Finite Group Databasebeta

← #34080272

Subgroups — #34080272

Order 19328.

326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752767C211yesmaximal, characteristic
2#23752767C211yesmaximal, characteristic
3#23752615C211yesmaximal, characteristic, complemented
4#23752564C211yesmaximal, characteristic, complemented
5#23752563C211yesmaximal, characteristic, complemented
6#23752556C214yesmaximal
7#23752522C214yesmaximal, complemented
8#23752263C211yesmaximal, characteristic
9#498×C151C211yesmaximal, characteristic, complemented
10#18012739C2211yescharacteristic
11#18012739C2211yescharacteristic
12#18012730—21no—
13#18012730C2212yes—
14#18012719—21no—
15#18012719C2212yes—
16#18012715—21no—
17#18012715—21no—
18Q8×Dic151—21no—
19Q8×Dic151—21no—
20#18012704—21no—
21#18012704C2212yes—
22#18012697—21no—
23#18012697C2212yes—
24C42×D151C2211yescharacteristic
25#18012672C2214yes—
26Dic151⋊C8C2212yes—
27#18012664C2214yes—
28#18012662C2214yes—
29(C2×D151)⋊C8C2212yes—
30C4×C151⋊C8C2211yescharacteristic
31C4⋊Q8×C151C2211yescharacteristic
32C4⋊Q8×C151C2211yescharacteristic
33#106×C151C2214yes—
34C4×C8×C151C2211yescharacteristic
35C2×Dic302—21no—
36C2×Dic302C2312yes—
37C2×C4×D151D411yescharacteristic
38C2×C4×D151D411yescharacteristic
39C2×C4×D151C2311yescharacteristic
40C2×C151⋊C8C2312yes—
41C4⋊Dic151—22no—
42C4⋊Dic151—22no—
43C4⋊Dic151—21no—
44C4⋊Dic151—21no—
45C4⋊Dic151—21no—
46C4⋊Dic151C2312yes—
47Dic151⋊C4—22no—
48Dic151⋊C4—22no—
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51C4×Dic151—22no—
52C4×Dic151—22no—
53C4×Dic151D411yescharacteristic
54C4×Dic151D411yescharacteristic
55C4×Dic151C2311yescharacteristic
56C2×Q8×C151—21no—
57C2×Q8×C151—21no—
58C2×C8×C151C2312yes—
59C4⋊C4×C151—21no—
60C4⋊C4×C151—21no—
61C4⋊C4×C151C2312yes—
62C4⋊C4×C151C2312yes—
63C42×C151C2311yescharacteristic
64C22×D151C2×D411yescharacteristic
65Dic302—24no—
66Dic302—42no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151C2×D411yescharacteristic
70C2×Dic151C2×D411yescharacteristic
71C2×Dic151C2×D411yescharacteristic
72C4×D151—22no—
73C4×D151—22no—
74C4×D151—22no—
75C151⋊C8—22no—
76Q8×C151—42no—
77Q8×C151—42no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2411yescharacteristic
83C8×C151—22no—
84C22×C151C22×D411yescharacteristic
85C2×D151—21no—
86C2×D151—21no—
87C2×D151—21no—
88C4×C151—42no—
89C4×C151—42no—
90C4×C151#13512yes—
91C4×C151#13712yes—
92C4×C1512−1+412yes—
93Dic151—21no—
94Dic151—21no—
95Dic151—21no—
96Dic151—42no—
97Dic151—42no—
98C2×C151#53611yescharacteristic
99C2×C151C2×#13511yescharacteristic
100C2×C151C2×#13711yescharacteristic
101D151—41no—
102C151#323111yescharacteristic, complemented, Sylow
103#3231—1511nomaximal, Sylow
104#533—1511no—
105#533—1511no—
106#500—1511no—
107#498D15111yescharacteristic, complemented
108#487—1511no—
109#487—1511no—
110#485—1514no—
111#479—1514no—
112#431—1511no—
113C4⋊Q8—1511no—
114C4⋊Q8—1511no—
115C4⋊Q8C2×D15111yescharacteristic
116C4⋊Q8C2×D15111yescharacteristic
117#125—3021no—
118#125—1512no—
119C22⋊Q8—3021no—
120C22⋊Q8—3021no—
121C22⋊Q8—3021no—
122C22⋊Q8—1512no—
123C4×Q8—3021no—
124C4×Q8—3021no—
125C4×Q8—3021no—
126C4×Q8—1512no—
127#117—3021no—
128#117—1512no—
129C2×C42—1511no—
130#107—1514no—
131#106C2×D15114yes—
132C4⋊C8—1512no—
133#103—1514no—
134#103—1514no—
135C22⋊C8—1512no—
136C4×C8—1511no—
137C4×C8C2×D15111yescharacteristic
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—3021no—
141C2×Q8—1512no—
142C22×C4—1511no—
143C22×C4—1511no—
144C22×C4—1511no—
145C2×C8—1512no—
146C2×C8C22×D15112yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—3022no—
150C4⋊C4—3022no—
151C4⋊C4—3022no—
152C4⋊C4—3022no—
153C4⋊C4—3021no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—1512no—
157C4⋊C4C22×D15112yes—
158C4⋊C4C22×D15112yes—
159C22⋊C4—3022no—
160C22⋊C4—3022no—
161C42—3022no—
162C42—3022no—
163C42—1511no—
164C42—1511no—
165C42—1511no—
166C42C22×D15111yescharacteristic
167C23—1511no—
168Q8—42no—
169Q8—42no—
170Q8—3024no—
171Q8—6042no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—3022no—
177C2×C4—3022no—
178C2×C4—3022no—
179C2×C4—1511no—
180C2×C4—1511no—
181C2×C4—1511no—
182C2×C4D4×D15111yescharacteristic
183C2×C4D4×D15111yescharacteristic
184C2×C4C23×D15111yescharacteristic
185C8—22no—
186C8—3022no—
187C22—3021no—
188C22—3021no—
189C22—3021no—
190C22C2×D4×D15111yescharacteristic
191C4—42no—
192C4—42no—
193C4—3021no—
194C4—3021no—
195C4—3021no—
196C4—6042no—
197C4—6042no—
198C4#1801276012yes—
199C4#1801276812yes—
200C4#1801278712yes—
201C2—6041no—
202C2#2375278711yescharacteristic
203C2C2×#1801276011yescharacteristic
204C2C2×#1801276811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#498×C151C2
socleC22×C151C22×D4
prime radicalC22×D151C2×D4
hypercenter#498D151
hypocenterC151#3231
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
3. #23752615C2semidirect
4. #23752564C2semidirect
5. #23752563C2semidirect
7. #23752522C2semidirect
9. #498×C151C2semidirect
102. C151#3231semidirect
107. #498D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
#237526152
#237525642
#237525632
#237525562
#237525222
#237522632
#498×C1512
#3231151