Finite Group Databasebeta

← #34080255

Subgroups — #34080255

Order 19328.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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
2C4⋊Q8×D151C211yesmaximal, characteristic
3#23752608C211yesmaximal, characteristic, complemented
4#23752564C211yesmaximal, characteristic, complemented
5#23752563C211yesmaximal, characteristic, complemented
6#23752544C214yesmaximal
7#23752496C214yesmaximal, complemented
8#23752263C211yesmaximal, characteristic
9#498×C151C211yesmaximal, characteristic, complemented
10C2×Q8×D151—21no—
11#18012739C2211yescharacteristic
12#18012739C2211yescharacteristic
13#18012738—21no—
14#18012738C2212yes—
15#18012737—21no—
16#18012730—21no—
17#18012719C2212yes—
18#18012715—21no—
19Q8×Dic151—21no—
20#18012704C2212yes—
21#18012697—21no—
22C4⋊C4×D151—21no—
23C4⋊C4×D151C2212yes—
24C42×D151C2211yescharacteristic
25#18012670C2214yes—
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—22no—
36C2×Dic302—21no—
37C2×Dic302C2312yes—
38Q8×D151—44no—
39C2×C4×D151—22no—
40C2×C4×D151D411yescharacteristic
41C2×C4×D151D411yescharacteristic
42C2×C4×D151C2311yescharacteristic
43C2×C151⋊C8C2312yes—
44C4⋊Dic151—22no—
45C4⋊Dic151—21no—
46C4⋊Dic151—21no—
47C4⋊Dic151—21no—
48C4⋊Dic151C2312yes—
49Dic151⋊C4—22no—
50Dic151⋊C4—22no—
51Dic151⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
54C4×Dic151D411yescharacteristic
55C4×Dic151D411yescharacteristic
56C4×Dic151C2311yescharacteristic
57C2×Q8×C151—21no—
58C2×Q8×C151—21no—
59C2×C8×C151C2312yes—
60C4⋊C4×C151—21no—
61C4⋊C4×C151—21no—
62C4⋊C4×C151C2312yes—
63C4⋊C4×C151C2312yes—
64C42×C151C2311yescharacteristic
65C22×D151C2×D411yescharacteristic
66Dic302—24no—
67Dic302—42no—
68Dic302—44no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151C2×D411yescharacteristic
72C2×Dic151C2×D411yescharacteristic
73C2×Dic151C2×D411yescharacteristic
74C4×D151—22no—
75C4×D151—22no—
76C4×D151—44no—
77C4×D151SD1614yes—
78C151⋊C8—22no—
79Q8×C151—42no—
80Q8×C151—42no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2411yescharacteristic
86C8×C151—22no—
87C22×C151C22×D411yescharacteristic
88C2×D151—21no—
89C2×D151—21no—
90C2×D151C2×SD1612yes—
91C4×C151—42no—
92C4×C151—42no—
93C4×C151C2×SD1612yes—
94C4×C151#13712yes—
95C4×C1512−1+412yes—
96Dic151—21no—
97Dic151—21no—
98Dic151—42no—
99Dic151—42no—
100Dic151C2×SD1612yes—
101C2×C151#53611yescharacteristic
102C2×C151C22×SD1611yescharacteristic
103C2×C151C2×#13711yescharacteristic
104D151—22no—
105C151#322911yescharacteristic, complemented, Sylow
106#3229—1511nomaximal, Sylow
107#533—1511no—
108C2×C4⋊Q8—1511no—
109#498—1511no—
110#498D15111yescharacteristic, complemented
111#487—1511no—
112#487—1511no—
113#483—1514no—
114#475—1514no—
115#431—1511no—
116C22×Q8—3021no—
117C4⋊Q8—3021no—
118C4⋊Q8—3021no—
119C4⋊Q8—1512no—
120C4⋊Q8—1511no—
121C4⋊Q8—1511no—
122C4⋊Q8C2×D15111yescharacteristic
123C4⋊Q8C2×D15111yescharacteristic
124#125—3021no—
125C22⋊Q8—3021no—
126C22⋊Q8—1512no—
127C4×Q8—3021no—
128C4×Q8—1512no—
129#117—3021no—
130C2×C4⋊C4—3021no—
131C2×C4⋊C4—1512no—
132C2×C42—1511no—
133#106—1514no—
134#106C2×D15114yes—
135C4⋊C8—1512no—
136#103—1514no—
137#103—1514no—
138C22⋊C8—1512no—
139C4×C8—1511no—
140C4×C8C2×D15111yescharacteristic
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—3022no—
144C2×Q8—3021no—
145C2×Q8—6044no—
146C2×Q8—1512no—
147C22×C4—3022no—
148C22×C4—1511no—
149C22×C4—1511no—
150C22×C4—1511no—
151C2×C8—1512no—
152C2×C8C22×D15112yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—3022no—
156C4⋊C4—3022no—
157C4⋊C4—3022no—
158C4⋊C4—3022no—
159C4⋊C4—3021no—
160C4⋊C4—3021no—
161C4⋊C4—3021no—
162C4⋊C4—1512no—
163C4⋊C4C22×D15112yes—
164C4⋊C4C22×D15112yes—
165C22⋊C4—3022no—
166C42—3022no—
167C42—1511no—
168C42—1511no—
169C42—1511no—
170C42C22×D15111yescharacteristic
171C23—1511no—
172Q8—42no—
173Q8—42no—
174Q8—3024no—
175Q8—6044no—
176Q8—6042no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—6044no—
184C2×C4—1511no—
185C2×C4—1511no—
186C2×C4—1511no—
187C2×C4—1514no—
188C2×C4D4×D15111yescharacteristic
189C2×C4D4×D15111yescharacteristic
190C2×C4C23×D15111yescharacteristic
191C8—22no—
192C8—3022no—
193C22—3021no—
194C22—3021no—
195C22—1512no—
196C22C2×D4×D15111yescharacteristic
197C4—42no—
198C4—42no—
199C4—3021no—
200C4—3021no—
201C4—6042no—
202C4—6042no—
203C4—1512no—
204C4SD16×D15112yes—
205C4#1801276812yes—
206C4#1801278712yes—
207C2—3022no—
208C2#2375278711yescharacteristic
209C2C2×SD16×D15111yescharacteristic
210C2C2×#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#3229
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. #23752608C2semidirect
4. #23752564C2semidirect
5. #23752563C2semidirect
7. #23752496C2semidirect
9. #498×C151C2semidirect
105. C151#3229semidirect
110. #498D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
C4⋊Q8×D1512
#237526082
#237525642
#237525632
#237525442
#237524962
#237522632
#498×C1512
#3229151