Finite Group Databasebeta

← #34055172

Subgroups — #34055172

Order 19072.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#18011937C212yesmaximal, complemented
2C2×#18011933C211yesmaximal, characteristic, complemented
3#23750192C212yesmaximal, complemented
4#23750013C214yesmaximal, complemented
5#23750008C212yesmaximal, complemented
6#23750000C212yesmaximal, complemented
7#23749580C211yesmaximal, characteristic, complemented
8C22×D8×C149C211yesmaximal, characteristic, complemented
9C2×#14558736C2212yes—
10#18011937—28no—
11#18011933—24no—
12C2×Dic596C2211yescharacteristic, complemented
13C2×#14558725C2212yescomplemented
14C2×#14558724C2214yescomplemented
15C2×D1192C2211yescharacteristic, complemented
16C2×#14558721C2214yescomplemented
17C2×#14558720C2211yescharacteristic
18#18011907C2214yescomplemented
19#18011898C2214yescomplemented
20#18011882—24no—
21#18011880—24no—
22#18011870C2211yescharacteristic
23#18011821C2212yescomplemented
24C8×Dic149C2212yescomplemented
25C22×D4×C149C2212yes—
26C2×D8×C149—24no—
27C2×D8×C149C2212yes—
28C2×D8×C149C2212yes—
29C22×C8×C149C2211yescharacteristic
30#14558736—24no—
31#14558736—24no—
32C2×Dic298C2312yes—
33C2×D596C2312yes—
34C2×C22⋊D149—28no—
35C2×C22⋊D149—22no—
36C2×C4×D149—22no—
37Dic596—22no—
38#14558725—24no—
39#14558724—28no—
40D1192—22no—
41#14558721—28no—
42#14558720D414yescomplemented
43C2×#11924746C2312yes—
44C4⋊Dic149D412yes—
45C22⋊Dic149—28no—
46C22⋊Dic149D412yes—
47C4×Dic149C2312yes—
48C24×C149—22no—
49C2×D4×C149—24no—
50C2×D4×C149—24no—
51C2×D4×C149—22no—
52C2×D4×C149C2314yes—
53C22×C4×C149C2311yescharacteristic
54D8×C149—24no—
55D8×C149—24no—
56C2×C8×C149D414yescomplemented
57C2×C8×C149C2311yescharacteristic
58C2×C8×C149C2311yescharacteristic
59C22×D149—22no—
60Dic298—22no—
61Dic298—22no—
62D596—22no—
63D596—22no—
64C22⋊D149—44no—
65C22⋊D149—88no—
66C2×Dic149—22no—
67C2×Dic149C2×D414yes—
68C4×D149—44no—
69#11924746C2×D414yes—
70C23×C149—24no—
71C23×C149—44no—
72C23×C149—84no—
73C23×C149C2×D411yescharacteristic
74D4×C149—24no—
75D4×C149—24no—
76D4×C149—44no—
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D412yes—
79C2×C4×C149C2×D412yes—
80C2×C4×C149C2411yescharacteristic
81C8×C149C2×D412yes—
82C8×C149C2×D412yes—
83C22×C149—22no—
84C22×C149—44no—
85C22×C149—48no—
86C22×C149—88no—
87C22×C149#12712yes—
88C22×C149C22×D411yescharacteristic
89C2×D149—42no—
90C2×D149—44no—
91C4×C149#12712yes—
92C4×C149C22×D411yescharacteristic
93C4×C149C22×D411yescharacteristic
94Dic149—24no—
95Dic149—42no—
96C2×C149—22no—
97C2×C149—84no—
98C2×C149C2×#12711yescharacteristic
99C2×C149#57612yes—
100D149—82no—
101C149#315511yescharacteristic, complemented, Sylow
102#3155—1491nomaximal, Sylow
103C2×AGL(1,ℤ/8)—1492no—
104C2×#135—1491no—
105C22×D8D14911yescharacteristic, complemented
106#535—1492no—
107#496—1494no—
108#495—1492no—
109#493—1492no—
110#405—1491no—
111C2×#41—1492no—
112C22×D4C2×D14912yes—
113AGL(1,ℤ/8)—2988no—
114#135—2984no—
115C2×Q16—1491no—
116C2×SD16—1494no—
117C2×SD16—1492no—
118C2×D8—24no—
119C2×D8—1494no—
120C2×D8—1491no—
121C2×D8C2×D14912yes—
122C2×D8C2×D14912yes—
123C2×M16—1491no—
124C22×C8C2×D14911yescharacteristic
125#127—1494no—
126#124—1494no—
127#121—2984no—
128#120—2984no—
129#117—1491no—
130#97—1492no—
131C4×C8—1492no—
132C24—22no—
133#41—2984no—
134#41—2984no—
135C2×Q8—1492no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—24no—
139C2×D4—2982no—
140C2×D4—2988no—
141C2×D4—1492no—
142C2×D4C22×D14914yes—
143C22×C4—2982no—
144C22×C4C22×D14911yescharacteristic
145Q16—2982no—
146SD16—2988no—
147SD16—2984no—
148D8—24no—
149D8—24no—
150D8—2988no—
151D8—2982no—
152M16—1494no—
153C2×C8—1492no—
154C2×C8C22⋊D14914yescomplemented
155C2×C8C22×D14911yescharacteristic
156C2×C8C22×D14911yescharacteristic
157C4⋊C4—1492no—
158C22⋊C4—2988no—
159C22⋊C4—1492no—
160C42—1492no—
161C23—24no—
162C23—44no—
163C23—84no—
164C23—2982no—
165C23D4×D14911yescharacteristic
166Q8—2982no—
167Q8—2982no—
168D4—24no—
169D4—24no—
170D4—44no—
171D4—2982no—
172D4—2982no—
173D4—5964no—
174D4—11928no—
175C2×C4—2982no—
176C2×C4—5964no—
177C2×C4—1494no—
178C2×C4D4×D14911yescharacteristic
179C2×C4D4×D14912yes—
180C2×C4C2×C22⋊D14912yes—
181C2×C4C23×D14911yescharacteristic
182C8—1494no—
183C8C2×C22⋊D14912yes—
184C8C2×C22⋊D14912yes—
185C22—22no—
186C22—44no—
187C22—48no—
188C22—88no—
189C22—5962no—
190C22—5964no—
191C22#1801190712yes—
192C22C2×D4×D14911yescharacteristic
193C4—2984no—
194C4—5962no—
195C4#1801190712yes—
196C4C2×D4×D14911yescharacteristic
197C4C22×C22⋊D14911yescharacteristic
198C2—22no—
199C2—84no—
200C2—11922no—
201C2C2×#1801190711yescharacteristic
202C2#2375042612yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×D8×C149C2
socleC22×C149C22×D4
hypercenterC22×D8D149
hypocenterC149#3155
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. C2×#18011933C2semidirect
3. #23750192C2semidirect
4. #23750013C2semidirect
5. #23750008C2semidirect
6. #23750000C2semidirect
7. #23749580C2semidirect
8. C22×D8×C149C2semidirect
12. C2×Dic596C22semidirect
13. C2×#14558725C22semidirect
14. C2×#14558724C22semidirect
15. C2×D1192C22semidirect
16. C2×#14558721C22semidirect
18. #18011907C22semidirect
19. #18011898C22semidirect
23. #18011821C22semidirect
24. C8×Dic149C22semidirect
42. #14558720D4semidirect
56. C2×C8×C149D4semidirect
101. C149#3155semidirect
105. C22×D8D149semidirect
154. C2×C8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
C2×#180119332
#237501922
#237500132
#237500082
#237500002
#237495802
C22×D8×C1492
#3155149