Finite Group Databasebeta

← #34047447

Subgroups — #34047447

Order 19072.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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×#18011890C211yesmaximal, characteristic
2#23749529C212yesmaximal, complemented
3#23749519C212yesmaximal
4#23749513C212yesmaximal
5#23749510C212yesmaximal, complemented
6#23749509C212yesmaximal, complemented
7#23749488C211yesmaximal, characteristic
8C4×#14558715C212yesmaximal, complemented
9C4×C22⋊C4×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11#18011890C418yescomplemented
12C2×C4⋊Dic149C2211yescharacteristic
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×C22⋊Dic149C2211yescharacteristic
17C2×C22⋊Dic149C2211yescharacteristic
18C2×C22⋊Dic149C2212yes—
19C2×C4×Dic149C2212yes—
20C2×C4×Dic149C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2212yes—
26#18011818C2212yes—
27C23×C4×C149C2211yescharacteristic
28C2×C22⋊C4×C149C2212yes—
29C2×C42×C149C2211yescharacteristic
30C2×C42×C149C2211yescharacteristic
31#95×C149C2212yes—
32C2×Dic298—41no—
33C2×Dic298—41no—
34C2×Dic298C2×C414yes—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C22×Dic149C2312yes—
39C4⋊Dic149C2×C414yes—
40#14558715—24no—
41#14558715—42no—
42#14558715C2×C418yes—
43C22⋊Dic149—41no—
44C22⋊Dic149—41no—
45C22⋊Dic149C2×C418yes—
46C4×Dic149—24no—
47C4×Dic149—42no—
48C24×C149C2311yescharacteristic
49C22×C4×C149—41no—
50C22×C4×C149—41no—
51C22×C4×C149C2×C414yes—
52C22×C4×C149C2312yes—
53C22×C4×C149C2311yescharacteristic
54C22×C4×C149C2311yescharacteristic
55C22×C4×C149C2312yes—
56C22⋊C4×C149—24no—
57C42×C149—41no—
58C42×C149—41no—
59Dic298—44no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—22no—
70C2×Dic149C22×C414yes—
71C2×Dic149C22×C414yes—
72C23×C149—22no—
73C23×C149—21no—
74C23×C149—21no—
75C23×C149—22no—
76C23×C149C22×C412yes—
77C23×C149C2411yescharacteristic
78C2×C4×C149—21no—
79C2×C4×C149—21no—
80C2×C4×C149—21no—
81C2×C4×C149—21no—
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149—44no—
88C2×C4×C149C22×C412yes—
89C2×C4×C149C22×C412yes—
90C2×C4×C149#4114yes—
91C22×C149—22no—
92C22×C149—22no—
93C22×C149—22no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149C23×C411yescharacteristic
97C22×C149C2×#4112yes—
98C22×C149H(5,𝔽2)11yescharacteristic
99C22×C149H(5,𝔽2)11yescharacteristic
100C22×C1492−1+412yes—
101C4×C149—22no—
102C4×C149—22no—
103C4×C149—24no—
104C4×C149—42no—
105Dic149—24no—
106Dic149—24no—
107Dic149—42no—
108Dic149—42no—
109C2×C149—42no—
110C2×C149C4×#4111yescharacteristic
111C2×C149#51811yescharacteristic
112C2×C149#51911yescharacteristic
113C2×C149#53912yes—
114C2×C149#54212yes—
115C149#233211yescharacteristic, complemented, Sylow
116#2332—1491nomaximal, Sylow
117C2×C22⋊Q8—1491no—
118#391—1492no—
119#388—1492no—
120#388—1492no—
121#387—1492no—
122#387—1492no—
123#381—1491no—
124C4×C4⋊C4—1492no—
125C4×C22⋊C4D14911yescharacteristic
126C22×Q8—1491no—
127C23×C4C2×D14911yescharacteristic
128C22⋊Q8—1498no—
129C2×C4⋊C4—1492no—
130C2×C4⋊C4—1492no—
131C2×C4⋊C4—1492no—
132C2×C4⋊C4—1491no—
133C2×C22⋊C4—1491no—
134C2×C22⋊C4—1491no—
135C2×C22⋊C4—1492no—
136C2×C22⋊C4C2×D14912yes—
137C2×C42—1492no—
138C2×C42—1492no—
139C2×C42C2×D14911yescharacteristic
140C2×C42C2×D14911yescharacteristic
141#95—1492no—
142#95—1492no—
143#95—1492no—
144#95—1492no—
145#95—1492no—
146#95—1492no—
147#95C2×D14912yes—
148C24C22×D14911yescharacteristic
149C2×Q8—5961no—
150C2×Q8—5961no—
151C2×Q8—1494no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—1492no—
155C22×C4—1492no—
156C22×C4—1492no—
157C22×C4—1492no—
158C22×C4C4×D14914yes—
159C22×C4C22×D14912yes—
160C22×C4C22×D14911yescharacteristic
161C22×C4C22×D14911yescharacteristic
162C22×C4C22×D14912yes—
163C4⋊C4—2984no—
164C4⋊C4—5962no—
165C4⋊C4—1498no—
166C4⋊C4—1494no—
167C22⋊C4—24no—
168C22⋊C4—5961no—
169C22⋊C4—5961no—
170C22⋊C4—1498no—
171C42—41no—
172C42—41no—
173C42—2984no—
174C42—5962no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D14912yes—
180C23C23×D14911yescharacteristic
181Q8—5964no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—2982no—
198C2×C4—2982no—
199C2×C4—2982no—
200C2×C4—2982no—
201C2×C4—2982no—
202C2×C4—1494no—
203C2×C4—1494no—
204C2×C4C2×C4×D14912yes—
205C2×C4C2×C4×D14912yes—
206C2×C4#1455873614yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D14911yescharacteristic
213C22C2×#1455873612yes—
214C22#1801195611yescharacteristic
215C22#1801195611yescharacteristic
216C22#1801195812yes—
217C4—24no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—2984no—
222C4—2984no—
223C4—5962no—
224C4—5962no—
225C2—42no—
226C2C4×#1455873611yescharacteristic
227C2#2375009811yescharacteristic
228C2#2375010211yescharacteristic
229C2#2375021712yes—
230C2#2375024012yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC24×C149C23
hypercenterC4×C22⋊C4D149
hypocenterC149#2332
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23749529C2semidirect
5. #23749510C2semidirect
6. #23749509C2semidirect
8. C4×#14558715C2semidirect
11. #18011890C4semidirect
115. C149#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#180118902
#237495292
#237495192
#237495132
#237495102
#237495092
#237494882
C4×#145587152
C4×C22⋊C4×C1492
#2332149