Finite Group Databasebeta

← #34068328

Subgroups — #34068328

Order 19328.

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

normal subgroups only

This group has 200 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#23752942C211yesmaximal, characteristic
2#23752494C211yesmaximal, characteristic
3#23752419C211yesmaximal, characteristic
4#23751961C211yesmaximal, characteristic
5#23751944C211yesmaximal, characteristic
6#23751944C211yesmaximal, characteristic
7#487×C151C211yesmaximal, characteristic
8C2×#14558994—21no—
9#18012738—21no—
10#18012738—21no—
11#18012737—22no—
12C4×Dic302C2211yescharacteristic
13C4×Dic302C2211yescharacteristic
14#18012704—21no—
15#18012704—21no—
16#18012670—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012663—21no—
20#18012662—21no—
21C4⋊Q8×C151C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23#103×C151—22no—
24C4×C8×C151C2211yescharacteristic
25C2×Dic302—22no—
26C2×Dic302D411yescharacteristic
27C2×Dic302D411yescharacteristic
28#14558994—42no—
29C2×C151⋊C8—21no—
30C2×C151⋊C8—21no—
31C4⋊Dic151D411yescharacteristic
32C4⋊Dic151D411yescharacteristic
33Dic151⋊C4—22no—
34Dic151⋊C4—22no—
35Dic151⋊C4—21no—
36Dic151⋊C4—21no—
37C4×Dic151—22no—
38C4×Dic151—21no—
39C4×Dic151—21no—
40C2×Q8×C151—21no—
41C2×Q8×C151D412yes—
42C2×C8×C151—21no—
43C4⋊C4×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C42×C151C2311yescharacteristic
48Dic302—21no—
49Dic302—21no—
50Dic302—82no—
51Dic302SD1612yes—
52Dic302Q1612yescomplemented
53C2×Dic151—21no—
54C2×Dic151—21no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C151⋊C8—41no—
58C151⋊C8—41no—
59Q8×C151—42no—
60Q8×C151—41no—
61Q8×C151—41no—
62C2×C4×C151—22no—
63C2×C4×C151—41no—
64C2×C4×C151C2×D411yescharacteristic
65C2×C4×C151C2×D411yescharacteristic
66C2×C4×C151C2×D411yescharacteristic
67C8×C151—41no—
68C22×C151#12011yescharacteristic
69C4×C151—21no—
70C4×C151—42no—
71C4×C151—81no—
72C4×C151C2×SD1611yescharacteristic
73C4×C151C2×Q1611yescharacteristic
74C4×C151#13711yescharacteristic
75C4×C151#13711yescharacteristic
76Dic151—22no—
77Dic151—22no—
78Dic151—41no—
79Dic151—41no—
80C2×C151#44811yescharacteristic
81C2×C151#45111yescharacteristic
82C2×C151#45511yescharacteristic
83C151#164511yescharacteristic, complemented, Sylow
84#1645—1511nomaximal, Sylow
85Q82—1511no—
86#487D15111yescharacteristic
87#475—1511no—
88#462—1511no—
89#333—1511no—
90Q8⋊C8—1511no—
91Q8⋊C8—1511no—
92C2×Q16—3021no—
93C4⋊Q8—3021no—
94C4⋊Q8—3021no—
95C4⋊Q8—3022no—
96C4⋊Q8C2×D15111yescharacteristic
97C4⋊Q8C2×D15111yescharacteristic
98C4×Q8—3021no—
99C4×Q8—3021no—
100C4×Q8—1511no—
101C4×Q8—1511no—
102#106—3021no—
103C4⋊C8—1511no—
104C4⋊C8—1511no—
105#103—22no—
106#103—3021no—
107#103—3021no—
108C4×C8C2×D15111yescharacteristic
109C2×Q8—21no—
110C2×Q8—3022no—
111C2×Q8—1511no—
112C2×Q8—1511no—
113C2×Q8C22⋊D15112yes—
114Q16—6042no—
115C2×C8—21no—
116C2×C8—3021no—
117C2×C8—3021no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—3022no—
123C4⋊C4—3022no—
124C4⋊C4—3021no—
125C4⋊C4—3021no—
126C4⋊C4—1511no—
127C4⋊C4—1511no—
128C42—3022no—
129C42—3021no—
130C42—3021no—
131C42C22×D15111yescharacteristic
132Q8—42no—
133Q8—41no—
134Q8—41no—
135Q8—3021no—
136Q8—3021no—
137Q8—1512no—
138Q8—1512no—
139Q8—12082no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—3021no—
143C2×C4—3021no—
144C2×C4—3021no—
145C2×C4—3021no—
146C2×C4D4×D15111yescharacteristic
147C2×C4D4×D15111yescharacteristic
148C2×C4C2×C22⋊D15111yescharacteristic
149C8—41no—
150C8—6041no—
151C8—6041no—
152C22#1801270711yescharacteristic
153C4—21no—
154C4—42no—
155C4—81no—
156C4—3022no—
157C4—3022no—
158C4—6041no—
159C4—6041no—
160C4SD16×D15111yescharacteristic
161C4Q16×D15111yescharacteristic
162C4#1801276811yescharacteristic
163C4#1801277111yescharacteristic
164C2#2375234911yescharacteristic
165C2#2375236611yescharacteristic
166C2#2375238911yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#487×C151C2
socle, prime radicalC22×C151#120
hypercenter#487D151
hypocenterC151#1645
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
52. Dic302Q16semidirect
83. C151#1645semidirect

Maximal subgroups

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

subgroupindex
#237529422
#237524942
#237524192
#237519612
#237519442
#487×C1512
#1645151