Finite Group Databasebeta

← #34060666

Subgroups — #34060666

Order 19072.

432 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 110 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×#11924753C211yesmaximal, characteristic, complemented
2C2×#18011968C212yesmaximal, complemented
3C2×C22⋊#11924753C211yesmaximal, characteristic, complemented
4#23750491C212yesmaximal, complemented
5C2×#18011871C211yesmaximal, characteristic
6C22×#11924753—24no—
7C22×#11924753—22no—
8C22×#11924753C2212yes—
9C22×#11924753C2212yes—
10#18011968—24no—
11C22⋊#11924753—22no—
12C22×C22⋊D149C411yescharacteristic
13C23×Dic149C2211yescharacteristic
14C22×C4×D149C2211yescharacteristic
15#18011871—22no—
16#18011871—22no—
17C2×#14558715C411yescharacteristic
18C2×#14558713C411yescharacteristic
19C2×C4×Dic149C2211yescharacteristic
20C2×C22⋊C4×C149C411yescharacteristic
21C2×#11924753—28no—
22C2×#11924753—22no—
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C2×#11924753D414yescomplemented
28C23×D149C2×C411yescharacteristic
29C2×C22⋊D149—22no—
30C2×C22⋊D149—22no—
31C2×C22⋊D149C814yescomplemented
32C22×Dic149—22no—
33C22×Dic149—22no—
34C22×Dic149C2×C411yescharacteristic
35C22×Dic149C2×C411yescharacteristic
36C22×Dic149D412yes—
37C22×Dic149D412yes—
38C22×Dic149C2311yescharacteristic
39C2×C4×D149—22no—
40C2×C4×D149—21no—
41C2×C4×D149—21no—
42C2×C4×D149—22no—
43#14558715—22no—
44#14558713—22no—
45C4×Dic149—21no—
46C4×Dic149—21no—
47C24×C149C2×C411yescharacteristic
48C22×C4×C149C2×C411yescharacteristic
49C22×C4×C149C2×C411yescharacteristic
50C22⋊C4×C149—22no—
51#11924753—24no—
52#11924753—42no—
53C22×D149—21no—
54C22×D149—22no—
55C22×D149—21no—
56C22×D149—22no—
57C22×D149C2×C812yescomplemented
58C22⋊D149—28no—
59C2×Dic149—21no—
60C2×Dic149—22no—
61C2×Dic149—21no—
62C2×Dic149—22no—
63C2×Dic149—24no—
64C2×Dic149—22no—
65C2×Dic149C22⋊C412yes—
66C2×Dic149C2×C812yescomplemented
67C2×Dic149C2×D412yes—
68C2×Dic149C2×D411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C2×Dic149#4112yes—
71C4×D149—41no—
72C4×D149—42no—
73C4×D149—41no—
74C23×C149—22no—
75C23×C149—22no—
76C23×C149C22⋊C412yes—
77C23×C149C2×C812yes—
78C23×C149M1612yes—
79C23×C149C22×C411yescharacteristic
80C2×C4×C149—21no—
81C2×C4×C149—21no—
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C22×C149—22no—
85C22×C149—22no—
86C22×C149—24no—
87C22×C149—24no—
88C22×C149C22⋊C814yescomplemented
89C22×C149C2×C22⋊C411yescharacteristic
90C22×C149C4×D412yes—
91C22×C149C22×C811yescharacteristic
92C22×C149C2×M1611yescharacteristic
93C22×C149#13112yes—
94C2×D149—22no—
95C2×D149—24no—
96C2×D149—41no—
97C2×D149—41no—
98C2×D149—42no—
99C4×C149—41no—
100C4×C149—41no—
101Dic149—22no—
102Dic149—22no—
103Dic149#12011yescharacteristic
104Dic149#12112yes—
105Dic149#12311yescharacteristic
106C2×C149—24no—
107C2×C149#38611yescharacteristic
108C2×C149C2×C22⋊C811yescharacteristic
109C2×C149#40811yescharacteristic
110C2×C149C8×D412yes—
111C2×C149#43512yes—
112D149—42no—
