Finite Group Databasebeta

← C4⋊C4×C22⋊D227 #44402633

Subgroups — C4⋊C4×C22⋊D227 #44402633

Order 29056.

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⋊D227C212yesmaximal
2C2×C4×C22⋊D227C211yesmaximal, characteristic
3C2×C4⋊C4×D227C211yesmaximal, characteristic, complemented
4#28408927C212yesmaximal, complemented
5#28408905C212yesmaximal, complemented
6#28408903C212yesmaximal, complemented
7#28408901C211yesmaximal, characteristic, complemented
8#28408892C211yesmaximal, characteristic, complemented
9#28408889C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic227C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C227C211yesmaximal, characteristic, complemented
12C22×C22⋊D227C2211yescharacteristic
13C22×C4×D227C2212yes—
14C22×C4×D227C2211yescharacteristic
15C4×C22⋊D227—28no—
16C4×C22⋊D227C418yescomplemented
17C2×C4⋊Dic227C2211yescharacteristic
18C2×C4⋊Dic227C2211yescharacteristic
19C2×Dic227⋊C4C2212yes—
20C2×Dic227⋊C4C2212yes—
21C2×Dic227⋊C4C2212yes—
22C2×Dic227⋊C4C2211yescharacteristic
23C4⋊C4×D227—24no—
24C2×C22⋊Dic227C2212yes—
25C2×C22⋊Dic227C2211yescharacteristic
26C2×(C2×D227)⋊C4C2212yes—
27C2×(C2×D227)⋊C4C2211yescharacteristic
28C2×C4×Dic227C2212yes—
29C2×C4×Dic227C2211yescharacteristic
30C227⋊#95C2212yes—
31C227⋊#95C2212yes—
32C227⋊#95C2212yes—
33C23×C4×C227C2212yes—
34C23×C4×C227C2211yescharacteristic
35C2×C4⋊C4×C227—24no—
36C2×C4⋊C4×C227C2211yescharacteristic
37C2×C4⋊C4×C227C2212yes—
38C2×C4⋊C4×C227C2211yescharacteristic
39C23×D227C2311yescharacteristic
40C2×C22⋊D227C2×C414yes—
41C2×C22⋊D227D414yes—
42C2×C22⋊D227Q814yes—
43C22×Dic227C2312yes—
44C22×Dic227C2312yes—
45C22×Dic227C2311yescharacteristic
46C22×Dic227C2311yescharacteristic
47C22×Dic227C2311yescharacteristic
48C2×C4×D227—24no—
49C2×C4×D227—22no—
50C2×C4×D227—24no—
51C2×C4×D227—22no—
52C2×C4×D227—42no—
53C2×C4×D227C2×C414yescomplemented
54C4⋊Dic227—22no—
55C4⋊Dic227—22no—
56Dic227⋊C4—24no—
57Dic227⋊C4—24no—
58Dic227⋊C4—42no—
59Dic227⋊C4C2×C414yescomplemented
60C22⋊Dic227—24no—
61C22⋊Dic227C2×C414yescomplemented
62(C2×D227)⋊C4—24no—
63(C2×D227)⋊C4C2×C414yescomplemented
64C4×Dic227—24no—
65C4×Dic227C2×C414yescomplemented
66C24×C227C2311yescharacteristic
67C22×C4×C227—22no—
68C22×C4×C227—22no—
69C22×C4×C227—24no—
70C22×C4×C227—24no—
71C22×C4×C227—42no—
72C22×C4×C227C2×C414yescomplemented
73C22×C4×C227C2312yes—
74C22×C4×C227C2311yescharacteristic
75C22×C4×C227C2312yes—
76C22×C4×C227C2311yescharacteristic
77C4⋊C4×C227—24no—
78C4⋊C4×C227—22no—
79C4⋊C4×C227D414yescomplemented
80C22×D227—21no—
81C22×D227—21no—
82C22×D227—21no—
83C22×D227—21no—
84C22×D227C22×C412yes—
85C22×D227C2×D412yes—
86C22×D227C2×Q812yes—
87C22⋊D227C4⋊C4116yesdirect product factor
88C2×Dic227—21no—
89C2×Dic227—21no—
90C2×Dic227—21no—
91C2×Dic227—21no—
92C2×Dic227—22no—
93C2×Dic227—22no—
94C2×Dic227—22no—
95C2×Dic227—22no—
96C2×Dic227—22no—
97C2×Dic227—22no—
98C2×Dic227C22×C412yes—
99C2×Dic227C22×C412yes—
100C2×Dic227C22×C412yes—
101C2×Dic227C2×D412yes—
102C2×Dic227C2×Q812yes—
103C4×D227—28no—
104C4×D227—48no—
105C23×C227—21no—
