Finite Group Databasebeta

← #34055338

Subgroups — #34055338

Order 19072.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#23750229C212yesmaximal, complemented
2#23750027C211yesmaximal, characteristic, complemented
3#23749989C212yesmaximal, complemented
4#23749875C212yesmaximal, complemented
5#23749858C212yesmaximal, complemented
6#23749737C212yesmaximal, complemented
7D8×Dic149C212yesmaximal, complemented
8#23749579C211yesmaximal, characteristic, complemented
9#493×C149C211yesmaximal, characteristic, complemented
10C2×#14558719C2211yescharacteristic
11C2×C8×D149C2211yescharacteristic
12#18011903C2212yes—
13#18011892—24no—
14#18011883—24no—
15#18011882C2214yes—
16D4×Dic149C2214yes—
17#18011868C2211yescharacteristic
18#18011845C2212yes—
19#18011843C2212yes—
20#18011832C2214yes—
21#18011832C2214yes—
22#18011822C2211yescharacteristic
23#18011821C2211yescharacteristic
24C8×Dic149C2211yescharacteristic
25C2×D8×C149C2212yes—
26C2×D8×C149C2212yes—
27#127×C149C2212yes—
28C4×C8×C149C2211yescharacteristic
29C2×C22⋊D149—24no—
30C22×Dic149—24no—
31C2×C4×D149C2311yescharacteristic
32#14558719—22no—
33C2×#11924746C2311yescharacteristic
34C2×#11924746C2311yescharacteristic
35C8×D149—22no—
36C4⋊Dic149C2314yes—
37#14558715—24no—
38#14558715D412yes—
39C22⋊Dic149—24no—
40C22⋊Dic149—24no—
41#14558713D412yes—
42C4×Dic149C2311yescharacteristic
43C2×D4×C149—24no—
44C2×D4×C149C2314yes—
45D8×C149—24no—
46D8×C149—24no—
47C2×C8×C149C2311yescharacteristic
48C2×C8×C149C2311yescharacteristic
49C42×C149C2311yescharacteristic
50C22×D149C2×D411yescharacteristic
51C22⋊D149—84no—
52C2×Dic149—24no—
53C2×Dic149—84no—
54C2×Dic149C2×D411yescharacteristic
55C2×Dic149C2×D412yes—
56C4×D149—21no—
57C4×D149—21no—
58#11924746—21no—
59#11924746—21no—
60C23×C149—24no—
61D4×C149—24no—
62D4×C149—24no—
63D4×C149—84no—
64C2×C4×C149C2×D412yes—
65C2×C4×C149C2411yescharacteristic
66C8×C149#4112yes—
67C8×C149#4112yes—
68C22×C149—44no—
69C22×C149—44no—
70C22×C149—44no—
71C22×C149C22×D411yescharacteristic
72C2×D149—21no—
73C2×D149—22no—
74C4×C149—22no—
75C4×C149C2×#4111yescharacteristic
76C4×C149C2×#4111yescharacteristic
77Dic149—21no—
78Dic149—22no—
79Dic149—44no—
80C2×C149—84no—
81C2×C149#53211yescharacteristic
82C2×C149#57612yes—
83D149—41no—
84C149#317611yescharacteristic, complemented, Sylow
85#3176—1491nomaximal, Sylow
86#540—1492no—
87#499—1491no—
88#493D14911yescharacteristic, complemented
89#490—1492no—
90#469—1492no—
91#466—1492no—
92#442—1492no—
93C4×D8—1492no—
94#405—1491no—
95C2×D8C2×D14912yes—
96C2×D8C2×D14912yes—
97C2×M16—1491no—
98C22×C8—1491no—
99#127C2×D14912yes—
100#125—1492no—
101#123—2984no—
102#121—2984no—
103#121—1494no—
104C4×D4—1494no—
105#117—1491no—
106#107—1492no—
107#106—1492no—
108#102—1494no—
109#102—1494no—
110#97—1491no—
111#97—1491no—
112C4×C8—1491no—
113C4×C8C2×D14911yescharacteristic
114C2×D4—24no—
115C2×D4—2984no—
116C2×D4C22×D14914yes—
117C22×C4—2984no—
118C22×C4—1491no—
119D8—24no—
120D8—24no—
121M16—2982no—
122C2×C8—2982no—
123C2×C8—1491no—
124C2×C8—1491no—
125C2×C8C22×D14911yescharacteristic
126C2×C8C22×D14911yescharacteristic
127C4⋊C4—2984no—
128C4⋊C4—1494no—
129C4⋊C4—1492no—
130C22⋊C4—2984no—
131C22⋊C4—2984no—
132C22⋊C4—1492no—
133C42—1491no—
134C42C22×D14911yescharacteristic
135C23—24no—
136C23—1491no—
137D4—24no—
138D4—24no—
139D4—84no—
140D4—11924no—
141C2×C4—2981no—
142C2×C4—2981no—
143C2×C4—2984no—
144C2×C4—1492no—
145C2×C4—1491no—
146C2×C4—11924no—
147C2×C4D4×D14912yes—
148C2×C4C23×D14911yescharacteristic
149C8—2981no—
150C8—2981no—
151C8#1455873512yes—
152C8#1455873512yes—
153C22—44no—
154C22—44no—
155C22—44no—
156C22—2982no—
157C22—2981no—
158C22C2×D4×D14911yescharacteristic
159C4—22no—
160C4—2982no—
161C4—2981no—
162C4—5964no—
163C4C2×#1455873511yescharacteristic
164C4C2×#1455873511yescharacteristic
165C2—84no—
166C2—5961no—
167C2#2375017311yescharacteristic
168C2#2375042612yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#493×C149C2
socleC22×C149C22×D4
hypercenter#493D149
hypocenterC149#3176
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #23750229C2semidirect
2. #23750027C2semidirect
3. #23749989C2semidirect
4. #23749875C2semidirect
5. #23749858C2semidirect
6. #23749737C2semidirect
7. D8×Dic149C2semidirect
8. #23749579C2semidirect
9. #493×C149C2semidirect
84. C149#3176semidirect
88. #493D149semidirect

Maximal subgroups

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

subgroupindex
#237502292
#237500272
#237499892
#237498752
#237498582
#237497372
D8×Dic1492
#237495792
#493×C1492
#3176149