Finite Group Databasebeta

← #34047558

Subgroups — #34047558

Order 19072.

604 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 221 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×#18011867C212yesmaximal
2C22×C4⋊Dic149C211yesmaximal, characteristic
3#23749523C212yesmaximal, complemented
4#23749510C214yesmaximal, complemented
5#23749486C212yesmaximal
6#23749485C211yesmaximal, characteristic
7C4×C4⋊Dic149C212yesmaximal, complemented
8C4×C22⋊C4×C149C211yesmaximal, characteristic
9C23×Dic149C2212yes—
10#18011867—28no—
11C2×C4⋊Dic149C418yescomplemented
12C2×C4⋊Dic149C2212yes—
13C2×C4⋊Dic149C2211yescharacteristic
14C2×C4⋊Dic149C2212yes—
15C2×C4⋊Dic149C2211yescharacteristic
16C2×#14558715C2214yes—
17C2×C22⋊Dic149C2212yes—
18C2×C4×Dic149C2214yes—
19#18011818C2214yes—
20#18011818C2212yes—
21#18011818C2214yes—
22C23×C4×C149C2211yescharacteristic
23C2×C22⋊C4×C149C2211yescharacteristic
24C2×C22⋊C4×C149C2211yescharacteristic
25C2×C42×C149C2212yes—
26#95×C149C2212yes—
27C22×Dic149—24no—
28C22×Dic149—24no—
29C22×Dic149C2×C418yes—
30C22×Dic149C2314yes—
31C22×Dic149C2312yes—
32C22×Dic149C2312yes—
33C4⋊Dic149—24no—
34C4⋊Dic149C2×C418yes—
35C4⋊Dic149C2×C414yes—
36C4⋊Dic149C2×C414yes—
37#14558715—28no—
38C22⋊Dic149—24no—
39C4×Dic149—28no—
40C24×C149C2311yescharacteristic
41C22×C4×C149—24no—
42C22×C4×C149C2×C414yes—
43C22×C4×C149C2312yes—
44C22×C4×C149C2311yescharacteristic
45C22×C4×C149C2312yes—
46C22×C4×C149C2311yescharacteristic
47C22⋊C4×C149—22no—
48C22⋊C4×C149D414yes—
49C42×C149—24no—
50C2×Dic149—216no—
51C2×Dic149—22no—
52C2×Dic149—22no—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—24no—
56C2×Dic149—24no—
57C2×Dic149—24no—
58C2×Dic149C22×C414yes—
59C2×Dic149C22×C414yes—
60C23×C149—22no—
61C23×C149—22no—
62C23×C149C22×C412yes—
63C23×C149C2×D412yes—
64C23×C149#4112yes—
65C23×C149C2411yescharacteristic
66C2×C4×C149—22no—
67C2×C4×C149—22no—
68C2×C4×C149—22no—
69C2×C4×C149—28no—
70C2×C4×C149—22no—
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149C22×C412yes—
74C2×C4×C149C22×C412yes—
75C2×C4×C149C2×D414yes—
76C2×C4×C149#4114yes—
77C22×C149—22no—
78C22×C149—22no—
79C22×C149—24no—
80C22×C149—24no—
81C22×C149C4×D414yes—
82C22×C149C23×C411yescharacteristic
83C22×C149C22×D411yescharacteristic
84C22×C149C2×#4112yes—
85C22×C149C2×#4111yescharacteristic
86C22×C1492−1+412yes—
87C4×C149—22no—
88C4×C149—24no—
89C4×C149—42no—
90C4×C149#11714yescomplemented
91Dic149—24no—
92Dic149—24no—
93Dic149—44no—
94C2×C149—24no—
95C2×C149C2×#11711yescharacteristic
96C2×C149C2×C4×D411yescharacteristic
97C2×C149#51911yescharacteristic
98C2×C149#54712yes—
99C2×C149#55212yes—
100C149#234411yescharacteristic, complemented, Sylow
101#2344—1491nomaximal, Sylow
102C2×#117—1492no—
103C22×C4⋊C4—1491no—
104#389—1492no—
105#387—1494no—
106#381—1492no—
107#380—1491no—
108C4×C4⋊C4—1492no—
109C4×C22⋊C4D14911yescharacteristic
110C23×C4—1492no—
111C23×C4C2×D14911yescharacteristic
112#117—2988no—
113C2×C4⋊C4—1494no—
114C2×C4⋊C4—1492no—
115C2×C4⋊C4—1498no—
116C2×C4⋊C4—1491no—
117C2×C4⋊C4—1492no—
118C2×C4⋊C4—1491no—
119C2×C22⋊C4—1492no—
120C2×C22⋊C4C2×D14911yescharacteristic
121C2×C22⋊C4C2×D14911yescharacteristic
122C2×C42—1494no—
123C2×C42C2×D14912yes—
124#95—1494no—
125#95—1492no—
126#95—1494no—
127#95C2×D14912yes—
128C24C22×D14911yescharacteristic
129C22×C4—24no—
130C22×C4—2984no—
131C22×C4—2984no—
132C22×C4—1494no—
133C22×C4—1498no—
134C22×C4—1492no—
135C22×C4—1492no—
136C22×C4C4×D14914yes—
137C22×C4C22×D14912yes—
138C22×C4C22×D14911yescharacteristic
139C22×C4C22×D14912yes—
140C22×C4C22×D14911yescharacteristic
141C4⋊C4—2988no—
142C4⋊C4—2984no—
143C4⋊C4—1498no—
144C4⋊C4—1494no—
145C4⋊C4—1494no—
146C22⋊C4—22no—
147C22⋊C4—2984no—
148C22⋊C4D59614yes—
149C42—24no—
150C42—2988no—
151C23—22no—
152C23—22no—
153C23C2×C4×D14912yes—
154C23C2×D59612yes—
155C23#1455873612yes—
156C23C23×D14911yescharacteristic
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—28no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—29816no—
169C2×C4—2984no—
170C2×C4—2984no—
171C2×C4—2984no—
172C2×C4—1494no—
173C2×C4—1494no—
174C2×C4C2×C4×D14912yes—
175C2×C4C2×C4×D14912yes—
176C2×C4C2×D59614yes—
177C2×C4#1455873514yes—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22C4×D59614yes—
183C22C22×C4×D14911yescharacteristic
184C22C22×D59611yescharacteristic
185C22C2×#1455873512yes—
186C22C2×#1455873611yescharacteristic
187C22#1801195812yes—
188C4—24no—
189C4—22no—
190C4—42no—
191C4—2984no—
192C4—2984no—
193C4—5964no—
194C4#1801186714yescomplemented
195C2—24no—
196C2C2×#1801186711yescharacteristic
197C2C2×C4×D59611yescharacteristic
198C2#2375010211yescharacteristic
199C2#2375027912yes—
200C2#2375031512yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC24×C149C23
hypercenterC4×C22⋊C4D149
hypocenterC149#2344
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #23749523C2semidirect
4. #23749510C2semidirect
7. C4×C4⋊Dic149C2semidirect
11. C2×C4⋊Dic149C4semidirect
90. C4×C149#117semidirect
100. C149#2344semidirect
194. C4#18011867semidirect

Maximal subgroups

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

subgroupindex
C2×#180118672
C22×C4⋊Dic1492
#237495232
#237495102
#237494862
#237494852
C4×C4⋊Dic1492
C4×C22⋊C4×C1492
#2344149