Finite Group Databasebeta

← #34080308

Subgroups — #34080308

Order 19328.

366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752762C211yesmaximal, characteristic
2#23752622C212yesmaximal, complemented
3#23752578C212yesmaximal, complemented
4#23752536C214yesmaximal, complemented
5#23752499C212yesmaximal, complemented
6#23752489C212yesmaximal, complemented
7#23752269C211yesmaximal, characteristic, complemented
8#533×C151C211yesmaximal, characteristic, complemented
9C2×#14559004—21no—
10#18012739C2211yescharacteristic
11#18012736C2211yescharacteristic
12#18012727—21no—
13#18012713—21no—
14#18012713C2212yes—
15C4×D604—21no—
16C4×D604C2212yes—
17#18012672C2214yes—
18#18012670C2214yes—
19C4⋊(C151⋊C8)C2212yes—
20#18012659C2214yes—
21#18012659C2214yes—
22C22⋊(C151⋊C8)C2212yes—
23#18012650C2212yes—
24C4⋊Q8×C151C2211yescharacteristic
25C4⋊Q8×C151C2211yescharacteristic
26#125×C151C2212yes—
27C22⋊Q8×C151—21no—
28C22⋊Q8×C151—21no—
29C4×Q8×C151—21no—
30C4×Q8×C151—21no—
31#117×C151C2212yes—
32C2×C42×C151C2211yescharacteristic
33#14559004—44no—
34C2×Dic302—21no—
35C2×D604—21no—
36C2×D604—21no—
37C2×D604C2312yes—
38C2×C22⋊D151—22no—
39C2×C4×D151—22no—
40C2×C151⋊C8C2314yes—
41C4⋊Dic151—21no—
42C4⋊Dic151C2312yes—
43(C2×D151)⋊C4—22no—
44(C2×D151)⋊C4—22no—
45C2×Q8×C151—21no—
46C2×Q8×C151—21no—
47C22×C4×C151D411yescharacteristic
48C22×C4×C151D411yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C4⋊C4×C151—22no—
51C4⋊C4×C151—22no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151—21no—
54C4⋊C4×C151C2312yes—
55C4⋊C4×C151C2312yes—
56C22⋊C4×C151—22no—
57C42×C151—22no—
58C42×C151D411yescharacteristic
59C42×C151D411yescharacteristic
60C42×C151C2311yescharacteristic
61C42×C151C2311yescharacteristic
62C22×D151—22no—
63Dic302—42no—
64D604—24no—
65D604—42no—
66D604—42no—
67C22⋊D151—44no—
68C2×Dic151—22no—
69C4×D151—44no—
70C151⋊C8—24no—
71C23×C151C2×D411yescharacteristic
72Q8×C151—42no—
73Q8×C151—42no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—41no—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2411yescharacteristic
85C22×C151—21no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151C22×D411yescharacteristic
89C2×D151—42no—
90C2×D151—42no—
91C2×D151—42no—
92C4×C151—21no—
93C4×C151—21no—
94C4×C151—21no—
95C4×C151—21no—
96C4×C151—42no—
97C4×C151—42no—
98C4×C151AGL(1,ℤ/8)12yes—
99C4×C1512−1+412yes—
100Dic151—42no—
101C2×C151—41no—
102C2×C151#53611yescharacteristic
103C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
104C2×C151#57511yescharacteristic
105D151—82no—
106C151#323511yescharacteristic, complemented, Sylow
107#3235—1511nomaximal, Sylow
108#533D15111yescharacteristic, complemented
109#532—1511no—
110#501—1512no—
111#490—1512no—
112#482—1514no—
113#476—1512no—
114#474—1512no—
115#432—1511no—
116C2×#41—3021no—
117C4⋊Q8—1511no—
118C4⋊Q8C2×D15111yescharacteristic
119C4⋊Q8C2×D15111yescharacteristic
120#127—1511no—
121#125C2×D15112yes—
122#124—3021no—
123C22⋊Q8—21no—
124C22⋊Q8—21no—
125#121—3021no—
126#121—1512no—
127C4×Q8—21no—
128C4×Q8—21no—
129C4×D4—3021no—
130C4×D4—1512no—
131#117C2×D15112yes—
132C2×C42C2×D15111yescharacteristic
133#107—1514no—
134#106—1514no—
135C4⋊C8—1512no—
136#102—1514no—
137#102—1514no—
138C22⋊C8—1512no—
139#97—1512no—
140#41—6044no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—3021no—
144C2×D4—3022no—
145C2×D4—3021no—
146C2×D4—3021no—
147C2×D4—1512no—
148C22×C4—3022no—
149C22×C4C22⋊D15111yescharacteristic
150C22×C4C22⋊D15111yescharacteristic
151C22×C4C22×D15111yescharacteristic
152C2×C8—1514no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—3021no—
158C4⋊C4—1512no—
159C4⋊C4C22×D15112yes—
160C4⋊C4C22×D15112yes—
161C22⋊C4—22no—
162C22⋊C4—3022no—
163C22⋊C4—3022no—
164C42—22no—
165C42C22⋊D15111yescharacteristic
166C42C22⋊D15111yescharacteristic
167C42C22×D15111yescharacteristic
168C42C22×D15111yescharacteristic
169C23—3022no—
170C23C2×C22⋊D15111yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—6042no—
174D4—3024no—
175D4—6042no—
176D4—6042no—
177D4—6044no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—3022no—
184C2×C4—6044no—
185C2×C4C2×C22⋊D15111yescharacteristic
186C2×C4C2×C22⋊D15111yescharacteristic
187C2×C4C2×C22⋊D15111yescharacteristic
188C2×C4C2×C22⋊D15111yescharacteristic
189C2×C4C2×C22⋊D15111yescharacteristic
190C2×C4C23×D15111yescharacteristic
191C8—3024no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—6042no—
196C22—6042no—
197C22—6042no—
198C22C22×C22⋊D15111yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—42no—
205C4—6042no—
206C4#1801276412yes—
207C4#1801278712yes—
208C2—41no—
209C2—12082no—
210C2#2375278611yescharacteristic
211C2C2×#1801276411yescharacteristic
212C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#533×C151C2
socleC22×C151C22×D4
prime radical#23752762C2
hypercenter#533D151
hypocenterC151#3235
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23752622C2semidirect
3. #23752578C2semidirect
4. #23752536C2semidirect
5. #23752499C2semidirect
6. #23752489C2semidirect
7. #23752269C2semidirect
8. #533×C151C2semidirect
106. C151#3235semidirect
108. #533D151semidirect

Maximal subgroups

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

subgroupindex
#237527622
#237526222
#237525782
#237525362
#237524992
#237524892
#237522692
#533×C1512
#3235151