22⋊Dic293C2216yescomplemented
16C2×#17989779C2216yescomplemented
17C2×C4×Dic293C2213yescomplemented
18C25×C293C2211yescharacteristic, complemented
19C22×D4×C293C2213yes—
20#120×C293C2218yescomplemented
21C2×C22⋊C4×C293C2213yescomplemented
22C23×D293—46no—
23C23×D293C2312yes—
24C23×D293C2314yescomplemented
25C2×Dic586—46no—
26C2×Dic586C23112yescomplemented
27C2×C22⋊D293—412no—
28C2×C22⋊D293C23124yes—
29C22×Dic293C2316yes—
30C22⋊Dic293C23112yescomplemented
31C22⋊Dic293C23124yescomplemented
32#17989779C23124yescomplemented
33C4×Dic293C23112yescomplemented
34C24×C293—46no—
35C24×C293C2313yes—
36C24×C293C2311yescharacteristic
37C24×C293C2314yescomplemented
38C2×D4×C293—46no—
39C2×D4×C293C23112yes—
40C22×C4×C293C2313yes—
41C22⋊C4×C293C23112yescomplemented
42C22×D293—212no—
43C22×D293—412no—
44C22×D293—416no—
45C22×D293C2414yes—
46Dic586—412no—
47C22⋊D293—424no—
48C2×Dic293—212no—
49C2×Dic293C24112yes—
50C23×C293—26no—
51C23×C293—26no—
52C23×C293—212no—
53C23×C293—412no—
54C23×C293—416no—
55C23×C293C2416yes—
56C23×C293C2412yes—
57C23×C293C2411yescharacteristic
58D4×C293—412no—
59C2×C4×C293—26no—
60C2×C4×C293C2416yes—
61C22×C293—26no—
62C22×C293—26no—
63C22×C293—212no—
64C22×C293—416no—
65C22×C293—412no—
66C22×C293—44no—
67C22×C293H(5,𝔽2)16yes—
68C22×C293C2511yescharacteristic
69C2×D293—212no—
70C2×D293—416no—
71C2×D293—48no—
72C4×C293—26no—
73Dic293—212no—
74C2×C293—42no—
75C2×C293—46no—
76C2×C293H(3,𝔽4)14yescomplemented
77C2×C293C2×H(5,𝔽2)13yes—
78D293—44no—
79C293C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—2931nomaximal, Sylow
81H(3,𝔽4)—29316no—
82C2×#124—2933no—
83C2×#124—2936no—
84C2×#120—2932no—
85C2×#120—2933no—
86C2×#120D29311yescharacteristic, complemented
87C25—2931no—
88C25C2×D29311yescharacteristic, complemented
89C22×Q8—2933no—
90C22×D4—2936no—
91C22×D4C2×D29313yes—
92#124—29324no—
93#124—29348no—
94#120—29316no—
95#120—29324no—
96#120C2×D29318yescomplemented
97C2×C22⋊C4—2933no—
98C2×C22⋊C4—2936no—
99C2×C22⋊C4—2936no—
100C2×C22⋊C4C2×D29313yescomplemented
101C2×C42—2933no—
102C24—46no—
103C24—2932no—
104C24—2934no—
105C24—11726no—
106C24C22×D29311yescharacteristic
107C24C22×D29313yes—
108C24C22×D29314yescomplemented
109C2×Q8—29312no—
110C2×Q8—11726no—
111C2×D4—46no—
112C2×D4—29324no—
113C2×D4—117212no—
114C2×D4C22×D293112yes—
115C22×C4—2936no—
116C22×C4C22×D29313yes—
117C22⋊C4—29312no—
118C22⋊C4—29324no—
119C22⋊C4—29324no—
120C22⋊C4C22×D293112yescomplemented
121C42—29312no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—2934no—
128C23—58612no—
129C23—117212no—
130C23—117216no—
131C23C23×D29312yes—
132C23C23×D29316yes—
133C23C23×D29311yescharacteristic
134Q8—117212no—
135D4—412no—
136D4—117224no—
137C2×C4—26no—
138C2×C4—29312no—
139C2×C4—58612no—
140C2×C4C23×D29316yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—58612no—
148C22—117216no—
149C22—11728no—
150C22#2262766916yes—
151C22C24×D29311yescharacteristic
152C4—26no—
153C4—58612no—
154C2—46no—
155C2—42no—
156C2—11724no—
157C2#3403687214yesdirect product factor
158C2C2×#2262766913yes—
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×#120×C293C2
socleC23×C293C24
hypercenterC2×#120D293
hypocenterC293C2×H(3,𝔽4)
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #34036872C2direct (N × H)
2. C2×#22627611C2semidirect
3. C2×#22627610C2semidirect
4. C2×#22627593C2semidirect
5. C2×#22627592C2semidirect
6. C2×#120×C293C2semidirect
7. C24×D293C22semidirect
8. C22×Dic586C22semidirect
10. #22627611C22semidirect
11. #22627610C22semidirect
12. #22627593C22semidirect
13. #22627592C22semidirect
14. C2×C22⋊Dic293C22semidirect
15. C2×C22⋊Dic293C22semidirect
16. C2×#17989779C22semidirect
17. C2×C4×Dic293C22semidirect
18. C25×C293C22semidirect
20. #120×C293C22semidirect
21. C2×C22⋊C4×C293C22semidirect
24. C23×D293C23semidirect
26. C2×Dic586C23semidirect
30. C22⋊Dic293C23semidirect
31. C22⋊Dic293C23semidirect
32. #17989779C23semidirect
33. C4×Dic293C23semidirect
37. C24×C293C23semidirect
41. C22⋊C4×C293C23semidirect
76. C2×C293H(3,𝔽4)semidirect
79. C293C2×H(3,𝔽4)semidirect
86. C2×#120D293semidirect
88. C25C2×D293semidirect
96. #120C2×D293semidirect
100. C2×C22⋊C4C2×D293semidirect
108. C24C22×D293semidirect
120. C22⋊C4C22×D293semidirect
157. C2#34036872direct (N × H)

Maximal subgroups

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

subgroupindex
#340368722
C2×#226276112
C2×#226276102
C2×#226275932
C2×#226275922
C2×#120×C2932
C2×H(3,𝔽4)293