Finite Group Databasebeta

← #2041×C151 #34065373

Subgroups — #2041×C151 #34065373

Order 19328.

402 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 108 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×#127×C151C211yesmaximal, characteristic
2C2×#102×C151C212yesmaximal, complemented
3C2×#102×C151C212yesmaximal, complemented
4#389×C151C211yesmaximal, characteristic, complemented
5#336×C151C211yesmaximal, characteristic, complemented
6C22×D4×C151—21no—
7C22×D4×C151—21no—
8C22×D4×C151C2212yes—
9C22×C8×C151C2212yes—
10#127×C151—24no—
11C2×C4⋊C4×C151—21no—
12C2×C4⋊C4×C151C2211yescharacteristic
13C2×C4⋊C4×C151C2211yescharacteristic
14C2×C42×C151C2211yescharacteristic
15#102×C151—24no—
16#102×C151—24no—
17#95×C151—21no—
18C24×C151—22no—
19C2×D4×C151—24no—
20C2×D4×C151—24no—
21C2×D4×C151—22no—
22C2×D4×C151—22no—
23C2×D4×C151—22no—
24C2×D4×C151—22no—
25C2×D4×C151—22no—
26C2×D4×C151—42no—
27C2×D4×C151—42no—
28C2×D4×C151—42no—
29C2×D4×C151—42no—
30C2×D4×C151D414yes—
31C22×C4×C151—21no—
32C22×C4×C151—21no—
33C22×C4×C151D411yescharacteristic
34C22×C4×C151D411yescharacteristic
35C22×C4×C151C2311yescharacteristic
36C2×C8×C151—22no—
37C2×C8×C151—22no—
38C2×C8×C151—22no—
39C4⋊C4×C151—21no—
40C4⋊C4×C151—22no—
41C4⋊C4×C151—42no—
42C4⋊C4×C151D412yescomplemented
43C42×C151—22no—
44C23×C151—24no—
45C23×C151—42no—
46C23×C151—42no—
47C23×C151—42no—
48C23×C151—42no—
49C23×C151—42no—
50C23×C151—42no—
51C23×C151C2×D411yescharacteristic
52D4×C151—24no—
53D4×C151—24no—
54D4×C151—48no—
55D4×C151—48no—
56D4×C151—42no—
57D4×C151—42no—
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151—21no—
62C2×C4×C151—22no—
63C2×C4×C151—41no—
64C2×C4×C151—41no—
65C2×C4×C151—41no—
66C2×C4×C151—41no—
67C2×C4×C151—41no—
68C2×C4×C151D812yes—
69C2×C4×C151SD1612yes—
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151C2×D412yes—
72C2×C4×C151#4112yes—
73C2×C4×C151#4111yescharacteristic
74C8×C151—42no—
75C22×C151—44no—
76C22×C151—44no—
77C22×C151—44no—
78C22×C151—82no—
79C22×C151—82no—
80C22×C151—82no—
81C22×C151—82no—
82C22×C151#12011yescharacteristic
83C22×C151#12111yescharacteristic
84C22×C151#12411yescharacteristic
85C22×C151C2×D811yescharacteristic
86C22×C151C2×SD1611yescharacteristic
87C22×C151AGL(1,ℤ/8)11yescharacteristic
88C22×C151AGL(1,ℤ/8)11yescharacteristic
89C4×C151—22no—
90C4×C151—22no—
91C4×C151—42no—
92C4×C151—81no—
93C4×C151#12112yes—
94C4×C151#12312yes—
95C2×C151—84no—
96C2×C151#39411yescharacteristic
97C2×C151#44711yescharacteristic
98C2×C151#45011yescharacteristic
99C2×C151#45911yescharacteristic
100C2×C151#46011yescharacteristic
101C2×C151#48611yescharacteristic
102C2×C151#49011yescharacteristic
103C151#204111yescharacteristic, direct product factor, Sylow
104#2041C15111yesmaximal, characteristic, direct product factor, Sylow
105C2×#127C2×C15111yescharacteristic
106C2×#102C2×C15112yescomplemented
107C2×#102C2×C15112yescomplemented
108#389C2×C15111yescharacteristic, complemented
109#336C2×C15111yescharacteristic, complemented
110C22×D4—21no—
111C22×D4—21no—
112C22×D4C22×C15112yes—
113C22×C8C22×C15112yes—
114#127—24no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4C22×C15111yescharacteristic
117C2×C4⋊C4C22×C15111yescharacteristic
118C2×C42C22×C15111yescharacteristic
119#102—24no—
120#102—24no—
121#95—21no—
122C24—22no—
123C2×D4—24no—
124C2×D4—24no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—42no—
131C2×D4—42no—
132C2×D4—42no—
133C2×D4—42no—
134C2×D4D4×C15114yes—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4D4×C15111yescharacteristic
138C22×C4D4×C15111yescharacteristic
139C22×C4C23×C15111yescharacteristic
140C2×C8—22no—
141C2×C8—22no—
142C2×C8—22no—
143C4⋊C4—21no—
144C4⋊C4—22no—
145C4⋊C4—42no—
146C4⋊C4D4×C15112yescomplemented
147C42—22no—
148C23—24no—
149C23—42no—
150C23—42no—
151C23—42no—
152C23—42no—
153C23—42no—
154C23—42no—
155C23C2×D4×C15111yescharacteristic
156D4—24no—
157D4—24no—
158D4—48no—
159D4—48no—
160D4—42no—
161D4—42no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4D8×C15112yes—
173C2×C4SD16×C15112yes—
174C2×C4C2×D4×C15111yescharacteristic
175C2×C4C2×D4×C15112yes—
176C2×C4#41×C15112yes—
177C2×C4#41×C15111yescharacteristic
178C8—42no—
179C22—44no—
180C22—44no—
181C22—44no—
182C22—82no—
183C22—82no—
184C22—82no—
185C22—82no—
186C22#120×C15111yescharacteristic
187C22#121×C15111yescharacteristic
188C22#124×C15111yescharacteristic
189C22C2×D8×C15111yescharacteristic
190C22C2×SD16×C15111yescharacteristic
191C22AGL(1,ℤ/8)×C15111yescharacteristic
192C22AGL(1,ℤ/8)×C15111yescharacteristic
193C4—22no—
194C4—22no—
195C4—42no—
196C4—81no—
197C4#121×C15112yes—
198C4#123×C15112yes—
199C2—84no—
200C2#394×C15111yescharacteristic
201C2#447×C15111yescharacteristic
202C2#450×C15111yescharacteristic
203C2#459×C15111yescharacteristic
204C2#460×C15111yescharacteristic
205C2#486×C15111yescharacteristic
206C2#490×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×D4
commutator, Frattini, cosocleC22×C4C23×C151
prime radicalC2×#127×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#102×C151C2semidirect
3. C2×#102×C151C2semidirect
4. #389×C151C2semidirect
5. #336×C151C2semidirect
42. C4⋊C4×C151D4semidirect
103. C151#2041direct (N × H)
104. #2041C151direct (N × H)
106. C2×#102C2×C151semidirect
107. C2×#102C2×C151semidirect
108. #389C2×C151semidirect
109. #336C2×C151semidirect
146. C4⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#127×C1512
C2×#102×C1512
#389×C1512
#336×C1512
#2041151