Finite Group Databasebeta

← #34077209

Subgroups — #34077209

Order 19328.

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

normal subgroups only

This group has 464 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#23752153C212yesmaximal, complemented
2#23752148C211yesmaximal, characteristic, complemented
3#23752140C212yesmaximal, complemented
4#23752135C212yesmaximal, complemented
5#23752126C212yesmaximal, complemented
6#23752126C212yesmaximal, complemented
7#23752092C212yesmaximal, complemented
8#23752084C211yesmaximal, characteristic, complemented
9#392×C151C211yesmaximal, characteristic
10C23×Dic151C2211yescharacteristic
11C2×C4⋊Dic151C2211yescharacteristic
12C2×Dic151⋊C4C2212yes—
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×C22⋊Dic151C2211yescharacteristic
16C2×C22⋊Dic151C2212yes—
17C2×C22⋊Dic151C2212yes—
18C2×C22⋊Dic151C2212yes—
19C2×C22⋊Dic151C2212yes—
20C2×C22⋊Dic151C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C22×D4×C151C2212yes—
27C22×D4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2211yescharacteristic
29C2×C22⋊C4×C151C2212yes—
30#95×C151C2211yescharacteristic
31C22×Dic151—41no—
32C22×Dic151—42no—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C4⋊Dic151—41no—
38Dic151⋊C4—42no—
39Dic151⋊C4—42no—
40Dic151⋊C4—42no—
41C22⋊Dic151—22no—
42C22⋊Dic151—42no—
43C22⋊Dic151—42no—
44C22⋊Dic151—42no—
45C22⋊Dic151—42no—
46C22⋊Dic151—42no—
47C24×C151C2312yes—
48C24×C151C2311yescharacteristic
49C2×D4×C151—24no—
50C2×D4×C151—42no—
51C2×D4×C151—42no—
52C2×D4×C151—42no—
53C2×D4×C151—41no—
54C22×C4×C151C2311yescharacteristic
55C22×C4×C151C2311yescharacteristic
56C22×C4×C151C2312yes—
57C22⋊C4×C151—42no—
58C22⋊C4×C151—41no—
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—
70C2×Dic151—22no—
71C2×Dic151—44no—
72C23×C151—22no—
73C23×C151—21no—
74C23×C151—22no—
75C23×C151—21no—
76C23×C151—22no—
77C23×C151—22no—
78C23×C151—22no—
79C23×C151—22no—
80C23×C151—22no—
81C23×C151—22no—
82C23×C151—22no—
83C23×C151#4112yes—
84C23×C151C2411yescharacteristic
85D4×C151—48no—
86D4×C151—44no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—21no—
92C2×C4×C151—22no—
93C2×C4×C151—21no—
94C22×C151—24no—
95C22×C151—22no—
96C22×C151—41no—
97C22×C151—41no—
98C22×C151—42no—
99C22×C151—42no—
100C22×C151—42no—
101C22×C151—42no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151C2×#4111yescharacteristic
107C22×C151H(5,𝔽2)12yes—
108C22×C151H(5,𝔽2)12yes—
109C22×C151H(5,𝔽2)11yescharacteristic
110C22×C1512−1+411yescharacteristic
111C4×C151—42no—
112C4×C151—41no—
113C4×C151—41no—
114Dic151—42no—
115Dic151—42no—
116Dic151—42no—
117Dic151—42no—
118C2×C151—42no—
119C2×C151—82no—
120C2×C151#53812yes—
121C2×C151#53911yescharacteristic
122C2×C151#56011yescharacteristic
123C2×C151#56011yescharacteristic
124C2×C151#56212yes—
125C151#282611yescharacteristic, complemented, Sylow
126#2826—1511nomaximal, Sylow
127#400—1512no—
128#399—1511no—
129#397—1512no—
130#396—1512no—
131#394—1512no—
132#394—1512no—
133#392D15111yescharacteristic
134#386—1512no—
135#385—1511no—
136C22×D4C2×D15112yes—
137C22×D4C2×D15111yescharacteristic
138C23×C4—1511no—
139C2×C4⋊C4—1512no—
140C2×C4⋊C4—1512no—
141C2×C4⋊C4—1512no—
142C2×C4⋊C4—1511no—
143C2×C22⋊C4—1511no—
144C2×C22⋊C4—1512no—
145C2×C22⋊C4—1512no—
146C2×C22⋊C4—1512no—
147C2×C22⋊C4—1512no—
148C2×C22⋊C4—1512no—
149C2×C22⋊C4C2×D15111yescharacteristic
150C2×C22⋊C4C2×D15112yes—
151#95—1512no—
152#95—1512no—
153#95—1512no—
154#95—1512no—
155#95—1511no—
156#95C2×D15111yescharacteristic
157C24C22×D15112yes—
158C24C22×D15111yescharacteristic
159C2×D4—24no—
160C2×D4—42no—
161C2×D4—41no—
162C2×D4—42no—
163C2×D4—42no—
164C22×C4—6041no—
165C22×C4—6042no—
166C22×C4—1512no—
167C22×C4—1512no—
168C22×C4—1512no—
169C22×C4—1512no—
170C22×C4C22×D15112yes—
171C22×C4C22×D15111yescharacteristic
172C22×C4C22×D15111yescharacteristic
173C4⋊C4—6042no—
174C4⋊C4—6042no—
175C4⋊C4—6042no—
176C4⋊C4—6041no—
177C22⋊C4—41no—
178C22⋊C4—42no—
179C22⋊C4—3022no—
180C22⋊C4—6042no—
181C22⋊C4—6042no—
182C22⋊C4—6042no—
183C22⋊C4—6042no—
184C22⋊C4—6042no—
185C23—21no—
186C23—22no—
187C23—22no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23#1455900312yes—
197C23C23×D15111yescharacteristic
198D4—48no—
199D4—44no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—3022no—
208C2×C4—3022no—
209C2×C4—3022no—
210C2×C4—3022no—
211C2×C4—3022no—
212C2×C4—3022no—
213C2×C4—3022no—
214C2×C4—3022no—
215C2×C4—3022no—
216C2×C4—3022no—
217C2×C4—3022no—
218C2×C4—3022no—
219C2×C4—6044no—
220C22—24no—
221C22—22no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22C2×#1455900311yescharacteristic
233C22#1801278412yes—
234C22#1801278412yes—
235C22#1801278411yescharacteristic
236C22#1801278611yescharacteristic
237C4—42no—
238C4—41no—
239C4—41no—
240C4—6042no—
241C4—6042no—
242C4—6042no—
243C4—6042no—
244C2—42no—
245C2—82no—
246C2#2375279712yes—
247C2#2375280711yescharacteristic
248C2#2375294911yescharacteristic
249C2#2375295111yescharacteristic
250C2#2375295712yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting, prime radical#392×C151C2
hypercenter#392D151
hypocenterC151#2826
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #23752153C2semidirect
2. #23752148C2semidirect
3. #23752140C2semidirect
4. #23752135C2semidirect
5. #23752126C2semidirect
6. #23752126C2semidirect
7. #23752092C2semidirect
8. #23752084C2semidirect
125. C151#2826semidirect

Maximal subgroups

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

subgroupindex
#237521532
#237521482
#237521402
#237521352
#237521262
#237520922
#237520842
#392×C1512
#2826151