Finite Group Databasebeta

← #344×D239 #44484288

Subgroups — #344×D239 #44484288

Order 30592.

388 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×D239C211yesmaximal, characteristic
2C2×M16×D239C211yesmaximal, characteristic
3#117×D239C211yesmaximal, characteristic
4#29504544C211yesmaximal, characteristic, complemented
5#29504543C211yesmaximal, characteristic, complemented
6#29504542C211yesmaximal, characteristic, complemented
7#344×C239C211yesmaximal, characteristic, complemented
8C22×C4×D239C2211yescharacteristic
9C2×#16838532C2211yescharacteristic
10C2×#16838532C2211yescharacteristic
11C2×#16838531—21no—
12C2×#16838531C412yescomplemented
13M16×D239—21no—
14M16×D239—21no—
15M16×D239—21no—
16M16×D239—21no—
17M16×D239—21no—
18M16×D239—21no—
19M16×D239C412yescomplemented
20M16×D239C412yescomplemented
21C2×C8×D239—21no—
22C2×C8×D239C412yescomplemented
23#21439919C2211yescharacteristic
24#21439918—21no—
25#21439917—21no—
26#21439916C412yes—
27C4⋊C4×D239—21no—
28C22⋊C4×D239C412yes—
29C42×D239—21no—
30C2×M16×C239C2211yescharacteristic
31C2×M16×C239C2211yescharacteristic
32#117×C239C2211yescharacteristic
33C23×D239C2×C411yescharacteristic
34C22×Dic239C2×C411yescharacteristic
35C2×C4×D239—22no—
36C2×C4×D239C2×C411yescharacteristic
37C2×C4×D239C2×C411yescharacteristic
38C2×C4×D239C2×C411yescharacteristic
39C2×C4×D239C2×C411yescharacteristic
40C2×C4×D239D411yescharacteristic
41C2×C4×D239D411yescharacteristic
42C2×C4×D239D411yescharacteristic
43C2×C4×D239D411yescharacteristic
44C2×C4×D239D411yescharacteristic
45C2×C4×D239D411yescharacteristic
46C2×C4×D239Q811yescharacteristic
47C2×C4×D239Q811yescharacteristic
48#16838532—21no—
49#16838532—21no—
50#16838532—21no—
51#16838532C2×C412yescomplemented
52#16838531—22no—
53#16838531—22no—
54#16838531—22no—
55#16838531—22no—
56C2×C239⋊C8—21no—
57C2×C239⋊C8C2×C412yescomplemented
58C8×D239—22no—
59C8×D239—22no—
60C8×D239—22no—
61C8×D239—22no—
62C4⋊Dic239—21no—
63Dic239⋊C4—22no—
64C22⋊Dic239C2×C412yes—
65(C2×D239)⋊C4—22no—
66C4×Dic239—22no—
67C4×Dic239—21no—
68C22×C4×C239C2311yescharacteristic
69M16×C239—21no—
70M16×C239—21no—
71M16×C239—21no—
72M16×C239C2×C412yescomplemented
73C2×C8×C239—21no—
74C2×C8×C239C2×C412yescomplemented
75C4⋊C4×C239—21no—
76C22⋊C4×C239C2×C412yes—
77C42×C239—21no—
78C22×D239—42no—
79C22×D239C4211yescharacteristic
80C22×D239C4211yescharacteristic
81C22×D239C22⋊C411yescharacteristic
82C22×D239C22⋊C411yescharacteristic
83C22×D239C4⋊C411yescharacteristic
84C22×D239C4⋊C411yescharacteristic
85C2×Dic239—22no—
86C2×Dic239C4211yescharacteristic
87C2×Dic239C4211yescharacteristic
88C2×Dic239C22⋊C411yescharacteristic
89C2×Dic239C22⋊C411yescharacteristic
90C2×Dic239C4⋊C411yescharacteristic
91C2×Dic239C4⋊C411yescharacteristic
92C4×D239—44no—
93C4×D239C22⋊C411yescharacteristic
