Finite Group Databasebeta

← #34068217

Subgroups — #34068217

Order 19328.

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

normal subgroups only

This group has 216 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#23752936C211yesmaximal, characteristic, complemented
2#23752409C211yesmaximal, characteristic, complemented
3#23752404C211yesmaximal, characteristic
4#23751958C211yesmaximal, characteristic, complemented
5#23751944C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7#486×C151C211yesmaximal, characteristic, complemented
8C2×#14558992—21no—
9C2×#14558989—21no—
10#18012734—22no—
11#18012728—21no—
12#18012719—21no—
13Q8×Dic151—21no—
14C4×Dic302C2211yescharacteristic
15C4×D604C2211yescharacteristic
16#18012697—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012660—21no—
20#18012660—21no—
21C4⋊Q8×C151C2211yescharacteristic
22#127×C151C2211yescharacteristic
23#102×C151—22no—
24C4×C8×C151C2211yescharacteristic
25C2×Dic302D411yescharacteristic
26C2×D604D411yescharacteristic
27C2×C4×D151—21no—
28#14558992—42no—
29#14558989—42no—
30C2×C151⋊C8—21no—
31C2×C151⋊C8—21no—
32C4⋊Dic151—22no—
33C4⋊Dic151D411yescharacteristic
34C4⋊Dic151D411yescharacteristic
35Dic151⋊C4—21no—
36(C2×D151)⋊C4—22no—
37(C2×D151)⋊C4—22no—
38(C2×D151)⋊C4—21no—
39C4×Dic151—22no—
40C4×Dic151—21no—
41C2×Q8×C151—21no—
42C2×D4×C151—21no—
43C2×D4×C151—21no—
44C2×D4×C151—21no—
45C2×C8×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D412yes—
48C42×C151C2311yescharacteristic
49C22×D151—21no—
50Dic302—21no—
51Dic302—21no—
52D604—21no—
53D604—21no—
54C2×Dic151—21no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C4×D151—41no—
58C4×D151—41no—
59C151⋊C8—41no—
60C151⋊C8—41no—
61C23×C151—41no—
62Q8×C151—41no—
63Q8×C151—41no—
64D4×C151—42no—
65D4×C151—41no—
66D4×C151—41no—
67D4×C151—41no—
68D4×C151—41no—
69C2×C4×C151—22no—
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C8×C151—41no—
74C22×C151—81no—
75C22×C151—81no—
76C22×C151—81no—
77C22×C151#12011yescharacteristic
78C2×D151—41no—
79C2×D151—41no—
80C2×D151—41no—
81C4×C151—21no—
82C4×C151—42no—
83C4×C151#13511yescharacteristic
84C4×C151#13511yescharacteristic
85C4×C151AGL(1,ℤ/8)11yescharacteristic
86C4×C151AGL(1,ℤ/8)11yescharacteristic
87Dic151—41no—
88Dic151—41no—
89Dic151—41no—
90C2×C151—161no—
91C2×C151#44911yescharacteristic
92C2×C151#44911yescharacteristic
93C2×C151#45411yescharacteristic
94D151—81no—
95C151#162811yescharacteristic, complemented, Sylow
96#1628—1511nomaximal, Sylow
97#556—1511no—
98#486D15111yescharacteristic, complemented
99#460—1511no—
100#459—1511no—
101#332—1511no—
102Q8⋊C8—1511no—
103D4⋊C8—1511no—
104C2×SD16—3021no—
105C2×D8—3021no—
106C4⋊Q8C2×D15111yescharacteristic
107#127C2×D15111yescharacteristic
108#126—3022no—
109#124—3021no—
110C22⋊Q8—3021no—
111C4×Q8—3021no—
112C4×Q8—1511no—
113C4×D4—1511no—
114#117—3021no—
115C4⋊C8—1511no—
116C4⋊C8—1511no—
117#102—22no—
118#102—3021no—
119#102—3021no—
120C4×C8C2×D15111yescharacteristic
121C2×Q8—21no—
122C2×Q8—1511no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—1511no—
127C22×C4—3021no—
128SD16—6042no—
129D8—6042no—
130C2×C8—21no—
131C2×C8—3021no—
132C2×C8—3021no—
133C4⋊C4—21no—
134C4⋊C4—3022no—
135C4⋊C4—3021no—
136C4⋊C4—1511no—
137C4⋊C4—1511no—
138C4⋊C4C22⋊D15112yes—
139C22⋊C4—3022no—
140C22⋊C4—3022no—
141C22⋊C4—3021no—
142C42—3022no—
143C42—3021no—
144C42C22×D15111yescharacteristic
145C23—41no—
146C23—3021no—
147Q8—41no—
148Q8—41no—
149Q8—3021no—
150Q8—3021no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—3021no—
157D4—3021no—
158C2×C4—22no—
159C2×C4—3021no—
160C2×C4—3021no—
161C2×C4—3021no—
162C2×C4—6041no—
163C2×C4—6041no—
164C2×C4D4×D15111yescharacteristic
165C2×C4D4×D15111yescharacteristic
166C2×C4C2×C22⋊D15111yescharacteristic
167C8—41no—
168C8—6041no—
169C8—6041no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—6041no—
174C22—6041no—
175C22—6041no—
176C22#1801270711yescharacteristic
177C4—21no—
178C4—42no—
179C4—6041no—
180C4—6041no—
181C4—6041no—
182C4#1801275811yescharacteristic
183C4#1801276011yescharacteristic
184C4#1801276311yescharacteristic
185C4#1801276611yescharacteristic
186C2—161no—
187C2—12081no—
188C2#2375235411yescharacteristic
189C2#2375235611yescharacteristic
190C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#486×C151C2
socleC22×C151#120
prime radical#23752404C2
hypercenter#486D151
hypocenterC151#1628
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23752936C2semidirect
2. #23752409C2semidirect
4. #23751958C2semidirect
5. #23751944C2semidirect
6. #23751941C2semidirect
7. #486×C151C2semidirect
95. C151#1628semidirect
98. #486D151semidirect

Maximal subgroups

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

subgroupindex
#237529362
#237524092
#237524042
#237519582
#237519442
#237519412
#486×C1512
#1628151