Finite Group Databasebeta

← #34080247

Subgroups — #34080247

Order 19328.

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

normal subgroups only

This group has 370 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, complemented
2#23752763C211yesmaximal, characteristic
3#23752615C211yesmaximal, characteristic, complemented
4#23752560C211yesmaximal, characteristic, complemented
5#23752559C211yesmaximal, characteristic, complemented
6#23752538C214yesmaximal, complemented
7#23752511C214yesmaximal, complemented
8#23752263C211yesmaximal, characteristic, complemented
9#498×C151C211yesmaximal, characteristic, complemented
10C2×#14559005—21no—
11#18012739C2211yescharacteristic
12#18012736C2211yescharacteristic
13#18012730C2212yes—
14#18012728—21no—
15#18012719—21no—
16#18012715—21no—
17#18012714—21no—
18#18012714C2212yes—
19Q8×Dic151—21no—
20#18012704—21no—
21#18012701—21no—
22#18012701C2212yes—
23#18012697C2212yes—
24C42×D151C2211yescharacteristic
25#18012672C2214yes—
26Dic151⋊C8C2212yes—
27#18012661C2214yes—
28#18012659C2214yes—
29(C2×D151)⋊C8C2212yes—
30C4×C151⋊C8C2211yescharacteristic
31C4⋊Q8×C151C2211yescharacteristic
32C4⋊Q8×C151C2211yescharacteristic
33#106×C151C2214yes—
34C4×C8×C151C2211yescharacteristic
35#14559005—44no—
36C2×Dic302—21no—
37C2×D604—22no—
38C2×D604—21no—
39C2×D604—21no—
40C2×D604C2312yes—
41C2×C4×D151—22no—
42C2×C4×D151D411yescharacteristic
43C2×C4×D151D411yescharacteristic
44C2×C4×D151C2311yescharacteristic
45C2×C151⋊C8C2312yes—
46C4⋊Dic151—22no—
47C4⋊Dic151—21no—
48C4⋊Dic151C2312yes—
49Dic151⋊C4—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊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×D151—22no—
66C22×D151C2×D411yescharacteristic
67Dic302—42no—
68D604—24no—
69D604—44no—
70D604—42no—
71D604—42no—
72C2×Dic151—22no—
73C2×Dic151C2×D411yescharacteristic
74C2×Dic151C2×D411yescharacteristic
75C2×Dic151C2×D411yescharacteristic
76C4×D151—22no—
77C4×D151—22no—
78C4×D151—22no—
79C4×D151—44no—
80C151⋊C8—22no—
81Q8×C151—42no—
82Q8×C151—42no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2×D411yescharacteristic
87C2×C4×C151C2411yescharacteristic
88C8×C151—22no—
89C22×C151C22×D411yescharacteristic
90C2×D151—21no—
91C2×D151—21no—
92C2×D151—21no—
93C2×D151—42no—
94C2×D151—42no—
95C2×D151—42no—
96C4×C151—42no—
97C4×C151—42no—
98C4×C151#13512yes—
99C4×C151AGL(1,ℤ/8)12yes—
100C4×C1512−1+412yes—
101Dic151—21no—
102Dic151—21no—
103Dic151—21no—
104Dic151—42no—
105C2×C151#53611yescharacteristic
106C2×C151C2×#13511yescharacteristic
107C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
108D151—41no—
109D151—82no—
110C151#322811yescharacteristic, complemented, Sylow
111#3228—1511nomaximal, Sylow
112#533—1511no—
113#532—1511no—
114#500—1511no—
115#498D15111yescharacteristic, complemented
116#486—1511no—
117#486—1511no—
118#482—1514no—
119#478—1514no—
120#431—1511no—
121C2×#41—3021no—
122C4⋊Q8—1511no—
123C4⋊Q8C2×D15111yescharacteristic
124C4⋊Q8C2×D15111yescharacteristic
125#127—1511no—
126#125—1512no—
127#124—3021no—
128C22⋊Q8—3021no—
129C22⋊Q8—3021no—
130#121—3021no—
131#121—1512no—
132C4×Q8—3021no—
133C4×Q8—3021no—
134C4×D4—3021no—
135C4×D4—1512no—
136#117—1512no—
137C2×C42—1511no—
138#107—1514no—
139#106C2×D15114yes—
140C4⋊C8—1512no—
141#102—1514no—
142#102—1514no—
143C22⋊C8—1512no—
144C4×C8—1511no—
145C4×C8C2×D15111yescharacteristic
146#41—6044no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—3021no—
150C2×D4—3022no—
151C2×D4—3021no—
152C2×D4—3021no—
153C2×D4—1512no—
154C22×C4—3022no—
155C22×C4—1511no—
156C22×C4—1511no—
157C22×C4—1511no—
158C2×C8—1512no—
159C2×C8C22×D15112yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—3022no—
163C4⋊C4—3022no—
164C4⋊C4—3021no—
165C4⋊C4—1512no—
166C4⋊C4C22×D15112yes—
167C4⋊C4C22×D15112yes—
168C22⋊C4—3022no—
169C22⋊C4—3022no—
170C22⋊C4—3022no—
171C42—3022no—
172C42—1511no—
173C42—1511no—
174C42—1511no—
175C42C22×D15111yescharacteristic
176C23—3022no—
177C23—1511no—
178Q8—42no—
179Q8—42no—
180Q8—6042no—
181D4—3024no—
182D4—6044no—
183D4—6042no—
184D4—6042no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—3022no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—3022no—
191C2×C4—6044no—
192C2×C4—1511no—
193C2×C4—1511no—
194C2×C4—1511no—
195C2×C4D4×D15111yescharacteristic
196C2×C4D4×D15111yescharacteristic
197C2×C4C23×D15111yescharacteristic
198C8—22no—
199C8—3022no—
200C22—3021no—
201C22—3021no—
202C22—3021no—
203C22—6042no—
204C22—6042no—
205C22—6042no—
206C22C2×D4×D15111yescharacteristic
207C4—42no—
208C4—42no—
209C4—3021no—
210C4—3021no—
211C4—3021no—
212C4—6042no—
213C4#1801276012yes—
214C4#1801276612yes—
215C4#1801278712yes—
216C2—6041no—
217C2—12082no—
218C2#2375278711yescharacteristic
219C2C2×#1801276011yescharacteristic
220C2C2×#1801276611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#498×C151C2
socleC22×C151C22×D4
prime radical#23752763C2
hypercenter#498D151
hypocenterC151#3228
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
1. #23752767C2semidirect
3. #23752615C2semidirect
4. #23752560C2semidirect
5. #23752559C2semidirect
6. #23752538C2semidirect
7. #23752511C2semidirect
8. #23752263C2semidirect
9. #498×C151C2semidirect
110. C151#3228semidirect
115. #498D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
#237527632
#237526152
#237525602
#237525592
#237525382
#237525112
#237522632
#498×C1512
#3228151