Finite Group Databasebeta

← #44487821

Subgroups — #44487821

Order 30592.

528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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×#21439925C211yesmaximal, characteristic, complemented
2C2×#21439918C211yesmaximal, characteristic
3#29504707C211yesmaximal, characteristic
4#29504706C212yesmaximal, complemented
5#29504696C212yesmaximal
6#29504692C211yesmaximal, characteristic, complemented
7#29504685C211yesmaximal, characteristic
8#29504623C211yesmaximal, characteristic, complemented
9#29504623C212yesmaximal, complemented
10#29504619C212yesmaximal
11#400×C239C211yesmaximal, characteristic, complemented
12C22×Dic478C2211yescharacteristic
13C22×C4×D239C2211yescharacteristic
14#21439925—24no—
15#21439918—24no—
16C2×C4⋊Dic239C2211yescharacteristic
17C2×Dic239⋊C4C2212yes—
18C2×Dic239⋊C4C2212yes—
19C2×Dic239⋊C4C2212yes—
20C2×Dic239⋊C4C2212yes—
21C2×(C2×D239)⋊C4C2212yes—
22C2×(C2×D239)⋊C4C2212yes—
23C2×(C2×D239)⋊C4C2211yescharacteristic
24C2×(C2×D239)⋊C4C2211yescharacteristic
25C2×C4×Dic239C2212yes—
26C2×C4×Dic239C2212yes—
27C2×C4×Dic239C2211yescharacteristic
28C2×C4×Dic239C2211yescharacteristic
29C239⋊#95C2212yes—
30C239⋊#95C2212yes—
31C239⋊#95C2211yescharacteristic
32C2×C4⋊C4×C239C2211yescharacteristic
33C2×C4⋊C4×C239C2211yescharacteristic
34#95×C239C2212yes—
35#95×C239C2211yescharacteristic
36#95×C239C2212yes—
37C23×D239C2311yescharacteristic
38C2×Dic478—24no—
39C2×Dic478—22no—
40C22×Dic239C2311yescharacteristic
41C22×Dic239C2311yescharacteristic
42C22×Dic239C2312yes—
43C22×Dic239C2312yes—
44C22×Dic239C2311yescharacteristic
45C2×C4×D239—22no—
46C2×C4×D239—22no—
47C2×C4×D239Q814yescomplemented
48C4⋊Dic239—22no—
49Dic239⋊C4—24no—
50Dic239⋊C4—24no—
51Dic239⋊C4—24no—
52Dic239⋊C4—24no—
53(C2×D239)⋊C4—22no—
54(C2×D239)⋊C4—24no—
55(C2×D239)⋊C4—24no—
56(C2×D239)⋊C4—22no—
57C4×Dic239—22no—
58C4×Dic239—24no—
59C4×Dic239—24no—
60C4×Dic239D414yes—
61C22×C4×C239C2312yes—
62C22×C4×C239C2311yescharacteristic
63C22×C4×C239C2312yes—
64C22×C4×C239C2311yescharacteristic
65C22×C4×C239C2311yescharacteristic
66C4⋊C4×C239—22no—
67C4⋊C4×C239—22no—
68C22×D239—21no—
69C22×D239—22no—
70C22×D239—22no—
71C22×D239—21no—
72C22×D239C2×Q812yes—
73Dic478—28no—
74C2×Dic239—22no—
75C2×Dic239—22no—
76C2×Dic239—22no—
77C2×Dic239—22no—
78C2×Dic239—22no—
79C2×Dic239—21no—
80C2×Dic239—22no—
81C2×Dic239C2×D412yes—
82C2×Dic239C2×D412yes—
83C2×Dic239C2×Q812yes—
84C2×Dic239#4114yes—
85C2×Dic239#4114yes—
86C2×Dic239#4112yes—
87C4×D239—28no—
88C23×C239C2411yescharacteristic
89C2×C4×C239—21no—
90C2×C4×C239—21no—
91C2×C4×C239—22no—
92C2×C4×C239—21no—
93C2×C4×C239—22no—
94C2×C4×C239—22no—
95C2×C4×C239—22no—
96C2×C4×C239—22no—
97C2×C4×C239—22no—
98C2×C4×C239—22no—
99C2×C4×C239—22no—
100C2×C4×C239C2×D412yes—
101C2×C4×C239C2×Q812yes—
102C22×C239C22×D411yescharacteristic
103C22×C239C22×Q811yescharacteristic
104C22×C239C2×#4111yescharacteristic
105C22×C239C2×#4112yes—
106C22×C239C2×#4112yes—
107C2×D239—22no—
108C2×D239—24no—
109C2×D239—41no—
110C2×D239—42no—
111C2×D239—41no—
112C4×C239—22no—
113C4×C239—22no—
114C4×C239—41no—
115C4×C239—42no—
116C4×C239—42no—
117Dic239—24no—
118Dic239—24no—
119Dic239—22no—
120Dic239—41no—
