Finite Group Databasebeta

← #34060555

Subgroups — #34060555

Order 19072.

336 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#23750628C212yesmaximal, complemented
2C2×#18011971C212yesmaximal
3#23750505C212yesmaximal, complemented
4C2×C4×C22⋊D149C211yesmaximal, characteristic
5C2×#14558745C2214yes—
6#18011978—22no—
7C4⋊#11924753—22no—
8#18011971—24no—
9C22×C22⋊D149C2211yescharacteristic
10C22×C4×D149C411yescharacteristic
11C4×C22⋊D149—22no—
12C4×C22⋊D149—22no—
13C2×#14558715C2211yescharacteristic
14C2×C22⋊Dic149C411yescharacteristic
15C2×#14558713C411yescharacteristic
16C2×C4×Dic149C2211yescharacteristic
17C23×C4×C149C411yescharacteristic
18#14558745—24no—
19#14558745—24no—
20C2×#11924753—24no—
21C23×D149C2×C411yescharacteristic
22C2×C22⋊D149—22no—
23C2×C22⋊D149—22no—
24C2×C22⋊D149D412yes—
25C2×C22⋊D149Q812yes—
26C22×Dic149C2×C411yescharacteristic
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2311yescharacteristic
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149—42no—
32#14558715—22no—
33C22⋊Dic149—22no—
34#14558713—22no—
35C4×Dic149D412yes—
36C4×Dic149D412yes—
37C24×C149C2×C411yescharacteristic
38C22×C4×C149—21no—
39C22×C4×C149—21no—
40C22×C4×C149—42no—
41C22×C4×C149C2×C411yescharacteristic
42C22×C4×C149C2×C411yescharacteristic
43#11924753—44no—
44C22×D149—21no—
45C22×D149—21no—
46C22×D149—41no—
47C22×D149—41no—
48C22×D149C4⋊C412yes—
49C22⋊D149—24no—
50C22⋊D149—24no—
51C2×Dic149—21no—
52C2×Dic149—41no—
53C2×Dic149—41no—
54C2×Dic149C22⋊C412yes—
55C2×Dic149C2×D411yescharacteristic
56C2×Dic149C2×D412yes—
57C2×Dic149C2×Q811yescharacteristic
58C2×Dic149#4112yes—
59C4×D149—42no—
60C4×D149—42no—
61C23×C149—21no—
62C23×C149—21no—
63C23×C149—41no—
64C23×C149—41no—
65C23×C149C4⋊C412yes—
66C23×C149C22×C411yescharacteristic
67C2×C4×C149—22no—
68C2×C4×C149—21no—
69C2×C4×C149—42no—
70C2×C4×C149—42no—
71C2×C4×C149—41no—
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22⋊C411yescharacteristic
74C22×C149—21no—
75C22×C149—21no—
76C22×C149—22no—
77C22×C149—42no—
78C22×C149—42no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149C2×C22⋊C411yescharacteristic
82C22×C149C2×C4⋊C411yescharacteristic
83C22×C149#11711yescharacteristic
84C2×D149—22no—
85C2×D149—42no—
86C2×D149—41no—
87C2×D149—41no—
88C2×D149—42no—
89C4×C149—21no—
90C4×C149—41no—
91C4×C149#10012yescomplemented
92Dic149—22no—
93Dic149—41no—
94Dic149#12112yes—
95Dic149C22⋊Q812yes—
96C2×C149—21no—
97C2×C149—21no—
98C2×C149—42no—
99C2×C149#38011yescharacteristic
100C2×C149C2×#10011yescharacteristic
101C2×C149#41311yescharacteristic
102D149—42no—
103C149#180011yescharacteristic, complemented, Sylow
104#1800—1491nomaximal, Sylow
105C2×C4×D4—1491no—
106#423—1492no—
107C2×#100—1492no—
108#343—1492no—
109C22×D4—1491no—
110C23×C4—1491no—
111C23×C4#1059701011yescharacteristic
112C2×M16—1494no—
113C4×D4—2982no—
114C4×D4—2982no—
115C2×C4⋊C4—1491no—
116C2×C22⋊C4—1491no—
117C2×C22⋊C4—1491no—
118C2×C42—1491no—
119C4⋊C8—2982no—
120C4⋊C8—2982no—
121#100—2984no—
122C24—1491no—
123C24C2×#1059701011yescharacteristic
124C2×D4—2982no—
125C2×D4—2982no—
126C2×D4—1492no—
127C2×D4—1492no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—42no—
131C22×C4—2981no—
132C22×C4—2981no—
133C22×C4—5962no—
134C22×C4—1491no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4C2×#1059701011yescharacteristic
138C22×C4C2×#1059701011yescharacteristic
139M16—2984no—
140M16—2984no—
141C2×C8—2984no—
142C4⋊C4—2982no—
143C22⋊C4—2982no—
144C22⋊C4—2982no—
145C42—1492no—
146C42—1492no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—2981no—
152C23—2981no—
153C23—5961no—
154C23—5961no—
155C23—1492no—
156C23C4⋊#1059701012yes—
157C23C22×#1059701011yescharacteristic
158D4—2984no—
159D4—2984no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—2981no—
166C2×C4—5962no—
167C2×C4—5961no—
168C2×C4—5962no—
169C2×C4—5961no—
170C2×C4—1492no—
171C2×C4—1492no—
172C2×C4—1491no—
173C2×C4—1491no—
174C2×C4—1492no—
175C2×C4C22⋊#1059701011yescharacteristic
176C2×C4C22⋊#1059701011yescharacteristic
177C8—5964no—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—2982no—
186C22—5962no—
187C22—5962no—
188C22—5961no—
189C22—5961no—
190C22C2×C22⋊#1059701011yescharacteristic
191C22C2×C4⋊#1059701011yescharacteristic
192C22#1801199011yescharacteristic
193C4—21no—
194C4—41no—
195C4—2982no—
196C4—5961no—
197C4—1492no—
198C4—1492no—
199C4#1801197112yescomplemented
200C2—21no—
201C2—21no—
202C2—42no—
203C2—5962no—
204C2#2375056711yescharacteristic
205C2C2×#1801197111yescharacteristic
206C2#2375061111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC23×C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×C22⋊D149C22
cosocleC22×Dic149C23
hypercenterC23×C4#10597010
hypocenterC149#1800
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #23750628C2semidirect
3. #23750505C2semidirect
91. C4×C149#100semidirect
103. C149#1800semidirect
199. C4#18011971semidirect

Maximal subgroups

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

subgroupindex
#237506282
C2×#180119712
#237505052
C2×C4×C22⋊D1492
#1800149