Finite Group Databasebeta

← C2×D149⋊#101 #34061297

Subgroups — C2×D149⋊#101 #34061297

Order 19072.

736 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 210 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×D149⋊M16C212yesmaximal
2D149⋊#101C218yesmaximal, direct product factor
3C2×#18011972C214yesmaximal, complemented
4C22×Q8×D149C211yesmaximal, characteristic
5C2×#14558746—22no—
6D149⋊M16—24no—
7D149⋊M16C2218yes—
8C2×#14558745C2214yes—
9C2×D149⋊C8—22no—
10#18011972C22116yescomplemented
11C22×Dic298C411yescharacteristic
12C22×Dic298C2212yes—
13C2×Q8×D149—22no—
14C2×Q8×D149—24no—
15C2×Q8×D149—22no—
16C2×Q8×D149C414yes—
17C2×Q8×D149C2214yes—
18C22×C4×D149C412yes—
19C22×C4×D149C2211yescharacteristic
20C22×Q8×C149C411yescharacteristic
21#14558746—28no—
22#14558745—24no—
23#14558745C2318yes—
24D149⋊C8—28no—
25C2×#11924753—24no—
26C23×D149C2×C411yescharacteristic
27C2×Dic298—24no—
28C2×Dic298—24no—
29C2×Dic298—22no—
30C2×Dic298—22no—
31C2×Dic298C2×C414yes—
32C2×Dic298C2×C414yes—
33C2×Dic298C2314yes—
34Q8×D149—28no—
35Q8×D149—28no—
36Q8×D149—28no—
37Q8×D149—28no—
38C22×Dic149C2×C412yes—
39C22×Dic149C2311yescharacteristic
40C2×C4×D149—24no—
41C2×C4×D149—22no—
42C2×C4×D149—22no—
43C2×C4×D149C2×C418yes—
44C2×C4×D149C2×C412yes—
45C2×C4×D149D412yes—
46C2×C4×D149D414yes—
47C2×C4×D149D412yes—
48C2×C4×D149C2312yes—
49C2×Q8×C149—22no—
50C2×Q8×C149—22no—
51C2×Q8×C149C2×C414yes—
52C22×C4×C149C2×C412yes—
53C22×C4×C149C2×C411yescharacteristic
54#11924753—28no—
55C22×D149—24no—
56C22×D149C22⋊C412yes—
57C22×D149C22⋊C411yescharacteristic
58C22×D149C22⋊C411yescharacteristic
59C22×D149C22×C412yes—
60Dic298—28no—
61Dic298—28no—
62Dic298—28no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149C22×C414yes—
66C2×Dic149C22×C411yescharacteristic
67C2×Dic149C2×D412yes—
68C2×Dic149C2×D412yes—
69C2×Dic149C2411yescharacteristic
70C4×D149—28no—
71C4×D149—28no—
72C4×D149C22⋊C414yes—
73C4×D149C22⋊C414yes—
74C4×D149C2×D414yes—
75C4×D149C2×D414yes—
76C23×C149C22×C411yescharacteristic
77Q8×C149—28no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149C22⋊C412yes—
81C2×C4×C149C22⋊C412yes—
82C2×C4×C149C22×C414yes—
83C2×C4×C149C22×C412yes—
84C22×C149—22no—
85C22×C149C2×C22⋊C411yescharacteristic
86C22×C149C2×C22⋊C411yescharacteristic
87C22×C149C23×C411yescharacteristic
88C2×D149—22no—
89C2×D149—24no—
90C2×D149—24no—
91C2×D149#10114yescomplemented
92C2×D149C2×C22⋊C412yes—
93C2×D149C2×C22⋊C412yes—
94C4×C149—24no—
95C4×C149C2×C22⋊C414yes—
96Dic149—24no—
97Dic149C2×C22⋊C412yes—
98Dic149C22×D412yes—
99C2×C149—21no—
100C2×C149—21no—
101C2×C149C2×#10112yescomplemented
102C2×C149C22×C22⋊C411yescharacteristic
103D149—22no—
104D149C2×#10114yescomplemented
