Finite Group Databasebeta

← #34068259

Subgroups — #34068259

Order 19328.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752866C211yesmaximal, characteristic
2#23752562C211yesmaximal, characteristic, complemented
3#23752499C211yesmaximal, characteristic, complemented
4#23751959C211yesmaximal, characteristic, complemented
5D4⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#476×C151C211yesmaximal, characteristic, complemented
8C2×#14559003—21no—
9#18012739C2211yescharacteristic
10#18012723—22no—
11#18012719—21no—
12#18012713—21no—
13C4×D604C2211yescharacteristic
14C2×C4⋊Dic151—21no—
15#18012670—21no—
16C4⋊(C151⋊C8)C2211yescharacteristic
17#18012663—22no—
18#18012659—21no—
19C4×C151⋊C8C2211yescharacteristic
20C4⋊Q8×C151C2211yescharacteristic
21C4×D4×C151C2211yescharacteristic
22#106×C151—21no—
23C4⋊C8×C151C2211yescharacteristic
24#102×C151—21no—
25#14559003—42no—
26#14559003—42no—
27C2×Dic302—21no—
28C2×D604D411yescharacteristic
29C2×C22⋊D151—22no—
30C22×Dic151—22no—
31C2×C4×D151—21no—
32C2×C151⋊C8—21no—
33C2×C151⋊C8—21no—
34C4⋊Dic151—22no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D412yes—
38(C2×D151)⋊C4—22no—
39(C2×D151)⋊C4—21no—
40C2×Q8×C151—21no—
41C2×D4×C151D411yescharacteristic
42C22×C4×C151—21no—
43C2×C8×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151D411yescharacteristic
47C22⋊C4×C151—21no—
48C42×C151C2311yescharacteristic
49C22×D151—21no—
50Dic302—41no—
51Dic302—41no—
52D604—21no—
53D604—21no—
54C22⋊D151—44no—
55C2×Dic151—21no—
56C2×Dic151—22no—
57C2×Dic151—44no—
58C4×D151—41no—
59C4×D151—41no—
60C151⋊C8—41no—
61C151⋊C8—41no—
62C23×C151—21no—
63Q8×C151—42no—
64D4×C151—21no—
65D4×C151SD1612yes—
66C2×C4×C151—21no—
67C2×C4×C151—41no—
68C2×C4×C151—41no—
69C2×C4×C151—41no—
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C8×C151—41no—
74C22×C151—22no—
75C22×C151—41no—
76C22×C151—41no—
77C22×C151#12011yescharacteristic
78C2×D151—41no—
79C2×D151—41no—
80C2×D151—41no—
81C4×C151—21no—
82C4×C151—41no—
83C4×C151—81no—
84C4×C151C2×SD1611yescharacteristic
85C4×C151#13511yescharacteristic
86C4×C151AGL(1,ℤ/8)11yescharacteristic
87C4×C151#13711yescharacteristic
88Dic151—41no—
89Dic151—42no—
90C2×C151—42no—
91C2×C151#45011yescharacteristic
92C2×C151#45211yescharacteristic
93C2×C151#45411yescharacteristic
94D151—81no—
95C151#163511yescharacteristic, complemented, Sylow
96#1635—1511nomaximal, Sylow
97#547—1511no—
98#487—1511no—
99#476—1511no—
100#476D15111yescharacteristic, complemented
101#332—1511no—
102D4⋊C8—1511no—
103D4⋊C8—1511no—
104C2×#41—3021no—
105C4⋊Q8—1511no—
106C4⋊Q8C2×D15111yescharacteristic
107#123—3022no—
108C22⋊Q8—3021no—
109#121—3021no—
110C4×D4—1511no—
111C4×D4C2×D15111yescharacteristic
112C2×C4⋊C4—3021no—
113#106—21no—
114#106—3021no—
115C4⋊C8—1511no—
116C4⋊C8C2×D15111yescharacteristic
117#103—3022no—
118#102—21no—
119#102—3021no—
120C4×C8—1511no—
121#41—6042no—
122#41—6042no—
123C2×Q8—21no—
124C2×Q8—3021no—
125C2×D4—3022no—
126C2×D4—1511no—
127C2×D4C22⋊D15111yescharacteristic
128C22×C4—21no—
129C22×C4—3022no—
130C22×C4—3021no—
131C2×C8—21no—
132C2×C8—3021no—
133C2×C8—3021no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—3022no—
137C4⋊C4—3021no—
138C4⋊C4—1512no—
139C4⋊C4—1511no—
140C4⋊C4C22⋊D15111yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—3022no—
143C22⋊C4—3021no—
144C42C22×D15111yescharacteristic
145C23—21no—
146C23—3021no—
147Q8—42no—
148Q8—6041no—
149Q8—6041no—
150D4—21no—
151D4—3021no—
152D4—3021no—
153D4—6044no—
154D4#1455899112yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—3021no—
160C2×C4—3022no—
161C2×C4—6044no—
162C2×C4—6041no—
163C2×C4—6041no—
164C2×C4D4×D15111yescharacteristic
165C2×C4D4×D15111yescharacteristic
166C2×C4C2×C22⋊D15111yescharacteristic
167C8—41no—
168C8—6041no—
169C8—6041no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—6041no—
174C22—6041no—
175C22—6041no—
176C22#1801270711yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—6041no—
181C4—6042no—
182C4C2×#1455899111yescharacteristic
183C4#1801276011yescharacteristic
184C4#1801276411yescharacteristic
185C4#1801276811yescharacteristic
186C2—42no—
187C2—12081no—
188C2#2375236211yescharacteristic
189C2#2375237111yescharacteristic
190C2#2375238311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#476×C151C2
socleC22×C151#120
prime radical#23752866C2
hypercenter#476D151
hypocenterC151#1635
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #23752562C2semidirect
3. #23752499C2semidirect
4. #23751959C2semidirect
5. D4⋊(C151⋊C8)C2semidirect
6. #23751939C2semidirect
7. #476×C151C2semidirect
95. C151#1635semidirect
100. #476D151semidirect

Maximal subgroups

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

subgroupindex
#237528662
#237525622
#237524992
#237519592
D4⋊(C151⋊C8)2
#237519392
#476×C1512
#1635151