Finite Group Databasebeta

← C2×#34036871 #49172905

Subgroups — C2×#34036871 #49172905

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#34036871C2116yesmaximal, direct product factor
2C2×#22627613C212yesmaximal, complemented
3C2×#22627612C212yesmaximal, complemented
4C2×#22627610C214yesmaximal, complemented
5C2×#22627594C214yesmaximal, complemented
6C2×#22627592C212yesmaximal, complemented
7C2×#124×C293C211yesmaximal, characteristic, complemented
8C24×D293C2212yescomplemented
9C22×Dic586C2212yescomplemented
10C22×D1172C2212yes—
11C22×D1172C2212yes—
12C22×C22⋊D293C2214yes—
13#22627613C22116yescomplemented
14#22627612C22116yescomplemented
15#22627610C22132yescomplemented
16#22627594C22132yescomplemented
17#22627592C22116yescomplemented
18C2×C22⋊Dic293C2212yescomplemented
19C2×#17989779C2214yescomplemented
20C2×#17989779C2214yescomplemented
21C2×#17989779C2214yescomplemented
22C2×C4×Dic293C2212yescomplemented
23C22×Q8×C293C2211yescharacteristic, complemented
24C22×D4×C293C2211yescharacteristic
25#124×C293C2218yescomplemented
26C2×C22⋊C4×C293C2214yescomplemented
27C2×C42×C293C2211yescharacteristic, complemented
28C23×D293—44no—
29C23×D293—48no—
30C23×D293C2314yes—
31C23×D293C2318yescomplemented
32C2×Dic586—44no—
33C2×Dic586C2318yescomplemented
34C2×D1172—44no—
35C2×D1172—44no—
36C2×D1172C2318yes—
37C2×D1172C2318yes—
38C2×C22⋊D293—48no—
39C2×C22⋊D293C23116yes—
40C22×Dic293C2314yes—
41C22⋊Dic293C2318yescomplemented
42#17989779C23116yescomplemented
43#17989779C23116yescomplemented
44#17989779C23116yescomplemented
45C4×Dic293C2318yescomplemented
46C24×C293C2312yes—
47C2×Q8×C293—42no—
48C2×Q8×C293C2314yescomplemented
49C2×D4×C293—42no—
50C2×D4×C293C2314yes—
51C22×C4×C293C2312yes—
52C22×C4×C293C2312yes—
53C22×C4×C293C2311yescharacteristic
54C22⋊C4×C293C23116yescomplemented
55C42×C293C2314yescomplemented
56C22×D293—28no—
57C22×D293—28no—
58C22×D293—28no—
59C22×D293—416no—
60C22×D293—48no—
61C22×D293—432no—
62C22×D293C2418yes—
63Dic586—48no—
64D1172—48no—
65D1172—48no—
66C22⋊D293—416no—
67C2×Dic293—28no—
68C2×Dic293C2418yes—
69C23×C293—24no—
70C23×C293—28no—
71C23×C293C2414yes—
72C23×C293C2411yescharacteristic
73Q8×C293—44no—
74D4×C293—44no—
75C2×C4×C293—22no—
76C2×C4×C293—24no—
77C2×C4×C293—24no—
78C2×C4×C293C2414yes—
79C2×C4×C293C2412yes—
80C2×C4×C293C2414yes—
81C22×C293—24no—
82C22×C293—28no—
83C22×C293—48no—
84C22×C293H(5,𝔽2)12yes—
85C22×C293H(5,𝔽2)14yes—
86C22×C293C2511yescharacteristic
87C2×D293—28no—
88C2×D293—28no—
89C2×D293—28no—
90C2×D293—432no—
91C2×D293—416no—
92C4×C293—22no—
93C4×C293—24no—
94C4×C293—24no—
95Dic293—28no—
96C2×C293—44no—
97C2×C293H(3,𝔽4)14yescomplemented
98C2×C293C2×H(5,𝔽2)11yescharacteristic
99C2×C293C2×H(5,𝔽2)12yes—
100D293—48no—
101C293C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C2×H(3,𝔽4)—2931nomaximal, Sylow
103H(3,𝔽4)—29316no—
104C2×#124—2932no—
105C2×#124—2934no—
106C2×#124—2932no—
107C2×#124D29311yescharacteristic, complemented
108C2×#120—2932no—
109C2×#120—2934no—
110C25—2932no—
111C22×Q8—2932no—
112C22×Q8C2×D29311yescharacteristic, complemented
113C22×D4—2934no—
114C22×D4—2932no—
115C22×D4—2932no—
116C22×D4C2×D29311yescharacteristic
117#124—29316no—
118#124—29332no—
119#124—29316no—
120#124C2×D29318yescomplemented
