Finite Group Databasebeta

← #34044600

Subgroups — #34044600

Order 19072.

852 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C23×C4×D149C211yesmaximal, characteristic
2C2×C22⋊#11924746C211yesmaximal, characteristic, complemented
3C2×#18011823C214yesmaximal, complemented
4C2×C22⋊C8×C149C211yesmaximal, characteristic, complemented
5C24×D149C411yescharacteristic
6C23×Dic149C411yescharacteristic
7C22×C4×D149—22no—
8C22×C4×D149—22no—
9C22×C4×D149—28no—
10C22×C4×D149C412yes—
11C22×C4×D149C2212yes—
12C22×#11924746C2212yescomplemented
13C22⋊#11924746—22no—
14#18011823—28no—
15C23×C4×C149C2211yescharacteristic
16C22×C8×C149C2212yescomplemented
17C22⋊C8×C149—22no—
18C23×D149—24no—
19C23×D149—24no—
20C23×D149—22no—
21C23×D149—22no—
22C23×D149C814yescomplemented
23C23×D149C2×C412yes—
24C22×Dic149—24no—
25C22×Dic149—22no—
26C22×Dic149C2×C412yes—
27C2×C4×D149—216no—
28C2×C4×D149—216no—
29C2×C4×D149—24no—
30C2×C4×D149—24no—
31C2×C4×D149—24no—
32C2×C4×D149—24no—
33C2×C4×D149—22no—
34C2×C4×D149—22no—
35C2×C4×D149D418yes—
36C2×#11924746—24no—
37C2×#11924746—22no—
38C24×C149C2×C411yescharacteristic
39C22×C4×C149—24no—
40C22×C4×C149C2×C411yescharacteristic
41C22×C4×C149D412yes—
42C22×C4×C149D412yes—
43C22×C4×C149C2311yescharacteristic
44C2×C8×C149—22no—
45C2×C8×C149—24no—
46C22×D149—28no—
47C22×D149—216no—
48C22×D149—28no—
49C22×D149—28no—
50C22×D149—22no—
51C22×D149—22no—
52C22×D149—22no—
53C22×D149—22no—
54C22×D149—216no—
55C22×D149C22⋊C414yes—
56C22×D149C2×C814yes—
57C22×D149M1614yes—
58C2×Dic149—28no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149C22⋊C414yes—
62C4×D149—216no—
63C4×D149—28no—
64C4×D149—28no—
65#11924746—42no—
66C23×C149—22no—
67C23×C149—22no—
68C23×C149C22⋊C412yes—
69C23×C149C2×C812yes—
70C23×C149M1612yes—
71C23×C149C22×C411yescharacteristic
72C2×C4×C149—22no—
73C2×C4×C149—24no—
74C2×C4×C149—24no—
75C2×C4×C149C22⋊C412yes—
76C2×C4×C149C2×D414yes—
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C8×C149—42no—
80C22×C149—22no—
81C22×C149—24no—
82C22×C149—22no—
83C22×C149—24no—
84C22×C149C22⋊C814yescomplemented
85C22×C149C2×C22⋊C412yes—
86C22×C149C2×C22⋊C411yescharacteristic
87C22×C149C22×C811yescharacteristic
88C22×C149C2×M1612yes—
89C22×C149C2×M1611yescharacteristic
90C2×D149—232no—
91C2×D149—24no—
92C2×D149—24no—
93C2×D149—24no—
94C2×D149—24no—
95C2×D149—24no—
96C2×D149—24no—
97C2×D149C22⋊C818yescomplemented
98C4×C149—22no—
99C4×C149#12012yes—
100C4×C149#12012yes—
101Dic149—24no—
102C2×C149—24no—
103C2×C149#37911yescharacteristic
104C2×C149C2×C22⋊C812yes—
105C2×C149C2×C22⋊C811yescharacteristic
106C2×C149#40712yes—
107C2×C149#40711yescharacteristic
108D149—28no—
109C149#177911yescharacteristic, complemented, Sylow
110#1779—1491nomaximal, Sylow
111C24×C4—1491no—
112C2×C22⋊C8—1491no—
113C2×C22⋊C8—1494no—
