Finite Group Databasebeta

← #34059950

Subgroups — #34059950

Order 19072.

300 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750646C212yesmaximal, complemented
2#23750469C212yesmaximal, complemented
3#23750468C212yesmaximal, complemented
4C2×C4×C22⋊D149C211yesmaximal, characteristic
5C4⋊#11924753—22no—
6C22⋊#11924753C2214yes—
7#18011966—22no—
8C22×C22⋊D149C411yescharacteristic
9C22×C4×D149C411yescharacteristic
10C4×C22⋊D149—22no—
11C4×C22⋊D149—22no—
12C2×#14558715C411yescharacteristic
13C2×C22⋊Dic149C2211yescharacteristic
14C2×#14558713C2211yescharacteristic
15C2×C4×Dic149C2211yescharacteristic
16C23×C4×C149C411yescharacteristic
17C2×#11924753—24no—
18C23×D149C2×C411yescharacteristic
19C2×C22⋊D149—22no—
20C2×C22⋊D149—22no—
21C2×C22⋊D149—22no—
22C22×Dic149C2×C411yescharacteristic
23C22×Dic149C2×C411yescharacteristic
24C22×Dic149C2311yescharacteristic
25C2×C4×D149—21no—
26C2×C4×D149—21no—
27C2×C4×D149—42no—
28#14558715—22no—
29C22⋊Dic149—22no—
30#14558713—22no—
31C4×Dic149D412yes—
32C4×Dic149D412yes—
33C24×C149C2×C411yescharacteristic
34C22×C4×C149—21no—
35C22×C4×C149—21no—
36C22×C4×C149—42no—
37C22×C4×C149C2×C411yescharacteristic
38C22×C4×C149C2×C411yescharacteristic
39#11924753—44no—
40C22×D149—21no—
41C22×D149—21no—
42C22×D149—41no—
43C22×D149—41no—
44C22×D149M1612yes—
45C22⋊D149—28no—
46C2×Dic149—21no—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—41no—
50C2×Dic149—41no—
51C2×Dic149C22⋊C412yes—
52C2×Dic149C2×D412yes—
53C4×D149—42no—
54C4×D149—42no—
55C23×C149—21no—
56C23×C149—21no—
57C23×C149—41no—
58C23×C149—41no—
59C23×C149M1612yes—
60C23×C149C22×C411yescharacteristic
61C2×C4×C149—22no—
62C2×C4×C149—21no—
63C2×C4×C149—42no—
64C2×C4×C149—42no—
65C2×C4×C149—41no—
66C2×C4×C149C22⋊C411yescharacteristic
67C2×C4×C149C22⋊C411yescharacteristic
68C22×C149—21no—
69C22×C149—21no—
70C22×C149—22no—
71C22×C149—42no—
72C22×C149—42no—
73C22×C149—41no—
74C22×C149—41no—
75C22×C149C2×C22⋊C411yescharacteristic
76C22×C149C2×M1611yescharacteristic
77C22×C149C2×M1611yescharacteristic
78C2×D149—22no—
79C2×D149—42no—
80C2×D149—41no—
81C2×D149—41no—
82C2×D149—42no—
83C4×C149—21no—
84C4×C149—41no—
85C4×C149#10012yes—
86Dic149—22no—
87Dic149—22no—
88Dic149—41no—
89C2×C149—21no—
90C2×C149—21no—
91C2×C149—42no—
92C2×C149#40711yescharacteristic
93C2×C149#41011yescharacteristic
94C2×C149C2×#10011yescharacteristic
95D149—42no—
96C149#146611yescharacteristic, complemented, Sylow
97#1466—1491nomaximal, Sylow
98C2×C4×D4—1491no—
99#432—1492no—
100#323—1492no—
101#323—1492no—
102C22×D4—1491no—
103C23×C4—1491no—
104C23×C4#1059701011yescharacteristic
105C4×D4—2982no—
106C4×D4—2982no—
107C2×C4⋊C4—1491no—
108C2×C22⋊C4—1491no—
109C2×C22⋊C4—1491no—
110C2×C42—1491no—
111C4⋊C8—2982no—
112C22⋊C8—1494no—
113#97—2982no—
114C24—1491no—
115C24C2×#1059701011yescharacteristic
116C2×D4—2982no—
117C2×D4—2982no—
118C2×D4—2982no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—42no—
122C22×C4—2981no—
123C22×C4—2981no—
124C22×C4—5962no—
125C22×C4—1491no—
126C22×C4—1491no—
127C22×C4—1491no—
128C22×C4C2×#1059701011yescharacteristic
129C22×C4C2×#1059701011yescharacteristic
130C2×C8—2984no—
131C4⋊C4—2982no—
132C22⋊C4—2982no—
133C22⋊C4—2982no—
134C42—1492no—
135C42—1492no—
136C23—21no—
137C23—21no—
138C23—41no—
139C23—41no—
140C23—2981no—
141C23—2981no—
142C23—5961no—
143C23—5961no—
144C23—1492no—
145C23#1455874612yes—
146C23C22×#1059701011yescharacteristic
147D4—2988no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—41no—
153C2×C4—2981no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—5962no—
157C2×C4—5961no—
158C2×C4—5962no—
159C2×C4—5961no—
160C2×C4—1492no—
161C2×C4—1492no—
162C2×C4C22⋊#1059701011yescharacteristic
163C2×C4C22⋊#1059701011yescharacteristic
164C8—5964no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—41no—
172C22—2982no—
173C22—5962no—
174C22—5962no—
175C22—5961no—
176C22—5961no—
177C22C2×C22⋊#1059701011yescharacteristic
178C22D149⋊M1611yescharacteristic
179C22C2×#1455874611yescharacteristic
180C4—21no—
181C4—41no—
182C4—2982no—
183C4—2982no—
184C4—5961no—
185C4#1801197112yes—
186C2—21no—
187C2—21no—
188C2—42no—
189C2—5962no—
190C2#2375059611yescharacteristic
191C2#2375060411yescharacteristic
192C2C2×#1801197111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC23×C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×C22⋊D149C4
cosocleC22×Dic149C23
hypercenterC23×C4#10597010
hypocenterC149#1466
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. #23750646C2semidirect
2. #23750469C2semidirect
3. #23750468C2semidirect
96. C149#1466semidirect

Maximal subgroups

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

subgroupindex
#237506462
#237504692
#237504682
C2×C4×C22⋊D1492
#1466149