Finite Group Databasebeta

← #491×D149 #34055028

Subgroups — #491×D149 #34055028

Order 19072.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D149C211yesmaximal, characteristic
2#125×D149C211yesmaximal, characteristic
3#23749995C211yesmaximal, characteristic, complemented
4#23749994C211yesmaximal, characteristic, complemented
5#23749993C211yesmaximal, characteristic, complemented
6#23749992C214yesmaximal, complemented
7#103×D149C214yesmaximal
8#97×D149C211yesmaximal, characteristic
9#491×C149C211yesmaximal, characteristic, complemented
10C2×Q8×D149C2212yes—
11C2×C8×D149C2212yes—
12#18011911C2211yescharacteristic
13#18011910—22no—
14#18011909C2212yes—
15#18011903C2211yescharacteristic
16#18011902C2212yes—
17#18011901—22no—
18C4⋊C4×D149—22no—
19C4⋊C4×D149—22no—
20C4⋊C4×D149C2212yes—
21C42×D149C2211yescharacteristic
22#18011836C2214yes—
23#18011835C2214yes—
24#18011834C2214yes—
25#18011822C2211yescharacteristic
26#18011821C2212yes—
27C4⋊Q8×C149C2211yescharacteristic
28#125×C149C2211yescharacteristic
29#103×C149C2214yes—
30#97×C149C2211yescharacteristic
31C2×Dic298—22no—
32C2×Dic298C2312yes—
33Q8×D149—28no—
34C2×C4×D149—22no—
35C2×C4×D149—22no—
36C2×C4×D149D412yes—
37C2×C4×D149C2311yescharacteristic
38C2×#11924746C2312yes—
39C8×D149—24no—
40C4⋊Dic149—22no—
41C4⋊Dic149—22no—
42C4⋊Dic149C2312yes—
43#14558715—24no—
44#14558715—22no—
45#14558715—22no—
46#14558715—22no—
47C4×Dic149D412yes—
48C4×Dic149C2311yescharacteristic
49C2×Q8×C149C2312yes—
50C2×C8×C149C2312yes—
51C4⋊C4×C149—22no—
52C4⋊C4×C149—22no—
53C4⋊C4×C149C2312yes—
54C42×C149C2311yescharacteristic
55C22×D149C2×D411yescharacteristic
56Dic298—24no—
57Dic298—44no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149C2×D412yes—
61C2×Dic149C2×D411yescharacteristic
62C4×D149—24no—
63C4×D149—44no—
64C4×D149—44no—
65C4×D149#4114yes—
66#11924746—22no—
67Q8×C149—24no—
68C2×C4×C149—22no—
69C2×C4×C149—22no—
70C2×C4×C149C2×D412yes—
71C2×C4×C149C2411yescharacteristic
72C8×C149—22no—
73C22×C149C22×D411yescharacteristic
74C2×D149#12412yes—
75C2×D149#13714yes—
76C4×C149—22no—
77C4×C149—42no—
78C4×C149—42no—
79C4×C149C2×#4112yes—
80Dic149—22no—
81Dic149—42no—
82Dic149—42no—
83Dic149#12412yes—
84C2×C149C2×#12411yescharacteristic
85C2×C149C2×#13712yes—
86D149#49114yesdirect product factor
87C149C2×#49111yescharacteristic, complemented, Sylow
88C2×#491—1491nomaximal, Sylow
89C2×C4⋊Q8—1491no—
90C2×#125—1491no—
91#491—1491no—
92#491—1491no—
93#491—1494no—
94#491—1491no—
95#491D14911yescharacteristic, direct product factor
96C2×#103—1494no—
97C2×#97—1491no—
98C22×Q8—1492no—
99C22×C8—1492no—
100C4⋊Q8—2982no—
101C4⋊Q8—1492no—
102C4⋊Q8—1491no—
103C4⋊Q8C2×D14911yescharacteristic
104#125—2982no—
105#125—1492no—
106#125—1491no—
107#125C2×D14911yescharacteristic
108C2×C4⋊C4—2982no—
109C2×C4⋊C4—2982no—
110C2×C4⋊C4—1492no—
111C2×C42—1491no—
112#103—1494no—
113#103—1494no—
114#103—1494no—
115#103C2×D14914yes—
116#97—1492no—
117#97—1491no—
118#97C2×D14911yescharacteristic
119C2×Q8—2982no—
120C2×Q8—2988no—
121C2×Q8—1492no—
122C2×Q8C22×D14912yes—
123C22×C4—2982no—
124C22×C4—2982no—
125C22×C4—1492no—
126C22×C4—1491no—
127C2×C8—2984no—
128C2×C8—1492no—
129C2×C8C22×D14912yes—
130C4⋊C4—22no—
131C4⋊C4—22no—
132C4⋊C4—2982no—
133C4⋊C4—2982no—
134C4⋊C4—2984no—
135C4⋊C4—2982no—
136C4⋊C4—2982no—
137C4⋊C4—2982no—
138C4⋊C4—1492no—
139C4⋊C4C22×D14912yes—
140C42—1492no—
141C42—1491no—
142C42C22×D14911yescharacteristic
143C23—1491no—
144Q8—24no—
145Q8—2984no—
146Q8—5964no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—2984no—
150C2×C4—2982no—
151C2×C4—2982no—
152C2×C4—5964no—
153C2×C4—5964no—
154C2×C4—1492no—
155C2×C4—1491no—
156C2×C4—1494no—
157C2×C4D4×D14912yes—
158C2×C4C23×D14911yescharacteristic
159C8—22no—
160C8—2982no—
161C22—1494no—
162C22—1492no—
163C22C2×D4×D14911yescharacteristic
164C4—22no—
165C4—42no—
166C4—42no—
167C4—2982no—
168C4—5962no—
169C4—5962no—
170C4—1492no—
171C4#41×D14912yes—
172C2—1494no—
173C2#124×D14911yescharacteristic
174C2#137×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#491×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#491D149
hypocenterC149C2×#491
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. #23749995C2semidirect
4. #23749994C2semidirect
5. #23749993C2semidirect
6. #23749992C2semidirect
9. #491×C149C2semidirect
86. D149#491direct (N × H)
87. C149C2×#491semidirect
95. #491D149direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1492
#125×D1492
#237499952
#237499942
#237499932
#237499922
#103×D1492
#97×D1492
#491×C1492
C2×#491149