94C4×D239C22⋊C411yescharacteristic
95C4×D239C22⋊C411yescharacteristic
96C4×D239C22⋊C411yescharacteristic
97C4×D239C22⋊C411yescharacteristic
98C4×D239C22⋊C411yescharacteristic
99C4×D239C22⋊C411yescharacteristic
100C4×D239C22⋊C411yescharacteristic
101C4×D239C4⋊C411yescharacteristic
102C4×D239C4⋊C411yescharacteristic
103C4×D239C4⋊C411yescharacteristic
104C4×D239C4⋊C411yescharacteristic
105C4×D239C4⋊C411yescharacteristic
106C4×D239C4⋊C411yescharacteristic
107C4×D239C4⋊C411yescharacteristic
108C4×D239C4⋊C411yescharacteristic
109C239⋊C8—22no—
110C239⋊C8—22no—
111C23×C239C22×C411yescharacteristic
112C2×C4×C239—22no—
113C2×C4×C239C22×C411yescharacteristic
114C2×C4×C239C22×C411yescharacteristic
115C2×C4×C239C2×D411yescharacteristic
116C2×C4×C239C2×D411yescharacteristic
117C2×C4×C239C2×D411yescharacteristic
118C2×C4×C239C2×Q811yescharacteristic
119C8×C239—22no—
120C8×C239—22no—
121C22×C239—41no—
122C22×C239C2×C4211yescharacteristic
123C22×C239C2×C22⋊C411yescharacteristic
124C22×C239C2×C4⋊C411yescharacteristic
125C2×D239—22no—
126C2×D239—22no—
127C2×D239—22no—
128C2×D239—41no—
129C2×D239—41no—
130C2×D239—41no—
131C2×D239#9511yescharacteristic
132C2×D239#9511yescharacteristic
133C2×D239#9511yescharacteristic
134C2×D239#9511yescharacteristic
135C4×C239—42no—
136C4×C239C2×C22⋊C411yescharacteristic
137C4×C239C2×C22⋊C411yescharacteristic
138C4×C239C2×C4⋊C411yescharacteristic
139C4×C239C2×C4⋊C411yescharacteristic
140Dic239—42no—
141Dic239#9511yescharacteristic
142Dic239#9511yescharacteristic
143Dic239#9511yescharacteristic
144Dic239#9511yescharacteristic
145C2×C239—21no—
146C2×C239—21no—
147C2×C239—21no—
148C2×C239C2×#9511yescharacteristic
149D239—21no—
150D239—21no—
151D239—21no—
152D239#34412yesdirect product factor
153C239C2×#34411yescharacteristic, complemented, Sylow
154C2×#344—2391nomaximal, Sylow
155C22×M16—2391no—
156C22×M16—2391no—
157C2×#117—2391no—
158#344—2391no—
159#344—2391no—
160#344—2391no—
161#344D23911yescharacteristic, direct product factor
162C23×C4—2391no—
163C2×M16—4781no—
164C2×M16—4781no—
165C2×M16—4781no—
166C2×M16—4781no—
167C2×M16—4781no—
168C2×M16—4781no—
169C2×M16—4781no—
170C2×M16—2391no—
171C2×M16—2392no—
172C2×M16—2392no—
173C2×M16—2391no—
174C2×M16—2392no—
175C2×M16C2×D23911yescharacteristic
176C2×M16C2×D23911yescharacteristic
177C22×C8—4781no—
178C22×C8—2392no—
179#117—4781no—
180#117—4781no—
181#117—2391no—
182#117—2392no—
183#117C2×D23911yescharacteristic
184C2×C4⋊C4—4781no—
185C2×C22⋊C4—2392no—
186C2×C42—4781no—
187C24—2391no—
188C22×C4—4782no—
189C22×C4—2391no—
190C22×C4—2391no—
191C22×C4—2391no—
192C22×C4—2391no—
193C22×C4—2391no—
194C22×C4—2391no—
195C22×C4—2391no—
196C22×C4—2391no—
197C22×C4—2391no—
198C22×C4—2391no—
199C22×C4—2391no—
200C22×C4—2391no—
201C22×C4—2391no—
202C22×C4C22×D23911yescharacteristic
