Finite Group Databasebeta

← #34068192

Subgroups — #34068192

Order 19328.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752927C211yesmaximal, characteristic, complemented
2#23752584C211yesmaximal, characteristic, complemented
3#23752404C211yesmaximal, characteristic, complemented
4#23751960C211yesmaximal, characteristic, complemented
5D4⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#459×C151C211yesmaximal, characteristic, complemented
8C2×#14558992—22no—
9C2×#14558989—21no—
10#18012739C2211yescharacteristic
11#18012725—22no—
12#18012713—21no—
13#18012710—21no—
14C4×D604C2211yescharacteristic
15#18012698—21no—
16#18012697—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18#18012660—21no—
19C4×C151⋊C8C2211yescharacteristic
20C2×D8×C151—21no—
21#127×C151C2211yescharacteristic
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24#102×C151—21no—
25C2×Dic302D412yes—
26C2×D604D411yescharacteristic
27C2×C22⋊D151—22no—
28C2×C4×D151—21no—
29#14558992—44no—
30#14558989—42no—
31C2×C151⋊C8—21no—
32C2×C151⋊C8—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151D411yescharacteristic
36C22⋊Dic151—22no—
37(C2×D151)⋊C4—22no—
38(C2×D151)⋊C4—21no—
39C4×Dic151—22no—
40C2×D4×C151—21no—
41C2×D4×C151—21no—
42C2×D4×C151—21no—
43C2×D4×C151D411yescharacteristic
44C22×C4×C151—21no—
45D8×C151—42no—
46C2×C8×C151—21no—
47C4⋊C4×C151D411yescharacteristic
48C22⋊C4×C151—21no—
49C42×C151C2311yescharacteristic
50C22×D151—21no—
51Dic302—42no—
52D604—21no—
53D604—21no—
54C22⋊D151—82no—
55C2×Dic151—21no—
56C2×Dic151—22no—
57C4×D151—41no—
58C4×D151—41no—
59C151⋊C8—22no—
60C151⋊C8—41no—
61C23×C151—21no—
62C23×C151—41no—
63D4×C151—21no—
64D4×C151—21no—
65D4×C151—42no—
66D4×C151—41no—
67D4×C151—41no—
68D4×C151—41no—
69D4×C151—41no—
70C2×C4×C151—21no—
71C2×C4×C151—41no—
72C2×C4×C151—41no—
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151C2×D411yescharacteristic
76C8×C151—41no—
77C22×C151—41no—
78C22×C151—41no—
79C22×C151—41no—
80C22×C151—81no—
81C22×C151—81no—
82C22×C151—81no—
83C22×C151#12011yescharacteristic
84C2×D151—41no—
85C2×D151—41no—
86C2×D151—41no—
87C4×C151—21no—
88C4×C151—41no—
89C4×C151#13511yescharacteristic
90C4×C151#13511yescharacteristic
91C4×C151AGL(1,ℤ/8)11yescharacteristic
92C4×C151AGL(1,ℤ/8)11yescharacteristic
93Dic151—41no—
94Dic151—42no—
95C2×C151—81no—
96C2×C151—161no—
97C2×C151#44911yescharacteristic
98C2×C151#44911yescharacteristic
99C2×C151#45311yescharacteristic
100D151—81no—
101C151#162411yescharacteristic, complemented, Sylow
102#1624—1511nomaximal, Sylow
103#555—1511no—
104#492—1511no—
105#459—1511no—
106#459D15111yescharacteristic, complemented
107#333—1511no—
108D4⋊C8—1511no—
109D4⋊C8—1511no—
110C2×SD16—3022no—
111C2×D8—21no—
112C2×D8—3021no—
113C4⋊Q8—1511no—
114#127C2×D15111yescharacteristic
115#124—3022no—
116#121—3021no—
117#121—3021no—
118C4×D4—1511no—
119C4×D4C2×D15111yescharacteristic
120#117—3021no—
121#117—3021no—
122C4⋊C8—1511no—
123C4⋊C8C2×D15111yescharacteristic
124#102—21no—
125#102—3021no—
126C4×C8—1511no—
127C2×Q8—1512no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—3022no—
132C2×D4—1511no—
133C2×D4C22⋊D15111yescharacteristic
134C22×C4—21no—
135C22×C4—3021no—
136SD16—6044no—
137D8—42no—
138D8—6042no—
139C2×C8—21no—
140C2×C8—3021no—
141C2×C8—3021no—
142C4⋊C4—3021no—
143C4⋊C4—3021no—
144C4⋊C4—1511no—
145C4⋊C4C22⋊D15111yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—3022no—
148C22⋊C4—3022no—
149C22⋊C4—3021no—
150C42—3022no—
151C42C22×D15111yescharacteristic
152C23—21no—
153C23—41no—
154C23—3021no—
155Q8—6042no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—3021no—
164D4—3021no—
165D4—12082no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3021no—
170C2×C4—3022no—
171C2×C4—6041no—
172C2×C4—6041no—
173C2×C4D4×D15111yescharacteristic
174C2×C4D4×D15111yescharacteristic
175C2×C4C2×C22⋊D15111yescharacteristic
176C8—41no—
177C8—3022no—
178C8—6041no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—6041no—
186C22—6041no—
187C22—6041no—
188C22#1801270711yescharacteristic
189C4—21no—
190C4—41no—
191C4—6041no—
192C4—6042no—
193C4#1801275811yescharacteristic
194C4#1801275911yescharacteristic
195C4#1801276311yescharacteristic
196C4#1801276511yescharacteristic
197C2—81no—
198C2—161no—
199C2—12081no—
200C2#2375235411yescharacteristic
201C2#2375235511yescharacteristic
202C2#2375237811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#459×C151C2
socleC22×C151#120
hypercenter#459D151
hypocenterC151#1624
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23752927C2semidirect
2. #23752584C2semidirect
3. #23752404C2semidirect
4. #23751960C2semidirect
5. D4⋊(C151⋊C8)C2semidirect
6. #23751939C2semidirect
7. #459×C151C2semidirect
101. C151#1624semidirect
106. #459D151semidirect

Maximal subgroups

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

subgroupindex
#237529272
#237525842
#237524042
#237519602
D4⋊(C151⋊C8)2
#237519392
#459×C1512
#1624151