Finite Group Databasebeta

← C2×#23750367 #34058811

Subgroups — C2×#23750367 #34058811

Order 19072.

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#23750367C2116yesmaximal, direct product factor
2C2×#18011900C212yesmaximal, complemented
3C2×#18011899C212yesmaximal, complemented
4C2×#18011897C214yesmaximal, complemented
5C2×#18011881C214yesmaximal, complemented
6C2×#18011879C212yesmaximal, complemented
7C2×#124×C149C211yesmaximal, characteristic, complemented
8C24×D149C2212yescomplemented
9C22×Dic298C2212yescomplemented
10C22×D596C2212yes—
11C22×D596C2212yes—
12C22×C22⋊D149C2214yes—
13#18011900C22116yescomplemented
14#18011899C22116yescomplemented
15#18011897C22132yescomplemented
16#18011881C22132yescomplemented
17#18011879C22116yescomplemented
18C2×C22⋊Dic149C2212yescomplemented
19C2×#14558713C2214yescomplemented
20C2×#14558713C2214yescomplemented
21C2×#14558713C2214yescomplemented
22C2×C4×Dic149C2212yescomplemented
23C22×Q8×C149C2211yescharacteristic, complemented
24C22×D4×C149C2211yescharacteristic
25#124×C149C2218yescomplemented
26C2×C22⋊C4×C149C2214yescomplemented
27C2×C42×C149C2211yescharacteristic, complemented
28C23×D149—48no—
29C23×D149—44no—
30C23×D149C2314yes—
31C23×D149C2318yescomplemented
32C2×Dic298—44no—
33C2×Dic298C2318yescomplemented
34C2×D596—44no—
35C2×D596—44no—
36C2×D596C2318yes—
37C2×D596C2318yes—
38C2×C22⋊D149—48no—
39C2×C22⋊D149C23116yes—
40C22×Dic149C2314yes—
41C22⋊Dic149C2318yescomplemented
42#14558713C23116yescomplemented
43#14558713C23116yescomplemented
44#14558713C23116yescomplemented
45C4×Dic149C2318yescomplemented
46C24×C149C2312yes—
47C2×Q8×C149—42no—
48C2×Q8×C149C2314yescomplemented
49C2×D4×C149—42no—
50C2×D4×C149C2314yes—
51C22×C4×C149C2312yes—
52C22×C4×C149C2312yes—
53C22×C4×C149C2311yescharacteristic
54C22⋊C4×C149C23116yescomplemented
55C42×C149C2314yescomplemented
56C22×D149—28no—
57C22×D149—28no—
58C22×D149—28no—
59C22×D149—416no—
60C22×D149—48no—
61C22×D149—432no—
62C22×D149C2418yes—
63Dic298—48no—
64D596—48no—
65D596—48no—
66C22⋊D149—416no—
67C2×Dic149—28no—
68C2×Dic149C2418yes—
69C23×C149—28no—
70C23×C149—24no—
71C23×C149C2414yes—
72C23×C149C2411yescharacteristic
73Q8×C149—44no—
74D4×C149—44no—
75C2×C4×C149—24no—
76C2×C4×C149—24no—
77C2×C4×C149—22no—
78C2×C4×C149C2414yes—
79C2×C4×C149C2414yes—
80C2×C4×C149C2412yes—
81C22×C149—24no—
82C22×C149—28no—
83C22×C149—48no—
84C22×C149H(5,𝔽2)12yes—
85C22×C149H(5,𝔽2)14yes—
86C22×C149C2511yescharacteristic
87C2×D149—28no—
88C2×D149—28no—
89C2×D149—28no—
90C2×D149—432no—
91C2×D149—416no—
92C4×C149—22no—
93C4×C149—24no—
94C4×C149—24no—
95Dic149—28no—
96C2×C149—44no—
97C2×C149H(3,𝔽4)14yescomplemented
98C2×C149C2×H(5,𝔽2)11yescharacteristic
99C2×C149C2×H(5,𝔽2)12yes—
100D149—48no—
101C149C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C2×H(3,𝔽4)—1491nomaximal, Sylow
103H(3,𝔽4)—14916no—
104C2×#124—1492no—
105C2×#124—1494no—
106C2×#124—1492no—
107C2×#124D14911yescharacteristic, complemented
108C2×#120—1492no—
109C2×#120—1494no—
110C25—1492no—
111C22×Q8—1492no—
112C22×Q8C2×D14911yescharacteristic, complemented
113C22×D4—1494no—
114C22×D4—1492no—
115C22×D4—1492no—
116C22×D4C2×D14911yescharacteristic
117#124—14916no—
118#124—14932no—
119#124—14916no—
120#124C2×D14918yescomplemented
