Finite Group Databasebeta

← C2×#13074479 #14920696

Subgroups — C2×#13074479 #14920696

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13074479C2116yesmaximal, direct product factor
4C2×#10622290C212yesmaximal, complemented
5C2×#10622269C212yesmaximal, complemented
6C2×#10622285C212yesmaximal
7C2×#10622286C212yesmaximal, complemented
8C2×#10622283C214yesmaximal, complemented
9C2×C11×#383C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2214yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2214yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2212yes—
22C2×#66928—28no—
23C2×#66928C2218yes—
24C2×C4×Dic22—28no—
25C2×C4×Dic22C2218yescomplemented
26C11×#383C2218yescomplemented
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2214yes—
31#10622290C22116yescomplemented
32#10622286C22116yescomplemented
33#10622285C22116yes—
34#10622283C22132yescomplemented
35#10622269C22116yescomplemented
36C24×D11C2312yes—
37C23×C4×C11C2314yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C22×D44—24no—
45C22×D44—44no—
46C22×D44C2314yes—
47C22×Dic22—24no—
48C22×Dic22—28no—
49C22×Dic22—24no—
50C22×Dic22—44no—
51C22×Dic22C2314yes—
52C22×Dic22C2314yes—
53C2×C42×C11D418yes—
54C2×C42×C11C2314yes—
55C2×(C2×D11)⋊C4—28no—
56C2×(C2×D11)⋊C4—28no—
57C2×(C2×D11)⋊C4—216no—
58C2×(C2×D11)⋊C4—48no—
59C2×(C2×D11)⋊C4C2318yes—
60C2×(C2×D11)⋊C4C2318yes—
61C2×(C2×D11)⋊C4C23116yes—
62C2×(C2×D11)⋊C4C23116yes—
63C2×C4⋊Dic11—24no—
64C2×C4⋊Dic11—48no—
65C2×C4⋊Dic11C2314yes—
66C2×C4⋊Dic11C23116yes—
67C2×Dic11⋊C4—28no—
68C2×Dic11⋊C4C2318yes—
69C2×C4×Dic11—28no—
70C2×C4×Dic11C2318yes—
71#66928—232no—
72C4×Dic22—232no—
73C11×#95C2318yes—
74C11×#95C2318yes—
75C11×#95C2318yes—
76C11⋊#95C23116yes—
77C2×#2632—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C23×D11—24no—
80C23×D11—28no—
81C23×D11—28no—
82C23×D11—28no—
83C23×D11C2414yes—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—28no—
88C22×C4×C11—28no—
89C22×C4×C11—28no—
90C22×C4×C11C2×D414yes—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×D414yes—
93C22×C4×C11C2418yes—
94C22×C4×C11C2412yes—
95C22×C4×C11C2412yes—
96C22×C4×C11C2412yes—
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—28no—
102C22×Dic11—28no—
103C22×Dic11#4118yes—
104C22×Dic11C2414yes—
105C22×Dic11C2414yes—
106C22×Dic11C2414yes—
107C2×D44—28no—
108C2×D44—48no—
109C2×D44—416no—
110C2×Dic22—232no—
111C2×Dic22—216no—
112C2×Dic22—28no—
113C2×Dic22—28no—
114C2×Dic22—48no—
115C2×Dic22—416no—
116C42×C11C2×D4116yes—
117(C2×D11)⋊C4—232no—
118(C2×D11)⋊C4—216no—
119(C2×D11)⋊C4—216no—
120(C2×D11)⋊C4—416no—
121C4⋊Dic11—28no—
