Finite Group Databasebeta

← D149⋊#355 #34060977

Subgroups — D149⋊#355 #34060977

Order 19072.

260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D149⋊#101C212yesmaximal, complemented
2#23750534C212yesmaximal, complemented
3#23750533C212yesmaximal, complemented
4#124×D149C211yesmaximal, characteristic
5D149⋊M16—22no—
6#18011972—22no—
7#18011972C2214yescomplemented
8C2×Q8×D149C2211yescharacteristic
9C2×D4×D149C411yescharacteristic
10#18011900C411yescharacteristic
11#18011899C2211yescharacteristic
12#18011898C2211yescharacteristic
13#18011897—22no—
14C22⋊C4×D149—22no—
15C42×D149C411yescharacteristic
16#124×C149C411yescharacteristic
17#14558746—42no—
18#14558745—24no—
19D149⋊C8—42no—
20C23×D149—21no—
21C2×Dic298D412yes—
22C2×Dic298C2311yescharacteristic
23Q8×D149—41no—
24Q8×D149—41no—
25C2×D596C2×C411yescharacteristic
26C2×C22⋊D149—21no—
27D4×D149—41no—
28D4×D149—41no—
29C2×C4×D149—21no—
30C2×C4×D149C2×C411yescharacteristic
31C2×C4×D149D412yes—
32C22⋊Dic149—22no—
33#14558713—22no—
34#14558713—22no—
35C4×Dic149—21no—
36C4×Dic149C2×C411yescharacteristic
37C2×Q8×C149C2×C411yescharacteristic
38C2×D4×C149C2×C411yescharacteristic
39C22⋊C4×C149—22no—
40C42×C149C2×C411yescharacteristic
41#11924753—44no—
42C22×D149—21no—
43C22×D149—44no—
44C22×D149—41no—
45C22×D149—41no—
46C22×D149C22⋊C411yescharacteristic
47Dic298—42no—
48Dic298—41no—
49D596—41no—
50C22⋊D149—42no—
51C2×Dic149—21no—
52C2×Dic149C22⋊C411yescharacteristic
53C2×Dic149C2×D412yes—
54C4×D149—21no—
55C4×D149—21no—
56C4×D149—22no—
57C4×D149—22no—
58C4×D149—42no—
59C23×C149—21no—
60Q8×C149—41no—
61D4×C149—41no—
62C2×C4×C149—21no—
63C2×C4×C149C22⋊C412yes—
64C2×C4×C149C22×C411yescharacteristic
65C22×C149—42no—
66C22×C149—41no—
67C22×C149C2×C22⋊C411yescharacteristic
68C2×D149—22no—
69C2×D149—42no—
70C2×D149—41no—
71C2×D149—82no—
72C2×D149—82no—
73C2×D149#9911yescharacteristic
74C2×D149#9911yescharacteristic
75C4×C149—22no—
76C4×C149—21no—
77C4×C149—41no—
78Dic149—21no—
79Dic149—22no—
80Dic149—41no—
81C2×C149—21no—
82C2×C149—81no—
83C2×C149C2×#9911yescharacteristic
84D149—21no—
85D149—81no—
86D149#35512yescomplemented
87C149C2×#35511yescharacteristic, complemented, Sylow
88C2×#355—1491nomaximal, Sylow
89C2×#124—1491no—
90C2×#101—1492no—
91#355—1492no—
92#355—1492no—
93C22×Q8—1491no—
94C22×D4—1491no—
95C2×M16—2982no—
96#124—2982no—
97#124—1491no—
98#124—1491no—
99#124—1491no—
100#124#1059701011yescharacteristic
101C2×C22⋊C4—2982no—
102C2×C42—1491no—
103#101—2982no—
104#101—1494no—
105C24—2981no—
106C2×Q8—5961no—
107C2×Q8—5961no—
108C2×Q8—1492no—
109C2×Q8—1491no—
110C2×Q8C2×#1059701011yescharacteristic
111C2×D4—2981no—
112C2×D4—5961no—
113C2×D4—5961no—
114C2×D4—1491no—
115C2×D4C2×#1059701011yescharacteristic
116C22×C4—2981no—
117C22×C4—1492no—
118C22×C4—1491no—
119M16—2984no—
120M16—5962no—
121C2×C8—5962no—
122C22⋊C4—22no—
123C22⋊C4—2982no—
124C22⋊C4—2982no—
125C22⋊C4—2982no—
126C42—2981no—
127C42—1491no—
128C42C2×#1059701011yescharacteristic
129C23—21no—
130C23—2981no—
131C23—5964no—
132C23—5961no—
133C23—5961no—
134C23—1491no—
135Q8—41no—
136Q8—5962no—
137Q8—5961no—
138D4—41no—
139D4—5961no—
140D4—5962no—
141C2×C4—21no—
142C2×C4—2982no—
143C2×C4—2982no—
144C2×C4—2981no—
145C2×C4—2981no—
146C2×C4—2981no—
147C2×C4—5962no—
148C2×C4—1491no—
149C2×C4—1492no—
150C2×C4C22⋊#1059701012yes—
151C2×C4C22×#1059701011yescharacteristic
152C8—5964no—
153C22—42no—
154C22—41no—
155C22—2982no—
156C22—5962no—
157C22—5961no—
158C22—1491no—
159C22—1491no—
160C22—11922no—
161C22—11922no—
162C22C2×C22⋊#1059701011yescharacteristic
163C4—22no—
164C4—21no—
165C4—41no—
166C4—2982no—
167C4—2981no—
168C4—5961no—
169C2—21no—
170C2—81no—
171C2—2981no—
172C2—1492no—
173C2—11921no—
174C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC2×C149C2×#99
prime radicalC2×D4×D149C4
cosocleC2×Dic298C23
hypercenter#124#10597010
hypocenterC149C2×#355
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D149⋊#101C2semidirect
2. #23750534C2semidirect
3. #23750533C2semidirect
7. #18011972C22semidirect
86. D149#355semidirect
87. C149C2×#355semidirect

Maximal subgroups

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

subgroupindex
D149⋊#1012
#237505342
#237505332
#124×D1492
C2×#355149