Finite Group Databasebeta

← C22×#10623094 #15660795

Subgroups — C22×#10623094 #15660795

Order 2816.

8710 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C2148yesmaximal, direct product factor
2C22×#66922C211yesmaximal, characteristic, complemented
3C22×#66938C214yesmaximal, complemented
4C22×#66983C212yesmaximal, complemented
5C22×#66991C212yesmaximal, complemented
6C22×C4×D44C211yesmaximal, characteristic, complemented
7C22×#66979C212yesmaximal, complemented
8C22×#66945C212yesmaximal, complemented
9C22×C4×D4×C11C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2212yes—
12C23×C22⋊D11C2214yes—
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2212yes—
16C2×C4×D4×C11C22124yescomplemented
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2214yes—
21C2×#66991C22148yescomplemented
22C2×#66983C22148yescomplemented
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2214yes—
25C2×#66979C22148yescomplemented
26C22×C4⋊Dic11C2212yes—
27C22×C4⋊Dic11C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4×Dic11C2214yes—
30#10623094C221256yesdirect product factor
31C2×#66945C22148yescomplemented
32C2×#66938C22196yescomplemented
33C2×C4×D44C22124yescomplemented
34C2×#66922C22124yescomplemented
35C25×C11C2312yes—
36C24×D11C2312yes—
37C22×D4×C11—28no—
38C22×D4×C11C23112yes—
39C23×C4×C11—216no—
40C23×C4×C11C2312yes—
41C23×C4×C11C23124yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—416no—
46C22×C22⋊D11C23148yes—
47C23×Dic11C2312yes—
48C23×Dic11C2314yes—
49C22×D44—28no—
50C22×D44C23112yes—
51C22×C4×D11—216no—
52C22×C4×D11C23124yes—
53C22×Dic22—48no—
54C22×Dic22C23124yes—
55C4×D4×C11C23164yescomplemented
56C2×C11×C4⋊C4C23112yes—
57C2×C11×C22⋊C4C23124yes—
58C2×C42×C11C23112yes—
59C2×C22⋊Dic11C23148yes—
60#66991C231128yescomplemented
61#66983C231128yescomplemented
62C2×(C2×D11)⋊C4C23124yes—
63C2×(C2×D11)⋊C4C23148yes—
64#66979C231128yescomplemented
65C2×C4⋊Dic11C23124yes—
66C2×C4⋊Dic11C23124yes—
67C2×C4⋊Dic11C23112yes—
68C2×C4×Dic11C23148yes—
69#66945C231128yescomplemented
70#66938C231256yescomplemented
71C4×D44C23164yescomplemented
72#66922C23164yescomplemented
73C22×#555—111nomaximal, Sylow
74C24×C11—28no—
75C24×C11—28no—
76C24×C11—28no—
77C24×C11C24112yes—
78C24×C11C2411yescharacteristic
79C23×D11—28no—
80C23×D11—28no—
81C23×D11—28no—
82C23×D11C24112yes—
83C2×D4×C11—248no—
84C2×D4×C11C24116yes—
85C22×C4×C11—28no—
86C22×C4×C11—24no—
87C22×C4×C11—296no—
88C22×C4×C11#4118yes—
89C22×C4×C11#4118yes—
90C22×C4×C11C24112yes—
91C22×C4×C11C24132yes—
92C22×C4×C11C2416yes—
93C22×C4×C11C2416yes—
94C22×C4×C11C2416yes—
95C2×C22⋊D11—496no—
96C2×C22⋊D11C24164yes—
97C22×Dic11—28no—
98C22×Dic11—216no—
99C22×Dic11C24112yes—
100C22×Dic11C24124yes—
101C2×D44—248no—
102C2×D44C24116yes—
103C2×C4×D11—296no—
104C2×C4×D11C24132yes—
105C2×Dic22—448no—
106C2×Dic22C24132yes—
107C11×C4⋊C4C24116yes—
108C11×C22⋊C4C24132yes—
109C42×C11C24116yes—
110C22⋊Dic11C24164yes—
111(C2×D11)⋊C4C24132yes—
112(C2×D11)⋊C4C24164yes—
