Finite Group Databasebeta

← #34068196

Subgroups — #34068196

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#23752865C211yesmaximal, characteristic, complemented
2#23752404C211yesmaximal, characteristic, complemented
3#23752404C211yesmaximal, characteristic, complemented
4#23751958C211yesmaximal, characteristic, complemented
5#23751941C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7#486×C151C211yesmaximal, characteristic, complemented
8C2×#14559005—21no—
9C2×#14558989—21no—
10C2×#14558989—21no—
11#18012724—22no—
12#18012715—21no—
13#18012714—21no—
14C4×D604C2211yescharacteristic
15C4×D604C2211yescharacteristic
16C4⋊C4×D151—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012660—21no—
20#18012660—21no—
21C4⋊Q8×C151C2211yescharacteristic
22#127×C151C2211yescharacteristic
23#102×C151—22no—
24C4×C8×C151C2211yescharacteristic
25#14559005—42no—
26#14559005—42no—
27C2×D604—22no—
28C2×D604D411yescharacteristic
29C2×D604D411yescharacteristic
30C2×C4×D151—22no—
31C2×C4×D151—21no—
32C2×C4×D151—21no—
33#14558989—42no—
34#14558989—42no—
35C2×C151⋊C8—21no—
36C2×C151⋊C8—21no—
37C4⋊Dic151D411yescharacteristic
38C4⋊Dic151D411yescharacteristic
39Dic151⋊C4—22no—
40(C2×D151)⋊C4—22no—
41(C2×D151)⋊C4—21no—
42(C2×D151)⋊C4—21no—
43C2×Q8×C151—21no—
44C2×D4×C151—21no—
45C2×D4×C151—21no—
46C2×D4×C151—21no—
47C2×C8×C151—21no—
48C4⋊C4×C151—21no—
49C4⋊C4×C151D412yes—
50C42×C151C2311yescharacteristic
51C22×D151—21no—
52C22×D151—21no—
53D604—21no—
54D604—21no—
55D604—21no—
56D604—44no—
57D604D812yescomplemented
58C2×Dic151—21no—
59C2×Dic151—21no—
60C4×D151—44no—
61C4×D151—41no—
62C4×D151—41no—
63C4×D151—41no—
64C4×D151—41no—
65C151⋊C8—41no—
66C151⋊C8—41no—
67C23×C151—41no—
68Q8×C151—41no—
69Q8×C151—41no—
70D4×C151—42no—
71D4×C151—41no—
72D4×C151—41no—
73D4×C151—41no—
74D4×C151—41no—
75C2×C4×C151—22no—
76C2×C4×C151C2×D411yescharacteristic
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×D411yescharacteristic
79C8×C151—41no—
80C22×C151—81no—
81C22×C151—81no—
82C22×C151—81no—
83C22×C151#12011yescharacteristic
84C2×D151—22no—
85C2×D151—41no—
86C2×D151—41no—
87C2×D151—41no—
88C2×D151—41no—
89C2×D151—41no—
90C4×C151—21no—
91C4×C151—42no—
92C4×C151C2×D811yescharacteristic
93C4×C151#13511yescharacteristic
94C4×C151AGL(1,ℤ/8)11yescharacteristic
95C4×C151AGL(1,ℤ/8)11yescharacteristic
96Dic151—41no—
97Dic151—41no—
98C2×C151—161no—
99C2×C151#44711yescharacteristic
100C2×C151#44911yescharacteristic
101C2×C151#45411yescharacteristic
102D151—42no—
103D151—81no—
104C151#162511yescharacteristic, complemented, Sylow
105#1625—1511nomaximal, Sylow
106#547—1511no—
107#486D15111yescharacteristic, complemented
108#459—1511no—
109#459—1511no—
110#332—1511no—
111D4⋊C8—1511no—
112D4⋊C8—1511no—
113C2×#41—3021no—
114C2×D8—3021no—
115C2×D8—3021no—
116C4⋊Q8C2×D15111yescharacteristic
117#127C2×D15111yescharacteristic
118#123—3022no—
119C22⋊Q8—3021no—
120#121—3021no—
121C4×D4—1511no—
122C4×D4—1511no—
123C2×C4⋊C4—3021no—
124C4⋊C8—1511no—
125C4⋊C8—1511no—
126#102—22no—
127#102—3021no—
128#102—3021no—
129C4×C8C2×D15111yescharacteristic
130#41—6042no—
131#41—6042no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—3022no—
137C2×D4—1511no—
138C2×D4—1511no—
139C22×C4—3022no—
140C22×C4—3021no—
141C22×C4—3021no—
142D8—6042no—
143D8—6042no—
144C2×C8—21no—
145C2×C8—3021no—
146C2×C8—3021no—
147C4⋊C4—21no—
148C4⋊C4—3022no—
149C4⋊C4—1511no—
150C4⋊C4—1511no—
151C4⋊C4C22⋊D15112yes—
152C22⋊C4—3022no—
153C22⋊C4—3021no—
154C22⋊C4—3021no—
155C42C22×D15111yescharacteristic
156C23—41no—
157C23—3021no—
158C23—3021no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—3021no—
167D4—3021no—
168D4—3021no—
169D4—6044no—
170D4—1512no—
171C2×C4—22no—
172C2×C4—3021no—
173C2×C4—3021no—
174C2×C4—6044no—
175C2×C4—6041no—
176C2×C4—6041no—
177C2×C4—6041no—
178C2×C4—6041no—
179C2×C4D4×D15111yescharacteristic
180C2×C4D4×D15111yescharacteristic
181C2×C4C2×C22⋊D15111yescharacteristic
182C8—41no—
183C8—6041no—
184C8—6041no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—3022no—
189C22—6041no—
190C22—6041no—
191C22—6041no—
192C22—6041no—
193C22—6041no—
194C22#1801270711yescharacteristic
195C4—21no—
196C4—42no—
197C4—6041no—
198C4—6041no—
199C4D8×D15111yescharacteristic
200C4#1801276011yescharacteristic
201C4#1801276311yescharacteristic
202C4#1801276611yescharacteristic
203C2—161no—
204C2—6042no—
205C2—12081no—
206C2#2375234411yescharacteristic
207C2#2375235611yescharacteristic
208C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#486×C151C2
socleC22×C151#120
hypercenter#486D151
hypocenterC151#1625
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23752865C2semidirect
2. #23752404C2semidirect
3. #23752404C2semidirect
4. #23751958C2semidirect
5. #23751941C2semidirect
6. #23751941C2semidirect
7. #486×C151C2semidirect
57. D604D8semidirect
104. C151#1625semidirect
107. #486D151semidirect

Maximal subgroups

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

subgroupindex
#237528652
#237524042
#237519582
#237519412
#486×C1512
#1625151