Finite Group Databasebeta

← #34068129

Subgroups — #34068129

Order 19328.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752774C211yesmaximal, characteristic
2#23752530C212yesmaximal, complemented
3#23751945C212yesmaximal, complemented
4#23751936C211yesmaximal, characteristic, complemented
5#399×C151C211yesmaximal, characteristic, complemented
6C22×C22⋊D151—21no—
7#18012723—22no—
8#18012713—21no—
9#18012713C2212yes—
10#18012709—22no—
11#18012670—22no—
12#18012659—22no—
13C22⋊(C151⋊C8)C2212yescomplemented
14C2×C4⋊C4×C151—21no—
15C2×C4⋊C4×C151C2211yescharacteristic, complemented
16C2×C22⋊C4×C151—21no—
17C2×C22⋊C4×C151C2211yescharacteristic
18#95×C151C2211yescharacteristic, complemented
19C23×D151—21no—
20C2×D604—21no—
21C2×D604D412yes—
22C2×C22⋊D151—22no—
23C2×C22⋊D151—22no—
24C2×C22⋊D151—42no—
25C2×C22⋊D151—42no—
26C22×Dic151—21no—
27C2×C151⋊C8—22no—
28C4⋊Dic151—21no—
29C4⋊Dic151D412yes—
30(C2×D151)⋊C4—22no—
31(C2×D151)⋊C4—22no—
32C24×C151D411yescharacteristic
33C22×C4×C151—21no—
34C22×C4×C151—21no—
35C22×C4×C151D411yescharacteristic
36C22×C4×C151C2311yescharacteristic
37C4⋊C4×C151—22no—
38C4⋊C4×C151—42no—
39C22⋊C4×C151—22no—
40C22⋊C4×C151—42no—
41C22×D151—22no—
42C22×D151—42no—
43C22×D151—81no—
44C22×D151—81no—
45D604—42no—
46D604—81no—
47C22⋊D151—44no—
48C22⋊D151—42no—
49C22⋊D151—42no—
50C2×Dic151—22no—
51C2×Dic151—42no—
52C151⋊C8—42no—
53C23×C151—21no—
54C23×C151—21no—
55C23×C151—41no—
56C23×C151—41no—
57C23×C151SD1612yes—
58C23×C151C2×D411yescharacteristic
59C2×C4×C151—22no—
60C2×C4×C151—21no—
61C2×C4×C151—41no—
62C2×C4×C151—41no—
63C2×C4×C151—41no—
64C2×C4×C151—41no—
65C2×C4×C151—41no—
66C2×C4×C151—41no—
67C2×C4×C151—41no—
68C2×C4×C151C2×D412yes—
69C22×C151—21no—
70C22×C151—21no—
71C22×C151—22no—
72C22×C151—42no—
73C22×C151—41no—
74C22×C151—41no—
75C22×C151—81no—
76C22×C151#12011yescharacteristic
77C22×C151C2×SD1611yescharacteristic
78C22×C151AGL(1,ℤ/8)11yescharacteristic
79C2×D151—42no—
80C2×D151—42no—
81C2×D151—42no—
82C2×D151—84no—
83C4×C151—22no—
84C4×C151—42no—
85C4×C151—41no—
86C4×C151—81no—
87Dic151—42no—
88C2×C151—21no—
89C2×C151—21no—
90C2×C151—42no—
91C2×C151#45011yescharacteristic
92C2×C151#45311yescharacteristic
93C2×C151#45811yescharacteristic
94D151—82no—
95C151#161311yescharacteristic, complemented, Sylow
96#1613—1511nomaximal, Sylow
97#534—1511no—
98#481—1512no—
99#399D15111yescharacteristic, complemented
100#327—1512no—
101#323—1511no—
102C22×D4—3021no—
103#123—3022no—
104#121—3021no—
105#121—1512no—
106#120—3022no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C2×D15111yescharacteristic, complemented
109C2×C22⋊C4—21no—
110C2×C22⋊C4C2×D15111yescharacteristic
111#106—3022no—
112#102—3022no—
113C22⋊C8—1512no—
114#95C2×D15111yescharacteristic, complemented
115C24—3021no—
116C24C22⋊D15111yescharacteristic
117C2×D4—3021no—
118C2×D4—3022no—
119C2×D4—3022no—
120C2×D4—6042no—
121C2×D4—6042no—
122C2×D4—1512no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—3021no—
126C22×C4C22⋊D15111yescharacteristic
127C22×C4C22×D15111yescharacteristic
128C2×C8—3022no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—3021no—
132C4⋊C4—1512no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—3022no—
136C22⋊C4—3022no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—3022no—
142C23—6042no—
143C23—12081no—
144C23—12081no—
145C23#1455899112yes—
146C23C2×C22⋊D15111yescharacteristic
147D4—6042no—
148D4—6044no—
149D4—6042no—
150D4—6042no—
151D4—12081no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—3022no—
162C2×C4—6042no—
163C2×C4D4×D15112yes—
164C8—6042no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—6042no—
173C22—6042no—
174C22—6042no—
175C22—12084no—
176C22#1801270711yescharacteristic
177C22C2×#1455899111yescharacteristic
178C22#1801276411yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—6042no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—12082no—
188C2#2375236211yescharacteristic
189C2#2375237911yescharacteristic
190C2#2375240111yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#399×C151C2
socleC22×C151#120
prime radical#23752774C2
hypercenter#399D151
hypocenterC151#1613
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #23752530C2semidirect
3. #23751945C2semidirect
4. #23751936C2semidirect
5. #399×C151C2semidirect
13. C22⋊(C151⋊C8)C22semidirect
15. C2×C4⋊C4×C151C22semidirect
18. #95×C151C22semidirect
95. C151#1613semidirect
99. #399D151semidirect
108. C2×C4⋊C4C2×D151semidirect
114. #95C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527742
#237525302
#237519452
#237519362
#399×C1512
#1613151