113C4⋊Dic11C24132yes—
114C4⋊Dic11C24132yes—
115C4⋊Dic11C24116yes—
116C4×Dic11C24164yes—
117C2×#555—1148no—
118C22×C4⋊Q8—111no—
119C22×#124—114no—
120C22×#121—112no—
121C22×#121—112no—
122C22×C4×D4—111no—
123C22×C4×D4D1111yescharacteristic, complemented
124C22×#117—112no—
125C22×#117—112no—
126C23×C11—224no—
127C23×C11—224no—
128C23×C11—224no—
129C23×C11—432no—
130C23×C11C2×#4114yes—
131C23×C11C2×#4114yes—
132C23×C11H(5,𝔽2)14yes—
133C23×C11C2518yes—
134C23×C11C2513yes—
135C22×D11—224no—
136C22×D11—224no—
137C22×D11—224no—
138C22×D11—432no—
139C22×D11C2518yes—
140D4×C11—232no—
141C2×C4×C11—224no—
142C2×C4×C11—212no—
143C2×C4×C11—264no—
144C2×C4×C11C2×#41124yes—
145C2×C4×C11C2×#41124yes—
146C2×C4×C11C2518yes—
147C2×C4×C11C2514yes—
148C2×C4×C11C2514yes—
149C2×C4×C11C2514yes—
150C22⋊D11—464no—
151C2×Dic11—224no—
152C2×Dic11—248no—
153C2×Dic11C2518yes—
154C2×Dic11C25116yes—
155D44—232no—
156C4×D11—264no—
157Dic22—432no—
158C23×Q8—112no—
159C23×D4—114no—
160C23×D4—111no—
161C23×D4C2×D1111yescharacteristic
162C24×C4—112no—
163C24×C4C2×D1112yes—
164#555—11256no—
165C2×C4⋊Q8—1124no—
166C2×#124—1196no—
167C2×#121—1148no—
168C2×#121—1148no—
169C2×C4×D4—1124no—
170C2×C4×D4C2×D11124yescomplemented
171C2×#117—1148no—
172C2×#117—1148no—
173C22×C4⋊C4—111no—
174C22×C4⋊C4—112no—
175C22×C4⋊C4—112no—
176C22×C4⋊C4C2×D1111yescharacteristic
177C22×C22⋊C4—114no—
178C22×C22⋊C4—114no—
179C22×C22⋊C4—112no—
180C22×C22⋊C4C2×D1112yes—
181C22×C42—114no—
182C22×C42C2×D1111yescharacteristic
183C22×C11—28no—
184C22×C11—28no—
185C22×C11—28no—
186C22×C11—448no—
187C22×C11#555116yescomplemented
188C22×C11C22×#4116yes—
189C22×C11C22×#4116yes—
190C22×C11C2×H(5,𝔽2)16yes—
191C22×C11C2611yescharacteristic
192C2×D11—28no—
193C2×D11—28no—
194C2×D11—28no—
195C2×D11—448no—
196C4×C11—28no—
197C4×C11—24no—
198C4×C11C22×#4118yes—
199C4×C11C22×#4118yes—
200Dic11—28no—
201Dic11—216no—
202C25—112no—
203C25C22×D1112yes—
204C22×Q8—1124no—
205C22×Q8—448no—
206C22×D4—28no—
207C22×D4—1148no—
208C22×D4—1112no—
209C22×D4—228no—
210C22×D4—4416no—
211C22×D4C22×D11112yes—
212C23×C4—216no—
213C23×C4—112no—
214C23×C4—114no—
215C23×C4—1124no—
216C23×C4—2216no—
217C23×C4C22×D11124yes—
218C23×C4C22×D1111yescharacteristic
219C23×C4C22×D1112yes—
220C23×C4C22×D1111yescharacteristic
221C23×C4C22×D1111yescharacteristic
222C4⋊Q8—1164no—
223#124—11256no—
224#121—11128no—
225#121—11128no—
226C4×D4—1164no—
227C4×D4C22×D11164yescomplemented
228#117—11128no—
229#117—11128no—
230C2×C4⋊C4—1112no—
231C2×C4⋊C4—1124no—
232C2×C4⋊C4—1124no—
233C2×C4⋊C4C22×D11112yes—
234C2×C22⋊C4—1148no—
235C2×C22⋊C4—1148no—
236C2×C22⋊C4—1124no—
237C2×C22⋊C4C22×D11124yes—
238C2×C42—1148no—
239C2×C42C22×D11112yes—
240C2×C11—48no—
241C2×C11C2×#555112yescomplemented
242C2×C11C23×#4111yescharacteristic
243C2×C11C23×#4111yescharacteristic
244C2×C11C22×H(5,𝔽2)11yescharacteristic
245D11—48no—
246C24—28no—
247C24—28no—
248C24—28no—
249C24—1112no—
250C24—228no—
251C24—228no—
252C24—228no—
253C24C23×D11112yes—
