Finite Group Databasebeta

← D149⋊#356 #34060980

Subgroups — D149⋊#356 #34060980

Order 19072.

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

normal subgroups only

This group has 240 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
2#23750536C212yesmaximal, complemented
3#23750535C212yesmaximal, complemented
4C4⋊Q8×D149C211yesmaximal, characteristic
5D149⋊M16—22no—
6#18011972—22no—
7#18011972C2214yes—
8C2×Q8×D149C411yescharacteristic
9C2×Q8×D149C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011910—22no—
12#18011909C411yescharacteristic
13#18011909C2211yescharacteristic
14C4⋊C4×D149—22no—
15C42×D149C411yescharacteristic
16C4⋊Q8×C149C411yescharacteristic
17#14558746—42no—
18#14558745—24no—
19D149⋊C8—42no—
20C2×Dic298—21no—
21C2×Dic298C2×C411yescharacteristic
22C2×Dic298D412yes—
23C2×Dic298C2311yescharacteristic
24Q8×D149—41no—
25Q8×D149—41no—
26Q8×D149—41no—
27Q8×D149—41no—
28C2×C4×D149—21no—
29C2×C4×D149—21no—
30C2×C4×D149C2×C411yescharacteristic
31C2×C4×D149D412yes—
32C4⋊Dic149—22no—
33#14558715—22no—
34#14558715—22no—
35C4×Dic149—21no—
36C4×Dic149C2×C411yescharacteristic
37C2×Q8×C149C2×C411yescharacteristic
38C2×Q8×C149C2×C411yescharacteristic
39C4⋊C4×C149—22no—
40C42×C149C2×C411yescharacteristic
41#11924753—44no—
42C22×D149C22⋊C411yescharacteristic
43Dic298—42no—
44Dic298—41no—
45Dic298—42no—
46Dic298—41no—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149C2×D412yes—
51C4×D149—24no—
52C4×D149—21no—
53C4×D149—21no—
54C4×D149—22no—
55C4×D149—22no—
56C4×D149—41no—
57C4×D149—41no—
58Q8×C149—41no—
59Q8×C149—41no—
60C2×C4×C149—21no—
61C2×C4×C149—21no—
62C2×C4×C149C22⋊C412yes—
63C2×C4×C149C22×C411yescharacteristic
64C22×C149C2×C22⋊C411yescharacteristic
65C2×D149—22no—
66C2×D149#9911yescharacteristic
67C2×D149#9911yescharacteristic
68C4×C149—22no—
69C4×C149—22no—
70C4×C149—21no—
71C4×C149—41no—
72Dic149—22no—
73Dic149—21no—
74Dic149—22no—
75Dic149—41no—
76C2×C149—21no—
77C2×C149C2×#9911yescharacteristic
78D149—21no—
79D149#35612yescomplemented
80C149C2×#35611yescharacteristic, complemented, Sylow
81C2×#356—1491nomaximal, Sylow
82C2×C4⋊Q8—1491no—
83C2×#101—1492no—
84#356—1492no—
85#356—1492no—
86C22×Q8—1491no—
87C22×Q8—1491no—
88C2×M16—2982no—
89C4⋊Q8—2982no—
90C4⋊Q8—1491no—
91C4⋊Q8—1491no—
92C4⋊Q8—1491no—
93C4⋊Q8#1059701011yescharacteristic
94C2×C4⋊C4—2982no—
95C2×C42—1491no—
96#101—2982no—
97#101—1494no—
98C2×Q8—2981no—
99C2×Q8—5961no—
100C2×Q8—5961no—
101C2×Q8—5961no—
102C2×Q8—5961no—
103C2×Q8—1491no—
104C2×Q8—1492no—
105C2×Q8—1491no—
106C2×Q8C2×#1059701011yescharacteristic
107C2×Q8C2×#1059701011yescharacteristic
108C22×C4—2981no—
109C22×C4—2981no—
110C22×C4—1492no—
111C22×C4—1491no—
112M16—2984no—
113M16—5962no—
114C2×C8—5962no—
115C4⋊C4—22no—
116C4⋊C4—2982no—
117C4⋊C4—2982no—
118C4⋊C4—2982no—
119C42—2981no—
120C42—1491no—
121C42C2×#1059701011yescharacteristic
122C23—1491no—
123Q8—41no—
124Q8—41no—
125Q8—5962no—
126Q8—5961no—
127Q8—5961no—
128Q8—5962no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—2984no—
132C2×C4—2982no—
133C2×C4—2982no—
134C2×C4—2981no—
135C2×C4—2981no—
136C2×C4—2981no—
137C2×C4—2981no—
138C2×C4—5961no—
139C2×C4—5961no—
140C2×C4—1491no—
141C2×C4—1492no—
142C2×C4C22⋊#1059701012yes—
143C2×C4C22×#1059701011yescharacteristic
144C8—5964no—
145C22—2982no—
146C22—1491no—
147C22—1491no—
148C22C2×C22⋊#1059701011yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—2982no—
154C4—2982no—
155C4—2981no—
156C4—5961no—
157C2—21no—
158C2—2981no—
159C2—1492no—
160C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC2×C149C2×#99
prime radicalC22×D149C22⋊C4
cosocleC2×Dic298C23
hypercenterC4⋊Q8#10597010
hypocenterC149C2×#356
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23750536C2semidirect
3. #23750535C2semidirect
79. D149#356semidirect
80. C149C2×#356semidirect

Maximal subgroups

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

subgroupindex
D149⋊#1012
#237505362
#237505352
C4⋊Q8×D1492
C2×#356149