Finite Group Databasebeta

← C2×#23750236 #34058058

Subgroups — C2×#23750236 #34058058

Order 19072.

1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.

normal subgroups only

This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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#23750236C2116yesmaximal, direct product factor
2C2×#18011906C214yesmaximal
3C2×#18011903C211yesmaximal, characteristic, complemented
4C2×#18011901C214yesmaximal, complemented
5C2×#18011887C212yesmaximal
6C2×Q8×Dic149C212yesmaximal, complemented
7C2×#18011868C211yesmaximal, characteristic
8C2×C4⋊Q8×C149C211yesmaximal, characteristic, complemented
9C22×C4×D149C2211yescharacteristic
10#18011906C22132yes—
11#18011903C2218yescomplemented
12#18011901C22132yescomplemented
13#18011887C22116yes—
14Q8×Dic149C22116yescomplemented
15#18011868C2218yes—
16C2×C4⋊Dic149C2214yes—
17C2×C4⋊Dic149C2212yes—
18C2×#14558715C2212yes—
19C2×#14558715C2214yes—
20C2×#14558715C2214yes—
21C2×#14558713C2212yes—
22C2×#14558713C2214yes—
23C2×C4×Dic149C2214yes—
24C2×C4×Dic149C2211yescharacteristic
25C22×Q8×C149C2212yes—
26C4⋊Q8×C149C2218yescomplemented
27C2×C4⋊C4×C149C2214yes—
28C2×C42×C149C2211yescharacteristic
29C23×D149C2311yescharacteristic
30C22×Dic149C2311yescharacteristic
31C22×Dic149C2312yes—
32C22×Dic149C2314yes—
33C2×C4×D149—24no—
34C2×C4×D149C2314yes—
35C4⋊Dic149C23116yes—
36C4⋊Dic149C2318yes—
37#14558715C23116yes—
38#14558715C2318yes—
39#14558715C23116yes—
40#14558713C2318yes—
41#14558713C23116yes—
42C4×Dic149C23116yes—
43C4×Dic149C2314yes—
44C2×Q8×C149—28no—
45C2×Q8×C149C2318yes—
46C22×C4×C149C2312yes—
47C22×C4×C149C2314yes—
48C22×C4×C149C2311yescharacteristic
49C4⋊C4×C149C23116yes—
50C42×C149C2314yes—
51C22×D149—22no—
52C22×D149—24no—
53C22×D149C2412yes—
54C2×Dic149—22no—
55C2×Dic149—24no—
56C2×Dic149—28no—
57C2×Dic149C2412yes—
58C2×Dic149C2414yes—
59C2×Dic149C2418yes—
60C4×D149—28no—
61C23×C149C2411yescharacteristic
62Q8×C149—216no—
63C2×C4×C149—28no—
64C2×C4×C149—24no—
65C2×C4×C149#4114yes—
66C2×C4×C149C2414yes—
67C2×C4×C149C2418yes—
68C2×C4×C149C2412yes—
69C22×C149C2×#4112yes—
70C22×C1492−1+414yes—
71C22×C149C2511yescharacteristic
72C2×D149—22no—
73C2×D149—24no—
74C2×D149—44no—
75C4×C149—28no—
76C4×C149—24no—
77C4×C149C2×#4114yes—
78Dic149—22no—
79Dic149—24no—
80Dic149—28no—
81C2×C149#54114yescomplemented
82C2×C149C22×#4111yescharacteristic
83C2×C149C2×2−1+412yes—
84D149—42no—
85C149C2×#54111yescharacteristic, complemented, Sylow
86C2×#541—1491nomaximal, Sylow
87#541—14916no—
88C2×C4⋊Q8D14911yescharacteristic, complemented
89C2×#126—1494no—
90C2×#125—1494no—
91C2×#125—1491no—
92C2×C22⋊Q8—1492no—
93C2×C4×Q8—1492no—
94C2×#117—1491no—
95C22×Q8C2×D14912yes—
96C23×C4—1491no—
97C4⋊Q8C2×D14918yescomplemented
98#126—14932no—
99#125—14932no—
100#125—1498no—
101C22⋊Q8—14916no—
102C4×Q8—14916no—
103#117—1498no—
104C2×C4⋊C4—1492no—
105C2×C4⋊C4—1492no—
106C2×C4⋊C4—1494no—
107C2×C4⋊C4—1494no—
108C2×C4⋊C4—1494no—
109C2×C4⋊C4C2×D14914yes—
110C2×C22⋊C4—1492no—
111C2×C22⋊C4—1494no—
112C2×C42—1491no—
113C2×C42—1494no—
114C2×C42C2×D14911yescharacteristic
115C24—1491no—
116C2×Q8—28no—
117C2×Q8C22×D14918yes—
118C22×C4—2984no—
119C22×C4—1492no—
120C22×C4—1494no—
121C22×C4—1491no—
122C22×C4—1494no—
123C22×C4C22×D14914yes—
124C22×C4C22×D14912yes—
125C22×C4C22×D14911yescharacteristic
126C4⋊C4—1498no—
127C4⋊C4—1498no—
128C4⋊C4—14916no—
129C4⋊C4—14916no—
130C4⋊C4—14916no—
131C4⋊C4C22×D149116yes—
132C22⋊C4—1498no—
133C22⋊C4—14916no—
134C42—1494no—
135C42—14916no—
136C42C22×D14914yes—
137C23—2982no—
138C23—2984no—
139C23—1492no—
140C23C23×D14911yescharacteristic
141Q8—216no—
142C2×C4—28no—
143C2×C4—24no—
144C2×C4—2982no—
145C2×C4—2984no—
146C2×C4—2988no—
147C2×C4—2988no—
148C2×C4—1494no—
149C2×C4—1498no—
150C2×C4—1492no—
151C2×C4#1455873514yes—
152C2×C4C23×D14918yes—
153C2×C4C23×D14914yes—
154C2×C4C23×D14912yes—
155C22—2982no—
156C22—2984no—
157C22—5964no—
158C22C2×#1455873512yes—
159C22#1801195914yes—
160C22C24×D14911yescharacteristic
161C4—28no—
162C4—24no—
163C4—2982no—
164C4—2984no—
165C4—2988no—
166C4C2×#1455873514yes—
167C2—5962no—
168C2#2375023614yesdirect product factor
169C2C22×#1455873511yescharacteristic
170C2C2×#1801195912yes—
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×C4⋊Q8×C149C2
socleC23×C149C24
prime radicalC23×D149C23
hypercenterC2×C4⋊Q8D149
hypocenterC149C2×#541
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23750236C2direct (N × H)
3. C2×#18011903C2semidirect
4. C2×#18011901C2semidirect
6. C2×Q8×Dic149C2semidirect
8. C2×C4⋊Q8×C149C2semidirect
11. #18011903C22semidirect
12. #18011901C22semidirect
14. Q8×Dic149C22semidirect
26. C4⋊Q8×C149C22semidirect
81. C2×C149#541semidirect
85. C149C2×#541semidirect
88. C2×C4⋊Q8D149semidirect
97. C4⋊Q8C2×D149semidirect
168. C2#23750236direct (N × H)

Maximal subgroups

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

subgroupindex
#237502362
C2×#180119062
C2×#180119032
C2×#180119012
C2×#180118872
C2×Q8×Dic1492
C2×#180118682
C2×C4⋊Q8×C1492
C2×#541149