Finite Group Databasebeta

← #34052763

Subgroups — #34052763

Order 19072.

456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#18011905C211yesmaximal, characteristic, complemented
2#23749558C213yesmaximal, complemented
3#23749548C213yesmaximal, complemented
4#23749547C213yesmaximal, complemented
5#23749541C213yesmaximal
6#23749495C211yesmaximal, characteristic, complemented
7C2×#126×C149C211yesmaximal, characteristic, complemented
8C22×C22⋊D149C2211yescharacteristic
9#18011905—24no—
10C2×C4⋊Dic149C2213yes—
11C2×C4⋊Dic149C2213yes—
12C2×#14558715C2213yes—
13C2×#14558715C2213yes—
14C2×C22⋊Dic149C2213yes—
15C2×#14558713C2213yes—
16C2×#14558713C2213yes—
17#18011818C2213yes—
18#18011818C2213yes—
19#126×C149—24no—
20C2×C4⋊C4×C149C2213yes—
21C2×C22⋊C4×C149C2213yes—
22C2×C42×C149C2211yescharacteristic
23C23×D149C2311yescharacteristic
24C2×C22⋊D149—43no—
25C22×Dic149C2311yescharacteristic
26C22×Dic149C2313yes—
27C22×Dic149C2313yes—
28C4⋊Dic149—43no—
29C4⋊Dic149—43no—
30#14558715—26no—
31#14558715—43no—
32C22⋊Dic149—43no—
33#14558713—26no—
34#14558713—43no—
35C24×C149C2311yescharacteristic
36C22×C4×C149C2313yes—
37C22×C4×C149C2313yes—
38C4⋊C4×C149—26no—
39C22⋊C4×C149—26no—
40C42×C149D414yescomplemented
41C22×D149—21no—
42C22×D149—23no—
43C22×D149—23no—
44C22⋊D149—44no—
45C2×Dic149—23no—
46C2×Dic149—23no—
47C2×Dic149—23no—
48C2×Dic149—23no—
49C2×Dic149—23no—
50C2×Dic149—23no—
51C2×Dic149—23no—
52C23×C149—21no—
53C23×C149—23no—
54C23×C149—23no—
55C23×C149C2411yescharacteristic
56C2×C4×C149—23no—
57C2×C4×C149—23no—
58C2×C4×C149—23no—
59C2×C4×C149—23no—
60C2×C4×C149—23no—
61C2×C4×C149C2×D416yes—
62C22×C149—43no—
63C22×C149—41no—
64C22×C149—43no—
65C22×C149C22×D411yescharacteristic
66C22×C149H(5,𝔽2)13yes—
67C22×C1492−1+413yes—
68C2×D149—43no—
69C2×D149—41no—
70C2×D149—43no—
71C4×C149—26no—
72C4×C149—43no—
73Dic149—43no—
74Dic149—43no—
75Dic149—41no—
76C2×C149—81no—
77C2×C149#53713yes—
78C2×C149#56011yescharacteristic
79C2×C149#56313yes—
80D149—81no—
81C149#282311yescharacteristic, complemented, Sylow
82#2823—1491nomaximal, Sylow
83C2×#126—1491no—
84C2×#126D14911yescharacteristic, complemented
85#398—1493no—
86#396—1493no—
87#396—1493no—
88#394—1493no—
89#384—1491no—
90C22×D4—1491no—
91#126—24no—
92#126—2984no—
93C2×C4⋊C4—1493no—
94C2×C4⋊C4—1493no—
95C2×C4⋊C4—1493no—
96C2×C4⋊C4—1493no—
97C2×C4⋊C4C2×D14913yes—
98C2×C22⋊C4—1493no—
99C2×C22⋊C4—1493no—
100C2×C22⋊C4—1493no—
101C2×C22⋊C4C2×D14913yes—
102C2×C42C2×D14911yescharacteristic
103#95—1493no—
104#95—1493no—
105C24—1491no—
106C24C22×D14911yescharacteristic
107C2×D4—5963no—
108C22×C4—1491no—
109C22×C4—1493no—
110C22×C4—1493no—
111C22×C4C22×D14913yes—
112C22×C4C22×D14913yes—
113C4⋊C4—26no—
114C4⋊C4—2986no—
115C4⋊C4—5963no—
116C4⋊C4—5963no—
117C4⋊C4—5963no—
118C22⋊C4—26no—
119C22⋊C4—2986no—
120C22⋊C4—5963no—
121C22⋊C4—5963no—
122C42C22⋊D14914yescomplemented
123C23—21no—
124C23—23no—
125C23—23no—
126C23—2981no—
127C23—2983no—
128C23—2983no—
129C23C23×D14911yescharacteristic
130D4—5964no—
131C2×C4—23no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—23no—
135C2×C4—23no—
136C2×C4—2983no—
137C2×C4—2983no—
138C2×C4—2983no—
139C2×C4—2983no—
140C2×C4—2983no—
141C2×C4—2983no—
142C2×C4—2983no—
143C2×C4C2×C22⋊D14916yes—
144C22—43no—
145C22—41no—
146C22—43no—
147C22—5963no—
148C22—5961no—
149C22—5963no—
150C22C22×C22⋊D14911yescharacteristic
151C22#1801195713yes—
152C22#1801195813yes—
153C4—26no—
154C4—43no—
155C4—5963no—
156C4—5961no—
157C4—5963no—
158C2—81no—
159C2—11921no—
160C2#2375020313yes—
161C2#2375036611yescharacteristic
162C2#2375037713yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
FittingC2×#126×C149C2
prime radicalC22×C22⋊D149C22
hypercenterC2×#126D149
hypocenterC149#2823
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#18011905C2semidirect
2. #23749558C2semidirect
3. #23749548C2semidirect
4. #23749547C2semidirect
6. #23749495C2semidirect
7. C2×#126×C149C2semidirect
40. C42×C149D4semidirect
81. C149#2823semidirect
84. C2×#126D149semidirect
122. C42C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119052
#237495582
#237495482
#237495472
#237495412
#237494952
C2×#126×C1492
#2823149