Finite Group Databasebeta

← #34071123

Subgroups — #34071123

Order 19328.

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

normal subgroups only

This group has 226 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
2#23752389C211yesmaximal, characteristic
3#23752007C211yesmaximal, characteristic, complemented
4#23752002C212yesmaximal, complemented
5#563×C151C211yesmaximal, characteristic, complemented
6#18012784C2211yescharacteristic
7#18012770—21no—
8#18012722—22no—
9#18012667—21no—
10#18012656C2211yescharacteristic
11#18012654C2212yes—
12#18012653—22no—
13C4⋊Q8×C151—21no—
14#126×C151—22no—
15#125×C151—21no—
16#124×C151C2211yescharacteristic
17#123×C151C2212yes—
18C22⋊Q8×C151—22no—
19#14559004—21no—
20#14559003—41no—
21C2×C22⋊D151—22no—
22D4×D151—41no—
23#14558994—41no—
24#14558991—41no—
25#14558988—21no—
26Dic151⋊C4—42no—
27C22⋊Dic151—22no—
28(C2×D151)⋊C4—42no—
29C2×Q8×C151—21no—
30C2×Q8×C151D411yescharacteristic
31C2×D4×C151C2311yescharacteristic
32C22×C4×C151D412yes—
33C4⋊C4×C151—21no—
34C4⋊C4×C151—22no—
35C4⋊C4×C151—22no—
36C4⋊C4×C151—21no—
37C4⋊C4×C151—22no—
38C22⋊C4×C151—22no—
39C22⋊C4×C151—22no—
40C22⋊C4×C151D412yes—
41C42×C151—21no—
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×C151C2×D412yes—
53Q8×C151—41no—
54Q8×C151—81no—
55D4×C151—41no—
56C2×C4×C151—21no—
57C2×C4×C151—22no—
58C2×C4×C151—22no—
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—42no—
69C4×C151—41no—
70C4×C151—42no—
71C4×C151—41no—
72Dic151—41no—
73Dic151—82no—
74C2×C151—21no—
75C2×C151—42no—
76C2×C151B(4,𝔽2)11yescharacteristic
77D151—81no—
78C151#220111yescharacteristic, complemented, Sylow
79#2201—1511nomaximal, Sylow
80#563D15111yescharacteristic, complemented
81#458—1512no—
82#455—1511no—
83#354—1511no—
84#352—1512no—
85H(5,𝔽2)—1511no—
86#137—3021no—
87C4⋊Q8—21no—
88#126—22no—
89#125—21no—
90#124C2×D15111yescharacteristic
91#123—3022no—
92#123C2×D15112yes—
93C22⋊Q8—22no—
94#104—3021no—
95#100—1511no—
96#99—3022no—
97#99—1512no—
98#41—3021no—
99#41—6041no—
100C2×Q8—21no—
101C2×Q8C22⋊D15111yescharacteristic
102C2×D4—3022no—
103C2×D4—6041no—
104C2×D4C22×D15111yescharacteristic
105C22×C4C22⋊D15112yes—
106Q16—6041no—
107SD16—6041no—
108M16—3021no—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—6042no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—3022no—
118C22⋊C4—6042no—
119C22⋊C4C22⋊D15112yes—
120C42—21no—
121C42C22⋊D15111yescharacteristic
122C23—3022no—
123C23C2×C22⋊D15112yes—
124Q8—41no—
125Q8—81no—
126Q8—3021no—
127D4—41no—
128D4—3021no—
129D4—6042no—
130D4—6041no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—3022no—
137C2×C4—6041no—
138C2×C4—6042no—
139C2×C4C2×C22⋊D15111yescharacteristic
140C8—6041no—
141C22—22no—
142C22—42no—
143C22—6041no—
144C22—12082no—
145C22#1801270811yescharacteristic
146C4—21no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—41no—
151C4—6041no—
152C4—12082no—
153C2—21no—
154C2—42no—
155C2—12081no—
156C2#2375239911yescharacteristic
subgroupG/H
centerC2#23752399
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#563×C151C2
socleC2×C151B(4,𝔽2)
prime radical#18012784C22
hypercenter#563D151
hypocenterC151#2201
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #563

Complements

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

NH ≅ G/Ntype
3. #23752007C2semidirect
4. #23752002C2semidirect
5. #563×C151C2semidirect
78. C151#2201semidirect
80. #563D151semidirect

Maximal subgroups

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

subgroupindex
#237524012
#237523892
#237520072
#237520022
#563×C1512
#2201151