Finite Group Databasebeta

← #34068119

Subgroups — #34068119

Order 19328.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#23752841C211yesmaximal, characteristic
2#23752543C211yesmaximal, characteristic
3#23752540C211yesmaximal, characteristic
4#23752144C211yesmaximal, characteristic
5#23751948C211yesmaximal, characteristic
6#23751937C211yesmaximal, characteristic
7#328×C151C211yesmaximal, characteristic
8#18012738—21no—
9#18012737—21no—
10#18012729—21no—
11#18012729—21no—
12#18012718C2211yescharacteristic
13#18012716—21no—
14#18012695—21no—
15C2×C4⋊Dic151—21no—
16C2×C4⋊Dic151C2211yescharacteristic
17C2×Dic151⋊C4C2211yescharacteristic
18#18012671—21no—
19#18012670—21no—
20#18012664—21no—
21#18012663—21no—
22C22⋊(C151⋊C8)C2211yescharacteristic
23C151⋊#95—21no—
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C2×Dic302—21no—
28C2×Dic302D411yescharacteristic
29C22×Dic151—21no—
30C22×Dic151D411yescharacteristic
31C22×Dic151D411yescharacteristic
32C2×C151⋊C8—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151—42no—
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41Dic151⋊C4—21no—
42Dic151⋊C4—21no—
43Dic151⋊C4—21no—
44Dic151⋊C4—21no—
45C22⋊Dic151—21no—
46C4×Dic151—21no—
47C4×Dic151—21no—
48C2×Q8×C151D411yescharacteristic
49C22×C4×C151—21no—
50C22×C4×C151C2311yescharacteristic
51C2×C8×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D411yescharacteristic
54C22⋊C4×C151—21no—
55Dic302—41no—
56Dic302—81no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—41no—
63C2×Dic151—41no—
64C2×Dic151—41no—
65C2×Dic151—41no—
66C2×Dic151SD1612yes—
67C151⋊C8—41no—
68C23×C151C2×D411yescharacteristic
69Q8×C151—41no—
70C2×C4×C151—22no—
71C2×C4×C151—21no—
72C2×C4×C151—21no—
73C2×C4×C151—41no—
74C2×C4×C151—41no—
75C2×C4×C151—41no—
76C2×C4×C151C2×D411yescharacteristic
77C2×C4×C151C2×D411yescharacteristic
78C8×C151—41no—
79C22×C151—21no—
80C22×C151—21no—
81C22×C151#12011yescharacteristic
82C22×C151C2×SD1611yescharacteristic
83C22×C151#13711yescharacteristic
84C4×C151—21no—
85C4×C151—21no—
86C4×C151—42no—
87C4×C151—41no—
88C4×C151—41no—
89Dic151—22no—
90Dic151—41no—
91Dic151—41no—
92Dic151—41no—
93Dic151—81no—
94C2×C151—21no—
95C2×C151—21no—
96C2×C151#44811yescharacteristic
97C2×C151#45611yescharacteristic
98C2×C151#45811yescharacteristic
99C151#161111yescharacteristic, complemented, Sylow
100#1611—1511nomaximal, Sylow
101#544—1511no—
102#483—1511no—
103#483—1511no—
104#398—1511no—
105#328—1511no—
106#328D15111yescharacteristic
107#324—1511no—
108C4⋊Q8—3021no—
109C4⋊Q8—3021no—
110#125—3021no—
111#125—3021no—
112C22⋊Q8—3021no—
113C22⋊Q8—1511no—
114C22⋊Q8C2×D15111yescharacteristic
115#117—3021no—
116C2×C4⋊C4—3021no—
117C2×C4⋊C4—1511no—
118C2×C4⋊C4—1511no—
119#106—3021no—
120#106—3021no—
121#103—3021no—
122#103—3021no—
123C22⋊C8—1511no—
124C22⋊C8C2×D15111yescharacteristic
125#95—3021no—
126#95C2×D15111yescharacteristic
127C2×Q8—3021no—
128C2×Q8—1511no—
129C2×Q8D60411yescharacteristic
130C22×C4—21no—
131C22×C4—3021no—
132C22×C4—1511no—
133C22×C4—1511no—
134C22×C4C22×D15111yescharacteristic
135C2×C8—21no—
136C2×C8—3021no—
137C4⋊C4—21no—
138C4⋊C4—3021no—
139C4⋊C4—3021no—
140C4⋊C4—3021no—
141C4⋊C4—3021no—
142C4⋊C4—3021no—
143C4⋊C4—3021no—
144C4⋊C4—3021no—
145C4⋊C4—3021no—
146C4⋊C4—3021no—
147C4⋊C4—3021no—
148C4⋊C4—6042no—
149C4⋊C4—1511no—
150C4⋊C4D60411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3021no—
153C42—3021no—
154C42—3021no—
155C23D4×D15111yescharacteristic
156Q8—41no—
157Q8—6041no—
158Q8—12081no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3021no—
166C2×C4—3021no—
167C2×C4—3021no—
168C2×C4—3021no—
169C2×C4—3021no—
170C2×C4—6041no—
171C2×C4—6041no—
172C2×C4—6041no—
173C2×C4—6041no—
174C2×C4—1512no—
175C2×C4D4×D15111yescharacteristic
176C2×C4C2×D60411yescharacteristic
177C8—41no—
178C8—6041no—
179C22—21no—
180C22—21no—
181C22#1801270911yescharacteristic
182C22SD16×D15111yescharacteristic
183C22#1801277111yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—3022no—
190C4—6041no—
191C4—6041no—
192C4—6041no—
193C4—12081no—
194C2—21no—
195C2—21no—
196C2#2375235211yescharacteristic
197C2#2375239611yescharacteristic
198C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#328D151
hypocenterC151#1611
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C151#1611semidirect

Maximal subgroups

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

subgroupindex
#237528412
#237525432
#237525402
#237521442
#237519482
#237519372
#328×C1512
#1611151