Finite Group Databasebeta

← #34068207

Subgroups — #34068207

Order 19328.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752937C211yesmaximal, characteristic, complemented
2#23752560C211yesmaximal, characteristic
3#23752413C211yesmaximal, characteristic
4#23752413C211yesmaximal, characteristic
5#23751942C211yesmaximal, characteristic, complemented
6#23751942C211yesmaximal, characteristic, complemented
7#332×C151C211yesmaximal, characteristic, complemented
8C2×#14558993—21no—
9C2×#14558993—21no—
10#18012737—21no—
11#18012736C2211yescharacteristic
12#18012730—21no—
13#18012729—22no—
14Q8×Dic151—21no—
15C4×Dic302C2211yescharacteristic
16C4×Dic302C2211yescharacteristic
17#18012704—21no—
18#18012661—21no—
19#18012661—21no—
20#18012659—22no—
21C4×C151⋊C8C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25C2×Dic302D411yescharacteristic
26C2×Dic302D411yescharacteristic
27C2×D604—21no—
28C2×D604—21no—
29C2×D604—21no—
30#14558993—42no—
31#14558993—42no—
32C2×C151⋊C8—21no—
33C4⋊Dic151—22no—
34C4⋊Dic151D411yescharacteristic
35C4⋊Dic151D411yescharacteristic
36Dic151⋊C4—22no—
37Dic151⋊C4—22no—
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40C4×Dic151—22no—
41C4×Dic151—21no—
42C4×Dic151—21no—
43C2×Q8×C151—21no—
44C2×C8×C151—21no—
45C2×C8×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D412yes—
48C42×C151C2311yescharacteristic
49C22×D151—41no—
50Dic302—21no—
51Dic302—21no—
52Dic302—21no—
53Dic302SD1612yescomplemented
54D604—42no—
55D604—41no—
56D604—41no—
57D604—41no—
58D604—41no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—21no—
63C151⋊C8—41no—
64Q8×C151—41no—
65Q8×C151—41no—
66C2×C4×C151—22no—
67C2×C4×C151C2×D411yescharacteristic
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C8×C151—41no—
71C8×C151—41no—
72C22×C151#12011yescharacteristic
73C2×D151—81no—
74C2×D151—81no—
75C2×D151—81no—
76C4×C151—21no—
77C4×C151—42no—
78C4×C151C2×SD1611yescharacteristic
79C4×C151#13511yescharacteristic
80C4×C151AGL(1,ℤ/8)11yescharacteristic
81C4×C151#13711yescharacteristic
82Dic151—22no—
83Dic151—41no—
84Dic151—41no—
85Dic151—41no—
86C2×C151#44811yescharacteristic
87C2×C151#44911yescharacteristic
88C2×C151#45411yescharacteristic
89D151—161no—
90C151#162611yescharacteristic, complemented, Sylow
91#1626—1511nomaximal, Sylow
92#557—1511no—
93#486—1511no—
94#460—1511no—
95#460—1511no—
96#332D15111yescharacteristic, complemented
97Q8⋊C8—1511no—
98Q8⋊C8—1511no—
99C2×SD16—3021no—
100C2×SD16—3021no—
101C4⋊Q8—3021no—
102C4⋊Q8C2×D15111yescharacteristic
103#127—1511no—
104#125—3021no—
105#125—3022no—
106C4×Q8—3021no—
107C4×Q8—3021no—
108C4×Q8—1511no—
109C4×Q8—1511no—
110C4⋊C8C2×D15111yescharacteristic
111C4⋊C8C2×D15111yescharacteristic
112#102—3021no—
113#102—3021no—
114#102—3022no—
115C4×C8—1511no—
116C2×Q8—21no—
117C2×Q8—1511no—
118C2×Q8—1511no—
119C2×D4—3021no—
120C2×D4—3021no—
121C2×D4—3021no—
122SD16—6042no—
123SD16—6042no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—3021no—
127C4⋊C4—21no—
128C4⋊C4—3022no—
129C4⋊C4—3022no—
130C4⋊C4—3022no—
131C4⋊C4—3021no—
132C4⋊C4—3021no—
133C4⋊C4—1511no—
134C4⋊C4—1511no—
135C4⋊C4D60412yes—
136C42—3022no—
137C42—3021no—
138C42—3021no—
139C42C22×D15111yescharacteristic
140C23—6041no—
141Q8—41no—
142Q8—41no—
143Q8—3021no—
144Q8—3021no—
145Q8—3021no—
146Q8—1512no—
147D4—6042no—
148D4—6041no—
149D4—6041no—
150D4—6041no—
151D4—6041no—
152C2×C4—22no—
153C2×C4—3021no—
154C2×C4—3021no—
155C2×C4—3021no—
156C2×C4—3021no—
157C2×C4D4×D15111yescharacteristic
158C2×C4D4×D15111yescharacteristic
159C2×C4C2×D60411yescharacteristic
160C8—41no—
161C8—41no—
162C8—6041no—
163C22—12081no—
164C22—12081no—
165C22—12081no—
166C22#1801270911yescharacteristic
167C4—21no—
168C4—42no—
169C4—3022no—
170C4—6041no—
171C4—6041no—
172C4—6041no—
173C4SD16×D15111yescharacteristic
174C4#1801276011yescharacteristic
175C4#1801276311yescharacteristic
176C4#1801277111yescharacteristic
177C2—24161no—
178C2#2375235211yescharacteristic
179C2#2375235811yescharacteristic
180C2#2375238711yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#332×C151C2
socleC22×C151#120
prime radical#18012736C22
hypercenter#332D151
hypocenterC151#1626
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #23752937C2semidirect
5. #23751942C2semidirect
6. #23751942C2semidirect
7. #332×C151C2semidirect
53. Dic302SD16semidirect
90. C151#1626semidirect
96. #332D151semidirect

Maximal subgroups

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

subgroupindex
#237529372
#237525602
#237524132
#237519422
#332×C1512
#1626151