Finite Group Databasebeta

← #34059776

Subgroups — #34059776

Order 19072.

234 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 44 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×#18011971C211yesmaximal, characteristic
2C2×#18011969C211yesmaximal, characteristic
3#23749502C211yesmaximal, characteristic
4C2×#14558745—21no—
5C2×C22⋊#10597010—21no—
6#18011971—21no—
7#18011971C412yescomplemented
8#18011969—21no—
9#18011969C412yescomplemented
10C22×C22⋊D149C2211yescharacteristic
11C23×Dic149C411yescharacteristic, complemented
12C2×#14558713—21no—
13#18011818—21no—
14C2×C22⋊C4×C149C411yescharacteristic, complemented
15C22×#10597010—41no—
16#14558745—22no—
17#14558745—41no—
18C2×#11924753—41no—
19C22⋊#10597010—22no—
20C22⋊#10597010—41no—
21C23×D149D411yescharacteristic
22C2×C22⋊D149—41no—
23C2×C22⋊D149—41no—
24C2×C22⋊D149C2×C411yescharacteristic
25C2×C22⋊D149C2×C411yescharacteristic
26C2×C22⋊D149D411yescharacteristic
27C2×C22⋊D149Q811yescharacteristic
28C22×Dic149—21no—
29C22×Dic149—41no—
30C22×Dic149—42no—
31C22×Dic149D411yescharacteristic
32#14558713—42no—
33C24×C149C2×C411yescharacteristic
34C22×C4×C149—21no—
35C22⋊C4×C149—41no—
36C2×#10597010—42no—
37C2×#10597010—81no—
38C2×#10597010—81no—
39#11924753—42no—
40C22×D149—21no—
41C22×D149—21no—
42C22×D149—41no—
43C22×D149—41no—
44C22×D149C22⋊C411yescharacteristic
45C22×D149C4⋊C411yescharacteristic
46C22⋊D149—41no—
47C22⋊D149—41no—
48C22⋊D149—41no—
49C22⋊D149—41no—
50C2×Dic149—21no—
51C2×Dic149—21no—
52C2×Dic149—22no—
53C2×Dic149—41no—
54C2×Dic149—42no—
55C2×Dic149—41no—
56C2×Dic149—42no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C4⋊C411yescharacteristic
59C23×C149—21no—
60C23×C149—21no—
61C23×C149—41no—
62C23×C149—41no—
63C23×C149C4211yescharacteristic
64C23×C149C22⋊C411yescharacteristic
65C23×C149C4⋊C411yescharacteristic
66C2×C4×C149—41no—
67C2×C4×C149—41no—
68C2×C4×C149—41no—
69C22×C149—21no—
70C22×C149—21no—
71C22×C149—21no—
72C22×C149—21no—
73C22×C149—41no—
74C22×C149—41no—
75C22×C149—42no—
76C22×C149—41no—
77C22×C149—41no—
78C22×C149#9511yescharacteristic
79C22×C149#9911yescharacteristic
80C22×C149#9911yescharacteristic
81C2×D149—21no—
82C2×D149—21no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—41no—
86C2×D149—41no—
87C2×D149—81no—
88#10597010—82no—
89C4×C149—81no—
90Dic149—21no—
91Dic149—21no—
92Dic149—42no—
93C2×C149—21no—
94C2×C149—21no—
95C2×C149—41no—
96C2×C149—41no—
97C2×C149#34211yescharacteristic
98C2×C149AΣL(1,𝔽16)11yescharacteristic
99C2×C149#35211yescharacteristic
100D149—41no—
101D149—41no—
102C149#139011yescharacteristic, complemented, Sylow
103#1390—1491nomaximal, Sylow
104C2×#100—1491no—
105C2×#99—1491no—
106#386—1491no—
107C22×D4—1491no—
108C23×C4—1491no—
109C2×M16—2981no—
110C2×C22⋊C4—2981no—
111C2×C22⋊C4—2981no—
112C2×C22⋊C4#1059701011yescharacteristic, complemented
113#100—2981no—
114#100—1492no—
115#99—2981no—
116#99—1492no—
117#95—2981no—
118C24—1491no—
119C24C2×#1059701011yescharacteristic
120C2×D4—5961no—
121C2×D4—5961no—
122C2×D4—1491no—
123C2×D4—1491no—
124C2×D4—1491no—
125C2×D4—1491no—
126C22×C4—21no—
127C22×C4—2981no—
128C22×C4—5962no—
129C22×C4—5961no—
130C22×C4—5961no—
131C22×C4—1491no—
132M16—2982no—
133M16—5961no—
134C2×C8—5961no—
135C22⋊C4—41no—
136C22⋊C4—2982no—
137C22⋊C4—5962no—
138C22⋊C4—5961no—
139C23—21no—
140C23—21no—
141C23—41no—
142C23—41no—
143C23—2981no—
144C23—2981no—
145C23—5961no—
146C23—5961no—
147C23—1491no—
148C23—1491no—
149C23C4×#1059701011yescharacteristic
150C23C22⋊#1059701011yescharacteristic
151C23C4⋊#1059701011yescharacteristic
152D4—5961no—
153D4—5961no—
154D4—5961no—
155D4—5961no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—2981no—
160C2×C4—2981no—
161C2×C4—2982no—
162C2×C4—5961no—
163C2×C4—5962no—
164C2×C4—5961no—
165C2×C4—5962no—
166C2×C4—5962no—
167C2×C4—1491no—
168C2×C4—1491no—
169C2×C4—11921no—
170C2×C4—11921no—
171C8—5962no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—2981no—
182C22—2981no—
183C22—5961no—
184C22—5961no—
185C22—5961no—
186C22—5961no—
187C22—11921no—
188C22(C2×#10597010)⋊C411yescharacteristic
189C22#1801196911yescharacteristic
190C22#1801197011yescharacteristic
191C4—81no—
192C4—2981no—
193C4—2981no—
194C4—5962no—
195C4—11922no—
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2—5961no—
201C2—5961no—
202C2#2375050311yescharacteristic
203C2#2375052611yescharacteristic
204C2#2375052811yescharacteristic
subgroupG/H
centerC22#18011970
commutatorC23×C149C42
FrattiniC24C2×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149#99
prime radical, cosocleC22×C22⋊D149C22
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1390
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
7. #18011971C4semidirect
9. #18011969C4semidirect
11. C23×Dic149C4semidirect
14. C2×C22⋊C4×C149C4semidirect
102. C149#1390semidirect
112. C2×C22⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119712
C2×#180119692
#237495022
#1390149