Finite Group Databasebeta

← #34068309

Subgroups — #34068309

Order 19328.

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

normal subgroups only

This group has 250 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#23752884C211yesmaximal, characteristic
2#23752560C211yesmaximal, characteristic, complemented
3#23752414C211yesmaximal, characteristic, complemented
4#23751955C211yesmaximal, characteristic, complemented
5Q8⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#475×C151C211yesmaximal, characteristic, complemented
8C2×#14559005—21no—
9C2×#14558991—21no—
10#18012736—21no—
11#18012736C2211yescharacteristic
12#18012714—21no—
13#18012714—22no—
14C4×D604—21no—
15C4×D604C2211yescharacteristic
16C4⋊(C151⋊C8)C2211yescharacteristic
17#18012663—21no—
18#18012659—22no—
19C4×C151⋊C8C2211yescharacteristic
20C4⋊Q8×C151C2211yescharacteristic
21C4×Q8×C151C2211yescharacteristic
22#106×C151—21no—
23C4⋊C8×C151C2211yescharacteristic
24#103×C151—21no—
25#14559005—42no—
26#14559005—42no—
27C2×D604—22no—
28C2×D604—22no—
29C2×D604—21no—
30C2×D604—21no—
31C2×D604D411yescharacteristic
32C2×D604D412yes—
33C2×C4×D151—22no—
34C2×C4×D151—21no—
35#14558991—42no—
36C2×C151⋊C8—21no—
37C2×C151⋊C8—21no—
38C4⋊Dic151D411yescharacteristic
39(C2×D151)⋊C4—22no—
40(C2×D151)⋊C4—21no—
41C2×Q8×C151—21no—
42C2×Q8×C151D411yescharacteristic
43C2×C8×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D411yescharacteristic
48C42×C151—21no—
49C42×C151C2311yescharacteristic
50C22×D151—21no—
51C22×D151—22no—
52D604—21no—
53D604—21no—
54D604—42no—
55D604—44no—
56D604—41no—
57D604—41no—
58D604—41no—
59D604—41no—
60D604—82no—
61C2×Dic151—21no—
62C4×D151—44no—
63C4×D151—41no—
64C4×D151—41no—
65C151⋊C8—41no—
66C151⋊C8—41no—
67Q8×C151—21no—
68Q8×C151—41no—
69Q8×C151—41no—
70Q8×C151SD1612yescomplemented
71C2×C4×C151—21no—
72C2×C4×C151—21no—
73C2×C4×C151—41no—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×D411yescharacteristic
77C8×C151—41no—
78C22×C151#12011yescharacteristic
79C2×D151—41no—
80C2×D151—42no—
81C2×D151—42no—
82C2×D151—41no—
83C2×D151—42no—
84C2×D151—41no—
85C4×C151—22no—
86C4×C151—21no—
87C4×C151—41no—
88C4×C151—81no—
89C4×C151C2×SD1611yescharacteristic
90C4×C151#13511yescharacteristic
91C4×C151AGL(1,ℤ/8)11yescharacteristic
92C4×C151AGL(1,ℤ/8)11yescharacteristic
93Dic151—41no—
94C2×C151#44911yescharacteristic
95C2×C151#45011yescharacteristic
96C2×C151#45511yescharacteristic
97D151—81no—
98D151—82no—
99C151#164211yescharacteristic, complemented, Sylow
100#1642—1511nomaximal, Sylow
101#550—1511no—
102#486—1511no—
103#475D15111yescharacteristic, complemented
104#461—1511no—
105#331—1511no—
106Q8⋊C8—1511no—
107D4⋊C8—1511no—
108C2×#41—3021no—
109C2×SD16—3021no—
110C4⋊Q8C2×D15111yescharacteristic
111#127—3021no—
112#127—1511no—
113#121—3022no—
114#121—3021no—
115C4×Q8C2×D15111yescharacteristic
116C4×D4—3021no—
117C4×D4—1511no—
118#106—21no—
119C4⋊C8—1511no—
120C4⋊C8C2×D15111yescharacteristic
121#103—21no—
122#103—3021no—
123#102—3022no—
124C4×C8—1511no—
125#41—6042no—
126#41—6042no—
127C2×Q8—21no—
128C2×Q8C22⋊D15111yescharacteristic
129C2×D4—3022no—
130C2×D4—3022no—
131C2×D4—3021no—
132C2×D4—3021no—
133C2×D4—1511no—
134C2×D4—1512no—
135C22×C4—3022no—
136C22×C4—3021no—
137SD16—6042no—
138C2×C8—21no—
139C2×C8—3021no—
140C2×C8—3021no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—1511no—
145C4⋊C4C22⋊D15111yescharacteristic
146C22⋊C4—3022no—
147C22⋊C4—3021no—
148C42—21no—
149C42C22×D15111yescharacteristic
150C23—3021no—
151C23—3022no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1455899112yescomplemented
156D4—3021no—
157D4—3021no—
158D4—6042no—
159D4—6044no—
160D4—6041no—
161D4—6041no—
162D4—6041no—
163D4—6041no—
164D4—12082no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—3021no—
169C2×C4—6044no—
170C2×C4—6041no—
171C2×C4—6041no—
172C2×C4D4×D15111yescharacteristic
173C2×C4D4×D15111yescharacteristic
174C2×C4C2×C22⋊D15111yescharacteristic
175C8—41no—
176C8—6041no—
177C8—6041no—
178C22—6041no—
179C22—6042no—
180C22—6042no—
181C22—6041no—
182C22—6042no—
183C22—6041no—
184C22#1801270711yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—81no—
189C4—6041no—
190C4C2×#1455899111yescharacteristic
191C4#1801276011yescharacteristic
192C4#1801276411yescharacteristic
193C4#1801276611yescharacteristic
194C2—12081no—
195C2—12082no—
196C2#2375235611yescharacteristic
197C2#2375236211yescharacteristic
198C2#2375238811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#475×C151C2
socleC22×C151#120
prime radical#23752884C2
hypercenter#475D151
hypocenterC151#1642
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #23752560C2semidirect
3. #23752414C2semidirect
4. #23751955C2semidirect
5. Q8⋊(C151⋊C8)C2semidirect
6. #23751939C2semidirect
7. #475×C151C2semidirect
70. Q8×C151SD16semidirect
99. C151#1642semidirect
103. #475D151semidirect
155. Q8#14558991semidirect

Maximal subgroups

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

subgroupindex
#237528842
#237525602
#237524142
#237519552
Q8⋊(C151⋊C8)2
#237519392
#475×C1512
#1642151