Finite Group Databasebeta

← #34047985

Subgroups — #34047985

Order 19072.

504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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×C4×Dic298C212yesmaximal
2#23749559C212yesmaximal
3#23749558C212yesmaximal
4#23749546C212yesmaximal
5#23749545C212yesmaximal
6C4×#14558715C212yesmaximal
7C4×C4⋊Dic149C211yesmaximal, characteristic
8#23749471C211yesmaximal, characteristic
9C4×C4⋊C4×C149C211yesmaximal, characteristic
10C22×Dic298C2212yes—
11C4×Dic298—28no—
12C2×C4⋊Dic149C2212yes—
13C2×C4⋊Dic149C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×C4×Dic149C2212yes—
19C2×C4×Dic149C2211yescharacteristic
20C2×C4×Dic149C2211yescharacteristic
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2211yescharacteristic
24#18011818C2211yescharacteristic
25#18011818C2212yes—
26#18011818C2212yes—
27C2×C4⋊C4×C149C2212yes—
28C2×C42×C149C2212yes—
29C2×C42×C149C2211yescharacteristic
30#95×C149C2211yescharacteristic
31#95×C149C2211yescharacteristic
32C2×Dic298—24no—
33C2×Dic298—24no—
34C2×Dic298—24no—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C22×Dic149C2312yes—
39C4⋊Dic149—24no—
40C4⋊Dic149—24no—
41#14558715—24no—
42#14558715—24no—
43#14558715—24no—
44#14558715—24no—
45C4×Dic149—24no—
46C4×Dic149D414yes—
47C4×Dic149Q814yescomplemented
48C22×C4×C149C2312yes—
49C22×C4×C149C2311yescharacteristic
50C22×C4×C149C2311yescharacteristic
51C22×C4×C149C2312yes—
52C22×C4×C149C2311yescharacteristic
53C4⋊C4×C149—24no—
54C42×C149—24no—
55C42×C149Q814yescomplemented
56Dic298—216no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149C2×D414yes—
67C2×Dic149C2×Q814yes—
68C2×Dic149#4114yes—
69C23×C149C2411yescharacteristic
70C2×C4×C149—22no—
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149C2×D412yes—
78C2×C4×C149C2×Q812yes—
79C2×C4×C149C2×Q812yes—
80C2×C4×C149C2×Q812yes—
81C2×C4×C149C2×Q812yes—
82C2×C4×C149#4114yes—
83C22×C149C22×D411yescharacteristic
84C22×C149C22×Q811yescharacteristic
85C22×C149C22×Q811yescharacteristic
86C22×C149C2×#4112yes—
87C22×C149C2×#4112yes—
88C4×C149—24no—
89C4×C149—22no—
90C4×C149—22no—
91C4×C149—42no—
92C4×C149C4⋊Q814yes—
93Dic149—24no—
94Dic149—24no—
95Dic149—24no—
96Dic149—42no—
97C2×C149#52512yes—
98C2×C149C2×C4⋊Q811yescharacteristic
99C2×C149#53311yescharacteristic
100C2×C149#53312yes—
101C2×C149#53311yescharacteristic
102C149#239911yescharacteristic, complemented, Sylow
103#2399—1491nomaximal, Sylow
104C2×C4×Q8—1492no—
105#398—1492no—
106#398—1492no—
107#395—1492no—
108#395—1492no—
109C4×C4⋊C4—1491no—
110C4×C4⋊C4—1492no—
111C4×C4⋊C4D14911yescharacteristic
112#376—1491no—
113C22×Q8—1492no—
114C4×Q8—2988no—
115C2×C4⋊C4—1492no—
116C2×C4⋊C4—1492no—
117C2×C4⋊C4—1492no—
118C2×C4⋊C4—1492no—
119C2×C4⋊C4—1492no—
120C2×C4⋊C4—1492no—
121C2×C4⋊C4C2×D14912yes—
122C2×C42—1492no—
123C2×C42—1491no—
124C2×C42—1491no—
125C2×C42C2×D14912yes—
126C2×C42C2×D14911yescharacteristic
127#95—1492no—
128#95—1492no—
129#95—1492no—
130#95—1491no—
131#95—1491no—
132#95—1492no—
133#95C2×D14911yescharacteristic
134#95C2×D14911yescharacteristic
135C2×Q8—2984no—
136C2×Q8—2984no—
137C2×Q8—2984no—
138C22×C4—1492no—
139C22×C4—1492no—
140C22×C4—1492no—
141C22×C4—1492no—
142C22×C4C22×D14912yes—
143C22×C4C22×D14911yescharacteristic
144C22×C4C22×D14911yescharacteristic
145C22×C4C22×D14912yes—
146C22×C4C22×D14911yescharacteristic
147C4⋊C4—24no—
148C4⋊C4—2984no—
149C4⋊C4—2984no—
150C4⋊C4—2984no—
151C4⋊C4—2984no—
152C4⋊C4—2984no—
153C4⋊C4—2984no—
154C42—24no—
155C42—2984no—
156C42—1494no—
157C42—1494no—
158C42Dic29814yescomplemented
159C23C23×D14911yescharacteristic
160Q8—29816no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—2982no—
171C2×C4—2982no—
172C2×C4—2982no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—1494no—
178C2×C4—1494no—
179C2×C4—1494no—
180C2×C4D4×D14912yes—
181C2×C4Q8×D14912yes—
182C2×C4C2×Dic29812yes—
183C2×C4C2×Dic29812yes—
184C2×C4C2×Dic29812yes—
185C2×C4#1455873614yes—
186C22C2×D4×D14911yescharacteristic
187C22C2×Q8×D14911yescharacteristic
188C22C22×Dic29811yescharacteristic
189C22#41×D14912yes—
190C22C2×#1455873612yes—
191C4—22no—
192C4—22no—
193C4—24no—
194C4—42no—
195C4—2984no—
196C4—2984no—
197C4—2984no—
198C4—5962no—
199C4#1801191014yes—
200C2#2375013412yes—
201C2C2×#1801191011yescharacteristic
202C2#2375017811yescharacteristic
203C2#2375017912yes—
204C2#2375018211yescharacteristic
subgroupG/H
centerC22×C4C22×D149
commutator, socle, prime radical, cosocleC23×C149C24
FrattiniC23C23×D149
FittingC4×C4⋊C4×C149C2
hypercenterC4×C4⋊C4D149
hypocenterC149#2399
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
47. C4×Dic149Q8semidirect
55. C42×C149Q8semidirect
102. C149#2399semidirect
158. C42Dic298semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic2982
#237495592
#237495582
#237495462
#237495452
C4×#145587152
C4×C4⋊Dic1492
#237494712
C4×C4⋊C4×C1492
#2399149