114C2×C22⋊C8D14911yescharacteristic, complemented
115C25—1491no—
116C23×C4—2988no—
117C23×C4—2982no—
118C23×C4—2982no—
119C23×C4—1491no—
120C23×C4—1492no—
121C23×C4—1492no—
122C23×C4C2×D14911yescharacteristic
123C22×C8—1492no—
124C22×C8C2×D14912yescomplemented
125C22⋊C8—22no—
126C22⋊C8—2988no—
127C22⋊C8—2982no—
128C24—2984no—
129C24—2984no—
130C24—2982no—
131C24—2982no—
132C24—1494no—
133C24—1492no—
134C24C4×D14911yescharacteristic
135C22×C4—24no—
136C22×C4—29816no—
137C22×C4—29816no—
138C22×C4—2984no—
139C22×C4—2984no—
140C22×C4—2982no—
141C22×C4—2984no—
142C22×C4—2984no—
143C22×C4—2982no—
144C22×C4—2982no—
145C22×C4—2984no—
146C22×C4—1492no—
147C22×C4—1498no—
148C22×C4C4×D14911yescharacteristic
149C22×C4C22⋊D14912yes—
150C22×C4D59612yes—
151C22×C4C22×D14911yescharacteristic
152C2×C8—24no—
153C2×C8—22no—
154C2×C8—2984no—
155C2×C8—2982no—
156C23—22no—
157C23—22no—
158C23—2988no—
159C23—29816no—
160C23—2988no—
161C23—29816no—
162C23—2982no—
163C23—2982no—
164C23—2988no—
165C23—2982no—
166C23—2982no—
167C23—1494no—
168C23—1494no—
169C23—1494no—
170C23#1455871312yes—
171C23C8×D14912yes—
172C23#1455871912yes—
173C23C2×C4×D14911yescharacteristic
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—29816no—
178C2×C4—2988no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2988no—
182C2×C4—2988no—
183C2×C4—1494no—
184C2×C4#1455871312yes—
185C2×C4D4×D14914yes—
186C2×C4C2×C22⋊D14911yescharacteristic
187C2×C4C2×D59611yescharacteristic
188C8—42no—
189C8—5962no—
190C22—22no—
191C22—24no—
192C22—24no—
193C22—22no—
194C22—29832no—
195C22—2984no—
196C22—2984no—
197C22—2984no—
198C22—2984no—
199C22—2984no—
200C22—2984no—
201C22—1498no—
202C22#1801182314yescomplemented
203C22C22⋊C4×D14912yes—
204C22C2×#1455871311yescharacteristic
205C22C2×C8×D14911yescharacteristic
206C22M16×D14912yes—
207C22C2×#1455871911yescharacteristic
208C4—22no—
209C4—2984no—
210C4#1801187912yes—
211C4#1801188112yes—
212C2—24no—
213C2—2988no—
214C2#2374948011yescharacteristic
215C2C22⋊C8×D14912yes—
216C2C2×#1801182311yescharacteristic
217C2#2374958712yes—
218C2#2374958811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D149
commutatorC22×C149C22×C8
FittingC2×C22⋊C8×C149C2
socleC23×C149C22×C4
prime radicalC24×D149C4
cosocleC22×C4×C149C23
hypercenterC2×C22⋊C8D149
hypocenterC149#1779
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#11924746C2semidirect
3. C2×#18011823C2semidirect
4. C2×C22⋊C8×C149C2semidirect
12. C22×#11924746C22semidirect
16. C22×C8×C149C22semidirect
22. C23×D149C8semidirect
84. C22×C149C22⋊C8semidirect
97. C2×D149C22⋊C8semidirect
109. C149#1779semidirect
114. C2×C22⋊C8D149semidirect
124. C22×C8C2×D149semidirect
202. C22#18011823semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1492
C2×C22⋊#119247462
C2×#180118232
C2×C22⋊C8×C1492
#1779149