Finite Group Databasebeta

← #34071125

Subgroups — #34071125

Order 19328.

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

normal subgroups only

This group has 226 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#23752403C212yesmaximal
3#23752389C211yesmaximal, characteristic
4#23752001C212yesmaximal, complemented
5#354×C151C211yesmaximal, characteristic, complemented
6#18012784C2211yescharacteristic
7#18012770—21no—
8#18012737—21no—
9#18012732—22no—
10#18012731—21no—
11#18012723—22no—
12#18012720C2212yes—
13#18012716—22no—
14#18012667—21no—
15#18012656C2211yescharacteristic
16#18012653—22no—
17#124×C151C2211yescharacteristic
18#99×C151C2212yes—
19#14559004—21no—
20#14559003—41no—
21C2×Dic302—21no—
22C2×C22⋊D151—22no—
23D4×D151—41no—
24C22×Dic151D412yes—
25#14558994—41no—
26#14558991—41no—
27#14558988—21no—
28C4⋊Dic151—21no—
29C4⋊Dic151—21no—
30C4⋊Dic151—42no—
31Dic151⋊C4—22no—
32Dic151⋊C4—22no—
33Dic151⋊C4—22no—
34C22⋊Dic151—22no—
35C22⋊Dic151D412yes—
36(C2×D151)⋊C4—42no—
37C4×Dic151—21no—
38C2×Q8×C151D411yescharacteristic
39C2×D4×C151C2311yescharacteristic
40C22⋊C4×C151—22no—
41C22⋊C4×C151—22no—
42C42×C151D411yescharacteristic
43C22×D151—22no—
44Dic302—21no—
45Dic302—81no—
46D604—21no—
47C22⋊D151—42no—
48C22⋊D151—41no—
49C2×Dic151—22no—
50C2×Dic151—22no—
51C2×Dic151—22no—
52C2×Dic151—42no—
53C4×D151—41no—
54C151⋊C8—41no—
55C23×C151C2×D412yes—
56Q8×C151—41no—
57D4×C151—41no—
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151—42no—
61C2×C4×C151C2×D411yescharacteristic
62C22×C151—22no—
63C22×C151—42no—
64C22×C151#12011yescharacteristic
65C2×D151—41no—
66C2×D151—82no—
67C4×C151—21no—
68C4×C151—41no—
69C4×C151—41no—
70C4×C151—82no—
71Dic151—42no—
72Dic151—41no—
73Dic151—42no—
74C2×C151—21no—
75C2×C151—42no—
76C2×C151B(4,𝔽2)11yescharacteristic
77D151—81no—
78C151#220111yescharacteristic, complemented, Sylow
79#2201—1511nomaximal, Sylow
80#563—1511no—
81#458—1512no—
82#455—1511no—
83#354D15111yescharacteristic, complemented
84#352—1512no—
85H(5,𝔽2)—1511no—
86#137—3021no—
87C4⋊Q8—3021no—
88#126—3022no—
89#125—3021no—
90#124C2×D15111yescharacteristic
91#123—3022no—
92#123—1512no—
93C22⋊Q8—3022no—
94#104—3021no—
95#100—1511no—
96#99—3022no—
97#99C2×D15112yes—
98#41—3021no—
99#41—6041no—
100C2×Q8—3021no—
101C2×Q8D60411yescharacteristic
102C2×D4—3022no—
103C2×D4—6041no—
104C2×D4C22×D15111yescharacteristic
105C22×C4—1512no—
106Q16—6041no—
107SD16—6041no—
108M16—3021no—
109C4⋊C4—3022no—
110C4⋊C4—3022no—
111C4⋊C4—3021no—
112C4⋊C4—3021no—
113C4⋊C4—3022no—
114C4⋊C4—6042no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—3022no—
118C22⋊C4—6042no—
119C22⋊C4—1512no—
120C42—3021no—
121C42D60411yescharacteristic
122C23—3022no—
123C23D4×D15112yes—
124Q8—41no—
125Q8—3021no—
126Q8—12081no—
127D4—41no—
128D4—3021no—
129D4—6042no—
130D4—6041no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—42no—
134C2×C4—3022no—
135C2×C4—3022no—
136C2×C4—3022no—
137C2×C4—6041no—
138C2×C4—6042no—
139C2×C4C2×D60411yescharacteristic
140C8—6041no—
141C22—22no—
142C22—42no—
143C22—6041no—
144C22—12082no—
145C22#1801270911yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—82no—
150C4—6042no—
151C4—6041no—
152C4—6042no—
153C2—21no—
154C2—42no—
155C2—12081no—
156C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#354×C151C2
socleC2×C151B(4,𝔽2)
prime radical#18012784C22
hypercenter#354D151
hypocenterC151#2201
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
1. #23752962C2semidirect
4. #23752001C2semidirect
5. #354×C151C2semidirect
78. C151#2201semidirect
83. #354D151semidirect

Maximal subgroups

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

subgroupindex
#237529622
#237524032
#237523892
#237520012
#354×C1512
#2201151