113C149#186911yescharacteristic, complemented, Sylow
114#1869—1491nomaximal, Sylow
115C23×C8—1491no—
116C2×C4×D4—1491no—
117C2×C22⋊C8—1491no—
118C2×C22⋊C8—1492no—
119#336—1492no—
120C22×D4—1491no—
121C23×C4—1491no—
122C23×C4—1491no—
123C22×C8—2982no—
124C22×C8—2984no—
125C22×C8—1492no—
126C22×C8—1492no—
127C4×D4—2982no—
128C4×D4—2982no—
129C2×C4⋊C4—1491no—
130C2×C22⋊C4—1491no—
131C2×C22⋊C4#1059701011yescharacteristic
132C2×C42—1491no—
133C22⋊C8—2982no—
134C22⋊C8—2984no—
135C24—1491no—
136C24C2×#1059701011yescharacteristic
137C2×D4—2982no—
138C2×D4—2982no—
139C2×D4—1494no—
140C22×C4—2982no—
141C22×C4—2981no—
142C22×C4—2981no—
143C22×C4—2982no—
144C22×C4—2982no—
145C22×C4—2982no—
146C22×C4—1492no—
147C22×C4—1492no—
148C22×C4—1491no—
149C22×C4—1491no—
150C22×C4—1491no—
151C22×C4C2×#1059701011yescharacteristic
152C22×C4C2×#1059701011yescharacteristic
153C2×C8—2988no—
154C2×C8—2982no—
155C2×C8—2982no—
156C2×C8—2982no—
157C2×C8—2982no—
158C2×C8—2982no—
159C2×C8—1494no—
160C4⋊C4—2982no—
161C22⋊C4—22no—
162C22⋊C4—2982no—
163C42—2981no—
164C42—2981no—
165C23—22no—
166C23—22no—
167C23—2981no—
168C23—2982no—
169C23—2981no—
170C23—2982no—
171C23—1492no—
172C23C22⋊#1059701012yes—
173C23D149⋊C812yes—
174C23#1455874612yes—
175C23C22×#1059701011yescharacteristic
176D4—2988no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—2981no—
182C2×C4—2982no—
183C2×C4—2981no—
184C2×C4—2982no—
185C2×C4—2984no—
186C2×C4—2982no—
187C2×C4—5961no—
188C2×C4—5962no—
189C2×C4—5961no—
190C2×C4—1492no—
191C2×C4—1492no—
192C2×C4—1491no—
193C2×C4—1491no—
194C2×C4—1492no—
195C2×C4—1492no—
196C8—2984no—
197C8—5962no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22—24no—
202C22—2982no—
203C22—2984no—
204C22—5961no—
205C22—5961no—
206C22—5962no—
207C22#1801196814yescomplemented
208C22C2×C22⋊#1059701011yescharacteristic
209C22D4×#1059701012yes—
210C22C2×D149⋊C811yescharacteristic
211C22C2×#1455874611yescharacteristic
212C22#1801199812yes—
213C4—41no—
214C4—41no—
215C4—2982no—
216C4—2982no—
217C4—1491no—
218C4—1492no—
219C4—1491no—
220C2—24no—
221C2—5962no—
222C2#2375057311yescharacteristic
223C2C2×#1801196811yescharacteristic
224C2#2375059811yescharacteristic
225C2#2375065212yes—
226C2#2375065412yes—
subgroupG/H
center, FrattiniC23C22×#10597010
commutatorC22×C149C22×C8
FittingC2×C22⋊C4×C149C4
socleC23×C149C22×C4
prime radicalC22×C22⋊D149C4
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1869
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#11924753C2semidirect
2. C2×#18011968C2semidirect
3. C2×C22⋊#11924753C2semidirect
4. #23750491C2semidirect
27. C2×#11924753D4semidirect
31. C2×C22⋊D149C8semidirect
57. C22×D149C2×C8semidirect
66. C2×Dic149C2×C8semidirect
88. C22×C149C22⋊C8semidirect
113. C149#1869semidirect
207. C22#18011968semidirect

Maximal subgroups

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

subgroupindex
C23×#119247532
C2×#180119682
C2×C22⋊#119247532
#237504912
C2×#180118712
#1869149