106C23×C227—21no—
107C23×C227—21no—
108C23×C227—21no—
109C23×C227C22×C412yes—
110C23×C227C2×D412yes—
111C23×C227C2×Q812yes—
112C23×C227C2411yescharacteristic
113C2×C4×C227—21no—
114C2×C4×C227—22no—
115C2×C4×C227—21no—
116C2×C4×C227—22no—
117C2×C4×C227—28no—
118C2×C4×C227—22no—
119C2×C4×C227—22no—
120C2×C4×C227—22no—
121C2×C4×C227—48no—
122C2×C4×C227C22×C412yes—
123C2×C4×C227C22×C412yes—
124C2×C4×C227C2×D414yes—
125C2×C4×C227C2×D412yes—
126C2×C4×C227#4112yes—
127C22×C227—22no—
128C22×C227—22no—
129C22×C227—22no—
130C22×C227—22no—
131C22×C227—22no—
132C22×C227—22no—
133C22×C227C2×C4⋊C414yescomplemented
134C22×C227C23×C411yescharacteristic
135C22×C227C22×D411yescharacteristic
136C22×C227C22×D411yescharacteristic
137C22×C227C22×Q811yescharacteristic
138C22×C227C2×#4111yescharacteristic
139C22×C227H(5,𝔽2)11yescharacteristic
140C22×C2272−1+411yescharacteristic
141C2×D227—22no—
142C2×D227—22no—
143C2×D227—22no—
144C2×D227—22no—
145C2×D227—22no—
146C2×D227—22no—
147C2×D227C2×C4⋊C414yescomplemented
148C4×C227—22no—
149C4×C227—24no—
150C4×C227—42no—
151C4×C227C4×D414yescomplemented
152Dic227—22no—
153Dic227—22no—
154Dic227—42no—
155Dic227—42no—
156Dic227C2×C4⋊C414yescomplemented
157C2×C227—24no—
158C2×C227C22×C4⋊C411yescharacteristic
159C2×C227C2×C4×D411yescharacteristic
160C2×C227#52011yescharacteristic
161C2×C227D4211yescharacteristic
162C2×C227#54711yescharacteristic
163C2×C227D4×Q811yescharacteristic
164C2×C227#55411yescharacteristic
165D227—24no—
166C227D4×C4⋊C411yescharacteristic, complemented, Sylow
167D4×C4⋊C4—2271nomaximal, Sylow
168C2×C4×D4—2272no—
169C2×C4×D4—2271no—
170C22×C4⋊C4—2271no—
171C22×C4⋊C4D22711yescharacteristic, complemented
172#389—2272no—
173#385—2272no—
174#385—2272no—
175#384—2271no—
176#380—2271no—
177#380—2271no—
178C4×C4⋊C4—2271no—
179C22×D4—2271no—
180C23×C4—2272no—
181C23×C4—2271no—
182C23×C4C2×D22712yes—
183C23×C4C2×D22711yescharacteristic
184C4×D4—4548no—
185C4×D4—2278no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—4544no—
188C2×C4⋊C4—2272no—
189C2×C4⋊C4—2271no—
190C2×C4⋊C4—2272no—
191C2×C4⋊C4—2272no—
192C2×C4⋊C4—2271no—
193C2×C4⋊C4—2271no—
194C2×C4⋊C4C2×D22711yescharacteristic
195C2×C4⋊C4C2×D22712yes—
196C2×C4⋊C4C2×D22711yescharacteristic
197C2×C22⋊C4—2272no—
198C2×C22⋊C4—2272no—
199C2×C22⋊C4—2271no—
200C2×C22⋊C4—2271no—
201C2×C42—2272no—
202C2×C42—2271no—
203#95—2272no—
204#95—2272no—
205#95—2272no—
206C24—2271no—
207C24C22×D22711yescharacteristic
208C2×D4—2274no—
209C2×D4—2274no—
210C2×D4—2274no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—42no—
216C22×C4—9082no—
217C22×C4—4544no—
218C22×C4—4544no—
219C22×C4—4542no—
220C22×C4—4542no—
221C22×C4—2272no—
222C22×C4—2272no—
223C22×C4—2271no—
224C22×C4—2271no—
225C22×C4—2274no—
226C22×C4—2271no—
227C22×C4C4×D22714yescomplemented
228C22×C4C22×D22712yes—
229C22×C4C22×D22711yescharacteristic
230C22×C4C22×D22712yes—
231C22×C4C22×D22711yescharacteristic
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—9082no—
235C4⋊C4—4544no—
236C4⋊C4—4544no—
237C4⋊C4—4542no—
238C4⋊C4—4542no—
