Finite Group Databasebeta

← #34077257

Subgroups — #34077257

Order 19328.

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

normal subgroups only

This group has 408 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#23752141C212yesmaximal, complemented
2#23752139C212yesmaximal, complemented
3#23752134C212yesmaximal, complemented
4#23752132C211yesmaximal, characteristic, complemented
5#23752129C212yesmaximal
6#23752125C212yesmaximal, complemented
7#23752113C211yesmaximal, characteristic
8#23752098C212yesmaximal, complemented
9#398×C151C211yesmaximal, characteristic, complemented
10C22×Dic302C2211yescharacteristic
11C22×D604C2211yescharacteristic
12C2×C4⋊Dic151C2212yes—
13C2×Dic151⋊C4C2212yes—
14C2×(C2×D151)⋊C4C2212yes—
15C2×(C2×D151)⋊C4C2212yes—
16C2×(C2×D151)⋊C4C2212yes—
17C2×(C2×D151)⋊C4C2212yes—
18C2×(C2×D151)⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×C4×Dic151C2211yescharacteristic
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C2×C4⋊C4×C151C2212yes—
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29#95×C151C2212yes—
30#95×C151C2211yescharacteristic
31C23×D151C2312yes—
32C2×Dic302—42no—
33C2×Dic302—41no—
34C2×D604—22no—
35C2×D604—41no—
36C2×D604—41no—
37C22×Dic151C2312yes—
38C22×Dic151C2312yes—
39C22×Dic151C2312yes—
40C4⋊Dic151—42no—
41Dic151⋊C4—42no—
42(C2×D151)⋊C4—42no—
43(C2×D151)⋊C4—42no—
44(C2×D151)⋊C4—42no—
45(C2×D151)⋊C4—42no—
46(C2×D151)⋊C4—42no—
47(C2×D151)⋊C4—42no—
48C4×Dic151—41no—
49C22×C4×C151C2311yescharacteristic
50C22×C4×C151C2312yes—
51C22×C4×C151C2311yescharacteristic
52C22×C4×C151C2312yes—
53C22×C4×C151C2311yescharacteristic
54C4⋊C4×C151—24no—
55C4⋊C4×C151—41no—
56C4⋊C4×C151—41no—
57C22×D151—22no—
58C22×D151—22no—
59C22×D151—22no—
60C22×D151—22no—
61C22×D151—22no—
62C22×D151—22no—
63C22×D151—22no—
64Dic302—44no—
65D604—44no—
66C2×Dic151—22no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C23×C151C2411yescharacteristic
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—21no—
86C2×C4×C151—21no—
87C2×C4×C151—22no—
88C2×C4×C151#4112yes—
89C22×C151C2×#4111yescharacteristic
90C22×C151H(5,𝔽2)11yescharacteristic
91C22×C151H(5,𝔽2)11yescharacteristic
92C22×C151H(5,𝔽2)12yes—
93C22×C1512−1+412yes—
94C2×D151—42no—
95C2×D151—42no—
96C2×D151—42no—
97C2×D151—42no—
98C2×D151—42no—
99C2×D151—42no—
100C2×D151—42no—
101C4×C151—22no—
102C4×C151—42no—
103C4×C151—42no—
104C4×C151—41no—
105C4×C151—41no—
106Dic151—42no—
107Dic151—42no—
108Dic151—42no—
109C2×C151#53811yescharacteristic
110C2×C151#54212yes—
111C2×C151#56011yescharacteristic
112C2×C151#56212yes—
113C2×C151#56311yescharacteristic
114D151—82no—
115C151#283011yescharacteristic, complemented, Sylow
116#2830—1511nomaximal, Sylow
117#398D15111yescharacteristic, complemented
118#397—1512no—
119#397—1512no—
120#396—1512no—
121#395—1511no—
122#394—1512no—
123#393—1512no—
124#390—1511no—
125#387—1512no—
126C22×Q8—1511no—
127C22×D4—1511no—
128C2×C4⋊C4—1512no—
129C2×C4⋊C4—1512no—
130C2×C4⋊C4C2×D15112yes—
131C2×C4⋊C4C2×D15111yescharacteristic
132C2×C4⋊C4C2×D15111yescharacteristic
133C2×C22⋊C4—1512no—
134C2×C22⋊C4—1512no—
135C2×C22⋊C4—1512no—
136C2×C22⋊C4—1512no—
137C2×C22⋊C4—1512no—
138C2×C22⋊C4—1512no—
139C2×C42—1511no—
140#95—1512no—
141#95—1512no—
142#95—1512no—
143#95—1512no—
144#95—1511no—
145#95C2×D15112yes—
146#95C2×D15111yescharacteristic
147C24—1512no—
148C2×Q8—6041no—
149C2×Q8—6042no—
150C2×D4—3022no—
151C2×D4—6041no—
152C2×D4—6041no—
153C22×C4—1512no—
154C22×C4—1512no—
155C22×C4—1512no—
156C22×C4C22×D15112yes—
157C22×C4C22×D15111yescharacteristic
158C22×C4C22×D15112yes—
159C22×C4C22×D15111yescharacteristic
160C22×C4C22×D15111yescharacteristic
161C4⋊C4—24no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—6042no—
165C4⋊C4—6042no—
166C22⋊C4—6042no—
167C22⋊C4—6042no—
168C22⋊C4—6042no—
169C22⋊C4—6042no—
170C22⋊C4—6042no—
171C22⋊C4—6042no—
172C42—6041no—
173C23—3022no—
174C23—3022no—
175C23—3022no—
176C23—3022no—
177C23—3022no—
178C23—3022no—
179C23—3022no—
180C23C23×D15111yescharacteristic
181Q8—6044no—
182D4—6044no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—3022no—
196C2×C4—3022no—
197C2×C4—3022no—
198C2×C4—3022no—
199C2×C4—3022no—
200C2×C4—3022no—
201C2×C4—3022no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4#1455900312yes—
205C22—6042no—
206C22—6042no—
207C22—6042no—
208C22—6042no—
209C22—6042no—
210C22—6042no—
211C22—6042no—
212C22C2×#1455900311yescharacteristic
213C22#1801278411yescharacteristic
214C22#1801278511yescharacteristic
215C22#1801278512yes—
216C22#1801278712yes—
217C4—22no—
218C4—42no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—6042no—
223C4—6042no—
224C4—6042no—
225C2—12082no—
226C2#2375279911yescharacteristic
227C2#2375283512yes—
228C2#2375295211yescharacteristic
229C2#2375296012yes—
230C2#2375296111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#398×C151C2
prime radicalC22×D604C22
hypercenter#398D151
hypocenterC151#2830
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #23752141C2semidirect
2. #23752139C2semidirect
3. #23752134C2semidirect
4. #23752132C2semidirect
6. #23752125C2semidirect
8. #23752098C2semidirect
9. #398×C151C2semidirect
115. C151#2830semidirect
117. #398D151semidirect

Maximal subgroups

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

subgroupindex
#237521412
#237521392
#237521342
#237521322
#237521292
#237521252
#237521132
#237520982
#398×C1512
#2830151