Finite Group Databasebeta

← C2×#34036870 #49172903

Subgroups — C2×#34036870 #49172903

Order 37504.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 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#34036870C2116yesmaximal, direct product factor
2C2×#22627621C211yesmaximal, characteristic, complemented
3C2×#22627618C211yesmaximal, characteristic, complemented
4C2×#22627609C213yesmaximal, complemented
5C2×#22627599C213yesmaximal, complemented
6C2×#22627597C213yesmaximal, complemented
7C2×#22627594C213yesmaximal, complemented
8C2×#126×C293C211yesmaximal, characteristic, complemented
9C24×D293C2211yescharacteristic
10C22×D1172C2213yes—
11C22×D1172C2213yes—
12C22×D1172C2213yescomplemented
13C22×C22⋊D293C2213yes—
14C22×C4×D293C2213yescomplemented
15#22627621C2218yescomplemented
16#22627618C2218yescomplemented
17#22627609C22124yescomplemented
18#22627599C22124yescomplemented
19#22627597C22124yescomplemented
20#22627594C22124yescomplemented
21C2×#17989781C2213yescomplemented
22C2×#17989779C2213yes—
23C2×#17989779C2213yes—
24C2×#17989779C2213yescomplemented
25#126×C293C2218yescomplemented
26C2×C4⋊C4×C293C2213yescomplemented
27C2×C22⋊C4×C293C2213yes—
28C2×C42×C293C2211yescharacteristic, complemented
29C23×D293—46no—
30C23×D293C2313yes—
31C23×D293C2311yescharacteristic
32C23×D293C2311yescharacteristic
33C23×D293C2314yes—
34C2×D1172—46no—
35C2×D1172—46no—
36C2×D1172—46no—
37C2×D1172C23112yes—
38C2×D1172C23112yes—
39C2×D1172C23112yescomplemented
40C2×C22⋊D293—46no—
41C2×C22⋊D293C23112yes—
42C22×Dic293C2313yes—
43C2×C4×D293—46no—
44C2×C4×D293C23112yescomplemented
45#17989781C23112yescomplemented
46#17989779C23112yes—
47#17989779C23112yes—
48#17989779C23112yescomplemented
49C24×C293C2311yescharacteristic
50C22×C4×C293C2313yes—
51C22×C4×C293C2313yes—
52C4⋊C4×C293C23112yescomplemented
53C22⋊C4×C293C23112yes—
54C42×C293C2314yescomplemented
55C22×D293—26no—
56C22×D293—26no—
57C22×D293—26no—
58C22×D293—26no—
59C22×D293—26no—
60C22×D293—412no—
61C22×D293—416no—
62C22×D293C2412yes—
63C22×D293C2412yes—
64C22×D293C2416yes—
65D1172—412no—
66D1172—412no—
67D1172—412no—
68C22⋊D293—412no—
69C2×Dic293—26no—
70C2×Dic293C2416yes—
71C4×D293—412no—
72C23×C293—26no—
73C23×C293C2412yes—
74C23×C293C2411yescharacteristic
75C2×C4×C293—26no—
76C2×C4×C293—26no—
77C2×C4×C293C2416yes—
78C2×C4×C293C2416yes—
79C22×C293—26no—
80C22×C293—44no—
81C22×C293H(5,𝔽2)16yes—
82C22×C293C2511yescharacteristic
83C2×D293—26no—
84C2×D293—26no—
85C2×D293—26no—
86C2×D293—26no—
87C2×D293—26no—
88C2×D293—416no—
89C2×D293—412no—
90C2×D293—44no—
91C2×D293—44no—
92C4×C293—26no—
93C4×C293—26no—
94Dic293—26no—
95C2×C293—42no—
96C2×C293#56014yescomplemented
97C2×C293C2×H(5,𝔽2)13yes—
98D293—46no—
99D293—42no—
100D293—42no—
101C293C2×#56011yescharacteristic, complemented, Sylow
102C2×#560—2931nomaximal, Sylow
103#560—29316no—
104C2×#127—2931no—
105C2×#126—2931no—
106C2×#126D29311yescharacteristic, complemented
107C2×#123—2933no—
108C2×#121—2933no—
109C2×#121—2933no—
110C2×#120—2933no—
111C25—2931no—
112C22×D4—2933no—
113C22×D4—2933no—
114C22×D4—2933no—
115C22×D4—2933no—
