Finite Group Databasebeta

← #34068407

Subgroups — #34068407

Order 19328.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752966C211yesmaximal, characteristic, complemented
2#23752599C211yesmaximal, characteristic
3#23752576C211yesmaximal, characteristic, complemented
4#23751954C211yesmaximal, characteristic, complemented
5#23751953C211yesmaximal, characteristic, complemented
6#23751951C211yesmaximal, characteristic, complemented
7#490×C151C211yesmaximal, characteristic, complemented
8C2×#14558992—21no—
9C2×#14558989—21no—
10#18012738—21no—
11#18012734—21no—
12#18012734—21no—
13#18012731C2211yescharacteristic
14#18012727C2211yescharacteristic
15#18012724—21no—
16#18012719—21no—
17#18012717—21no—
18#18012660—21no—
19#18012660—21no—
20#18012650C2211yescharacteristic
21#18012650C2211yescharacteristic
22#127×C151C2211yescharacteristic
23#125×C151C2211yescharacteristic
24#102×C151—21no—
25#102×C151—21no—
26#97×C151C2211yescharacteristic
27C2×Dic302—21no—
28C2×Dic302D411yescharacteristic
29C2×D604D411yescharacteristic
30C2×C4×D151—21no—
31#14558992—42no—
32#14558989—42no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41(C2×D151)⋊C4—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46C4×Dic151—21no—
47C2×D4×C151—21no—
48C2×D4×C151—21no—
49C2×D4×C151—21no—
50C2×C8×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D411yescharacteristic
54C4⋊C4×C151D411yescharacteristic
55C42×C151C2311yescharacteristic
56C22×D151—21no—
57Dic302—41no—
58Dic302—81no—
59D604—41no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—21no—
63C4×D151—81no—
64C151⋊C8—22no—
65C151⋊C8—41no—
66C23×C151—41no—
67D4×C151—41no—
68D4×C151—41no—
69D4×C151—42no—
70D4×C151—42no—
71C2×C4×C151—21no—
72C2×C4×C151—21no—
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151C2×D411yescharacteristic
76C8×C151—41no—
77C22×C151—81no—
78C22×C151—81no—
79C22×C151—81no—
80C22×C151#12011yescharacteristic
81C2×D151—41no—
82C2×D151—41no—
83C2×D151—41no—
84C4×C151—21no—
85C4×C151—21no—
86C4×C151—21no—
87C4×C151—41no—
88C4×C151—41no—
89Dic151—41no—
90Dic151—41no—
91Dic151—41no—
92C2×C151—161no—
93C2×C151#45311yescharacteristic
94C2×C151#45411yescharacteristic
95C2×C151#45411yescharacteristic
96D151—81no—
97C151#165711yescharacteristic, complemented, Sylow
98#1657—1511nomaximal, Sylow
99#563—1511no—
100#496—1511no—
101#490—1511no—
102#490D15111yescharacteristic, complemented
103#330—1511no—
104#330—1511no—
105#329—1511no—
106C2×SD16—3021no—
107C2×D8—3021no—
108C4⋊Q8—3021no—
109#127C2×D15111yescharacteristic
110#126—3021no—
111#126—3021no—
112#125—1511no—
113#125C2×D15111yescharacteristic
114#124—1511no—
115#123—3021no—
116C22⋊Q8—3021no—
117C22⋊Q8—3021no—
118#102—21no—
119#102—21no—
120#102—3021no—
121#102—3021no—
122#97—1511no—
123#97—1511no—
124#97C2×D15111yescharacteristic
125C2×Q8—3021no—
126C2×Q8—1511no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—1511no—
131C22×C4—3021no—
132SD16—6042no—
133D8—6042no—
134C2×C8—21no—
135C2×C8—3021no—
136C2×C8—3021no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—3021no—
140C4⋊C4—3021no—
141C4⋊C4—3021no—
142C4⋊C4—3021no—
143C4⋊C4—1511no—
144C4⋊C4—1511no—
145C4⋊C4C22⋊D15111yescharacteristic
146C4⋊C4C22⋊D15111yescharacteristic
147C22⋊C4—3021no—
148C22⋊C4—3021no—
149C22⋊C4—3021no—
150C22⋊C4—3021no—
151C22⋊C4—3021no—
152C42—3021no—
153C42C22×D15111yescharacteristic
154C23—41no—
155C23—3021no—
156Q8—6041no—
157Q8—12081no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—6041no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—3021no—
166C2×C4—3021no—
167C2×C4—3021no—
168C2×C4—12081no—
169C2×C4D4×D15111yescharacteristic
170C2×C4D4×D15111yescharacteristic
171C2×C4C2×C22⋊D15111yescharacteristic
172C8—41no—
173C8—3022no—
174C8—6041no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—6041no—
179C22—6041no—
180C22—6041no—
181C22#1801270711yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—6041no—
188C4—6041no—
189C4—6041no—
190C2—161no—
191C2—12081no—
192C2#2375237811yescharacteristic
193C2#2375238311yescharacteristic
194C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#490×C151C2
socleC22×C151#120
prime radical#23752599C2
hypercenter#490D151
hypocenterC151#1657
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23752966C2semidirect
3. #23752576C2semidirect
4. #23751954C2semidirect
5. #23751953C2semidirect
6. #23751951C2semidirect
7. #490×C151C2semidirect
97. C151#1657semidirect
102. #490D151semidirect

Maximal subgroups

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

subgroupindex
#237529662
#237525992
#237525762
#237519542
#237519532
#237519512
#490×C1512
#1657151