Finite Group Databasebeta

← #34068447

Subgroups — #34068447

Order 19328.

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

normal subgroups only

This group has 184 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#23752962C211yesmaximal, characteristic
2#23752621C211yesmaximal, characteristic, complemented
3#23752581C211yesmaximal, characteristic, complemented
4#23752571C211yesmaximal, characteristic
5#23751953C211yesmaximal, characteristic, complemented
6#23751953C211yesmaximal, characteristic, complemented
7#329×C151C211yesmaximal, characteristic
8#18012739C2211yescharacteristic
9#18012737—21no—
10#18012732—21no—
11#18012732—21no—
12#18012731C2211yescharacteristic
13#18012731C2211yescharacteristic
14#18012720—21no—
15#18012716—21no—
16#18012716—21no—
17#18012673—21no—
18#18012671—21no—
19#18012664—21no—
20#18012664—21no—
21#18012663—21no—
22#18012660—21no—
23#18012650C2211yescharacteristic
24#124×C151C2211yescharacteristic
25#97×C151C2211yescharacteristic
26#97×C151C2211yescharacteristic
27C2×Dic302—21no—
28C2×Dic302—21no—
29C22×Dic151—21no—
30C2×C151⋊C8—21no—
31C4⋊Dic151—21no—
32C4⋊Dic151—21no—
33C4⋊Dic151D411yescharacteristic
34C4⋊Dic151D411yescharacteristic
35C4⋊Dic151D411yescharacteristic
36C4⋊Dic151D411yescharacteristic
37Dic151⋊C4—21no—
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41Dic151⋊C4—21no—
42Dic151⋊C4—21no—
43C22⋊Dic151—21no—
44C22⋊Dic151—21no—
45C22⋊Dic151—21no—
46C4×Dic151—21no—
47C2×Q8×C151D411yescharacteristic
48C2×D4×C151D411yescharacteristic
49C2×C8×C151—21no—
50C2×C8×C151—21no—
51C22⋊C4×C151—21no—
52C22⋊C4×C151—21no—
53C42×C151C2311yescharacteristic
54Dic302—42no—
55Dic302—81no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—21no—
60C2×Dic151—41no—
61C2×Dic151—81no—
62C151⋊C8—41no—
63C23×C151—21no—
64Q8×C151—41no—
65D4×C151—41no—
66C2×C4×C151—21no—
67C2×C4×C151C2×D411yescharacteristic
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C8×C151—22no—
71C8×C151—41no—
72C22×C151—41no—
73C22×C151—41no—
74C22×C151—41no—
75C22×C151#12011yescharacteristic
76C4×C151—21no—
77C4×C151—21no—
78C4×C151—21no—
79C4×C151—41no—
80Dic151—41no—
81Dic151—41no—
82Dic151—41no—
83Dic151—41no—
84Dic151—81no—
85C2×C151—81no—
86C2×C151#45411yescharacteristic
87C2×C151#45511yescharacteristic
88C2×C151#45611yescharacteristic
89C151#166411yescharacteristic, complemented, Sylow
90#1664—1511nomaximal, Sylow
91#563—1511no—
92#501—1511no—
93#491—1511no—
94#489—1511no—
95#330—1511no—
96#330—1511no—
97#329D15111yescharacteristic
98C4⋊Q8—3021no—
99C4⋊Q8—1511no—
100#126—3021no—
101#126—3021no—
102#125—1511no—
103#125—1511no—
104#124C2×D15111yescharacteristic
105#123—3021no—
106C22⋊Q8—3021no—
107C22⋊Q8—3021no—
108#107—3021no—
109#106—3021no—
110#103—3021no—
111#103—3021no—
112#103—3021no—
113#102—3021no—
114#97—1511no—
115#97C2×D15111yescharacteristic
116#97C2×D15111yescharacteristic
117C2×Q8—3021no—
118C2×Q8—3021no—
119C2×Q8D60411yescharacteristic
120C2×D4D60411yescharacteristic
121C22×C4—3021no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—3021no—
125C4⋊C4—3021no—
126C4⋊C4—3021no—
127C4⋊C4—3021no—
128C4⋊C4—3021no—
129C4⋊C4—3021no—
130C4⋊C4—3021no—
131C4⋊C4—3021no—
132C4⋊C4—3021no—
133C4⋊C4—1511no—
134C4⋊C4—1511no—
135C4⋊C4—1511no—
136C4⋊C4—1511no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—3021no—
140C22⋊C4—3021no—
141C22⋊C4—3021no—
142C42—3021no—
143C42C22×D15111yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—6042no—
147Q8—12081no—
148D4—41no—
149C2×C4—21no—
150C2×C4—3021no—
151C2×C4—3021no—
152C2×C4—3021no—
153C2×C4—3021no—
154C2×C4—6041no—
155C2×C4—12081no—
156C2×C4D4×D15111yescharacteristic
157C2×C4D4×D15111yescharacteristic
158C2×C4C2×D60411yescharacteristic
159C8—22no—
160C8—41no—
161C8—6041no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1801270911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—6041no—
171C4—6041no—
172C4—6041no—
173C4—6041no—
174C4—12081no—
175C2—81no—
176C2#2375238611yescharacteristic
177C2#2375239211yescharacteristic
178C2#2375239611yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#329×C151C2
socleC22×C151#120
prime radicalC2×D4×C151D4
hypercenter#329D151
hypocenterC151#1664
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23752621C2semidirect
3. #23752581C2semidirect
5. #23751953C2semidirect
6. #23751953C2semidirect
89. C151#1664semidirect

Maximal subgroups

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

subgroupindex
#237529622
#237526212
#237525812
#237525712
#237519532
#329×C1512
#1664151