Finite Group Databasebeta

← #34068143

Subgroups — #34068143

Order 19328.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#23752809C211yesmaximal, characteristic
2#23752548C211yesmaximal, characteristic, complemented
3#23752531C211yesmaximal, characteristic
4#23752151C211yesmaximal, characteristic, complemented
5#23751950C211yesmaximal, characteristic, complemented
6#23751947C211yesmaximal, characteristic
7#324×C151C211yesmaximal, characteristic, complemented
8#18012734—21no—
9#18012729—21no—
10#18012724—21no—
11#18012722—21no—
12#18012718C2211yescharacteristic
13#18012717—21no—
14#18012713C2211yescharacteristic
15C4×C22⋊D151—21no—
16C2×C4⋊Dic151C2211yescharacteristic
17#18012673—21no—
18#18012671—21no—
19#18012664—21no—
20#18012661—21no—
21C151⋊#95—21no—
22C151⋊#95—21no—
23C151⋊#95C2211yescharacteristic
24C2×C4⋊C4×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26C22⋊C8×C151C2211yescharacteristic
27C2×Dic302D411yescharacteristic
28C2×D604D411yescharacteristic
29C2×C22⋊D151—21no—
30C22×Dic151—21no—
31C22×Dic151—21no—
32C2×C4×D151—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151D411yescharacteristic
36C4⋊Dic151D411yescharacteristic
37Dic151⋊C4—21no—
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41C22⋊Dic151—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46C4×Dic151—21no—
47C22×C4×C151D411yescharacteristic
48C22×C4×C151D411yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C2×C8×C151—21no—
51C2×C8×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151—21no—
54C22×D151—21no—
55Dic302—41no—
56D604—41no—
57C22⋊D151—41no—
58C22⋊D151—41no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—41no—
63C2×Dic151—41no—
64C2×Dic151—42no—
65C2×Dic151—41no—
66C2×Dic151—41no—
67C4×D151—81no—
68C23×C151C2×D411yescharacteristic
69C2×C4×C151—21no—
70C2×C4×C151—21no—
71C2×C4×C151—21no—
72C2×C4×C151—21no—
73C2×C4×C151—41no—
74C2×C4×C151—41no—
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×D411yescharacteristic
77C8×C151—41no—
78C8×C151—41no—
79C22×C151—21no—
80C22×C151—21no—
81C22×C151#12011yescharacteristic
82C22×C151#13511yescharacteristic
83C22×C151#13711yescharacteristic
84C2×D151—41no—
85C2×D151—41no—
86C2×D151—41no—
87C4×C151—21no—
88C4×C151—21no—
89C4×C151—41no—
90C4×C151—41no—
91Dic151—41no—
92Dic151—41no—
93Dic151—41no—
94Dic151—81no—
95Dic151—81no—
96C2×C151—21no—
97C2×C151—21no—
98C2×C151#45211yescharacteristic
99C2×C151#45411yescharacteristic
100C2×C151#45811yescharacteristic
101D151—81no—
102C151#161511yescharacteristic, complemented, Sylow
103#1615—1511nomaximal, Sylow
104#539—1511no—
105#484—1511no—
106#481—1511no—
107#400—1511no—
108#328—1511no—
109#327—1511no—
110#324D15111yescharacteristic, complemented
111#126—3021no—
112#125—3021no—
113#123—3021no—
114#123—3021no—
115C22⋊Q8—3021no—
116C22⋊Q8—1511no—
117#121—1511no—
118C4×D4—3021no—
119C2×C4⋊C4—1511no—
120C2×C4⋊C4C2×D15111yescharacteristic
121#107—3021no—
122#106—3021no—
123#103—3021no—
124#102—3021no—
125C22⋊C8C2×D15111yescharacteristic
126C22⋊C8C2×D15111yescharacteristic
127#95—3021no—
128#95—3021no—
129#95—1511no—
130C2×Q8—1511no—
131C2×D4—3021no—
132C2×D4—1511no—
133C22×C4—3021no—
134C22×C4—3021no—
135C22×C4—3021no—
136C22×C4D60411yescharacteristic
137C22×C4D60411yescharacteristic
138C22×C4C22×D15111yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3021no—
144C4⋊C4—3021no—
145C4⋊C4—3021no—
146C4⋊C4—3021no—
147C4⋊C4—3021no—
148C4⋊C4—3021no—
149C4⋊C4—1511no—
150C4⋊C4—1511no—
151C22⋊C4—3021no—
152C22⋊C4—3021no—
153C22⋊C4—3021no—
154C22⋊C4—3021no—
155C22⋊C4—3021no—
156C42—3021no—
157C23—3021no—
158C23C2×D60411yescharacteristic
159Q8—6041no—
160D4—6041no—
161D4—6041no—
162D4—6041no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3021no—
170C2×C4—3021no—
171C2×C4—3021no—
172C2×C4—6041no—
173C2×C4—6041no—
174C2×C4—6042no—
175C2×C4—6041no—
176C2×C4—6041no—
177C2×C4—12081no—
178C2×C4D4×D15111yescharacteristic
179C2×C4D4×D15111yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—6041no—
185C22—6041no—
186C22—6041no—
187C22#1801270911yescharacteristic
188C22#1801276111yescharacteristic
189C22#1801277211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—6041no—
195C4—6041no—
196C4—6041no—
197C4—12081no—
198C4—12081no—
199C2—21no—
200C2—21no—
201C2—12081no—
202C2#2375237611yescharacteristic
203C2#2375238711yescharacteristic
204C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#324×C151C2
socleC22×C151#120
prime radical#18012713C22
hypercenter#324D151
hypocenterC151#1615
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #23752548C2semidirect
4. #23752151C2semidirect
5. #23751950C2semidirect
7. #324×C151C2semidirect
102. C151#1615semidirect
110. #324D151semidirect

Maximal subgroups

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

subgroupindex
#237528092
#237525482
#237525312
#237521512
#237519502
#237519472
#324×C1512
#1615151