Finite Group Databasebeta

← #34071106

Subgroups — #34071106

Order 19328.

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

normal subgroups only

This group has 246 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#23752401C212yesmaximal, complemented
2#23752379C211yesmaximal, characteristic
3#23752005C211yesmaximal, characteristic, complemented
4#23752002C212yesmaximal, complemented
5#559×C151C211yesmaximal, characteristic, complemented
6#18012784C2211yescharacteristic
7#18012765—21no—
8#18012722—22no—
9#18012667—21no—
10#18012656C2211yescharacteristic
11#18012654C2212yes—
12#18012653—22no—
13#127×C151C2211yescharacteristic
14#124×C151—22no—
15#123×C151—21no—
16#123×C151C2212yes—
17C4×Q8×C151—21no—
18C4×D4×C151—22no—
19#14559004—21no—
20#14559003—41no—
21C2×C22⋊D151—22no—
22D4×D151—41no—
23#14558992—41no—
24#14558989—41no—
25#14558988—21no—
26Dic151⋊C4—42no—
27C22⋊Dic151—22no—
28(C2×D151)⋊C4—42no—
29C2×Q8×C151—21no—
30C2×D4×C151—22no—
31C2×D4×C151D411yescharacteristic
32C2×D4×C151C2311yescharacteristic
33C22×C4×C151—21no—
34C22×C4×C151D412yes—
35C4⋊C4×C151—21no—
36C4⋊C4×C151—22no—
37C22⋊C4×C151—22no—
38C22⋊C4×C151—21no—
39C22⋊C4×C151—22no—
40C22⋊C4×C151D412yes—
41C42×C151—22no—
42C42×C151D411yescharacteristic
43C22×D151—22no—
44Dic302—21no—
45D604—21no—
46C22⋊D151—42no—
47C22⋊D151—41no—
48C2×Dic151—22no—
49C2×Dic151—42no—
50C4×D151—41no—
51C151⋊C8—41no—
52C23×C151—21no—
53C23×C151C2×D412yes—
54Q8×C151—42no—
55D4×C151—41no—
56D4×C151—41no—
57D4×C151—44no—
58C2×C4×C151—21no—
59C2×C4×C151—22no—
60C2×C4×C151—22no—
61C2×C4×C151—42no—
62C2×C4×C151—81no—
63C2×C4×C151C2×D411yescharacteristic
64C22×C151—22no—
65C22×C151—42no—
66C22×C151—42no—
67C22×C151—41no—
68C22×C151#12011yescharacteristic
69C2×D151—41no—
70C2×D151—82no—
71C4×C151—22no—
72C4×C151—21no—
73C4×C151—42no—
74C4×C151—42no—
75Dic151—41no—
76Dic151—82no—
77C2×C151—21no—
78C2×C151—42no—
79C2×C151—81no—
80C2×C151B(4,𝔽2)11yescharacteristic
81D151—81no—
82C151#219811yescharacteristic, complemented, Sylow
83#2198—1511nomaximal, Sylow
84#559D15111yescharacteristic, complemented
85#458—1512no—
86#453—1511no—
87#353—1511no—
88#352—1512no—
89H(5,𝔽2)—1511no—
90AGL(1,ℤ/8)—3021no—
91#127C2×D15111yescharacteristic
92#124—22no—
93#123—21no—
94#123—3022no—
95#123C2×D15112yes—
96C4×Q8—21no—
97C4×D4—22no—
98#104—3021no—
99#100—1511no—
100#99—3022no—
101#99—1512no—
102#41—3021no—
103#41—6041no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—3022no—
107C2×D4—6041no—
108C2×D4C22⋊D15111yescharacteristic
109C2×D4C22×D15111yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D15112yes—
112SD16—6041no—
113D8—6041no—
114M16—3021no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—6042no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—3022no—
122C22⋊C4—6042no—
123C22⋊C4C22⋊D15112yes—
124C42—22no—
125C42C22⋊D15111yescharacteristic
126C23—21no—
127C23—3022no—
128C23C2×C22⋊D15112yes—
129Q8—42no—
130Q8—3021no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—3021no—
135D4—6042no—
136D4—6041no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—3022no—
143C2×C4—6041no—
144C2×C4—6042no—
145C2×C4C2×C22⋊D15111yescharacteristic
146C8—6041no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—6041no—
152C22—12082no—
153C22#1801270811yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—6041no—
159C4—12082no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—12081no—
164C2#2375239911yescharacteristic
subgroupG/H
centerC2#23752399
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#559×C151C2
socleC2×C151B(4,𝔽2)
prime radical#23752379C2
hypercenter#559D151
hypocenterC151#2198
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #23752401C2semidirect
3. #23752005C2semidirect
4. #23752002C2semidirect
5. #559×C151C2semidirect
82. C151#2198semidirect
84. #559D151semidirect

Maximal subgroups

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

subgroupindex
#237524012
#237523792
#237520052
#237520022
#559×C1512
#2198151