Finite Group Databasebeta

← #34068276

Subgroups — #34068276

Order 19328.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752877C211yesmaximal, characteristic
2#23752564C211yesmaximal, characteristic, complemented
3#23752508C211yesmaximal, characteristic, complemented
4#23752503C211yesmaximal, characteristic
5#23751942C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic
7#332×C151C211yesmaximal, characteristic, complemented
8C2×Q8×D151—21no—
9#18012739C2211yescharacteristic
10#18012738—21no—
11#18012717—22no—
12#18012715—21no—
13C4×Dic302C2211yescharacteristic
14C4×D604C2211yescharacteristic
15#18012701—21no—
16#18012673—21no—
17#18012671—21no—
18#18012664—21no—
19#18012662—22no—
20#18012661—21no—
21C4×C151⋊C8C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25C2×Dic302—22no—
26C2×Dic302—21no—
27C2×Dic302D411yescharacteristic
28Q8×D151—42no—
29Q8×D151—42no—
30C2×D604D411yescharacteristic
31C2×C4×D151—22no—
32C2×C4×D151—21no—
33C2×C151⋊C8—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—22no—
39Dic151⋊C4—21no—
40(C2×D151)⋊C4—22no—
41(C2×D151)⋊C4—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—21no—
50Dic302—21no—
51Dic302—44no—
52Dic302—42no—
53Dic302SD1612yes—
54D604—21no—
55D604Q1612yes—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—41no—
60C4×D151—44no—
61C4×D151—41no—
62C4×D151—41no—
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—22no—
74C2×D151—41no—
75C2×D151—41no—
76C4×C151—21no—
77C4×C151—42no—
78C4×C151C2×SD1611yescharacteristic
79C4×C151C2×Q1611yescharacteristic
80C4×C151AGL(1,ℤ/8)11yescharacteristic
81C4×C151#13711yescharacteristic
82Dic151—22no—
83Dic151—41no—
84Dic151—41no—
85Dic151—81no—
86C2×C151#45011yescharacteristic
87C2×C151#45111yescharacteristic
88C2×C151#45411yescharacteristic
89D151—42no—
90C151#163711yescharacteristic, complemented, Sylow
91#1637—1511nomaximal, Sylow
92D4×Q8—1511no—
93#487—1511no—
94#477—1511no—
95#476—1511no—
96#332D15111yescharacteristic, complemented
97Q8⋊C8—1511no—
98D4⋊C8—1511no—
99C22×Q8—3021no—
100C4⋊Q8—3021no—
101C4⋊Q8—1511no—
102C4⋊Q8C2×D15111yescharacteristic
103C22⋊Q8—3021no—
104C22⋊Q8—3022no—
105C4×Q8—1511no—
106C4×D4—3021no—
107C4×D4—1511no—
108#107—3021no—
109#106—3021no—
110C4⋊C8C2×D15111yescharacteristic
111C4⋊C8C2×D15111yescharacteristic
112#103—3021no—
113#103—3022no—
114#102—3021no—
115C4×C8—1511no—
116C2×Q8—21no—
117C2×Q8—3022no—
118C2×Q8—3021no—
119C2×Q8—6042no—
120C2×Q8—6042no—
121C2×Q8—1511no—
122C2×D4—1511no—
123C22×C4—3022no—
124C22×C4—3021no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—3021no—
128C4⋊C4—21no—
129C4⋊C4—3022no—
130C4⋊C4—3021no—
131C4⋊C4—3021no—
132C4⋊C4—3021no—
133C4⋊C4—1511no—
134C4⋊C4—1511no—
135C4⋊C4D60412yes—
136C22⋊C4—3022no—
137C22⋊C4—3021no—
138C42—3021no—
139C42C22×D15111yescharacteristic
140C23—3021no—
141Q8—41no—
142Q8—41no—
143Q8—3021no—
144Q8—6042no—
145Q8—6044no—
146Q8—1512no—
147D4—3021no—
148D4—1512no—
149C2×C4—22no—
150C2×C4—3021no—
151C2×C4—3021no—
152C2×C4—3021no—
153C2×C4—6044no—
154C2×C4—6041no—
155C2×C4—6041no—
156C2×C4—6041no—
157C2×C4D4×D15111yescharacteristic
158C2×C4D4×D15111yescharacteristic
159C2×C4C2×D60411yescharacteristic
160C8—41no—
161C8—41no—
162C8—6041no—
163C22—3022no—
164C22—6041no—
165C22—6041no—
166C22#1801270911yescharacteristic
167C4—21no—
168C4—42no—
169C4—3022no—
170C4—6041no—
171C4—6041no—
172C4—12081no—
173C4SD16×D15111yescharacteristic
174C4Q16×D15111yescharacteristic
175C4#1801276311yescharacteristic
176C4#1801276811yescharacteristic
177C2—6042no—
178C2#2375236411yescharacteristic
179C2#2375236911yescharacteristic
180C2#2375238711yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#332×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#332D151
hypocenterC151#1637
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #23752564C2semidirect
3. #23752508C2semidirect
5. #23751942C2semidirect
7. #332×C151C2semidirect
90. C151#1637semidirect
96. #332D151semidirect

Maximal subgroups

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

subgroupindex
#237528772
#237525642
#237525082
#237525032
#237519422
#237519392
#332×C1512
#1637151