Finite Group Databasebeta

← #34077253

Subgroups — #34077253

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#23752142C211yesmaximal, characteristic, complemented
2#23752140C212yesmaximal, complemented
3#23752140C212yesmaximal, complemented
4#23752135C212yesmaximal, complemented
5#23752132C211yesmaximal, characteristic, complemented
6#23752126C212yesmaximal
7#23752124C212yesmaximal, complemented
8#23752096C212yesmaximal, complemented
9#390×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×C4⋊Dic151C2211yescharacteristic
12C2×Dic151⋊C4C2212yes—
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×C22⋊Dic151C2212yes—
16C2×C22⋊Dic151C2212yes—
17C2×C22⋊Dic151C2212yes—
18C2×C22⋊Dic151C2212yes—
19C151⋊#95C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2211yescharacteristic
25C151⋊#95C2211yescharacteristic
26C22×D4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2212yes—
29C2×C22⋊C4×C151C2212yes—
30C2×C42×C151C2211yescharacteristic
31C2×Dic302—42no—
32C2×Dic302—41no—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C4⋊Dic151—41no—
38Dic151⋊C4—24no—
39Dic151⋊C4—42no—
40Dic151⋊C4—42no—
41C22⋊Dic151—42no—
42C22⋊Dic151—42no—
43C22⋊Dic151—42no—
44C22⋊Dic151—42no—
45C24×C151C2312yes—
46C2×D4×C151—22no—
47C2×D4×C151—41no—
48C2×D4×C151—41no—
49C22×C4×C151C2311yescharacteristic
50C22×C4×C151C2312yes—
51C22×C4×C151C2311yescharacteristic
52C22×C4×C151C2311yescharacteristic
53C4⋊C4×C151—41no—
54C22⋊C4×C151—42no—
55C22⋊C4×C151—42no—
56C42×C151—41no—
57Dic302—44no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C23×C151—22no—
71C23×C151—22no—
72C23×C151—22no—
73C23×C151—22no—
74C23×C151—22no—
75C23×C151—22no—
76C23×C151—22no—
77C23×C151C2411yescharacteristic
78D4×C151—44no—
79C2×C4×C151—21no—
80C2×C4×C151—21no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151—21no—
84C2×C4×C151—22no—
85C2×C4×C151—21no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151#4112yes—
89C22×C151—42no—
90C22×C151—42no—
91C22×C151—42no—
92C22×C151—42no—
93C22×C151—42no—
94C22×C151—42no—
95C22×C151—42no—
96C22×C151C2×#4111yescharacteristic
97C22×C151H(5,𝔽2)11yescharacteristic
98C22×C151H(5,𝔽2)11yescharacteristic
99C22×C151H(5,𝔽2)12yes—
100C22×C1512−1+412yes—
101C4×C151—22no—
102C4×C151—41no—
103C4×C151—41no—
104C4×C151—42no—
105Dic151—42no—
106Dic151—42no—
107Dic151—42no—
108Dic151—42no—
109C2×C151—82no—
110C2×C151#53811yescharacteristic
111C2×C151#54212yes—
112C2×C151#56011yescharacteristic
113C2×C151#56212yes—
114C2×C151#56311yescharacteristic
115C151#283011yescharacteristic, complemented, Sylow
116#2830—1511nomaximal, Sylow
117#398—1511no—
118#397—1512no—
119#397—1512no—
120#396—1512no—
121#395—1511no—
122#394—1512no—
123#393—1512no—
124#390D15111yescharacteristic
125#387—1512no—
126C22×Q8—1511no—
127C22×D4C2×D15111yescharacteristic
128C2×C4⋊C4—1512no—
129C2×C4⋊C4—1512no—
130C2×C4⋊C4—1512no—
131C2×C4⋊C4—1511no—
132C2×C4⋊C4C2×D15111yescharacteristic
133C2×C22⋊C4—1512no—
134C2×C22⋊C4—1512no—
135C2×C22⋊C4—1512no—
136C2×C22⋊C4—1512no—
137C2×C22⋊C4C2×D15112yes—
138C2×C22⋊C4C2×D15112yes—
139C2×C42C2×D15111yescharacteristic
140#95—1512no—
141#95—1512no—
142#95—1512no—
143#95—1512no—
144#95—1512no—
145#95—1511no—
146#95—1511no—
147C24C22×D15112yes—
148C2×Q8—6042no—
149C2×Q8—6041no—
150C2×D4—22no—
151C2×D4—41no—
152C2×D4—41no—
153C22×C4—1512no—
154C22×C4—1512no—
155C22×C4—1512no—
156C22×C4—1512no—
157C22×C4C22×D15112yes—
158C22×C4C22×D15111yescharacteristic
159C22×C4C22×D15111yescharacteristic
160C22×C4C22×D15111yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—3024no—
163C4⋊C4—6042no—
164C4⋊C4—6042no—
165C4⋊C4—6041no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C22⋊C4—6042no—
169C22⋊C4—6042no—
170C22⋊C4—6042no—
171C22⋊C4—6042no—
172C42—41no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23C23×D15111yescharacteristic
181Q8—6044no—
182D4—44no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—3022no—
193C2×C4—3022no—
194C2×C4—3022no—
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#1455900412yes—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22C2×#1455900411yescharacteristic
213C22#1801278411yescharacteristic
214C22#1801278411yescharacteristic
215C22#1801278412yes—
216C22#1801278612yes—
217C4—22no—
218C4—41no—
219C4—41no—
220C4—42no—
221C4—6042no—
222C4—6042no—
223C4—6042no—
224C4—6042no—
225C2—82no—
226C2#2375280011yescharacteristic
227C2#2375282712yes—
228C2#2375294911yescharacteristic
229C2#2375295712yes—
230C2#2375296211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#390×C151C2
prime radicalC22×D4×C151C22
hypercenter#390D151
hypocenterC151#2830
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #23752142C2semidirect
2. #23752140C2semidirect
3. #23752140C2semidirect
4. #23752135C2semidirect
5. #23752132C2semidirect
7. #23752124C2semidirect
8. #23752096C2semidirect
115. C151#2830semidirect

Maximal subgroups

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

subgroupindex
#237521422
#237521402
#237521352
#237521322
#237521262
#237521242
#237520962
#390×C1512
#2830151