Finite Group Databasebeta

← D149⋊#354 #34060960

Subgroups — D149⋊#354 #34060960

Order 19072.

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

normal subgroups only

This group has 284 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⋊#99C212yesmaximal
2#23750532C212yesmaximal, complemented
3#23750531C212yesmaximal, complemented
4#124×D149C211yesmaximal, characteristic
5C2×C22⋊#10597010—22no—
6#18011970C2214yes—
7#18011969—22no—
8C2×Q8×D149C411yescharacteristic, complemented
9C2×D4×D149C2211yescharacteristic
10#18011900C2211yescharacteristic
11#18011899C2211yescharacteristic
12#18011898C411yescharacteristic, complemented
13#18011897—22no—
14C22⋊C4×D149—22no—
15C42×D149C411yescharacteristic, complemented
16#124×C149C411yescharacteristic, complemented
17C22×#10597010—42no—
18C22⋊#10597010—24no—
19C22⋊#10597010—42no—
20C23×D149D412yes—
21C2×Dic298—21no—
22C2×Dic298C2×C411yescharacteristic, complemented
23Q8×D149—41no—
24Q8×D149—41no—
25C2×D596C2311yescharacteristic
26C2×C22⋊D149D412yes—
27D4×D149—41no—
28D4×D149—41no—
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149C2×C411yescharacteristic
32C22⋊Dic149—22no—
33#14558713—22no—
34#14558713—22no—
35C4×Dic149—21no—
36C4×Dic149C2×C411yescharacteristic, complemented
37C2×Q8×C149C2×C411yescharacteristic, complemented
38C2×D4×C149C2×C411yescharacteristic
39C22⋊C4×C149—22no—
40C42×C149C2×C411yescharacteristic, complemented
41C2×#10597010—44no—
42C2×#10597010—84no—
43C22×D149—22no—
44C22×D149—22no—
45C22×D149—44no—
46C22×D149C22⋊C411yescharacteristic
47C22×D149C2×D412yes—
48Dic298—42no—
49Dic298—41no—
50D596—41no—
51C22⋊D149—42no—
52C2×Dic149—21no—
53C2×Dic149—21no—
54C2×Dic149C22⋊C411yescharacteristic
55C4×D149—21no—
56C4×D149—21no—
57C4×D149—42no—
58C4×D149—41no—
59C4×D149—41no—
60C23×C149C22⋊C412yes—
61Q8×C149—41no—
62D4×C149—41no—
63C2×C4×C149—21no—
64C2×C4×C149—21no—
65C2×C4×C149C22×C411yescharacteristic
66C22×C149—22no—
67C22×C149—42no—
68C22×C149C2×C22⋊C411yescharacteristic
69C2×D149—22no—
70C2×D149—22no—
71C2×D149—44no—
72C2×D149—42no—
73C2×D149—82no—
74C2×D149#9911yescharacteristic
75C2×D149#9911yescharacteristic
76#10597010—84no—
77C4×C149—21no—
78C4×C149—41no—
79C4×C149—41no—
80Dic149—21no—
81Dic149—41no—
82Dic149—41no—
83C2×C149—21no—
84C2×C149—42no—
85C2×C149C2×#9911yescharacteristic
86D149—21no—
87D149—42no—
88D149#35412yescomplemented
89C149C2×#35411yescharacteristic, complemented, Sylow
90C2×#354—1491nomaximal, Sylow
91C2×#124—1491no—
92C2×#99—1492no—
93#354—1492no—
94#354—1492no—
95C22×Q8—1491no—
96C22×D4—1491no—
97#124—2982no—
98#124—1491no—
99#124—1491no—
100#124—1491no—
101#124#1059701011yescharacteristic, complemented
102C2×C22⋊C4—2982no—
103C2×C22⋊C4—2982no—
104C2×C42—1491no—
105#99—2982no—
106#99—1494no—
107C24—1492no—
108C2×Q8—2981no—
109C2×Q8—5961no—
110C2×Q8—5961no—
111C2×Q8—1491no—
112C2×Q8C2×#1059701011yescharacteristic, complemented
113C2×D4—5961no—
114C2×D4—5961no—
115C2×D4—1492no—
116C2×D4—1491no—
117C2×D4C2×#1059701011yescharacteristic
118C22×C4—2981no—
119C22×C4—2981no—
120C22×C4—5962no—
121C22×C4—1491no—
122C22⋊C4—22no—
123C22⋊C4—2982no—
124C22⋊C4—2982no—
125C22⋊C4—2982no—
126C22⋊C4—2984no—
127C22⋊C4—5962no—
128C42—2981no—
129C42—1491no—
130C42C2×#1059701011yescharacteristic, complemented
131C23—2982no—
132C23—2982no—
133C23—5964no—
134C23—1491no—
135C23—1492no—
136C23C22⋊#1059701012yes—
137Q8—41no—
138Q8—5961no—
139Q8—5962no—
140D4—41no—
141D4—5961no—
142D4—5962no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2981no—
146C2×C4—2981no—
147C2×C4—2981no—
148C2×C4—2981no—
149C2×C4—5962no—
150C2×C4—5961no—
151C2×C4—5961no—
152C2×C4—5964no—
153C2×C4—1491no—
154C2×C4—11924no—
155C2×C4C22×#1059701011yescharacteristic
156C22—22no—
157C22—42no—
158C22—2982no—
159C22—2982no—
160C22—5962no—
161C22—5964no—
162C22—1491no—
163C22—1491no—
164C22—11922no—
165C22C2×C22⋊#1059701011yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—2981no—
170C4—5961no—
171C4—5961no—
172C4—11924no—
173C2—21no—
174C2—42no—
175C2—2981no—
176C2—5962no—
177C2—1492no—
178C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC2×C149C2×#99
prime radicalC2×D4×D149C22
cosocleC2×D596C23
hypercenter#124#10597010
hypocenterC149C2×#354
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #23750532C2semidirect
3. #23750531C2semidirect
8. C2×Q8×D149C4semidirect
12. #18011898C4semidirect
15. C42×D149C4semidirect
16. #124×C149C4semidirect
22. C2×Dic298C2×C4semidirect
36. C4×Dic149C2×C4semidirect
37. C2×Q8×C149C2×C4semidirect
40. C42×C149C2×C4semidirect
88. D149#354semidirect
89. C149C2×#354semidirect
101. #124#10597010semidirect
112. C2×Q8C2×#10597010semidirect
130. C42C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#992
#237505322
#237505312
#124×D1492
C2×#354149