Finite Group Databasebeta

← #34052758

Subgroups — #34052758

Order 19072.

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

normal subgroups only

This group has 380 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×#18011903C211yesmaximal, characteristic
2#23749564C212yesmaximal
3#23749563C212yesmaximal
4#23749558C214yesmaximal
5#23749556C212yesmaximal
6#23749555C212yesmaximal
7#23749491C211yesmaximal, characteristic
8C2×#125×C149C211yesmaximal, characteristic
9#18011903—24no—
10C2×C4⋊Dic149C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12C2×C4⋊Dic149C2212yes—
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2214yes—
16#18011818C2212yes—
17#18011818C2212yes—
18#18011818C2214yes—
19#18011818C2214yes—
20#18011818C2214yes—
21#125×C149—24no—
22C2×C4⋊C4×C149C2212yes—
23C2×C4⋊C4×C149C2211yescharacteristic
24C2×C4⋊C4×C149C2212yes—
25C2×C4⋊C4×C149C2211yescharacteristic
26C2×C42×C149C2211yescharacteristic
27C22×Dic149C2314yes—
28C22×Dic149C2312yes—
29C22×Dic149C2312yes—
30C4⋊Dic149—22no—
31C4⋊Dic149—22no—
32C4⋊Dic149—42no—
33#14558715—24no—
34#14558715—24no—
35#14558715—44no—
36C22×C4×C149C2312yes—
37C22×C4×C149C2312yes—
38C22×C4×C149C2311yescharacteristic
39C22×C4×C149C2311yescharacteristic
40C22×C4×C149C2311yescharacteristic
41C4⋊C4×C149—22no—
42C4⋊C4×C149—24no—
43C4⋊C4×C149—22no—
44C4⋊C4×C149—24no—
45C42×C149D414yes—
46C2×Dic149—22no—
47C2×Dic149—22no—
48C2×Dic149—22no—
49C2×Dic149—24no—
50C2×Dic149—22no—
51C2×Dic149—24no—
52C2×Dic149—24no—
53C2×Dic149—24no—
54C23×C149C2411yescharacteristic
55C2×C4×C149—21no—
56C2×C4×C149—22no—
57C2×C4×C149—21no—
58C2×C4×C149—22no—
59C2×C4×C149—22no—
60C2×C4×C149—22no—
61C2×C4×C149—22no—
62C2×C4×C149—24no—
63C2×C4×C149—22no—
64C2×C4×C149C2×D412yes—
65C2×C4×C149C2×D412yes—
66C2×C4×C149C2×D412yes—
67C22×C149C22×D411yescharacteristic
68C22×C149H(5,𝔽2)11yescharacteristic
69C22×C1492−1+412yes—
70C22×C1492−1+411yescharacteristic
71C22×C1492−1+412yes—
72C4×C149—22no—
73C4×C149—22no—
74C4×C149—22no—
75C4×C149—42no—
76C4×C149—42no—
77Dic149—42no—
78Dic149—42no—
79Dic149—44no—
80C2×C149#53611yescharacteristic
81C2×C149#53611yescharacteristic
82C2×C149#53711yescharacteristic
83C2×C149#56312yes—
84C2×C149#56412yes—
85C149#282211yescharacteristic, complemented, Sylow
86#2822—1491nomaximal, Sylow
87C2×#125—1491no—
88C2×#125D14911yescharacteristic
89#400—1492no—
90#400—1492no—
91#398—1492no—
92#398—1492no—
93#398—1494no—
94#382—1491no—
95#125—24no—
96#125—2984no—
97C2×C4⋊C4—1492no—
98C2×C4⋊C4—1491no—
99C2×C4⋊C4—1492no—
100C2×C4⋊C4—1491no—
101C2×C4⋊C4—1492no—
102C2×C4⋊C4—1494no—
103C2×C4⋊C4C2×D14912yes—
104C2×C4⋊C4C2×D14911yescharacteristic
105C2×C4⋊C4C2×D14912yes—
106C2×C4⋊C4C2×D14911yescharacteristic
107C2×C42C2×D14911yescharacteristic
108#95—1492no—
109#95—1492no—
110#95—1494no—
111#95—1494no—
112#95—1494no—
113C22×C4—1494no—
114C22×C4—1492no—
115C22×C4—1492no—
116C22×C4C22×D14912yes—
117C22×C4C22×D14912yes—
118C22×C4C22×D14911yescharacteristic
119C22×C4C22×D14911yescharacteristic
120C22×C4C22×D14911yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—2984no—
126C4⋊C4—2984no—
127C4⋊C4—2982no—
128C4⋊C4—2982no—
129C4⋊C4—5964no—
130C4⋊C4—5962no—
131C42C22⋊D14914yes—
132C23C23×D14911yescharacteristic
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—22no—
142C2×C4—2982no—
143C2×C4—2982no—
144C2×C4—2982no—
145C2×C4—2984no—
146C2×C4—2982no—
147C2×C4—2984no—
148C2×C4—2984no—
149C2×C4—2984no—
150C2×C4C2×C22⋊D14912yes—
151C2×C4C2×C22⋊D14912yes—
152C2×C4C2×C22⋊D14912yes—
153C22C22×C22⋊D14911yescharacteristic
154C22#1801195711yescharacteristic
155C22#1801195812yes—
156C22#1801195811yescharacteristic
157C22#1801195912yes—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—5962no—
164C4—5962no—
165C4—5964no—
166C2#2375019611yescharacteristic
167C2#2375019911yescharacteristic
168C2#2375020311yescharacteristic
169C2#2375037912yes—
170C2C149⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, prime radical, cosocleC23×C149C24
FittingC2×#125×C149C2
hypercenterC2×#125D149
hypocenterC149#2822
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
85. C149#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#180119032
#237495642
#237495632
#237495582
#237495562
#237495552
#237494912
C2×#125×C1492
#2822149