Finite Group Databasebeta

← #34054167

Subgroups — #34054167

Order 19072.

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

normal subgroups only

This group has 584 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
2C4×#14558736C211yesmaximal, characteristic, complemented
3#23749822C214yesmaximal, complemented
4#23749817C214yesmaximal, complemented
5#23749649C211yesmaximal, characteristic, complemented
6#23749630C212yesmaximal, complemented
7C2×#127×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011937—28no—
10C2×#14558724C2214yescomplemented
11C2×#14558721C2214yescomplemented
12C2×#14558720C2212yes—
13C4×Dic298C2212yescomplemented
14C4×D596C2212yescomplemented
15C4×C22⋊D149—22no—
16#18011870C2211yescharacteristic
17#18011868—21no—
18C42×D149—21no—
19C4⋊#11924746C2214yescomplemented
20#18011832C2218yescomplemented
21C22×D4×C149—22no—
22C22×D4×C149C2212yes—
23#127×C149—21no—
24#127×C149—21no—
25#127×C149C2214yes—
26C2×C42×C149C2211yescharacteristic
27#14558736—22no—
28#14558736D414yescomplemented
29C2×Dic298C2311yescharacteristic
30C2×D596C2311yescharacteristic
31C2×C22⋊D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149—22no—
34#14558724—28no—
35#14558721—28no—
36#14558720—24no—
37C2×#11924746C2314yes—
38C4⋊Dic149C2312yes—
39#14558715—22no—
40C22⋊Dic149—21no—
41#14558713—22no—
42C4×Dic149—21no—
43C4×Dic149—22no—
44C24×C149—22no—
45C2×D4×C149—24no—
46C2×D4×C149—22no—
47C2×D4×C149—24no—
48C2×D4×C149—24no—
49C2×D4×C149—24no—
50C2×D4×C149—48no—
51C2×D4×C149C2314yes—
52C22×C4×C149D412yes—
53C22×C4×C149C2311yescharacteristic
54C42×C149D411yescharacteristic
55C42×C149D411yescharacteristic
56C42×C149C2312yes—
57C22×D149—21no—
58Dic298—21no—
59Dic298C2×D412yescomplemented
60D596—21no—
61D596C2×D412yescomplemented
62C22⋊D149—24no—
63C2×Dic149—21no—
64C2×Dic149—22no—
65C4×D149—24no—
66C4×D149—44no—
67#11924746—24no—
68C23×C149—24no—
69C23×C149—48no—
70C23×C149—44no—
71C23×C149C2×D411yescharacteristic
72D4×C149—24no—
73D4×C149—24no—
74D4×C149—48no—
75D4×C149—44no—
76D4×C149—48no—
77C2×C4×C149—24no—
78C2×C4×C149C2×D412yes—
79C2×C4×C149C2×D412yes—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D412yes—
82C2×C4×C149#4112yes—
83C2×C4×C149C2411yescharacteristic
84C22×C149—22no—
85C22×C149—44no—
86C22×C149—48no—
87C22×C149—88no—
88C22×C149#12112yes—
89C22×C149C22×D411yescharacteristic
90C2×D149—22no—
91C2×D149—42no—
92C4×C149—22no—
93C4×C149#12112yes—
94C4×C149AGL(1,ℤ/8)14yescomplemented
95C4×C149C22×D411yescharacteristic
96C4×C149C2×#4111yescharacteristic
97Dic149—22no—
98Dic149—42no—
99C2×C149—22no—
100C2×C149—84no—
101C2×C149C2×#12111yescharacteristic
102C2×C149C2×AGL(1,ℤ/8)12yes—
103D149—42no—
104C149#303811yescharacteristic, complemented, Sylow
105#3038—1491nomaximal, Sylow
106C2×AGL(1,ℤ/8)—1492no—
107C2×#127D14911yescharacteristic, complemented
108C4×#41—1491no—
109#460—1494no—
110#459—1494no—
111#423—1491no—
112#418—1492no—
113C2×#41—1491no—
114C22×D4—22no—
115C22×D4C2×D14912yes—
116AGL(1,ℤ/8)—2988no—
117C2×SD16—1494no—
118C2×D8—1494no—
119C2×M16—1492no—
120#127—21no—
121#127—21no—
122#127C2×D14914yes—
123C4×Q8—1492no—
124C4×D4—2982no—
125C4×D4—1492no—
126#117—2981no—
127#117—1491no—
128C2×C42—2981no—
129C2×C42C2×D14911yescharacteristic
130C4⋊C8—1494no—
131#102—1498no—
132C24—22no—
133#41—2982no—
134#41—1494no—
135C2×Q8—1491no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—24no—
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—48no—
142C2×D4—2981no—
143C2×D4—1491no—
144C2×D4C22×D14914yes—
145C22×C4—2981no—
146C22×C4—2982no—
147C22×C4C22⋊D14912yes—
148C22×C4C22×D14911yescharacteristic
149SD16—2988no—
150D8—2988no—
151M16—2984no—
152C2×C8—1494no—
153C4⋊C4—2982no—
154C4⋊C4—1492no—
155C22⋊C4—2981no—
156C22⋊C4—2982no—
157C42—2981no—
158C42—2982no—
159C42C22⋊D14911yescharacteristic
160C42C22⋊D14911yescharacteristic
161C42C22×D14912yes—
162C23—24no—
163C23—48no—
164C23—44no—
165C23—2981no—
166C23C2×C22⋊D14911yescharacteristic
167Q8—2981no—
168Q8—1492no—
169D4—24no—
170D4—24no—
171D4—48no—
172D4—48no—
173D4—44no—
174D4—2984no—
175D4—2981no—
176D4—1492no—
177C2×C4—24no—
178C2×C4—2981no—
179C2×C4—2984no—
180C2×C4—2982no—
181C2×C4—5964no—
182C2×C4D4×D14912yes—
183C2×C4C2×C22⋊D14912yes—
184C2×C4C2×C22⋊D14912yes—
185C2×C4C2×C22⋊D14911yescharacteristic
186C2×C4#1455873512yes—
187C2×C4C23×D14911yescharacteristic
188C8—2984no—
189C22—22no—
190C22—48no—
191C22—44no—
192C22—88no—
193C22—2982no—
194C22—5962no—
195C22#1801188212yes—
196C22C22×C22⋊D14911yescharacteristic
197C4—22no—
198C4—2982no—
199C4—5962no—
200C4#1801188212yes—
201C4#1801193714yescomplemented
202C4C2×D4×D14911yescharacteristic
203C4C2×#1455873511yescharacteristic
204C2—22no—
205C2—84no—
206C2—5962no—
207C2C2×#1801188211yescharacteristic
208C2C2×#1801193712yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#127×C149C2
socleC22×C149C22×D4
hypercenterC2×#127D149
hypocenterC149#3038
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. C4×#14558736C2semidirect
3. #23749822C2semidirect
4. #23749817C2semidirect
5. #23749649C2semidirect
6. #23749630C2semidirect
7. C2×#127×C149C2semidirect
10. C2×#14558724C22semidirect
11. C2×#14558721C22semidirect
13. C4×Dic298C22semidirect
14. C4×D596C22semidirect
19. C4⋊#11924746C22semidirect
20. #18011832C22semidirect
28. #14558736D4semidirect
59. Dic298C2×D4semidirect
61. D596C2×D4semidirect
94. C4×C149AGL(1,ℤ/8)semidirect
104. C149#3038semidirect
107. C2×#127D149semidirect
201. C4#18011937semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
C4×#145587362
#237498222
#237498172
#237496492
#237496302
C2×#127×C1492
#3038149