121#120—29316no—
122#120—29332no—
123C2×C22⋊C4—2932no—
124C2×C22⋊C4—2934no—
125C2×C22⋊C4—2934no—
126C2×C22⋊C4—2934no—
127C2×C22⋊C4C2×D29314yescomplemented
128C2×C42—2932no—
129C2×C42C2×D29311yescharacteristic, complemented
130C24—2934no—
131C24—2938no—
132C24—11724no—
133C24—11728no—
134C24C22×D29312yes—
135C2×Q8—42no—
136C2×Q8—2938no—
137C2×Q8—11724no—
138C2×Q8C22×D29314yescomplemented
139C2×D4—42no—
140C2×D4—29316no—
141C2×D4—2938no—
142C2×D4—2938no—
143C2×D4—11724no—
144C2×D4—11724no—
145C2×D4—11728no—
146C2×D4C22×D29314yes—
147C22×C4—2934no—
148C22×C4C22×D29312yes—
149C22×C4C22×D29311yescharacteristic
150C22×C4C22×D29312yes—
151C22⋊C4—2938no—
152C22⋊C4—29316no—
153C22⋊C4—29316no—
154C22⋊C4—29316no—
155C22⋊C4C22×D293116yescomplemented
156C42—2938no—
157C42C22×D29314yescomplemented
158C23—24no—
159C23—28no—
160C23—2938no—
161C23—5868no—
162C23—5868no—
163C23—5868no—
164C23—11728no—
165C23—117216no—
166C23—117232no—
167C23C23×D29314yes—
168C23C23×D29311yescharacteristic
169Q8—44no—
170Q8—11728no—
171D4—44no—
172D4—11728no—
173D4—11728no—
174D4—117216no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—2938no—
179C2×C4—5868no—
180C2×C4C23×D29314yes—
181C2×C4C23×D29312yes—
182C2×C4C23×D29314yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—5868no—
187C22—5868no—
188C22—5868no—
189C22—117232no—
190C22—117216no—
191C22#2262766912yes—
192C22#2262767014yes—
193C22C24×D29311yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—5868no—
198C2—44no—
199C2—11728no—
200C2#3403687114yesdirect product factor
201C2C2×#2262766911yescharacteristic
202C2C2×#2262767012yes—
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×#124×C293C2
socleC23×C293C24
hypercenterC2×#124D293
hypocenterC293C2×H(3,𝔽4)
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #34036871C2direct (N × H)
2. C2×#22627613C2semidirect
3. C2×#22627612C2semidirect
4. C2×#22627610C2semidirect
5. C2×#22627594C2semidirect
6. C2×#22627592C2semidirect
7. C2×#124×C293C2semidirect
8. C24×D293C22semidirect
9. C22×Dic586C22semidirect
13. #22627613C22semidirect
14. #22627612C22semidirect
15. #22627610C22semidirect
16. #22627594C22semidirect
17. #22627592C22semidirect
18. C2×C22⋊Dic293C22semidirect
19. C2×#17989779C22semidirect
20. C2×#17989779C22semidirect
21. C2×#17989779C22semidirect
22. C2×C4×Dic293C22semidirect
23. C22×Q8×C293C22semidirect
25. #124×C293C22semidirect
26. C2×C22⋊C4×C293C22semidirect
27. C2×C42×C293C22semidirect
31. C23×D293C23semidirect
33. C2×Dic586C23semidirect
41. C22⋊Dic293C23semidirect
42. #17989779C23semidirect
43. #17989779C23semidirect
44. #17989779C23semidirect
45. C4×Dic293C23semidirect
48. C2×Q8×C293C23semidirect
54. C22⋊C4×C293C23semidirect
55. C42×C293C23semidirect
97. C2×C293H(3,𝔽4)semidirect
101. C293C2×H(3,𝔽4)semidirect
107. C2×#124D293semidirect
112. C22×Q8C2×D293semidirect
120. #124C2×D293semidirect
127. C2×C22⋊C4C2×D293semidirect
129. C2×C42C2×D293semidirect
138. C2×Q8C22×D293semidirect
155. C22⋊C4C22×D293semidirect
157. C42C22×D293semidirect
200. C2#34036871direct (N × H)

Maximal subgroups

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

subgroupindex
#340368712
C2×#226276132
C2×#226276122
C2×#226276102
C2×#226275942
C2×#226275922
C2×#124×C2932
C2×H(3,𝔽4)293