105C149C22×#10111yescharacteristic, complemented, Sylow
106C22×#101—1491nomaximal, Sylow
107C23×Q8—1491no—
108C22×M16—1492no—
109C2×#101—1494no—
110C2×#101—1498no—
111C22×Q8—2982no—
112C22×Q8—2984no—
113C22×Q8—2982no—
114C22×Q8—1494no—
115C22×Q8—1494no—
116C22×Q8—1492no—
117C22×Q8—1491no—
118C22×Q8#1059701011yescharacteristic
119C23×C4—1492no—
120C23×C4—1491no—
121C2×M16—2984no—
122C2×M16—2982no—
123C2×M16—1494no—
124C2×M16—1498no—
125C22×C8—2982no—
126#101—14916no—
127C24—1491no—
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—2984no—
131C2×Q8—2984no—
132C2×Q8—2988no—
133C2×Q8—2988no—
134C2×Q8—2988no—
135C2×Q8—2988no—
136C2×Q8—2982no—
137C2×Q8—2982no—
138C2×Q8—1494no—
139C2×Q8—1494no—
140C2×Q8—1494no—
141C2×Q8C2×#1059701014yes—
142C22×C4—2984no—
143C22×C4—2982no—
144C22×C4—2982no—
145C22×C4—1492no—
146C22×C4—1498no—
147C22×C4—1491no—
148C22×C4—1492no—
149C22×C4—1494no—
150C22×C4—1492no—
151C22×C4—1492no—
152C22×C4—1492no—
153C22×C4C2×#1059701012yes—
154C22×C4C2×#1059701011yescharacteristic
155M16—2984no—
156M16—2988no—
157M16—1498no—
158C2×C8—2984no—
159C2×C8—2988no—
160C23—2984no—
161C23—1492no—
162C23—1491no—
163C23—1492no—
164C23—1491no—
165C23C22×#1059701011yescharacteristic
166Q8—28no—
167Q8—2988no—
168Q8—2988no—
169Q8—2988no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—2988no—
173C2×C4—2988no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—1494no—
177C2×C4—1492no—
178C2×C4—1492no—
179C2×C4—1491no—
180C2×C4—1491no—
181C2×C4—1494no—
182C2×C4—1494no—
183C2×C4—1494no—
184C2×C4—1494no—
185C2×C4C22⋊#1059701012yes—
186C2×C4C22⋊#1059701012yes—
187C2×C4C22×#1059701014yes—
188C2×C4C22×#1059701012yes—
189C8—2988no—
190C22—22no—
191C22—2984no—
192C22—2984no—
193C22—2982no—
194C22—1492no—
195C22—1492no—
196C22—1494no—
197C22C2×C22⋊#1059701011yescharacteristic
198C22C2×C22⋊#1059701011yescharacteristic
199C22C23×#1059701011yescharacteristic
200C4—24no—
201C4—2984no—
202C4—1492no—
203C4—1492no—
204C4C2×C22⋊#1059701014yes—
205C2—21no—
206C2—21no—
207C2—2982no—
208C2—1494no—
209C2D149⋊#10112yesdirect product factor
210C2C22×C22⋊#1059701011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC22×C149C23×C4
FrattiniC22C23×#10597010
FittingC22×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC2×Dic149C24
hypercenterC22×Q8#10597010
hypocenterC149C22×#101
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. D149⋊#101C2direct (N × H)
3. C2×#18011972C2semidirect
10. #18011972C22semidirect
91. C2×D149#101semidirect
101. C2×C149C2×#101semidirect
104. D149C2×#101semidirect
105. C149C22×#101semidirect
209. C2D149⋊#101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D149⋊M162
D149⋊#1012
C2×#180119722
C22×Q8×D1492
C22×#101149