Finite Group Databasebeta

← #34047497

Subgroups — #34047497

Order 19072.

428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 217 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#23749524C212yesmaximal
2#23749511C212yesmaximal
3#23749511C212yesmaximal
4#23749511C212yesmaximal
5#23749511C212yesmaximal
6#23749493C211yesmaximal, characteristic
7C4⋊C4×Dic149C212yesmaximal
8C4×C4⋊Dic149C211yesmaximal, characteristic
9C2×#125×C149C211yesmaximal, characteristic
10C2×C4⋊Dic149C2212yes—
11C2×C4⋊Dic149C2212yes—
12C2×C4⋊Dic149C2212yes—
13C2×C4×Dic149C2212yes—
14C2×C4×Dic149C2211yescharacteristic
15C2×C4×Dic149C2211yescharacteristic
16C2×C4×Dic149C2212yes—
17#18011818C2212yes—
18#18011818C2212yes—
19#18011818C2212yes—
20#18011818C2211yescharacteristic
21#18011818C2212yes—
22#18011818C2211yescharacteristic
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2212yes—
26#125×C149C418yescomplemented
27C2×C4⋊C4×C149C2212yes—
28C2×C4⋊C4×C149C2211yescharacteristic
29C2×C4⋊C4×C149C2211yescharacteristic
30C2×C4⋊C4×C149C2212yes—
31C2×C42×C149C2211yescharacteristic
32C22×Dic149C2312yes—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C4⋊Dic149—24no—
37C4⋊Dic149—24no—
38C4⋊Dic149—42no—
39C4×Dic149—24no—
40C4×Dic149—41no—
41C4×Dic149—41no—
42C4×Dic149—42no—
43C22×C4×C149C2311yescharacteristic
44C22×C4×C149C2311yescharacteristic
45C22×C4×C149C2311yescharacteristic
46C22×C4×C149C2312yes—
47C22×C4×C149C2312yes—
48C4⋊C4×C149C2×C418yes—
49C4⋊C4×C149C2×C414yes—
50C4⋊C4×C149C2×C414yes—
51C4⋊C4×C149C2×C418yes—
52C42×C149C2×C414yes—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—22no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149#4114yes—
65C23×C149C2411yescharacteristic
66C2×C4×C149—22no—
67C2×C4×C149—22no—
68C2×C4×C149—22no—
69C2×C4×C149—21no—
70C2×C4×C149—22no—
71C2×C4×C149—21no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149C22×C412yes—
75C2×C4×C149C22×C412yes—
76C2×C4×C149C22×C412yes—
77C2×C4×C149C22×C414yes—
78C2×C4×C149C22×C414yes—
79C22×C149C23×C411yescharacteristic
80C22×C149C2×#4112yes—
81C22×C149H(5,𝔽2)11yescharacteristic
82C22×C1492−1+411yescharacteristic
83C22×C1492−1+412yes—
84C4×C149—24no—
85C4×C149—22no—
86C4×C149—22no—
87C4×C149—22no—
88C4×C149—24no—
89Dic149—24no—
90Dic149—42no—
91Dic149—42no—
92Dic149—42no—
93C2×C149C4×#4111yescharacteristic
94C2×C149#51911yescharacteristic
95C2×C149#52011yescharacteristic
96C2×C149#53912yes—
97C2×C149#54112yes—
98C149#233611yescharacteristic, complemented, Sylow
99#2336—1491nomaximal, Sylow
100C2×#125D14911yescharacteristic
101#389—1492no—
102#387—1492no—
103#387—1492no—
104#387—1492no—
105#387—1492no—
106#383—1491no—
107C4×C4⋊C4—1492no—
108C4×C4⋊C4—1491no—
109#125Dic14918yescomplemented
110C2×C4⋊C4—1492no—
111C2×C4⋊C4—1492no—
112C2×C4⋊C4—1492no—
113C2×C4⋊C4C2×D14912yes—
114C2×C4⋊C4C2×D14911yescharacteristic
115C2×C4⋊C4C2×D14911yescharacteristic
116C2×C4⋊C4C2×D14912yes—
117C2×C42—1492no—
118C2×C42—1491no—
119C2×C42—1491no—
120C2×C42—1492no—
121C2×C42C2×D14911yescharacteristic
122#95—1492no—
123#95—1492no—
124#95—1492no—
125#95—1491no—
126#95—1492no—
127#95—1491no—
128#95—1492no—
129#95—1492no—
130#95—1492no—
131C22×C4—1492no—
132C22×C4—1492no—
133C22×C4—1492no—
134C22×C4—1492no—
135C22×C4C22×D14911yescharacteristic
136C22×C4C22×D14911yescharacteristic
137C22×C4C22×D14912yes—
138C22×C4C22×D14912yes—
139C22×C4C22×D14911yescharacteristic
140C4⋊C4—2984no—
141C4⋊C4—2984no—
142C4⋊C4—5962no—
143C4⋊C4C2×Dic14918yes—
144C4⋊C4C2×Dic14914yes—
145C4⋊C4C2×Dic14914yes—
146C4⋊C4C2×Dic14918yes—
147C42—2984no—
148C42—5961no—
149C42—5961no—
150C42—5962no—
151C42C2×Dic14914yes—
152C23C23×D14911yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—2982no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—2982no—
171C2×C4—2982no—
172C2×C4—1494no—
173C2×C4C22×Dic14912yes—
174C2×C4C22×Dic14912yes—
175C2×C4C22×Dic14912yes—
176C2×C4C22×Dic14914yes—
177C2×C4C22×Dic14914yes—
178C22C23×Dic14911yescharacteristic
179C22#41×D14912yes—
180C22#1801195711yescharacteristic
181C22#1801195811yescharacteristic
182C22#1801195912yes—
183C4—24no—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—24no—
188C4—2984no—
189C4—5962no—
190C4—5962no—
191C4—5962no—
192C2#41×Dic14911yescharacteristic
193C2#2375010311yescharacteristic
194C2#2375010811yescharacteristic
195C2#2375022312yes—
196C2#2375023412yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC2×#125×C149C2
socle, prime radical, cosocleC23×C149C24
hypercenterC2×#125D149
hypocenterC149#2336
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
26. #125×C149C4semidirect
98. C149#2336semidirect
109. #125Dic149semidirect

Maximal subgroups

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

subgroupindex
#237495242
#237495112
#237494932
C4⋊C4×Dic1492
C4×C4⋊Dic1492
C2×#125×C1492
#2336149