Finite Group Databasebeta

← C4⋊C4×C22⋊D61 #21448718

Subgroups — C4⋊C4×C22⋊D61 #21448718

Order 7808.

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⋊D61C212yesmaximal
2C2×C4×C22⋊D61C211yesmaximal, characteristic
3C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839657C212yesmaximal, complemented
5#16839635C212yesmaximal, complemented
6#16839633C212yesmaximal, complemented
7#16839631C211yesmaximal, characteristic, complemented
8#16839622C211yesmaximal, characteristic, complemented
9#16839619C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C4×D61C2212yes—
14C22×C4×D61C2211yescharacteristic
15C4×C22⋊D61—28no—
16C4×C22⋊D61C418yescomplemented
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×#11758196C2211yescharacteristic
23C4⋊C4×D61—24no—
24C2×C22⋊Dic61C2212yes—
25C2×C22⋊Dic61C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2211yescharacteristic
28C2×C4×Dic61C2212yes—
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33C23×C4×C61C2212yes—
34C23×C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61—24no—
36C2×C4⋊C4×C61C2211yescharacteristic
37C2×C4⋊C4×C61C2212yes—
38C2×C4⋊C4×C61C2211yescharacteristic
39C24×C61C2311yescharacteristic
40C23×D61C2311yescharacteristic
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—24no—
44C22×C4×C61—24no—
45C22×C4×C61—42no—
46C22×C4×C61C2×C414yescomplemented
47C22×C4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2312yes—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61C2×C414yes—
52C2×C22⋊D61D414yes—
53C2×C22⋊D61Q814yes—
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56C22×Dic61C2311yescharacteristic
57C22×Dic61C2311yescharacteristic
58C22×Dic61C2311yescharacteristic
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61—24no—
62C2×C4×D61—24no—
63C2×C4×D61—42no—
64C2×C4×D61C2×C414yescomplemented
65C4⋊C4×C61—24no—
66C4⋊C4×C61—22no—
67C4⋊C4×C61D414yescomplemented
68C22⋊Dic61—24no—
69C22⋊Dic61C2×C414yescomplemented
70#11758198—24no—
71#11758198C2×C414yescomplemented
72C4⋊Dic61—22no—
73C4⋊Dic61—22no—
74#11758196—24no—
75#11758196—24no—
76#11758196—42no—
77#11758196C2×C414yescomplemented
78C4×Dic61—24no—
79C4×Dic61C2×C414yescomplemented
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61C22×C412yes—
85C23×C61C2×D412yes—
86C23×C61C2×Q812yes—
87C23×C61C2411yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—21no—
92C22×D61C22×C412yes—
93C22×D61C2×D412yes—
94C22×D61C2×Q812yes—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—28no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—48no—
104C2×C4×C61C22×C412yes—
105C2×C4×C61C22×C412yes—
106C2×C4×C61C2×D414yes—
107C2×C4×C61C2×D412yes—
108C2×C4×C61#4112yes—
109C22⋊D61C4⋊C4116yesdirect product factor
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61C22×C412yes—
121C2×Dic61C22×C412yes—
122C2×Dic61C22×C412yes—
123C2×Dic61C2×D412yes—
124C2×Dic61C2×Q812yes—
125C4×D61—28no—
126C4×D61—48no—
127C22×C61—22no—
128C22×C61—22no—
129C22×C61—22no—
130C22×C61—22no—
131C22×C61—22no—
132C22×C61—22no—
133C22×C61C2×C4⋊C414yescomplemented
134C22×C61C23×C411yescharacteristic
135C22×C61C22×D411yescharacteristic
136C22×C61C22×D411yescharacteristic
137C22×C61C22×Q811yescharacteristic
138C22×C61C2×#4111yescharacteristic
139C22×C61H(5,𝔽2)11yescharacteristic
140C22×C612−1+411yescharacteristic
141C2×D61—22no—
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—22no—
147C2×D61C2×C4⋊C414yescomplemented
148C4×C61—22no—
149C4×C61—24no—
150C4×C61—42no—
151C4×C61C4×D414yescomplemented
152Dic61—22no—
153Dic61—22no—
154Dic61—42no—
155Dic61—42no—
156Dic61C2×C4⋊C414yescomplemented
157D4×C4⋊C4—611nomaximal, Sylow
158C2×C61—24no—
159C2×C61C22×C4⋊C411yescharacteristic
160C2×C61C2×C4×D411yescharacteristic
161C2×C61#52011yescharacteristic
162C2×C61D4211yescharacteristic
163C2×C61#54711yescharacteristic
164C2×C61D4×Q811yescharacteristic
165C2×C61#55411yescharacteristic
166D61—24no—
167C2×C4×D4—611no—
168C2×C4×D4—612no—
169C22×C4⋊C4—611no—
170C22×C4⋊C4D6111yescharacteristic, complemented