121#120—14916no—
122#120—14932no—
123C2×C22⋊C4—1492no—
124C2×C22⋊C4—1494no—
125C2×C22⋊C4—1494no—
126C2×C22⋊C4—1494no—
127C2×C22⋊C4C2×D14914yescomplemented
128C2×C42—1492no—
129C2×C42C2×D14911yescharacteristic, complemented
130C24—5964no—
131C24—5968no—
132C24—1494no—
133C24—1498no—
134C24C22×D14912yes—
135C2×Q8—42no—
136C2×Q8—5964no—
137C2×Q8—1498no—
138C2×Q8C22×D14914yescomplemented
139C2×D4—42no—
140C2×D4—5964no—
141C2×D4—5964no—
142C2×D4—5968no—
143C2×D4—14916no—
144C2×D4—1498no—
145C2×D4—1498no—
146C2×D4C22×D14914yes—
147C22×C4—1494no—
148C22×C4C22×D14912yes—
149C22×C4C22×D14911yescharacteristic
150C22×C4C22×D14912yes—
151C22⋊C4—1498no—
152C22⋊C4—14916no—
153C22⋊C4—14916no—
154C22⋊C4—14916no—
155C22⋊C4C22×D149116yescomplemented
156C42—1498no—
157C42C22×D14914yescomplemented
158C23—24no—
159C23—28no—
160C23—2988no—
161C23—2988no—
162C23—2988no—
163C23—5968no—
164C23—59616no—
165C23—59632no—
166C23—1498no—
167C23C23×D14914yes—
168C23C23×D14911yescharacteristic
169Q8—44no—
170Q8—5968no—
171D4—44no—
172D4—5968no—
173D4—5968no—
174D4—59616no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—2988no—
179C2×C4—1498no—
180C2×C4C23×D14914yes—
181C2×C4C23×D14912yes—
182C2×C4C23×D14914yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—2988no—
187C22—2988no—
188C22—2988no—
189C22—59632no—
190C22—59616no—
191C22#1801195612yes—
192C22#1801195714yes—
193C22C24×D14911yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—2988no—
198C2—44no—
199C2—5968no—
200C2#2375036714yesdirect product factor
201C2C2×#1801195611yescharacteristic
202C2C2×#1801195712yes—
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#124×C149C2
socleC23×C149C24
hypercenterC2×#124D149
hypocenterC149C2×H(3,𝔽4)
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #23750367C2direct (N × H)
2. C2×#18011900C2semidirect
3. C2×#18011899C2semidirect
4. C2×#18011897C2semidirect
5. C2×#18011881C2semidirect
6. C2×#18011879C2semidirect
7. C2×#124×C149C2semidirect
8. C24×D149C22semidirect
9. C22×Dic298C22semidirect
13. #18011900C22semidirect
14. #18011899C22semidirect
15. #18011897C22semidirect
16. #18011881C22semidirect
17. #18011879C22semidirect
18. C2×C22⋊Dic149C22semidirect
19. C2×#14558713C22semidirect
20. C2×#14558713C22semidirect
21. C2×#14558713C22semidirect
22. C2×C4×Dic149C22semidirect
23. C22×Q8×C149C22semidirect
25. #124×C149C22semidirect
26. C2×C22⋊C4×C149C22semidirect
27. C2×C42×C149C22semidirect
31. C23×D149C23semidirect
33. C2×Dic298C23semidirect
41. C22⋊Dic149C23semidirect
42. #14558713C23semidirect
43. #14558713C23semidirect
44. #14558713C23semidirect
45. C4×Dic149C23semidirect
48. C2×Q8×C149C23semidirect
54. C22⋊C4×C149C23semidirect
55. C42×C149C23semidirect
97. C2×C149H(3,𝔽4)semidirect
101. C149C2×H(3,𝔽4)semidirect
107. C2×#124D149semidirect
112. C22×Q8C2×D149semidirect
120. #124C2×D149semidirect
127. C2×C22⋊C4C2×D149semidirect
129. C2×C42C2×D149semidirect
138. C2×Q8C22×D149semidirect
155. C22⋊C4C22×D149semidirect
157. C42C22×D149semidirect
200. C2#23750367direct (N × H)

Maximal subgroups

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

subgroupindex
#237503672
C2×#180119002
C2×#180118992
C2×#180118972
C2×#180118812
C2×#180118792
C2×#124×C1492
C2×H(3,𝔽4)149