Finite Group Databasebeta

← #34077146

Subgroups — #34077146

Order 19328.

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

normal subgroups only

This group has 444 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
1C2×#18012719C211yesmaximal, characteristic
2C2×#18012717C211yesmaximal, characteristic
3#23752154C212yesmaximal, complemented
4#23752150C211yesmaximal, characteristic, complemented
5#23752141C212yesmaximal
6#23752139C212yesmaximal
7#23752133C211yesmaximal, characteristic, complemented
8#23752133C212yesmaximal, complemented
9#23752132C211yesmaximal, characteristic, complemented
10#23752074C211yesmaximal, characteristic
11#400×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×Dic302C2211yescharacteristic
14C22×C4×D151C2211yescharacteristic
15#18012719—24no—
16#18012717—24no—
17C2×C4⋊Dic151C2212yes—
18C2×C4⋊Dic151C2212yes—
19C2×Dic151⋊C4C2211yescharacteristic
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2212yes—
22C2×(C2×D151)⋊C4C2211yescharacteristic
23C2×(C2×D151)⋊C4C2211yescharacteristic
24C2×(C2×D151)⋊C4C2212yes—
25C2×(C2×D151)⋊C4C2212yes—
26C151⋊#95C2211yescharacteristic
27C151⋊#95C2212yes—
28C151⋊#95C2212yes—
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C2×C4⋊C4×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2211yescharacteristic
34#95×C151C2211yescharacteristic
35#95×C151C2212yes—
36#95×C151C2212yes—
37C23×D151C2311yescharacteristic
38C2×Dic302—22no—
39C2×Dic302—22no—
40C2×Dic302—42no—
41C2×Dic302—42no—
42C22×Dic151C2311yescharacteristic
43C22×Dic151C2311yescharacteristic
44C22×Dic151C2312yes—
45C22×Dic151C2312yes—
46C22×Dic151C2311yescharacteristic
47C2×C4×D151—42no—
48C2×C4×D151D414yes—
49C4⋊Dic151—24no—
50C4⋊Dic151—42no—
51Dic151⋊C4—22no—
52Dic151⋊C4—22no—
53Dic151⋊C4—42no—
54(C2×D151)⋊C4—22no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—24no—
57(C2×D151)⋊C4—42no—
58C22×C4×C151C2311yescharacteristic
59C22×C4×C151C2311yescharacteristic
60C22×C4×C151C2312yes—
61C22×C4×C151C2312yes—
62C22×C4×C151C2311yescharacteristic
63C4⋊C4×C151—22no—
64C4⋊C4×C151—22no—
65C22×D151—22no—
66C22×D151—22no—
67C22×D151—21no—
68C22×D151—21no—
69C22×D151C2×D412yes—
70Dic302—44no—
71Dic302—44no—
72C2×Dic151—22no—
73C2×Dic151—21no—
74C2×Dic151—21no—
75C2×Dic151—22no—
76C2×Dic151—22no—
77C2×Dic151—22no—
78C2×Dic151—22no—
79C2×Dic151—22no—
80C2×Dic151—21no—
81C2×Dic151—22no—
82C2×Dic151—21no—
83C2×Dic151—22no—
84C2×Dic151C2×D412yes—
85C4×D151—44no—
86C23×C151C2411yescharacteristic
87C2×C4×C151—22no—
88C2×C4×C151—21no—
89C2×C4×C151—22no—
90C2×C4×C151—21no—
91C2×C4×C151—22no—
92C2×C4×C151—22no—
93C2×C4×C151—21no—
94C2×C4×C151—24no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—21no—
98C2×C4×C151C2×D412yes—
99C22×C151C22×D411yescharacteristic
100C22×C151H(5,𝔽2)12yes—
101C22×C1512−1+411yescharacteristic
102C22×C1512−1+412yes—
103C22×C1512−1+411yescharacteristic
104C2×D151—22no—
105C2×D151—22no—
106C2×D151—22no—
107C2×D151—42no—
108C2×D151—42no—
109C4×C151—22no—
110C4×C151—41no—
111C4×C151—42no—
112C4×C151—41no—
113C4×C151—42no—
114Dic151—22no—
115Dic151—41no—
116Dic151—42no—
117Dic151—41no—