171#389—612no—
172#385—612no—
173#385—612no—
174#384—611no—
175#380—611no—
176#380—611no—
177C4×C4⋊C4—611no—
178C61D4×C4⋊C411yescharacteristic, complemented, Sylow
179C22×D4—611no—
180C23×C4—611no—
181C23×C4—612no—
182C23×C4C2×D6112yes—
183C23×C4C2×D6111yescharacteristic
184C4×D4—618no—
185C4×D4—1228no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—612no—
190C2×C4⋊C4—612no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—612no—
193C2×C4⋊C4—1224no—
194C2×C4⋊C4C2×D6111yescharacteristic
195C2×C4⋊C4C2×D6112yes—
196C2×C4⋊C4C2×D6111yescharacteristic
197C2×C22⋊C4—611no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4—612no—
200C2×C22⋊C4—612no—
201C2×C42—611no—
202C2×C42—612no—
203#95—612no—
204#95—612no—
205#95—612no—
206C24—611no—
207C24C22×D6111yescharacteristic
208C2×D4—614no—
209C2×D4—614no—
210C2×D4—614no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—42no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—614no—
220C22×C4—612no—
221C22×C4—612no—
222C22×C4—1224no—
223C22×C4—1222no—
224C22×C4—1222no—
225C22×C4—1224no—
226C22×C4—2442no—
227C22×C4C4×D6114yescomplemented
228C22×C4C22×D6112yes—
229C22×C4C22×D6111yescharacteristic
230C22×C4C22×D6112yes—
231C22×C4C22×D6111yescharacteristic
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—614no—
235C4⋊C4—1224no—
236C4⋊C4—1222no—
237C4⋊C4—1224no—
238C4⋊C4—1222no—
239C4⋊C4—2442no—
240C4⋊C4C22⋊D6114yesdirect product factor
241C22⋊C4—614no—
242C22⋊C4—614no—
243C22⋊C4—1224no—
244C22⋊C4—1224no—
245C42—614no—
246C42—1224no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—612no—
252C23—612no—
253C23—612no—
254C23—1221no—
255C23—1221no—
256C23—1221no—
257C23—1221no—
258C23C2×C4×D6112yes—
259C23D4×D6112yes—
260C23Q8×D6112yes—
261C23C23×D6111yescharacteristic
262D4—6116no—
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—612no—
273C2×C4—612no—
274C2×C4—612no—
275C2×C4—612no—
276C2×C4—612no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1228no—
282C2×C4—1222no—
283C2×C4—1222no—
284C2×C4—1222no—
285C2×C4—1222no—
286C2×C4—1222no—
287C2×C4—1222no—
288C2×C4—2448no—
289C2×C4C2×C4×D6112yes—
290C2×C4C2×C4×D6112yes—
291C2×C4#1175822212yes—
292C2×C4C2×C22⋊D6114yes—
293C2×C4C2×C22⋊D6112yes—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—614no—
301C22—1222no—
302C22—1222no—
303C22—1222no—
304C22—1222no—
305C22—1222no—
306C22—1222no—
307C22C4⋊C4×D6114yescomplemented
308C22C22×C4×D6111yescharacteristic
309C22C2×D4×D6111yescharacteristic
310C22C22×C22⋊D6111yescharacteristic
311C22C2×Q8×D6111yescharacteristic
312C22C2×#1175822211yescharacteristic
313C22#1451982211yescharacteristic
314C22#1451982511yescharacteristic
315C4—22no—
316C4—24no—
317C4—42no—
318C4—614no—
319C4—1222no—
320C4—1222no—
321C4—2442no—
322C4—2442no—
323C4C4×C22⋊D6114yescomplemented
324C2—24no—
325C2—1224no—
326C2C2×C4⋊C4×D6111yescharacteristic
327C2C2×C4×C22⋊D6111yescharacteristic
328C2#1684024311yescharacteristic
329C2D4×C22⋊D6111yescharacteristic
330C2#1684041311yescharacteristic
331C2Q8×C22⋊D6111yescharacteristic
332C2#1684046711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC22×C4⋊C4×C61C2
socleC23×C61C24
hypercenterC22×C4⋊C4D61
hypocenterC61D4×C4⋊C4
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D61C2semidirect
4. #16839657C2semidirect
5. #16839635C2semidirect
6. #16839633C2semidirect
7. #16839631C2semidirect
8. #16839622C2semidirect
9. #16839619C2semidirect
10. C4⋊C4×Dic61C2semidirect
11. C22×C4⋊C4×C61C2semidirect
16. C4×C22⋊D61C4semidirect
46. C22×C4×C61C2×C4semidirect
64. C2×C4×D61C2×C4semidirect
67. C4⋊C4×C61D4semidirect
69. C22⋊Dic61C2×C4semidirect
71. #11758198C2×C4semidirect
77. #11758196C2×C4semidirect
79. C4×Dic61C2×C4semidirect
109. C22⋊D61C4⋊C4direct (N × H)
133. C22×C61C2×C4⋊C4semidirect
147. C2×D61C2×C4⋊C4semidirect
151. C4×C61C4×D4semidirect
156. Dic61C2×C4⋊C4semidirect
170. C22×C4⋊C4D61semidirect
178. C61D4×C4⋊C4semidirect
227. C22×C4C4×D61semidirect
240. C4⋊C4C22⋊D61direct (N × H)
307. C22C4⋊C4×D61semidirect
323. C4C4×C22⋊D61semidirect