Finite Group Databasebeta

← C4×#10623329 #14912008

Subgroups — C4×#10623329 #14912008

Order 2816.

4186 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623329C212yesmaximal
2#13070977C218yesmaximal, complemented
3#13070973C212yesmaximal, complemented
4#13070969C214yesmaximal, complemented
5C4×D4×Dic11C218yesmaximal, complemented
6C4×#66979C212yesmaximal, complemented
7C2×C4×C22⋊Dic11C214yesmaximal, complemented
8C22×C4×D4×C11C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11C2212yes—
11C2×C4×D4×C11C4116yescomplemented
12C2×C4×D4×C11C2214yes—
13C2×C4×D4×C11C2214yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2218yes—
18#10623329C4132yesdirect product factor
19C2×D4×Dic11C22116yes—
20C2×#66979C2214yes—
21C22×C4×Dic11C2218yescomplemented
22C4×C22⋊Dic11C2214yes—
23C4×C22⋊Dic11C2218yes—
24C4×C22⋊Dic11C2214yes—
25C4×C22⋊Dic11C2218yescomplemented
26C4×C22⋊Dic11C2218yescomplemented
27C2×C11⋊#95C2218yescomplemented
28C4⋊C4×Dic11C22116yescomplemented
29C22⋊C4×Dic11C22132yescomplemented
30C4×C4⋊Dic11C2214yescomplemented
31C4×C4⋊Dic11C2214yescomplemented
32#10622545C2214yescomplemented
33C42×Dic11C2214yescomplemented
34C25×C11C2312yes—
35C22×D4×C11C2×C4116yes—
36C22×D4×C11C2×C418yes—
37C22×D4×C11C2314yes—
38C23×C4×C11—48no—
39C23×C4×C11C2×C4116yescomplemented
40C23×C4×C11C2314yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2314yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C23116yes—
47C4×D4×C11C2×C4132yescomplemented
48C4×D4×C11C2×C4132yescomplemented
49C2×C11×C4⋊C4C2×C418yescomplemented
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C22⋊C4C2×C4116yescomplemented
52C2×C11×C22⋊C4C2318yes—
53C2×C42×C11C2×C418yescomplemented
54C2×C42×C11C2312yes—
55C2×C42×C11C2312yes—
56C2×C22⋊Dic11C2×C4164yescomplemented
57C2×C22⋊Dic11C2318yes—
58C2×C22⋊Dic11C23116yes—
59D4×Dic11C2×C41128yescomplemented
60#66979C2×C4132yescomplemented
61C2×C4⋊Dic11C2318yes—
62C2×C4×Dic11—416no—
63C2×C4×Dic11C2318yes—
64C2×C4×Dic11C2318yes—
65C2×C4×Dic11C23116yes—
66C2×C4×Dic11C2318yes—
67C11⋊#95C2318yes—
68C11⋊#95C2318yes—
69C11⋊#95C23116yes—
70C4×#518—111nomaximal, Sylow
71C24×C11—44no—
72C24×C11—44no—
73C24×C11C22×C4116yes—
74C24×C11C22×C418yes—
75C24×C11C2411yescharacteristic
76C24×C11C2414yes—
77C2×D4×C11C42164yescomplemented
78C2×D4×C11C22×C4132yes—
79C2×D4×C11C22×C4116yes—
80C22×C4×C11—216no—
81C22×C4×C11—24no—
82C22×C4×C11—432no—
83C22×C4×C11—44no—
84C22×C4×C11—48no—
85C22×C4×C11—42no—
86C22×C4×C11C22×C414yes—
87C22×C4×C11C22×C4116yes—
88C22×C4×C11C22×C414yes—
89C22×C4×C11C22×C418yes—
90C22×C4×C11C22×C4116yes—
91C22×C4×C11C22×C418yes—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C2411yescharacteristic
94C22×C4×C11C2412yes—
95C22×C4×C11C2414yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—416no—
99C22×Dic11—416no—
100C22×Dic11C22×C4164yescomplemented
101C22×Dic11C24116yes—
102C11×C4⋊C4C22×C4116yes—
103C11×C22⋊C4C22×C4132yes—
104C42×C11C22×C418yes—
105C42×C11C22×C418yes—
106C22⋊Dic11C22×C4132yes—
107C22⋊Dic11C22×C4164yescomplemented
108C4⋊Dic11C22×C4132yescomplemented
109C4×Dic11—216no—
110C4×Dic11—416no—
111C4×Dic11—48no—
112C4×Dic11C22×C4132yescomplemented
113C2×#518—112no—
114C22×C4×D4D1111yescharacteristic
115#2275—118no—
116#2274—112no—
117#2273—114no—
118C42×D4—118no—
119C4×#117—112no—
120C2×C4×C22⋊C4—114no—
121C23×C11—28no—
122C23×C11—22no—
123C23×C11—28no—
