Finite Group Databasebeta

← C4⋊C4×C22⋊D239 #44487447

Subgroups — C4⋊C4×C22⋊D239 #44487447

Order 30592.

776 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D239C212yesmaximal
2C2×C4×C22⋊D239C211yesmaximal, characteristic
3C2×C4⋊C4×D239C211yesmaximal, characteristic, complemented
4#29504667C212yesmaximal, complemented
5#29504645C212yesmaximal, complemented
6#29504643C212yesmaximal, complemented
7#29504641C211yesmaximal, characteristic, complemented
8#29504632C211yesmaximal, characteristic, complemented
9#29504629C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic239C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C239C211yesmaximal, characteristic, complemented
12C22×C22⋊D239C2211yescharacteristic
13C22×C4×D239C2212yes—
14C22×C4×D239C2211yescharacteristic
15C4×C22⋊D239—28no—
16C4×C22⋊D239C418yescomplemented
17C2×C4⋊Dic239C2211yescharacteristic
18C2×C4⋊Dic239C2211yescharacteristic
19C2×Dic239⋊C4C2212yes—
20C2×Dic239⋊C4C2212yes—
21C2×Dic239⋊C4C2212yes—
22C2×Dic239⋊C4C2211yescharacteristic
23C4⋊C4×D239—24no—
24C2×C22⋊Dic239C2212yes—
25C2×C22⋊Dic239C2211yescharacteristic
26C2×(C2×D239)⋊C4C2212yes—
27C2×(C2×D239)⋊C4C2211yescharacteristic
28C2×C4×Dic239C2212yes—
29C2×C4×Dic239C2211yescharacteristic
30C239⋊#95C2212yes—
31C239⋊#95C2212yes—
32C239⋊#95C2212yes—
33C23×C4×C239C2212yes—
34C23×C4×C239C2211yescharacteristic
35C2×C4⋊C4×C239—24no—
36C2×C4⋊C4×C239C2211yescharacteristic
37C2×C4⋊C4×C239C2212yes—
38C2×C4⋊C4×C239C2211yescharacteristic
39C23×D239C2311yescharacteristic
40C2×C22⋊D239C2×C414yes—
41C2×C22⋊D239D414yes—
42C2×C22⋊D239Q814yes—
43C22×Dic239C2312yes—
44C22×Dic239C2312yes—
45C22×Dic239C2311yescharacteristic
46C22×Dic239C2311yescharacteristic
47C22×Dic239C2311yescharacteristic
48C2×C4×D239—24no—
49C2×C4×D239—22no—
50C2×C4×D239—24no—
51C2×C4×D239—22no—
52C2×C4×D239—42no—
53C2×C4×D239C2×C414yescomplemented
54C4⋊Dic239—22no—
55C4⋊Dic239—22no—
56Dic239⋊C4—24no—
57Dic239⋊C4—24no—
58Dic239⋊C4—42no—
59Dic239⋊C4C2×C414yescomplemented
60C22⋊Dic239—24no—
61C22⋊Dic239C2×C414yescomplemented
62(C2×D239)⋊C4—24no—
63(C2×D239)⋊C4C2×C414yescomplemented
64C4×Dic239—24no—
65C4×Dic239C2×C414yescomplemented
66C24×C239C2311yescharacteristic
67C22×C4×C239—22no—
68C22×C4×C239—22no—
69C22×C4×C239—24no—
70C22×C4×C239—24no—
71C22×C4×C239—42no—
72C22×C4×C239C2×C414yescomplemented
73C22×C4×C239C2312yes—
74C22×C4×C239C2311yescharacteristic
75C22×C4×C239C2312yes—
76C22×C4×C239C2311yescharacteristic
77C4⋊C4×C239—24no—
78C4⋊C4×C239—22no—
79C4⋊C4×C239D414yescomplemented
80C22×D239—21no—
81C22×D239—21no—
82C22×D239—21no—
83C22×D239—21no—
84C22×D239C22×C412yes—
85C22×D239C2×D412yes—
86C22×D239C2×Q812yes—
87C22⋊D239C4⋊C4116yesdirect product factor
88C2×Dic239—21no—
89C2×Dic239—21no—
90C2×Dic239—21no—
91C2×Dic239—21no—
92C2×Dic239—22no—
93C2×Dic239—22no—
94C2×Dic239—22no—
95C2×Dic239—22no—
96C2×Dic239—22no—
97C2×Dic239—22no—
98C2×Dic239C22×C412yes—
99C2×Dic239C22×C412yes—
100C2×Dic239C22×C412yes—
101C2×Dic239C2×D412yes—
102C2×Dic239C2×Q812yes—
103C4×D239—28no—
104C4×D239—48no—