254C24C23×D1111yescharacteristic
255C2×Q8—1132no—
256C2×Q8—4448no—
257C2×D4—248no—
258C2×D4—1164no—
259C2×D4—1116no—
260C2×D4—2248no—
261C2×D4—4496no—
262C2×D4C23×D11116yes—
263C22×C4—28no—
264C22×C4—24no—
265C22×C4—296no—
266C22×C4—1112no—
267C22×C4—1124no—
268C22×C4—1132no—
269C22×C4—228no—
270C22×C4—2216no—
271C22×C4—2296no—
272C22×C4#433918yes—
273C22×C4#434118yes—
274C22×C4C23×D11112yes—
275C22×C4C23×D1116yes—
276C22×C4C23×D11132yes—
277C22×C4C23×D1116yes—
278C22×C4C23×D1116yes—
279C4⋊C4—1116no—
280C4⋊C4—1132no—
281C4⋊C4—1132no—
282C4⋊C4C23×D11116yes—
283C22⋊C4—1164no—
284C22⋊C4—1164no—
285C22⋊C4—1132no—
286C22⋊C4C23×D11132yes—
287C42—1164no—
288C42C23×D11116yes—
289C11C22×#55511yescharacteristic, complemented, Sylow
290C23—224no—
291C23—224no—
292C23—224no—
293C23—432no—
294C23—118no—
295C23—2224no—
296C23—2224no—
297C23—2224no—
298C23—4432no—
299C23C2×#433914yes—
300C23C2×#434114yes—
301C23#6704214yes—
302C23C24×D1118yes—
303C23C24×D1113yes—
304Q8—4432no—
305D4—232no—
306D4—2232no—
307D4—4464no—
308C2×C4—224no—
309C2×C4—212no—
310C2×C4—264no—
311C2×C4—118no—
312C2×C4—1116no—
313C2×C4—2224no—
314C2×C4—2248no—
315C2×C4—2264no—
316C2×C4C2×#4339124yes—
317C2×C4C2×#4341124yes—
318C2×C4C24×D1118yes—
319C2×C4C24×D1114yes—
320C2×C4C24×D1114yes—
321C2×C4C24×D1114yes—
322C22—28no—
323C22—28no—
324C22—28no—
325C22—448no—
326C22—228no—
327C22—228no—
328C22—228no—
329C22—4448no—
330C22#10623094116yesdirect product factor
331C22C22×#433916yes—
332C22C22×#434116yes—
333C22C2×#6704216yes—
334C22C25×D1111yescharacteristic
335C4—28no—
336C4—24no—
337C4—228no—
338C4—2216no—
339C4C22×#433918yes—
340C4C22×#434118yes—
341C2—48no—
342C2—448no—
343C2C2×#10623094112yesdirect product factor
344C2C23×#434111yescharacteristic
345C2C23×#433911yescharacteristic
346C2C22×#6704211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C22×#555
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2direct (N × H)
2. C22×#66922C2semidirect
3. C22×#66938C2semidirect
4. C22×#66983C2semidirect
5. C22×#66991C2semidirect
6. C22×C4×D44C2semidirect
7. C22×#66979C2semidirect
8. C22×#66945C2semidirect
9. C22×C4×D4×C11C2semidirect
16. C2×C4×D4×C11C22semidirect
21. C2×#66991C22semidirect
22. C2×#66983C22semidirect
25. C2×#66979C22semidirect
30. #10623094C22direct (N × H)
31. C2×#66945C22semidirect
32. C2×#66938C22semidirect
33. C2×C4×D44C22semidirect
34. C2×#66922C22semidirect
55. C4×D4×C11C23semidirect
60. #66991C23semidirect
61. #66983C23semidirect
64. #66979C23semidirect
69. #66945C23semidirect
70. #66938C23semidirect
71. C4×D44C23semidirect
72. #66922C23semidirect
123. C22×C4×D4D11semidirect
170. C2×C4×D4C2×D11semidirect
187. C22×C11#555semidirect
227. C4×D4C22×D11semidirect
241. C2×C11C2×#555semidirect
289. C11C22×#555semidirect
330. C22#10623094direct (N × H)
343. C2C2×#10623094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C22×#669222
C22×#669382
C22×#669832
C22×#669912
C22×C4×D442
C22×#669792
C22×#669452
C22×C4×D4×C112
C22×#55511