Finite Group Databasebeta

← #34068198

Subgroups — #34068198

Order 19328.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752867C211yesmaximal, characteristic, complemented
2#23752558C211yesmaximal, characteristic, complemented
3#23752404C211yesmaximal, characteristic, complemented
4#23751957C211yesmaximal, characteristic, complemented
5D4⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#459×C151C211yesmaximal, characteristic, complemented
8C2×#14559004—21no—
9C2×#14558989—21no—
10#18012739C2211yescharacteristic
11#18012721—22no—
12#18012718—21no—
13#18012710—21no—
14C4×D604C2211yescharacteristic
15C4⋊C4×D151—21no—
16C4⋊(C151⋊C8)C2211yescharacteristic
17#18012660—22no—
18#18012660—21no—
19C4×C151⋊C8C2211yescharacteristic
20C2×D8×C151—21no—
21#127×C151C2211yescharacteristic
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24#102×C151—21no—
25#14559004—42no—
26#14559004—42no—
27C2×Dic302—21no—
28C2×D604D411yescharacteristic
29C2×C22⋊D151—22no—
30C2×C4×D151—22no—
31C2×C4×D151—21no—
32#14558989—42no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D412yes—
38Dic151⋊C4—22no—
39C22⋊Dic151—22no—
40(C2×D151)⋊C4—21no—
41C2×D4×C151—21no—
42C2×D4×C151—21no—
43C2×D4×C151—21no—
44C2×D4×C151D411yescharacteristic
45C22×C4×C151—21no—
46D8×C151—42no—
47C2×C8×C151—21no—
48C4⋊C4×C151D411yescharacteristic
49C22⋊C4×C151—21no—
50C42×C151C2311yescharacteristic
51C22×D151—21no—
52Dic302—41no—
53Dic302—41no—
54D604—21no—
55D604D812yescomplemented
56C22⋊D151—44no—
57C2×Dic151—21no—
58C2×Dic151—22no—
59C4×D151—44no—
60C4×D151—41no—
61C4×D151—41no—
62C151⋊C8—41no—
63C151⋊C8—41no—
64C23×C151—21no—
65C23×C151—41no—
66D4×C151—21no—
67D4×C151—21no—
68D4×C151—42no—
69D4×C151—41no—
70D4×C151—41no—
71D4×C151—41no—
72D4×C151—41no—
73C2×C4×C151—21no—
74C2×C4×C151—41no—
75C2×C4×C151—41no—
76C2×C4×C151C2×D411yescharacteristic
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×D411yescharacteristic
79C8×C151—41no—
80C22×C151—41no—
81C22×C151—41no—
82C22×C151—41no—
83C22×C151—81no—
84C22×C151—81no—
85C22×C151—81no—
86C22×C151#12011yescharacteristic
87C2×D151—22no—
88C2×D151—41no—
89C2×D151—41no—
90C4×C151—21no—
91C4×C151—41no—
92C4×C151C2×D811yescharacteristic
93C4×C151#13511yescharacteristic
94C4×C151AGL(1,ℤ/8)11yescharacteristic
95C4×C151AGL(1,ℤ/8)11yescharacteristic
96Dic151—42no—
97Dic151—41no—
98C2×C151—81no—
99C2×C151—161no—
100C2×C151#44711yescharacteristic
101C2×C151#44911yescharacteristic
102C2×C151#45411yescharacteristic
103D151—42no—
104C151#162511yescharacteristic, complemented, Sylow
105#1625—1511nomaximal, Sylow
106#547—1511no—
107#486—1511no—
108#459—1511no—
109#459D15111yescharacteristic, complemented
110#332—1511no—
111D4⋊C8—1511no—
112D4⋊C8—1511no—
113C2×#41—3021no—
114C2×D8—21no—
115C2×D8—3021no—
116C4⋊Q8—1511no—
117#127C2×D15111yescharacteristic
118#123—3022no—
119C22⋊Q8—3021no—
120#121—3021no—
121C4×D4—1511no—
122C4×D4C2×D15111yescharacteristic
123C2×C4⋊C4—3021no—
124C4⋊C8—1511no—
125C4⋊C8C2×D15111yescharacteristic
126#102—21no—
127#102—3021no—
128#102—3022no—
129C4×C8—1511no—
130#41—6042no—
131#41—6042no—
132C2×Q8—3021no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—3022no—
137C2×D4—1511no—
138C2×D4C22⋊D15111yescharacteristic
139C22×C4—21no—
140C22×C4—3022no—
141C22×C4—3021no—
142D8—42no—
143D8—6042no—
144C2×C8—21no—
145C2×C8—3021no—
146C2×C8—3021no—
147C4⋊C4—3022no—
148C4⋊C4—3021no—
149C4⋊C4—1511no—
150C4⋊C4—1512no—
151C4⋊C4C22⋊D15111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3022no—
154C22⋊C4—3021no—
155C42C22×D15111yescharacteristic
156C23—21no—
157C23—41no—
158C23—3021no—
159Q8—6041no—
160Q8—6041no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—3021no—
169D4—6044no—
170D4—1512no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3021no—
175C2×C4—3022no—
176C2×C4—6044no—
177C2×C4—6041no—
178C2×C4—6041no—
179C2×C4D4×D15111yescharacteristic
180C2×C4D4×D15111yescharacteristic
181C2×C4C2×C22⋊D15111yescharacteristic
182C8—41no—
183C8—6041no—
184C8—6041no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—3022no—
192C22—6041no—
193C22—6041no—
194C22#1801270711yescharacteristic
195C4—21no—
196C4—41no—
197C4—6042no—
198C4—6041no—
199C4D8×D15111yescharacteristic
200C4#1801275911yescharacteristic
201C4#1801276311yescharacteristic
202C4#1801276511yescharacteristic
203C2—81no—
204C2—161no—
205C2—6042no—
206C2#2375234411yescharacteristic
207C2#2375235511yescharacteristic
208C2#2375238311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#459×C151C2
socleC22×C151#120
hypercenter#459D151
hypocenterC151#1625
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. #23752867C2semidirect
2. #23752558C2semidirect
3. #23752404C2semidirect
4. #23751957C2semidirect
5. D4⋊(C151⋊C8)C2semidirect
6. #23751939C2semidirect
7. #459×C151C2semidirect
55. D604D8semidirect
104. C151#1625semidirect
109. #459D151semidirect

Maximal subgroups

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

subgroupindex
#237528672
#237525582
#237524042
#237519572
D4⋊(C151⋊C8)2
#237519392
#459×C1512
#1625151