116C23×C4—2933no—
117#127—2938no—
118#126—2938no—
119#126C2×D29318yescomplemented
120#123—29324no—
121#121—29324no—
122#121—29324no—
123#120—29324no—
124C2×C4⋊C4—2933no—
125C2×C4⋊C4C2×D29313yescomplemented
126C2×C22⋊C4—2933no—
127C2×C22⋊C4—2933no—
128C2×C22⋊C4—2933no—
129C2×C22⋊C4C2×D29313yes—
130C2×C42C2×D29311yescharacteristic, complemented
131C24—2931no—
132C24—2931no—
133C24—2933no—
134C24—2934no—
135C24—11726no—
136C24C22×D29311yescharacteristic
137C2×D4—29312no—
138C2×D4—29312no—
139C2×D4—29312no—
140C2×D4—29312no—
141C2×D4—11726no—
142C2×D4—11726no—
143C2×D4—11726no—
144C2×D4—11726no—
145C22×C4—2933no—
146C22×C4—29312no—
147C22×C4—11726no—
148C22×C4C22×D29313yes—
149C22×C4C22×D29313yes—
150C4⋊C4—29312no—
151C4⋊C4C22×D293112yescomplemented
152C22⋊C4—29312no—
153C22⋊C4—29312no—
154C22⋊C4—29312no—
155C22⋊C4C22×D293112yes—
156C42C22×D29314yescomplemented
157C23—26no—
158C23—2932no—
159C23—2932no—
160C23—2936no—
161C23—5866no—
162C23—5866no—
163C23—5866no—
164C23—5866no—
165C23—5866no—
166C23—117212no—
167C23—117216no—
168C23C23×D29312yes—
169C23C23×D29311yescharacteristic
170D4—117212no—
171D4—117212no—
172D4—117212no—
173D4—117212no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—2936no—
177C2×C4—5866no—
178C2×C4—117212no—
179C2×C4C23×D29316yes—
180C2×C4C23×D29316yes—
181C22—26no—
182C22—44no—
183C22—5866no—
184C22—5866no—
185C22—5866no—
186C22—5866no—
187C22—5866no—
188C22—117216no—
189C22—11724no—
190C22—11724no—
191C22—117212no—
192C22#2262767016yes—
193C22C24×D29311yescharacteristic
194C4—26no—
195C4—26no—
196C4—5866no—
197C2—42no—
198C2—11722no—
199C2—11722no—
200C2—11726no—
201C2#3403687014yesdirect product factor
202C2C2×#2262767013yes—
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×#126×C293C2
socleC23×C293C24
hypercenterC2×#126D293
hypocenterC293C2×#560
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #34036870C2direct (N × H)
2. C2×#22627621C2semidirect
3. C2×#22627618C2semidirect
4. C2×#22627609C2semidirect
5. C2×#22627599C2semidirect
6. C2×#22627597C2semidirect
7. C2×#22627594C2semidirect
8. C2×#126×C293C2semidirect
12. C22×D1172C22semidirect
14. C22×C4×D293C22semidirect
15. #22627621C22semidirect
16. #22627618C22semidirect
17. #22627609C22semidirect
18. #22627599C22semidirect
19. #22627597C22semidirect
20. #22627594C22semidirect
21. C2×#17989781C22semidirect
24. C2×#17989779C22semidirect
25. #126×C293C22semidirect
26. C2×C4⋊C4×C293C22semidirect
28. C2×C42×C293C22semidirect
39. C2×D1172C23semidirect
44. C2×C4×D293C23semidirect
45. #17989781C23semidirect
48. #17989779C23semidirect
52. C4⋊C4×C293C23semidirect
54. C42×C293C23semidirect
96. C2×C293#560semidirect
101. C293C2×#560semidirect
106. C2×#126D293semidirect
119. #126C2×D293semidirect
125. C2×C4⋊C4C2×D293semidirect
130. C2×C42C2×D293semidirect
151. C4⋊C4C22×D293semidirect
156. C42C22×D293semidirect
201. C2#34036870direct (N × H)

Maximal subgroups

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

subgroupindex
#340368702
C2×#226276212
C2×#226276182
C2×#226276092
C2×#226275992
C2×#226275972
C2×#226275942
C2×#126×C2932
C2×#560293