105C23×C239—21no—
106C23×C239—21no—
107C23×C239—21no—
108C23×C239—21no—
109C23×C239C22×C412yes—
110C23×C239C2×D412yes—
111C23×C239C2×Q812yes—
112C23×C239C2411yescharacteristic
113C2×C4×C239—21no—
114C2×C4×C239—22no—
115C2×C4×C239—21no—
116C2×C4×C239—22no—
117C2×C4×C239—28no—
118C2×C4×C239—22no—
119C2×C4×C239—22no—
120C2×C4×C239—22no—
121C2×C4×C239—48no—
122C2×C4×C239C22×C412yes—
123C2×C4×C239C22×C412yes—
124C2×C4×C239C2×D414yes—
125C2×C4×C239C2×D412yes—
126C2×C4×C239#4112yes—
127C22×C239—22no—
128C22×C239—22no—
129C22×C239—22no—
130C22×C239—22no—
131C22×C239—22no—
132C22×C239—22no—
133C22×C239C2×C4⋊C414yescomplemented
134C22×C239C23×C411yescharacteristic
135C22×C239C22×D411yescharacteristic
136C22×C239C22×D411yescharacteristic
137C22×C239C22×Q811yescharacteristic
138C22×C239C2×#4111yescharacteristic
139C22×C239H(5,𝔽2)11yescharacteristic
140C22×C2392−1+411yescharacteristic
141C2×D239—22no—
142C2×D239—22no—
143C2×D239—22no—
144C2×D239—22no—
145C2×D239—22no—
146C2×D239—22no—
147C2×D239C2×C4⋊C414yescomplemented
148C4×C239—22no—
149C4×C239—24no—
150C4×C239—42no—
151C4×C239C4×D414yescomplemented
152Dic239—22no—
153Dic239—22no—
154Dic239—42no—
155Dic239—42no—
156Dic239C2×C4⋊C414yescomplemented
157C2×C239—24no—
158C2×C239C22×C4⋊C411yescharacteristic
159C2×C239C2×C4×D411yescharacteristic
160C2×C239#52011yescharacteristic
161C2×C239D4211yescharacteristic
162C2×C239#54711yescharacteristic
163C2×C239D4×Q811yescharacteristic
164C2×C239#55411yescharacteristic
165D239—24no—
166C239D4×C4⋊C411yescharacteristic, complemented, Sylow
167D4×C4⋊C4—2391nomaximal, Sylow
168C2×C4×D4—2392no—
169C2×C4×D4—2391no—
170C22×C4⋊C4—2391no—
171C22×C4⋊C4D23911yescharacteristic, complemented
172#389—2392no—
173#385—2392no—
174#385—2392no—
175#384—2391no—
176#380—2391no—
177#380—2391no—
178C4×C4⋊C4—2391no—
179C22×D4—2391no—
180C23×C4—2392no—
181C23×C4—2391no—
182C23×C4C2×D23912yes—
183C23×C4C2×D23911yescharacteristic
184C4×D4—4788no—
185C4×D4—2398no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—4784no—
188C2×C4⋊C4—2392no—
189C2×C4⋊C4—2391no—
190C2×C4⋊C4—2392no—
191C2×C4⋊C4—2392no—
192C2×C4⋊C4—2391no—
193C2×C4⋊C4—2391no—
194C2×C4⋊C4C2×D23911yescharacteristic
195C2×C4⋊C4C2×D23912yes—
196C2×C4⋊C4C2×D23911yescharacteristic
197C2×C22⋊C4—2392no—
198C2×C22⋊C4—2392no—
199C2×C22⋊C4—2391no—
200C2×C22⋊C4—2391no—
201C2×C42—2392no—
202C2×C42—2391no—
203#95—2392no—
204#95—2392no—
205#95—2392no—
206C24—2391no—
207C24C22×D23911yescharacteristic
208C2×D4—2394no—
209C2×D4—2394no—
210C2×D4—2394no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—42no—
216C22×C4—9562no—
217C22×C4—4784no—
218C22×C4—4784no—
219C22×C4—4782no—
220C22×C4—4782no—
221C22×C4—2392no—
222C22×C4—2392no—
223C22×C4—2391no—
224C22×C4—2391no—
225C22×C4—2394no—
226C22×C4—2391no—
227C22×C4C4×D23914yescomplemented
228C22×C4C22×D23912yes—
229C22×C4C22×D23911yescharacteristic
230C22×C4C22×D23912yes—
231C22×C4C22×D23911yescharacteristic
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—9562no—
235C4⋊C4—4784no—
236C4⋊C4—4784no—
237C4⋊C4—4782no—