118Dic151—42no—
119C2×C151#53411yescharacteristic
120C2×C151#53611yescharacteristic
121C2×C151#53611yescharacteristic
122C2×C151#56312yes—
123C2×C151#56312yes—
124D151—42no—
125C151#281711yescharacteristic, complemented, Sylow
126#2817—1511nomaximal, Sylow
127C2×C22⋊Q8—1511no—
128C2×C22⋊Q8—1511no—
129#400—1511no—
130#400—1512no—
131#400D15111yescharacteristic, complemented
132#397—1512no—
133#397—1512no—
134#395—1511no—
135#395—1512no—
136#395—1511no—
137#381—1511no—
138C22×Q8—1511no—
139C22×Q8—1511no—
140C23×C4—1511no—
141C22⋊Q8—3024no—
142C22⋊Q8—3024no—
143C2×C4⋊C4—1511no—
144C2×C4⋊C4—1511no—
145C2×C4⋊C4—1512no—
146C2×C4⋊C4—1512no—
147C2×C4⋊C4—1512no—
148C2×C4⋊C4C2×D15111yescharacteristic
149C2×C4⋊C4C2×D15111yescharacteristic
150C2×C22⋊C4—1511no—
151C2×C22⋊C4—1511no—
152C2×C22⋊C4—1512no—
153C2×C22⋊C4—1512no—
154#95—1511no—
155#95—1512no—
156#95—1512no—
157#95—1512no—
158#95—1512no—
159#95—1512no—
160#95C2×D15111yescharacteristic
161#95C2×D15112yes—
162#95C2×D15112yes—
163C24—1511no—
164C2×Q8—3022no—
165C2×Q8—3022no—
166C2×Q8—6042no—
167C2×Q8—6042no—
168C22×C4—6042no—
169C22×C4—1512no—
170C22×C4—1511no—
171C22×C4—1511no—
172C22×C4—1512no—
173C22×C4—1511no—
174C22×C4—1514no—
175C22×C4C22×D15112yes—
176C22×C4C22×D15112yes—
177C22×C4C22×D15111yescharacteristic
178C22×C4C22×D15111yescharacteristic
179C22×C4C22×D15111yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—3022no—
183C4⋊C4—3024no—
184C4⋊C4—3022no—
185C4⋊C4—6042no—
186C4⋊C4—6042no—
187C22⋊C4—3022no—
188C22⋊C4—3024no—
189C22⋊C4—3022no—
190C22⋊C4—6042no—
191C23—3022no—
192C23—3022no—
193C23—3021no—
194C23—3021no—
195C23—1512no—
196C23C23×D15111yescharacteristic
197Q8—6044no—
198Q8—6044no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—24no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—3022no—
211C2×C4—3021no—
212C2×C4—3022no—
213C2×C4—3021no—
214C2×C4—3022no—
215C2×C4—3022no—
216C2×C4—3022no—
217C2×C4—3022no—
218C2×C4—3022no—
219C2×C4—3021no—
220C2×C4—3022no—
221C2×C4—3021no—
222C2×C4—6044no—
223C2×C4—1512no—
224C2×C4D4×D15112yes—
225C22—3022no—
226C22—3022no—
227C22—3022no—
228C22—6042no—
229C22—6042no—
230C22C2×D4×D15111yescharacteristic
231C22#1801278512yes—
232C22#1801278611yescharacteristic
233C22#1801278612yes—
234C22#1801278711yescharacteristic
235C4—22no—
236C4—42no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—3022no—
241C4—6042no—
242C4—6042no—
243C4—6041no—
244C4—6041no—
245C2—6042no—
246C2#2375277311yescharacteristic
247C2#2375278211yescharacteristic
248C2#2375278511yescharacteristic
249C2#2375296412yes—
250C2#2375296612yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#400×C151C2
prime radicalC23×D151C23
hypercenter#400D151
hypocenterC151#2817
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #23752154C2semidirect
4. #23752150C2semidirect
7. #23752133C2semidirect
8. #23752133C2semidirect
9. #23752132C2semidirect
11. #400×C151C2semidirect
125. C151#2817semidirect
131. #400D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127192
C2×#180127172
#237521542
#237521502
#237521412
#237521392
#237521332
#237521322
#237520742
#400×C1512
#2817151