Finite Group Databasebeta

← #34071131

Subgroups — #34071131

Order 19328.

216 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752394C212yesmaximal, complemented
2#23752384C211yesmaximal, characteristic
3#23752011C212yesmaximal, complemented
4#23752009C211yesmaximal, characteristic, complemented
5#563×C151C211yesmaximal, characteristic, complemented
6#18012787C2211yescharacteristic
7#18012770—22no—
8#18012765—21no—
9#18012667—21no—
10#18012667—22no—
11#18012658C2212yes—
12#18012658C2211yescharacteristic
13C4⋊Q8×C151C2212yes—
14#126×C151—22no—
15#125×C151—21no—
16#124×C151C2211yescharacteristic
17#123×C151—21no—
18C22⋊Q8×C151—22no—
19#14559005—41no—
20#14559004—21no—
21#14559004—22no—
22Q8×D151—41no—
23#14558994—42no—
24#14558992—41no—
25#14558991—42no—
26#14558989—41no—
27#14558988—21no—
28#14558988—22no—
29C2×Q8×C151D412yes—
30C2×Q8×C151C2311yescharacteristic
31C2×D4×C151D411yescharacteristic
32C22×C4×C151—21no—
33C4⋊C4×C151—21no—
34C4⋊C4×C151—22no—
35C4⋊C4×C151—21no—
36C4⋊C4×C151—22no—
37C4⋊C4×C151—22no—
38C22⋊C4×C151—22no—
39C22⋊C4×C151—21no—
40C22⋊C4×C151—22no—
41C42×C151D411yescharacteristic
42C42×C151D412yes—
43Dic302—21no—
44Dic302—22no—
45D604—21no—
46D604—22no—
47C22⋊D151—41no—
48C4×D151—41no—
49C4×D151—42no—
50C151⋊C8—41no—
51C151⋊C8—42no—
52C23×C151—21no—
53Q8×C151—41no—
54Q8×C151—42no—
55D4×C151—41no—
56C2×C4×C151—22no—
57C2×C4×C151—21no—
58C2×C4×C151—22no—
59C2×C4×C151—81no—
60C2×C4×C151C2×D412yes—
61C2×C4×C151C2×D411yescharacteristic
62C22×C151—42no—
63C22×C151—41no—
64C22×C151#12011yescharacteristic
65C2×D151—41no—
66C4×C151—21no—
67C4×C151—22no—
68C4×C151—41no—
69C4×C151—42no—
70C4×C151—42no—
71Dic151—41no—
72C2×C151—21no—
73C2×C151—81no—
74C2×C151B(4,𝔽2)11yescharacteristic
75D151—81no—
76C151#220311yescharacteristic, complemented, Sylow
77#2203—1511nomaximal, Sylow
78#563D15111yescharacteristic, complemented
79#456—1512no—
80#454—1511no—
81#356—1512no—
82#355—1511no—
832−1+4—1511no—
84#137—3022no—
85AGL(1,ℤ/8)—3021no—
86C4⋊Q8C2×D15112yes—
87#126—22no—
88#125—21no—
89#124C2×D15111yescharacteristic
90#123—21no—
91C22⋊Q8—22no—
92#104—3021no—
93#104—3022no—
94#101—1512no—
95#101—1511no—
96#41—3021no—
97#41—3022no—
98#41—6041no—
99C2×Q8—6041no—
100C2×Q8C22⋊D15112yes—
101C2×Q8C22×D15111yescharacteristic
102C2×D4C22⋊D15111yescharacteristic
103C22×C4—21no—
104Q16—6042no—
105SD16—6041no—
106SD16—6042no—
107D8—6041no—
108M16—3021no—
109M16—3022no—
110C4⋊C4—21no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—21no—
117C22⋊C4—22no—
118C42C22⋊D15111yescharacteristic
119C42C22⋊D15112yes—
120C23—21no—
121Q8—41no—
122Q8—42no—
123Q8—3021no—
124Q8—3022no—
125D4—41no—
126D4—3021no—
127D4—3022no—
128D4—6041no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—81no—
133C2×C4—6041no—
134C2×C4—6042no—
135C2×C4C2×C22⋊D15112yes—
136C2×C4C2×C22⋊D15111yescharacteristic
137C8—6041no—
138C8—6042no—
139C22—42no—
140C22—41no—
141C22—6041no—
142C22#1801270811yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—42no—
147C4—42no—
148C4—6041no—
149C2—21no—
150C2—81no—
151C2—12081no—
152C2#2375239911yescharacteristic
subgroupG/H
centerC2#23752399
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#563×C151C2
socleC2×C151B(4,𝔽2)
prime radical#23752384C2
hypercenter#563D151
hypocenterC151#2203
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #23752394C2semidirect
3. #23752011C2semidirect
4. #23752009C2semidirect
5. #563×C151C2semidirect
76. C151#2203semidirect
78. #563D151semidirect

Maximal subgroups

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

subgroupindex
#237523942
#237523842
#237520112
#237520092
#563×C1512
#2203151