Finite Group Databasebeta

← #34071133

Subgroups — #34071133

Order 19328.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752962C211yesmaximal, characteristic, complemented
2#23752397C212yesmaximal, complemented
3#23752384C211yesmaximal, characteristic
4#23752010C212yesmaximal, complemented
5#355×C151C211yesmaximal, characteristic, complemented
6#18012787C2211yescharacteristic
7#18012772—22no—
8#18012765—21no—
9#18012737C2212yes—
10#18012732—22no—
11#18012731—21no—
12#18012720—21no—
13#18012716—22no—
14#18012667—21no—
15#18012665—22no—
16#18012658C2211yescharacteristic
17#124×C151C2211yescharacteristic
18#101×C151C2212yes—
19#14559005—41no—
20#14559004—21no—
21#14559004—22no—
22C2×Dic302D412yes—
23Q8×D151—41no—
24C22×Dic151—21no—
25Dic604—42no—
26#14558993—42no—
27#14558992—41no—
28#14558989—41no—
29#14558988—21no—
30C4⋊Dic151—21no—
31C4⋊Dic151—21no—
32Dic151⋊C4—22no—
33Dic151⋊C4—22no—
34Dic151⋊C4—22no—
35C22⋊Dic151—22no—
36C22⋊Dic151—21no—
37C4×Dic151D412yes—
38C2×Q8×C151C2311yescharacteristic
39C2×D4×C151D411yescharacteristic
40M16×C151—22no—
41C22⋊C4×C151—22no—
42C42×C151D411yescharacteristic
43Dic302—21no—
44Dic302—22no—
45Dic302—42no—
46D604—21no—
47D604—22no—
48C22⋊D151—41no—
49C2×Dic151—22no—
50C2×Dic151—22no—
51C2×Dic151—81no—
52C4×D151—42no—
53C4×D151—41no—
54C151⋊C8—41no—
55C23×C151—21no—
56Q8×C151—41no—
57D4×C151—41no—
58C2×C4×C151—21no—
59C2×C4×C151C2×D412yes—
60C2×C4×C151C2×D411yescharacteristic
61C8×C151—42no—
62C22×C151—42no—
63C22×C151—41no—
64C22×C151#12011yescharacteristic
65C2×D151—41no—
66C4×C151—22no—
67C4×C151—21no—
68C4×C151—41no—
69Dic151—42no—
70Dic151—41no—
71Dic151—42no—
72C2×C151—21no—
73C2×C151—81no—
74C2×C151B(4,𝔽2)11yescharacteristic
75D151—81no—
76C151#220311yescharacteristic, complemented, Sylow
77#2203—1511nomaximal, Sylow
78#563—1511no—
79#456—1512no—
80#454—1511no—
81#356—1512no—
82#355D15111yescharacteristic, complemented
832−1+4—1511no—
84#137—3022no—
85AGL(1,ℤ/8)—3021no—
86C4⋊Q8—1512no—
87#126—3022no—
88#125—3021no—
89#124C2×D15111yescharacteristic
90#123—3021no—
91C22⋊Q8—3022no—
92#104—3022no—
93#104—3021no—
94#101—1511no—
95#101C2×D15112yes—
96#41—3022no—
97#41—3021no—
98#41—6041no—
99C2×Q8—6041no—
100C2×Q8—1512no—
101C2×Q8C22×D15111yescharacteristic
102C2×D4D60411yescharacteristic
103C22×C4—3021no—
104Q16—6042no—
105SD16—6042no—
106SD16—6041no—
107D8—6041no—
108M16—22no—
109M16—3021no—
110C4⋊C4—3022no—
111C4⋊C4—3021no—
112C4⋊C4—3021no—
113C4⋊C4—3022no—
114C4⋊C4—3022no—
115C22⋊C4—22no—
116C22⋊C4—3022no—
117C22⋊C4—3021no—
118C42—1512no—
119C42D60411yescharacteristic
120C23—21no—
121Q8—41no—
122Q8—3021no—
123Q8—3022no—
124Q8—6042no—
125D4—41no—
126D4—3021no—
127D4—3022no—
128D4—6041no—
129C2×C4—21no—
130C2×C4—3022no—
131C2×C4—3022no—
132C2×C4—6042no—
133C2×C4—6041no—
134C2×C4—12081no—
135C2×C4D4×D15112yes—
136C2×C4C2×D60411yescharacteristic
137C8—42no—
138C8—6041no—
139C22—42no—
140C22—41no—
141C22—6041no—
142C22#1801270911yescharacteristic
143C4—22no—
144C4—21no—
145C4—41no—
146C4—6042no—
147C4—6042no—
148C4—6041no—
149C2—21no—
150C2—81no—
151C2—12081no—
152C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#355×C151C2
socleC2×C151B(4,𝔽2)
prime radical#23752384C2
hypercenter#355D151
hypocenterC151#2203
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #23752962C2semidirect
2. #23752397C2semidirect
4. #23752010C2semidirect
5. #355×C151C2semidirect
76. C151#2203semidirect
82. #355D151semidirect

Maximal subgroups

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

subgroupindex
#237529622
#237523972
#237523842
#237520102
#355×C1512
#2203151