238C4⋊C4—4782no—
239C4⋊C4—2394no—
240C4⋊C4C22⋊D23914yesdirect product factor
241C22⋊C4—4784no—
242C22⋊C4—4784no—
243C22⋊C4—2394no—
244C22⋊C4—2394no—
245C42—4784no—
246C42—2394no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—4781no—
252C23—4781no—
253C23—4781no—
254C23—4781no—
255C23—2392no—
256C23—2392no—
257C23—2392no—
258C23C2×C4×D23912yes—
259C23D4×D23912yes—
260C23Q8×D23912yes—
261C23C23×D23911yescharacteristic
262D4—23916no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—28no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—48no—
272C2×C4—9568no—
273C2×C4—4782no—
274C2×C4—4782no—
275C2×C4—4782no—
276C2×C4—4782no—
277C2×C4—4782no—
278C2×C4—4782no—
279C2×C4—4781no—
280C2×C4—4781no—
281C2×C4—4781no—
282C2×C4—4781no—
283C2×C4—4788no—
284C2×C4—2392no—
285C2×C4—2392no—
286C2×C4—2392no—
287C2×C4—2392no—
288C2×C4—2392no—
289C2×C4C2×C4×D23912yes—
290C2×C4C2×C4×D23912yes—
291C2×C4C2×C22⋊D23914yes—
292C2×C4C2×C22⋊D23912yes—
293C2×C4#1683854812yes—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—4782no—
301C22—4782no—
302C22—4782no—
303C22—4782no—
304C22—4782no—
305C22—4782no—
306C22—2394no—
307C22C4⋊C4×D23914yescomplemented
308C22C22×C4×D23911yescharacteristic
309C22C2×D4×D23911yescharacteristic
310C22C22×C22⋊D23911yescharacteristic
311C22C2×Q8×D23911yescharacteristic
312C22C2×#1683854811yescharacteristic
313C22#2144000511yescharacteristic
314C22#2144000811yescharacteristic
315C4—24no—
316C4—22no—
317C4—42no—
318C4—9562no—
319C4—9562no—
320C4—4782no—
321C4—4782no—
322C4—2394no—
323C4C4×C22⋊D23914yescomplemented
324C2—24no—
325C2—4784no—
326C2C2×C4⋊C4×D23911yescharacteristic
327C2C2×C4×C22⋊D23911yescharacteristic
328C2#2950525311yescharacteristic
329C2D4×C22⋊D23911yescharacteristic
330C2#2950542311yescharacteristic
331C2Q8×C22⋊D23911yescharacteristic
332C2#2950547711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
FittingC22×C4⋊C4×C239C2
socle, cosocleC23×C239C24
prime radicalC22×C22⋊D239C22
hypercenterC22×C4⋊C4D239
hypocenterC239D4×C4⋊C4
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D239C2semidirect
4. #29504667C2semidirect
5. #29504645C2semidirect
6. #29504643C2semidirect
7. #29504641C2semidirect
8. #29504632C2semidirect
9. #29504629C2semidirect
10. C4⋊C4×Dic239C2semidirect
11. C22×C4⋊C4×C239C2semidirect
16. C4×C22⋊D239C4semidirect
53. C2×C4×D239C2×C4semidirect
59. Dic239⋊C4C2×C4semidirect
61. C22⋊Dic239C2×C4semidirect
63. (C2×D239)⋊C4C2×C4semidirect
65. C4×Dic239C2×C4semidirect
72. C22×C4×C239C2×C4semidirect
79. C4⋊C4×C239D4semidirect
87. C22⋊D239C4⋊C4direct (N × H)
133. C22×C239C2×C4⋊C4semidirect
147. C2×D239C2×C4⋊C4semidirect
151. C4×C239C4×D4semidirect
156. Dic239C2×C4⋊C4semidirect
166. C239D4×C4⋊C4semidirect
171. C22×C4⋊C4D239semidirect
227. C22×C4C4×D239semidirect
240. C4⋊C4C22⋊D239direct (N × H)
307. C22C4⋊C4×D239semidirect
323. C4C4×C22⋊D239semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D2392
C2×C4⋊C4×D2392
#295046672
#295046452
#295046432
#295046412
#295046322
#295046292
C4⋊C4×Dic2392
C22×C4⋊C4×C2392
D4×C4⋊C4239