121Dic239C22⋊Q814yes—
122C2×C239C2×C22⋊Q811yescharacteristic
123C2×C239#52511yescharacteristic
124C2×C239#52912yes—
125C2×C239#53211yescharacteristic
126C2×C239#53312yes—
127D239—42no—
128C239#239611yescharacteristic, complemented, Sylow
129#2396—2391nomaximal, Sylow
130C2×C4×Q8—2391no—
131C2×#117—2391no—
132#400D23911yescharacteristic, complemented
133#399—2391no—
134#398—2392no—
135#396—2392no—
136#395—2391no—
137#393—2391no—
138C4×C4⋊C4—2392no—
139C4×C4⋊C4—2391no—
140C4×C22⋊C4—2392no—
141C22×Q8—2391no—
142C23×C4—2391no—
143C4×Q8—4784no—
144#117—4784no—
145C2×C4⋊C4—2391no—
146C2×C4⋊C4—2392no—
147C2×C4⋊C4—2392no—
148C2×C4⋊C4—2392no—
149C2×C4⋊C4—2392no—
150C2×C4⋊C4C2×D23911yescharacteristic
151C2×C4⋊C4C2×D23911yescharacteristic
152C2×C22⋊C4—2391no—
153C2×C22⋊C4—2391no—
154C2×C22⋊C4—2392no—
155C2×C22⋊C4—2392no—
156C2×C42—2391no—
157C2×C42—2392no—
158C2×C42—2392no—
159C2×C42—2391no—
160#95—2392no—
161#95—2392no—
162#95—2391no—
163#95C2×D23912yes—
164#95C2×D23911yescharacteristic
165#95C2×D23912yes—
166C24—2391no—
167C2×Q8—4784no—
168C2×Q8—4782no—
169C22×C4—4782no—
170C22×C4—4782no—
171C22×C4—2391no—
172C22×C4—2392no—
173C22×C4—2392no—
174C22×C4—2391no—
175C22×C4—2394no—
176C22×C4—2391no—
177C22×C4C22×D23912yes—
178C22×C4C22×D23912yes—
179C22×C4C22×D23911yescharacteristic
180C22×C4C22×D23911yescharacteristic
181C22×C4C22×D23911yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—4782no—
185C4⋊C4—4784no—
186C4⋊C4—4784no—
187C4⋊C4—4784no—
188C4⋊C4—4784no—
189C22⋊C4—4782no—
190C22⋊C4—4784no—
191C22⋊C4—4784no—
192C22⋊C4—4782no—
193C42—4782no—
194C42—4784no—
195C42—4784no—
196C42—2394no—
197C23—4782no—
198C23—4782no—
199C23—4781no—
200C23—4781no—
201C23—2392no—
202C23C23×D23911yescharacteristic
203Q8—4788no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—4788no—
216C2×C4—4782no—
217C2×C4—4781no—
218C2×C4—4782no—
219C2×C4—4782no—
220C2×C4—4782no—
221C2×C4—4782no—
222C2×C4—4782no—
223C2×C4—2394no—
224C2×C4—2394no—
225C2×C4—2392no—
226C2×C4—2392no—
227C2×C4—2392no—
228C2×C4—2392no—
229C2×C4D4×D23912yes—
230C2×C4Q8×D23912yes—
231C22—9561no—
232C22—9562no—
233C22—9561no—
234C22—4784no—
235C22—4782no—
236C22C2×D4×D23911yescharacteristic
237C22C2×Q8×D23911yescharacteristic
238C22#41×D23912yes—
239C22#41×D23911yescharacteristic
240C22#41×D23912yes—
241C4—22no—
242C4—22no—
243C4—41no—
244C4—42no—
245C4—42no—
246C4—9561no—
247C4—4784no—
248C4—4784no—
249C4—4782no—
250C4—2394no—
251C2—9562no—
252C2C22⋊Q8×D23911yescharacteristic
253C2#2950528011yescharacteristic
254C2#2950530512yes—
255C2#2950532111yescharacteristic
256C2#2950532812yes—
subgroupG/H
center, FrattiniC23C23×D239
commutator, socle, cosocleC23×C239C24
Fitting#400×C239C2
prime radicalC23×D239C23
hypercenter#400D239
hypocenterC239#2396
LCSG ▷ C23×C239 ▷ C239
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#21439925C2semidirect
4. #29504706C2semidirect
6. #29504692C2semidirect
8. #29504623C2semidirect
9. #29504623C2semidirect
11. #400×C239C2semidirect
47. C2×C4×D239Q8semidirect
128. C239#2396semidirect
132. #400D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399252
C2×#214399182
#295047072
#295047062
#295046962
#295046922
#295046852
#295046232
#295046192
#400×C2392
#2396239