Finite Group Databasebeta

← #1459×C149 #34040372

Subgroups — #1459×C149 #34040372

Order 19072.

332 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 124 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×C4×D4×C149C211yesmaximal, characteristic
2C2×C22⋊C8×C149C212yesmaximal, complemented
3#324×C149C212yesmaximal, complemented
4#323×C149C212yesmaximal, complemented
5C22×D4×C149C411yescharacteristic
6C23×C4×C149C411yescharacteristic
7C23×C4×C149C2211yescharacteristic
8C22×C8×C149—22no—
9C4×D4×C149—22no—
10C4×D4×C149—22no—
11C2×C4⋊C4×C149C2211yescharacteristic
12C2×C22⋊C4×C149C411yescharacteristic
13C2×C22⋊C4×C149C2211yescharacteristic
14C2×C42×C149C411yescharacteristic
15C22⋊C8×C149—22no—
16C22⋊C8×C149C2214yes—
17C24×C149C2×C411yescharacteristic
18C24×C149C2×C411yescharacteristic
19C2×D4×C149—22no—
20C2×D4×C149—22no—
21C2×D4×C149C814yescomplemented
22C22×C4×C149—21no—
23C22×C4×C149—21no—
24C22×C4×C149—42no—
25C22×C4×C149—42no—
26C22×C4×C149C2×C411yescharacteristic
27C22×C4×C149C2×C411yescharacteristic
28C22×C4×C149C2×C411yescharacteristic
29C22×C4×C149C2×C411yescharacteristic
30C22×C4×C149D412yes—
31C22×C4×C149D412yes—
32C22×C4×C149C2311yescharacteristic
33C2×C8×C149—24no—
34C2×C8×C149—44no—
35C4⋊C4×C149—22no—
36C22⋊C4×C149—22no—
37C22⋊C4×C149—22no—
38C42×C149—21no—
39C42×C149—21no—
40C23×C149—21no—
41C23×C149—21no—
42C23×C149—41no—
43C23×C149—41no—
44C23×C149—41no—
45C23×C149—41no—
46C23×C149C22⋊C412yes—
47C23×C149C2×C812yes—
48C23×C149C2×C812yescomplemented
49C23×C149M1612yes—
50C23×C149C22×C411yescharacteristic
51D4×C149—28no—
52C2×C4×C149—21no—
53C2×C4×C149—21no—
54C2×C4×C149—24no—
55C2×C4×C149—22no—
56C2×C4×C149—21no—
57C2×C4×C149—21no—
58C2×C4×C149—42no—
59C2×C4×C149—41no—
60C2×C4×C149—42no—
61C2×C4×C149—42no—
62C2×C4×C149—41no—
63C2×C4×C149—41no—
64C2×C4×C149C22⋊C411yescharacteristic
65C2×C4×C149C22⋊C411yescharacteristic
66C2×C4×C149C2×C812yescomplemented
67C2×C4×C149C2×D412yes—
68C8×C149—44no—
69C22×C149—21no—
70C22×C149—22no—
71C22×C149—21no—
72C22×C149—22no—
73C22×C149—22no—
74C22×C149—42no—
75C22×C149—42no—
76C22×C149—42no—
77C22×C149—42no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149C22⋊C814yes—
81C22×C149C2×C22⋊C411yescharacteristic
82C22×C149C22×C811yescharacteristic
83C22×C149C2×M1611yescharacteristic
84C4×C149—22no—
85C4×C149—22no—
86C4×C149—21no—
87C4×C149—41no—
88C4×C149—41no—
89C4×C149#9912yes—
90C2×C149—21no—
91C2×C149—21no—
92C2×C149—24no—
93C2×C149—42no—
94C2×C149C2×C22⋊C811yescharacteristic
95C2×C149C2×#9911yescharacteristic
96C2×C149#41311yescharacteristic
97C149#145911yescharacteristic, direct product factor, Sylow
98#1459C14911yesmaximal, characteristic, direct product factor, Sylow
99C2×C4×D4C2×C14911yescharacteristic
100C2×C22⋊C8C2×C14912yescomplemented
101#324C2×C14912yescomplemented
102#323C2×C14912yescomplemented
103C22×D4C4×C14911yescharacteristic
104C23×C4C4×C14911yescharacteristic
105C23×C4C22×C14911yescharacteristic
106C22×C8—22no—
107C4×D4—22no—
108C4×D4—22no—
109C2×C4⋊C4C22×C14911yescharacteristic
110C2×C22⋊C4C4×C14911yescharacteristic
111C2×C22⋊C4C22×C14911yescharacteristic
112C2×C42C4×C14911yescharacteristic
113C22⋊C8—22no—
114C22⋊C8C22×C14914yes—
115C24C2×C4×C14911yescharacteristic
116C24C2×C4×C14911yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4C8×C14914yescomplemented
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—42no—
123C22×C4—42no—
124C22×C4C2×C4×C14911yescharacteristic
125C22×C4C2×C4×C14911yescharacteristic
126C22×C4C2×C4×C14911yescharacteristic
127C22×C4C2×C4×C14911yescharacteristic
128C22×C4D4×C14912yes—
129C22×C4D4×C14912yes—
130C22×C4C23×C14911yescharacteristic
131C2×C8—24no—
132C2×C8—44no—
133C4⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C42—21no—
137C42—21no—
138C23—21no—
139C23—21no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—41no—
144C23C22⋊C4×C14912yes—
145C23C2×C8×C14912yes—
146C23C2×C8×C14912yescomplemented
147C23M16×C14912yes—
148C23C22×C4×C14911yescharacteristic
149D4—28no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4C22⋊C4×C14911yescharacteristic
163C2×C4C22⋊C4×C14911yescharacteristic
164C2×C4C2×C8×C14912yescomplemented
165C2×C4C2×D4×C14912yes—
166C8—44no—
167C22—21no—
168C22—22no—
169C22—21no—
170C22—22no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22C22⋊C8×C14914yes—
179C22C2×C22⋊C4×C14911yescharacteristic
180C22C22×C8×C14911yescharacteristic
181C22C2×M16×C14911yescharacteristic
182C4—22no—
183C4—22no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4#99×C14912yes—
188C2—21no—
189C2—21no—
190C2—24no—
191C2—42no—
192C2C2×C22⋊C8×C14911yescharacteristic
193C2C2×#99×C14911yescharacteristic
194C2#413×C14911yescharacteristic
subgroupG/H
centerC2×C4×C149C22⋊C4
commutatorC22C22×C8×C149
Frattini, cosocleC22×C4C23×C149
socleC22×C149C2×C22⋊C4
prime radicalC22×D4×C149C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×C149C2semidirect
3. #324×C149C2semidirect
4. #323×C149C2semidirect
21. C2×D4×C149C8semidirect
48. C23×C149C2×C8semidirect
66. C2×C4×C149C2×C8semidirect
97. C149#1459direct (N × H)
98. #1459C149direct (N × H)
100. C2×C22⋊C8C2×C149semidirect
101. #324C2×C149semidirect
102. #323C2×C149semidirect
119. C2×D4C8×C149semidirect
146. C23C2×C8×C149semidirect
164. C2×C4C2×C8×C149semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C1492
C2×C22⋊C8×C1492
#324×C1492
#323×C1492
#1459149