Finite Group Databasebeta

← #34080265

Subgroups — #34080265

Order 19328.

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

normal subgroups only

This group has 326 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#23752769C211yesmaximal, characteristic
2#23752615C211yesmaximal, characteristic, complemented
3#23752608C211yesmaximal, characteristic, complemented
4#23752562C211yesmaximal, characteristic, complemented
5#23752562C211yesmaximal, characteristic, complemented
6#23752550C214yesmaximal
7#23752519C214yesmaximal, complemented
8#23752265C211yesmaximal, characteristic
9#533×C151C211yesmaximal, characteristic
10#18012739C2211yescharacteristic
11#18012739C2211yescharacteristic
12#18012731C2212yes—
13#18012718—21no—
14#18012718—21no—
15C4×Dic302—21no—
16C4×Dic302—21no—
17#18012698C2212yes—
18#18012672C2214yes—
19#18012670C2214yes—
20C4⋊(C151⋊C8)C2212yes—
21#18012663C2214yes—
22#18012663C2214yes—
23C22⋊(C151⋊C8)C2212yes—
24C4×C151⋊C8C2211yescharacteristic
25C4×C151⋊C8C2211yescharacteristic
26C4⋊Q8×C151C2211yescharacteristic
27C4⋊Q8×C151C2211yescharacteristic
28#125×C151—21no—
29C22⋊Q8×C151—21no—
30C22⋊Q8×C151C2212yes—
31C4×Q8×C151—21no—
32C4×Q8×C151C2212yes—
33#117×C151—21no—
34C2×C42×C151C2211yescharacteristic
35C2×Dic302—21no—
36C2×Dic302—21no—
37C2×C151⋊C8C2312yes—
38C2×C151⋊C8C2312yes—
39C4⋊Dic151—21no—
40C4⋊Dic151—21no—
41C4⋊Dic151C2312yes—
42C4⋊Dic151C2312yes—
43Dic151⋊C4—22no—
44Dic151⋊C4—22no—
45C22⋊Dic151—22no—
46C4×Dic151—22no—
47C2×Q8×C151—21no—
48C2×Q8×C151C2312yes—
49C22×C4×C151D411yescharacteristic
50C22×C4×C151D411yescharacteristic
51C22×C4×C151C2311yescharacteristic
52C4⋊C4×C151—21no—
53C4⋊C4×C151—21no—
54C4⋊C4×C151—21no—
55C4⋊C4×C151—22no—
56C4⋊C4×C151—22no—
57C4⋊C4×C151C2312yes—
58C22⋊C4×C151—22no—
59C42×C151—22no—
60C42×C151D411yescharacteristic
61C42×C151D411yescharacteristic
62C42×C151C2311yescharacteristic
63C42×C151C2311yescharacteristic
64Dic302—42no—
65Dic302—42no—
66C2×Dic151—22no—
67C2×Dic151—22no—
68C151⋊C8—22no—
69C151⋊C8—22no—
70C23×C151C2×D411yescharacteristic
71Q8×C151—24no—
72Q8×C151—42no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2411yescharacteristic
84C22×C151—21no—
85C22×C151—21no—
86C22×C151—21no—
87C22×C151C22×D411yescharacteristic
88C4×C151—21no—
89C4×C151—21no—
90C4×C151—21no—
91C4×C151—42no—
92C4×C151—42no—
93C4×C151#13512yes—
94C4×C151#13712yes—
95C4×C1512−1+412yes—
96Dic151—42no—
97Dic151—42no—
98C2×C151—41no—
99C2×C151#53611yescharacteristic
100C2×C151C2×#13511yescharacteristic
101C2×C151C2×#13711yescharacteristic
102C151#323111yescharacteristic, complemented, Sylow
103#3231—1511nomaximal, Sylow
104#533—1511no—
105#533D15111yescharacteristic
106#500—1511no—
107#498—1511no—
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—21no—
118#125—1512no—
119C22⋊Q8—21no—
120C22⋊Q8—3021no—
121C22⋊Q8—3021no—
122C22⋊Q8C2×D15112yes—
123C4×Q8—21no—
124C4×Q8—3021no—
125C4×Q8—3021no—
126C4×Q8C2×D15112yes—
127#117—21no—
128#117—1512no—
129C2×C42C2×D15111yescharacteristic
130#107—1514no—
131#106—1514no—
132C4⋊C8—1512no—
133#103—1514no—
134#103—1514no—
135C22⋊C8—1512no—
136C4×C8—1511no—
137C4×C8—1511no—
138C2×Q8—21no—
139C2×Q8—3021no—
140C2×Q8—3021no—
141C2×Q8C22×D15112yes—
142C22×C4C22⋊D15111yescharacteristic
143C22×C4C22⋊D15111yescharacteristic
144C22×C4C22×D15111yescharacteristic
145C2×C8—1512no—
146C2×C8—1512no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—3022no—
153C4⋊C4—3022no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—1512no—
157C4⋊C4—1512no—
158C4⋊C4C22×D15112yes—
159C22⋊C4—22no—
160C22⋊C4—3022no—
161C42—22no—
162C42—3022no—
163C42C22⋊D15111yescharacteristic
164C42C22⋊D15111yescharacteristic
165C42C22×D15111yescharacteristic
166C42C22×D15111yescharacteristic
167C23C2×C22⋊D15111yescharacteristic
168Q8—24no—
169Q8—42no—
170Q8—6042no—
171Q8—6042no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—3022no—
178C2×C4—3022no—
179C2×C4C2×C22⋊D15111yescharacteristic
180C2×C4C2×C22⋊D15111yescharacteristic
181C2×C4C2×C22⋊D15111yescharacteristic
182C2×C4C2×C22⋊D15111yescharacteristic
183C2×C4C2×C22⋊D15111yescharacteristic
184C2×C4C23×D15111yescharacteristic
185C8—3022no—
186C8—3022no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22C22×C22⋊D15111yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—6042no—
197C4—6042no—
198C4#1801275912yes—
199C4#1801277012yes—
200C4#1801278612yes—
201C2—41no—
202C2#2375278311yescharacteristic
203C2C2×#1801275911yescharacteristic
204C2C2×#1801277011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#533×C151C2
socleC22×C151C22×D4
prime radicalC23×C151C2×D4
hypercenter#533D151
hypocenterC151#3231
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. #23752615C2semidirect
3. #23752608C2semidirect
4. #23752562C2semidirect
5. #23752562C2semidirect
7. #23752519C2semidirect
102. C151#3231semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237526152
#237526082
#237525622
#237525502
#237525192
#237522652
#533×C1512
#3231151