124C23×C11—22no—
125C23×C11—48no—
126C23×C11—432no—
127C23×C11—48no—
128C23×C11C2×C42132yescomplemented
129C23×C11C23×C414yes—
130C23×C11C23×C4116yes—
131C23×C11C23×C418yes—
132C23×C11C23×C412yes—
133C23×C11C2511yescharacteristic
134D4×C11C2×C42164yescomplemented
135C2×C4×C11—28no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—28no—
139C2×C4×C11—232no—
140C2×C4×C11—416no—
141C2×C4×C11—48no—
142C2×C4×C11—44no—
143C2×C4×C11C2×C42116yescomplemented
144C2×C4×C11C23×C418yes—
145C2×C4×C11C23×C414yes—
146C2×C4×C11C23×C412yes—
147C2×C4×C11C23×C418yes—
148C2×C4×C11C23×C412yes—
149C2×C4×C11C23×C414yes—
150C2×C4×C11H(5,𝔽2)14yes—
151C2×Dic11—216no—
152C2×Dic11—216no—
153C2×Dic11—464no—
154C2×Dic11C23×C4132yes—
155C23×D4C2×D1111yescharacteristic
156C24×C4C2×D1112yes—
157#518—1132no—
158C2×C4×D4—1116no—
159C2×C4×D4Dic11116yescomplemented
160C2×C4×D4C2×D1114yes—
161C2×C4×D4C2×D1114yes—
162C2×#117—114no—
163C22×C4⋊C4C2×D1111yescharacteristic
164C22×C22⋊C4—118no—
165C22×C22⋊C4C2×D1112yes—
166C22×C42—118no—
167C22×C42C2×D1111yescharacteristic
168C4×C4⋊C4—1116no—
169C4×C4⋊C4—114no—
170C4×C4⋊C4—114no—
171C4×C22⋊C4—114no—
172C4×C22⋊C4—118no—
173C4×C22⋊C4—114no—
174C4×C22⋊C4—118no—
175C4×C22⋊C4—118no—
176C4×C22⋊C4—1132no—
177#376—114no—
178C2×#95—118no—
179C43—114no—
180C22×C11—22no—
181C22×C11—28no—
182C22×C11—22no—
183C22×C11—28no—
184C22×C11—28no—
185C22×C11—232no—
186C22×C11—432no—
187C22×C11C22×C4214yes—
188C22×C11C22×C42116yes—
189C22×C11C24×C412yes—
190C22×C11C24×C411yescharacteristic
191C22×C11C2×H(5,𝔽2)12yes—
192C22×C11#58512yes—
193C4×C11—22no—
194C4×C11—28no—
195C4×C11—24no—
196C4×C11C22×C4218yes—
197C4×C11#51814yescomplemented
198Dic11—232no—
199C25C22×D1112yes—
200C22×D4C4×D11116yes—
201C22×D4C2×Dic1118yes—
202C22×D4C22×D1114yes—
203C23×C4—48no—
204C23×C4—1116no—
205C23×C4C2×Dic11116yescomplemented
206C23×C4C22×D1114yes—
207C23×C4C22×D1111yescharacteristic
208C23×C4C22×D1111yescharacteristic
209C23×C4C22×D1112yes—
210C23×C4C22×D1114yes—
211C23×C4C22×D1111yescharacteristic
212C4×D4—11128no—
213C4×D4C2×Dic11132yescomplemented
214C4×D4C2×Dic11132yescomplemented
215#117—1132no—
216C2×C4⋊C4—118no—
217C2×C4⋊C4C2×Dic1118yescomplemented
218C2×C4⋊C4C22×D1114yes—
219C2×C22⋊C4—1164no—
220C2×C22⋊C4—118no—
221C2×C22⋊C4—1116no—
222C2×C22⋊C4C2×Dic11116yescomplemented
223C2×C22⋊C4C22×D1118yes—
224C2×C42—118no—
225C2×C42—118no—
226C2×C42—118no—
227C2×C42—1116no—
228C2×C42—4416no—
229C2×C42C2×Dic1118yescomplemented
230C2×C42C22×D1112yes—
231C2×C42C22×D1112yes—
232#95—118no—
233#95—1116no—
234#95—118no—
235C2×C11—24no—
236C2×C11—216no—
237C2×C11C23×C4211yescharacteristic
238C2×C11C2×#51811yescharacteristic
239C2×C11#342811yescharacteristic
240C2×C11C4×H(5,𝔽2)14yes—
241C24—44no—
242C24—44no—
243C24C2×C4×D11116yes—
244C24C22×Dic1118yes—
245C24C23×D1111yescharacteristic
246C24C23×D1114yes—
247C2×D4C4×Dic11164yescomplemented
248C2×D4C2×C4×D11132yes—
249C2×D4C22×Dic11116yes—
250C22×C4—216no—
251C22×C4—24no—
252C22×C4—432no—
253C22×C4—44no—
254C22×C4—48no—
255C22×C4—42no—
256C22×C4—1116no—
257C22×C4—1164no—
258C22×C4—4416no—
259C22×C4—4416no—
260C22×C4C2×C4×D1118yes—
261C22×C4C22×Dic1114yes—
262C22×C4C22×Dic11116yes—
263C22×C4C22×Dic1114yes—
264C22×C4C22×Dic1118yes—
265C22×C4C22×Dic11116yes—
266C22×C4C22×Dic1114yes—
267C22×C4C23×D1111yescharacteristic
268C22×C4C23×D1112yes—
269C22×C4C23×D1114yes—
270C22×C4C23×D1112yes—
