Finite Group Databasebeta

← #34055090

Subgroups — #34055090

Order 19072.

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

normal subgroups only

This group has 392 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#23750173C211yesmaximal, characteristic
2#125×D149C211yesmaximal, characteristic, complemented
3#23749995C211yesmaximal, characteristic, complemented
4#23749994C211yesmaximal, characteristic, complemented
5#23749989C211yesmaximal, characteristic, complemented
6#23749978C214yesmaximal, complemented
7#23749623C214yesmaximal, complemented
8#23749577C211yesmaximal, characteristic, complemented
9#490×C149C211yesmaximal, characteristic, complemented
10C2×#14558735C2212yes—
11C2×#14558719C2212yes—
12#18011911C2211yescharacteristic
13#18011903C2211yescharacteristic
14#18011902C2212yes—
15#18011901—22no—
16#18011898C2212yes—
17#18011882—22no—
18D4×Dic149—22no—
19C4⋊C4×D149—22no—
20C4⋊C4×D149C2212yes—
21C42×D149C2211yescharacteristic
22#18011836C2214yes—
23#18011834C2214yes—
24#18011832C2214yes—
25#18011822C2211yescharacteristic
26C8×Dic149C2212yes—
27#127×C149C2211yescharacteristic
28#125×C149C2211yescharacteristic
29#102×C149C2214yes—
30#97×C149C2211yescharacteristic
31#14558735—28no—
32C2×Dic298C2312yes—
33C2×C22⋊D149—22no—
34C22×Dic149—22no—
35C2×C4×D149—22no—
36C2×C4×D149D412yes—
37C2×C4×D149C2311yescharacteristic
38#14558719—24no—
39C2×#11924746C2312yes—
40C4⋊Dic149—22no—
41C4⋊Dic149—22no—
42C4⋊Dic149C2312yes—
43#14558715—22no—
44#14558715—22no—
45#14558715—22no—
46C22⋊Dic149—24no—
47C4×Dic149D412yes—
48C4×Dic149C2311yescharacteristic
49C2×D4×C149—22no—
50C2×D4×C149C2312yes—
51C2×C8×C149C2312yes—
52C4⋊C4×C149—22no—
53C4⋊C4×C149C2312yes—
54C42×C149C2311yescharacteristic
55C22×D149C2×D411yescharacteristic
56Dic298—24no—
57C22⋊D149—44no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—44no—
61C2×Dic149C2×D412yes—
62C2×Dic149C2×D411yescharacteristic
63C4×D149—42no—
64C4×D149—44no—
65C4×D149#4114yes—
66#11924746—22no—
67C23×C149—22no—
68D4×C149—24no—
69D4×C149—44no—
70C2×C4×C149—22no—
71C2×C4×C149C2×D412yes—
72C2×C4×C149C2411yescharacteristic
73C8×C149—22no—
74C22×C149—42no—
75C22×C149—44no—
76C22×C149C22×D411yescharacteristic
77C2×D149—22no—
78C2×D149#12412yes—
79C4×C149—22no—
80C4×C149—42no—
81C4×C149C2×#4112yes—
82Dic149—22no—
83Dic149—42no—
84Dic149—42no—
85Dic149#12412yes—
86C2×C149—82no—
87C2×C149C2×#12411yescharacteristic
88C2×C149#57512yes—
89D149—22no—
90C149#314211yescharacteristic, complemented, Sylow
91#3142—1491nomaximal, Sylow
92#532—1491no—
93C2×#125—1491no—
94#491—1491no—
95#491—1491no—
96#490—1491no—
97#490D14911yescharacteristic, complemented
98#488—1494no—
99#417—1494no—
100C4×M16—1491no—
101C2×#41—1492no—
102C2×M16—1492no—
103C4⋊Q8—1491no—
104#127C2×D14911yescharacteristic
105#125—2982no—
106#125—1492no—
107#125—1491no—
108#125C2×D14911yescharacteristic
109#124—1492no—
110#121—2982no—
111C4×D4—2982no—
112C2×C4⋊C4—2982no—
113C2×C4⋊C4—1492no—
114C2×C42—1491no—
115#103—1494no—
116#103—1494no—
117#102—1494no—
118#102C2×D14914yes—
119#97—1491no—
120#97C2×D14911yescharacteristic
121C4×C8—1492no—
122#41—2988no—
123C2×Q8—1492no—
124C2×D4—22no—
125C2×D4—2982no—
126C2×D4C22×D14912yes—
127C22×C4—2982no—
128C22×C4—2982no—
129C22×C4—1492no—
130C22×C4—1491no—
131M16—2984no—
132C2×C8—1492no—
133C2×C8C22×D14912yes—
134C4⋊C4—22no—
135C4⋊C4—2982no—
136C4⋊C4—2982no—
137C4⋊C4—2982no—
138C4⋊C4—2982no—
139C4⋊C4—2982no—
140C4⋊C4—1492no—
141C4⋊C4C22×D14912yes—
142C22⋊C4—2984no—
143C42—1492no—
144C42—1491no—
145C42C22×D14911yescharacteristic
146C23—22no—
147C23—1491no—
148Q8—2984no—
149D4—24no—
150D4—44no—
151D4—5964no—
152C2×C4—22no—
153C2×C4—2982no—
154C2×C4—2982no—
155C2×C4—5962no—
156C2×C4—5964no—
157C2×C4—5964no—
158C2×C4—1492no—
159C2×C4—1491no—
160C2×C4—1494no—
161C2×C4D4×D14912yes—
162C2×C4C23×D14911yescharacteristic
163C8—22no—
164C8—2982no—
165C22—44no—
166C22—42no—
167C22—2982no—
168C22—1492no—
169C22C2×D4×D14911yescharacteristic
170C4—22no—
171C4—42no—
172C4—2982no—
173C4—5962no—
174C4—5962no—
175C4—1492no—
176C4#41×D14912yes—
177C2—82no—
178C2—2982no—
179C2#124×D14911yescharacteristic
180C2#2375042112yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#490×C149C2
socleC22×C149C22×D4
prime radical#23750173C2
hypercenter#490D149
hypocenterC149#3142
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D149C2semidirect
3. #23749995C2semidirect
4. #23749994C2semidirect
5. #23749989C2semidirect
6. #23749978C2semidirect
7. #23749623C2semidirect
8. #23749577C2semidirect
9. #490×C149C2semidirect
90. C149#3142semidirect
97. #490D149semidirect

Maximal subgroups

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

subgroupindex
#237501732
#125×D1492
#237499952
#237499942
#237499892
#237499782
#237496232
#237495772
#490×C1492
#3142149