203M16—21no—
204M16—21no—
205M16—21no—
206M16—4782no—
207M16—4782no—
208M16—4782no—
209M16—4782no—
210M16—4781no—
211M16—4781no—
212M16—4781no—
213M16—2392no—
214M16C4×D23912yescomplemented
215C2×C8—21no—
216C2×C8—4782no—
217C2×C8—4782no—
218C2×C8—4782no—
219C2×C8—4782no—
220C2×C8—4781no—
221C2×C8—2392no—
222C2×C8C4×D23912yescomplemented
223C4⋊C4—21no—
224C4⋊C4—4782no—
225C4⋊C4—4781no—
226C22⋊C4—4782no—
227C22⋊C4—2392no—
228C22⋊C4C4×D23912yes—
229C42—21no—
230C42—4782no—
231C42—4781no—
232C23—9562no—
233C23—2391no—
234C23—2391no—
235C23—2391no—
236C23—2391no—
237C23—2391no—
238C23—2391no—
239C23C2×C4×D23911yescharacteristic
240C2×C4—22no—
241C2×C4—9564no—
242C2×C4—4782no—
243C2×C4—2391no—
244C2×C4—2391no—
245C2×C4—2391no—
246C2×C4—2391no—
247C2×C4—2391no—
248C2×C4—2391no—
249C2×C4—2391no—
250C2×C4—2391no—
251C2×C4—2391no—
252C2×C4—2391no—
253C2×C4—2391no—
254C2×C4—2391no—
255C2×C4—2391no—
256C2×C4—2391no—
257C2×C4—2391no—
258C2×C4—2391no—
259C2×C4—2391no—
260C2×C4—2391no—
261C2×C4—2391no—
262C2×C4—2391no—
263C2×C4—2391no—
264C2×C4—2391no—
265C2×C4C2×C4×D23911yescharacteristic
266C2×C4C2×C4×D23911yescharacteristic
267C2×C4D4×D23911yescharacteristic
268C2×C4D4×D23911yescharacteristic
269C2×C4D4×D23911yescharacteristic
270C2×C4Q8×D23911yescharacteristic
271C8—22no—
272C8—22no—
273C8—4782no—
274C8—4782no—
275C22—41no—
276C22—9561no—
277C22—9561no—
278C22—9561no—
279C22—4782no—
280C22—4782no—
281C22—4782no—
282C22—2391no—
283C22—2391no—
284C22—2391no—
285C22—2391no—
286C22C42×D23911yescharacteristic
287C22C22⋊C4×D23911yescharacteristic
288C22C4⋊C4×D23911yescharacteristic
289C4—42no—
290C4—9562no—
291C4—2391no—
292C4—2391no—
293C4—2391no—
294C4—2391no—
295C4C22⋊C4×D23911yescharacteristic
296C4C22⋊C4×D23911yescharacteristic
297C4C4⋊C4×D23911yescharacteristic
298C4C4⋊C4×D23911yescharacteristic
299C2—21no—
300C2—21no—
301C2—21no—
302C2—4781no—
303C2—4781no—
304C2—4781no—
305C2—2392no—
306C2#95×D23911yescharacteristic
subgroupG/H
centerC4C22⋊C4×D239
commutatorC22×C239C2×C42
FrattiniC22×C4C22×D239
Fitting#344×C239C2
socleC2×C239C2×#95
prime radicalC23×D239C2×C4
cosocleC22×C4×C239C23
hypercenter#344D239
hypocenterC239C2×#344
LCSG ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. #29504544C2semidirect
5. #29504543C2semidirect
6. #29504542C2semidirect
7. #344×C239C2semidirect
12. C2×#16838531C4semidirect
19. M16×D239C4semidirect
20. M16×D239C4semidirect
22. C2×C8×D239C4semidirect
51. #16838532C2×C4semidirect
57. C2×C239⋊C8C2×C4semidirect
72. M16×C239C2×C4semidirect
74. C2×C8×C239C2×C4semidirect
152. D239#344direct (N × H)
153. C239C2×#344semidirect
161. #344D239direct (N × H)
214. M16C4×D239semidirect
222. C2×C8C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D2392
#117×D2392
#295045442
#295045432
#295045422
#344×C2392
C2×#344239