271C22×C4C23×D1111yescharacteristic
272C4⋊C4—1132no—
273C4⋊C4C22×Dic11116yes—
274C22⋊C4—1132no—
275C22⋊C4—1164no—
276C22⋊C4C22×Dic11132yes—
277C42—1132no—
278C42—2216no—
279C42—4416no—
280C42—448no—
281C42C22×Dic1118yes—
282C42C22×Dic1118yes—
283C11C4×#51811yescharacteristic, complemented, Sylow
284C23—22no—
285C23—28no—
286C23—22no—
287C23—28no—
288C23—48no—
289C23—432no—
290C23—48no—
291C23C2×C4×Dic11132yescomplemented
292C23C22×C4×D1114yes—
293C23C22×C4×D11116yes—
294C23C23×Dic1118yes—
295C23C23×Dic1112yes—
296C23C24×D1111yescharacteristic
297D4C2×C4×Dic11164yescomplemented
298C2×C4—28no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—28no—
302C2×C4—232no—
303C2×C4—416no—
304C2×C4—48no—
305C2×C4—44no—
306C2×C4—1132no—
307C2×C4—2216no—
308C2×C4—2216no—
309C2×C4—4464no—
310C2×C4C2×C4×Dic11116yescomplemented
311C2×C4C22×C4×D1118yes—
312C2×C4#6703714yes—
313C2×C4C23×Dic1114yes—
314C2×C4C23×Dic1112yes—
315C2×C4C23×Dic1118yes—
316C2×C4C23×Dic1114yes—
317C2×C4C23×Dic1112yes—
318C22—22no—
319C22—28no—
320C22—22no—
321C22—28no—
322C22—232no—
323C22—28no—
324C22—432no—
325C22C22×C4×Dic1114yes—
326C22C22×C4×Dic11116yes—
327C22C23×C4×D1112yes—
328C22C2×#6703712yes—
329C22#1062345312yes—
330C22C24×Dic1111yescharacteristic
331C4—22no—
332C4—28no—
333C4—24no—
334C4—2232no—
335C4C22×C4×Dic1118yes—
336C4#1062332914yesdirect product factor
337C2—24no—
338C2—216no—
339C2C23×C4×Dic1111yescharacteristic
340C2C2×#1062332911yescharacteristic
341C2#1308181911yescharacteristic
342C2C4×#6703714yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC2×C11C23×C42
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socle, cosocleC23×C11C25
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11C4×#518
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. #13070977C2semidirect
3. #13070973C2semidirect
4. #13070969C2semidirect
5. C4×D4×Dic11C2semidirect
6. C4×#66979C2semidirect
7. C2×C4×C22⋊Dic11C2semidirect
11. C2×C4×D4×C11C4semidirect
18. #10623329C4direct (N × H)
21. C22×C4×Dic11C22semidirect
25. C4×C22⋊Dic11C22semidirect
26. C4×C22⋊Dic11C22semidirect
27. C2×C11⋊#95C22semidirect
28. C4⋊C4×Dic11C22semidirect
29. C22⋊C4×Dic11C22semidirect
30. C4×C4⋊Dic11C22semidirect
31. C4×C4⋊Dic11C22semidirect
32. #10622545C22semidirect
33. C42×Dic11C22semidirect
39. C23×C4×C11C2×C4semidirect
47. C4×D4×C11C2×C4semidirect
48. C4×D4×C11C2×C4semidirect
49. C2×C11×C4⋊C4C2×C4semidirect
51. C2×C11×C22⋊C4C2×C4semidirect
53. C2×C42×C11C2×C4semidirect
56. C2×C22⋊Dic11C2×C4semidirect
59. D4×Dic11C2×C4semidirect
60. #66979C2×C4semidirect
77. C2×D4×C11C42semidirect
100. C22×Dic11C22×C4semidirect
107. C22⋊Dic11C22×C4semidirect
108. C4⋊Dic11C22×C4semidirect
112. C4×Dic11C22×C4semidirect
128. C23×C11C2×C42semidirect
134. D4×C11C2×C42semidirect
143. C2×C4×C11C2×C42semidirect
159. C2×C4×D4Dic11semidirect
197. C4×C11#518semidirect
205. C23×C4C2×Dic11semidirect
213. C4×D4C2×Dic11semidirect
214. C4×D4C2×Dic11semidirect
217. C2×C4⋊C4C2×Dic11semidirect
222. C2×C22⋊C4C2×Dic11semidirect
229. C2×C42C2×Dic11semidirect
247. C2×D4C4×Dic11semidirect
283. C11C4×#518semidirect
291. C23C2×C4×Dic11semidirect
297. D4C2×C4×Dic11semidirect
310. C2×C4C2×C4×Dic11semidirect
336. C4#10623329direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233292
#130709772
#130709732
#130709692
C4×D4×Dic112
C4×#669792
C2×C4×C22⋊Dic112
C22×C4×D4×C112
C4×#51811