Finite Group Databasebeta

← #34060553

Subgroups — #34060553

Order 19072.

380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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×#18011969C212yesmaximal
2#23750567C212yesmaximal, complemented
3#23750503C212yesmaximal, complemented
4C2×#18011871C211yesmaximal, characteristic
5C2×C4⋊#10597010—22no—
6C2×C22⋊#10597010C2214yes—
7#18011969—24no—
8(C2×#10597010)⋊C4—22no—
9C22×C22⋊D149C2211yescharacteristic
10C23×Dic149C411yescharacteristic, complemented
11C22×C4×D149C2211yescharacteristic
12#18011871—22no—
13#18011871—22no—
14C2×#14558715C411yescharacteristic, complemented
15C2×#14558713C2211yescharacteristic
16C2×C4×Dic149C411yescharacteristic, complemented
17C2×C22⋊C4×C149C411yescharacteristic, complemented
18C22×#10597010—24no—
19C4⋊#10597010—44no—
20C22⋊#10597010—24no—
21C22⋊#10597010—24no—
22C23×D149C2311yescharacteristic
23C2×C22⋊D149—22no—
24C2×C22⋊D149—22no—
25C2×C22⋊D149D412yes—
26C2×C22⋊D149Q812yes—
27C22×Dic149—21no—
28C22×Dic149—21no—
29C22×Dic149—42no—
30C22×Dic149C2×C411yescharacteristic
31C22×Dic149C2×C411yescharacteristic
32C22×Dic149C2×C411yescharacteristic
33C2×C4×D149—42no—
34C2×C4×D149D412yes—
35C2×C4×D149D412yes—
36#14558715—22no—
37#14558713—22no—
38C4×Dic149—21no—
39C4×Dic149—21no—
40C24×C149C2×C411yescharacteristic
41C22×C4×C149C2×C411yescharacteristic
42C22×C4×C149C2×C411yescharacteristic
43C22⋊C4×C149—22no—
44C2×#10597010—44no—
45C2×#10597010—44no—
46C2×#10597010—44no—
47C22×D149—41no—
48C22×D149—41no—
49C22×D149C2×D412yes—
50C22×D149C2×D411yescharacteristic
51C22×D149C2×Q811yescharacteristic
52C22×D149#4112yes—
53C22⋊D149—24no—
54C22⋊D149—24no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149—22no—
58C2×Dic149—21no—
59C2×Dic149—42no—
60C2×Dic149—42no—
61C2×Dic149—41no—
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C4⋊C412yescomplemented
65C4×D149—24no—
66C4×D149—42no—
67C23×C149—21no—
68C23×C149—21no—
69C23×C149—41no—
70C23×C149—41no—
71C23×C149C4⋊C412yescomplemented
72C23×C149C22×C411yescharacteristic
73C2×C4×C149—21no—
74C2×C4×C149—41no—
75C2×C4×C149—41no—
76C2×C4×C149C22⋊C412yes—
77C22×C149—21no—
78C22×C149—21no—
79C22×C149—22no—
80C22×C149—42no—
81C22×C149—42no—
82C22×C149—41no—
83C22×C149—41no—
84C22×C149C2×C22⋊C411yescharacteristic
85C22×C149C2×C4⋊C411yescharacteristic
86C22×C149#11711yescharacteristic
87C2×D149—22no—
88C2×D149—22no—
89C2×D149—41no—
90C2×D149—41no—
91C2×D149—42no—
92C2×D149#12112yes—
93C2×D149C22⋊Q812yes—
94#10597010—84no—
95C4×C149—22no—
96C4×C149—41no—
97Dic149—22no—
98Dic149—21no—
99Dic149—41no—
100Dic149#9912yescomplemented
101C2×C149—21no—
102C2×C149—21no—
103C2×C149—42no—
104C2×C149#38011yescharacteristic
105C2×C149C2×#9911yescharacteristic
106C2×C149#41011yescharacteristic
107D149—22no—
108D149—22no—
109C149#179911yescharacteristic, complemented, Sylow
110#1799—1491nomaximal, Sylow
111C2×C4×D4—1491no—
112C2×#99—1492no—
113#380—1492no—
114#342—1492no—
115C22×D4—1491no—
116C23×C4—1491no—
117C23×C4—1491no—
118C4×D4—2982no—
119C4×D4—2982no—
120C2×C4⋊C4—2982no—
121C2×C4⋊C4—1491no—
122C2×C22⋊C4—1494no—
123C2×C22⋊C4—1491no—
124C2×C22⋊C4#1059701011yescharacteristic, complemented
125C2×C42—1491no—
126#99—2984no—
127#95—2982no—
128C24—1491no—
129C24C2×#1059701011yescharacteristic
130C2×D4—2982no—
131C2×D4—2982no—
132C2×D4—1492no—
133C2×D4—1492no—
134C22×C4—2981no—
135C22×C4—2981no—
136C22×C4—2984no—
137C22×C4—5962no—
138C22×C4—5962no—
139C22×C4—1491no—
140C22×C4—1491no—
141C22×C4—1492no—
142C22×C4—1491no—
143C22×C4—1492no—
144C22×C4C2×#1059701011yescharacteristic
145C22×C4C2×#1059701011yescharacteristic
146C4⋊C4—2982no—
147C4⋊C4—5964no—
148C22⋊C4—22no—
149C22⋊C4—2982no—
150C22⋊C4—2984no—
151C22⋊C4—2984no—
152C42—2981no—
153C42—2981no—
154C23—21no—
155C23—21no—
156C23—41no—
157C23—41no—
158C23—5961no—
159C23—5961no—
160C23—1492no—
161C23—1491no—
162C23—1491no—
163C23—1492no—
164C23C4⋊#1059701012yescomplemented
165C23C22×#1059701011yescharacteristic
166D4—2984no—
167D4—2984no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2984no—
172C2×C4—2981no—
173C2×C4—2981no—
174C2×C4—2982no—
175C2×C4—2981no—
176C2×C4—5962no—
177C2×C4—5962no—
178C2×C4—5962no—
179C2×C4—5961no—
180C2×C4—5964no—
181C2×C4—5964no—
182C2×C4—5964no—
183C2×C4—1491no—
184C2×C4—1492no—
185C2×C4—1491no—
186C2×C4C22⋊#1059701012yes—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—2982no—
195C22—2982no—
196C22—5961no—
197C22—5961no—
198C22—5962no—
199C22—1492no—
200C22—1492no—
201C22C2×C22⋊#1059701011yescharacteristic
202C22C2×C4⋊#1059701011yescharacteristic
203C22#1801199011yescharacteristic
204C4—22no—
205C4—41no—
206C4—2982no—
207C4—2981no—
208C4—5961no—
209C4—1492no—
210C4—11924no—
211C2—21no—
212C2—21no—
213C2—42no—
214C2—2982no—
215C2—2982no—
216C2#2375056711yescharacteristic
217C2D149⋊#9911yescharacteristic
218C2#2375060511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×C22⋊D149C22
cosocleC23×D149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1799
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23750567C2semidirect
3. #23750503C2semidirect
10. C23×Dic149C4semidirect
14. C2×#14558715C4semidirect
16. C2×C4×Dic149C4semidirect
17. C2×C22⋊C4×C149C4semidirect
64. C2×Dic149C4⋊C4semidirect
71. C23×C149C4⋊C4semidirect
100. Dic149#99semidirect
109. C149#1799semidirect
124. C2×C22⋊C4#10597010semidirect
164. C23C4⋊#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119692
#237505672
#237505032
C2×#180118712
#1799149