239C4⋊C4—2274no—
240C4⋊C4C22⋊D22714yesdirect product factor
241C22⋊C4—4544no—
242C22⋊C4—4544no—
243C22⋊C4—2274no—
244C22⋊C4—2274no—
245C42—4544no—
246C42—2274no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—4541no—
252C23—4541no—
253C23—4541no—
254C23—4541no—
255C23—2272no—
256C23—2272no—
257C23—2272no—
258C23C2×C4×D22712yes—
259C23D4×D22712yes—
260C23Q8×D22712yes—
261C23C23×D22711yescharacteristic
262D4—22716no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—28no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—48no—
272C2×C4—9088no—
273C2×C4—4542no—
274C2×C4—4542no—
275C2×C4—4542no—
276C2×C4—4542no—
277C2×C4—4542no—
278C2×C4—4542no—
279C2×C4—4541no—
280C2×C4—4541no—
281C2×C4—4541no—
282C2×C4—4541no—
283C2×C4—4548no—
284C2×C4—2272no—
285C2×C4—2272no—
286C2×C4—2272no—
287C2×C4—2272no—
288C2×C4—2272no—
289C2×C4C2×C4×D22712yes—
290C2×C4C2×C4×D22712yes—
291C2×C4C2×C22⋊D22714yes—
292C2×C4C2×C22⋊D22712yes—
293C2×C4#1681388412yes—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—4542no—
301C22—4542no—
302C22—4542no—
303C22—4542no—
304C22—4542no—
305C22—4542no—
306C22—2274no—
307C22C4⋊C4×D22714yescomplemented
308C22C22×C4×D22711yescharacteristic
309C22C2×D4×D22711yescharacteristic
310C22C22×C22⋊D22711yescharacteristic
311C22C2×Q8×D22711yescharacteristic
312C22C2×#1681388411yescharacteristic
313C22#2030033311yescharacteristic
314C22#2030033611yescharacteristic
315C4—24no—
316C4—22no—
317C4—42no—
318C4—9082no—
319C4—9082no—
320C4—4542no—
321C4—4542no—
322C4—2274no—
323C4C4×C22⋊D22714yescomplemented
324C2—24no—
325C2—4544no—
326C2C2×C4⋊C4×D22711yescharacteristic
327C2C2×C4×C22⋊D22711yescharacteristic
328C2#2840951311yescharacteristic
329C2D4×C22⋊D22711yescharacteristic
330C2#2840968311yescharacteristic
331C2Q8×C22⋊D22711yescharacteristic
332C2#2840973711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D227
commutatorC22×C227C23×C4
FittingC22×C4⋊C4×C227C2
socle, cosocleC23×C227C24
prime radicalC22×C22⋊D227C22
hypercenterC22×C4⋊C4D227
hypocenterC227D4×C4⋊C4
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D227C2semidirect
4. #28408927C2semidirect
5. #28408905C2semidirect
6. #28408903C2semidirect
7. #28408901C2semidirect
8. #28408892C2semidirect
9. #28408889C2semidirect
10. C4⋊C4×Dic227C2semidirect
11. C22×C4⋊C4×C227C2semidirect
16. C4×C22⋊D227C4semidirect
53. C2×C4×D227C2×C4semidirect
59. Dic227⋊C4C2×C4semidirect
61. C22⋊Dic227C2×C4semidirect
63. (C2×D227)⋊C4C2×C4semidirect
65. C4×Dic227C2×C4semidirect
72. C22×C4×C227C2×C4semidirect
79. C4⋊C4×C227D4semidirect
87. C22⋊D227C4⋊C4direct (N × H)
133. C22×C227C2×C4⋊C4semidirect
147. C2×D227C2×C4⋊C4semidirect
151. C4×C227C4×D4semidirect
156. Dic227C2×C4⋊C4semidirect
166. C227D4×C4⋊C4semidirect
171. C22×C4⋊C4D227semidirect
227. C22×C4C4×D227semidirect
240. C4⋊C4C22⋊D227direct (N × H)
307. C22C4⋊C4×D227semidirect
323. C4C4×C22⋊D227semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D2272
C2×C4⋊C4×D2272
#284089272
#284089052
#284089032
#284089012
#284088922
#284088892
C4⋊C4×Dic2272
C22×C4⋊C4×C2272
D4×C4⋊C4227