122C4⋊Dic11—416no—
123Dic11⋊C4—216no—
124C4×Dic11—216no—
125C22×#124—111no—
126C22×C4×Q8—111no—
127#2632—1116no—
128C2×#399—112no—
129C2×#395—112no—
130C2×#394—112no—
131C2×#393—112no—
132C2×#388—114no—
133C2×#383D1111yescharacteristic, complemented
134C23×C11C22×D412yes—
135C23×C11C2×#4114yes—
136C23×C11H(5,𝔽2)14yes—
137C23×C112−1+414yes—
138C23×C11C2511yescharacteristic
139C22×D11—24no—
140C22×D11—28no—
141C22×D11—28no—
142C22×D11—28no—
143C22×D11—48no—
144C22×D11—48no—
145C22×D11—48no—
146C22×D11—432no—
147C2×C4×C11—28no—
148C2×C4×C11—28no—
149C2×C4×C11—28no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—28no—
154C2×C4×C11—28no—
155C2×C4×C11—28no—
156C2×C4×C11—416no—
157C2×C4×C11C22×D414yes—
158C2×C4×C11C22×D414yes—
159C2×C4×C11C22×D414yes—
160C2×Dic11—216no—
161C2×Dic11—24no—
162C2×Dic11—24no—
163C2×Dic11—24no—
164C2×Dic11—24no—
165C2×Dic11—28no—
166C2×Dic11—28no—
167C2×Dic11—48no—
168C2×Dic11—48no—
169C2×Dic11C2×#4118yes—
170D44—416no—
171Dic22—232no—
172Dic22—416no—
173C23×Q8—111no—
174C23×Q8—111no—
175C23×D4—111no—
176C2×#124—118no—
177C2×#124—228no—
178C2×C4×Q8—118no—
179C2×C4×Q8—228no—
180C22×C4⋊C4—112no—
181C22×C4⋊C4—111no—
182C22×C4⋊C4—114no—
183C22×C22⋊C4—114no—
184C22×C22⋊C4—112no—
185C22×C22⋊C4—112no—
186C22×C22⋊C4—114no—
187C22×C42—112no—
188C22×C42C2×D1111yescharacteristic
189#399—1116no—
190#395—1116no—
191#394—1116no—
192#393—1116no—
193#388—1132no—
194#383C2×D1118yescomplemented
195C2×#95—114no—
196C2×#95C2×D1112yes—
197C2×#95C2×D1112yes—
198C2×#95C2×D1112yes—
199C22×C11#52514yes—
200C22×C11#53514yes—
201C22×C11#53614yes—
202C22×C11#542116yes—
203C22×C11C23×D411yescharacteristic
204C22×C11C22×#4112yes—
205C22×C11C2×H(5,𝔽2)12yes—
206C22×C11C2×2−1+412yes—
207C2×D11—44no—
208C2×D11—44no—
209C2×D11—44no—
210C2×D11—416no—
211C2×D11—816no—
212C4×C11—24no—
213C4×C11—24no—
214C4×C11—24no—
215C4×C11—48no—
216Dic11—28no—
217Dic11—44no—
218Dic11—44no—
219C25—112no—
220C22×Q8—114no—
221C22×Q8—114no—
222C22×Q8—228no—
223C22×Q8—224no—
224C22×Q8—224no—
225C22×Q8—444no—
226C22×D4—114no—
227C22×D4—224no—
228C22×D4—444no—
229C23×C4—112no—
230C23×C4—112no—
231C23×C4—112no—
232C23×C4C22×D1114yes—
233C23×C4C22×D1111yescharacteristic
234C23×C4C22×D1111yescharacteristic
235C23×C4C22×D1111yescharacteristic
236#124—2232no—
237C4×Q8—2232no—
238C2×C4⋊C4—118no—
239C2×C4⋊C4—114no—
240C2×C4⋊C4—1116no—
241C2×C4⋊C4—228no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—448no—
244C2×C22⋊C4—118no—
245C2×C22⋊C4—118no—
246C2×C22⋊C4—1116no—
247C2×C22⋊C4—1116no—
248C2×C22⋊C4—2216no—
249C2×C22⋊C4—228no—
250C2×C22⋊C4—228no—
251C2×C22⋊C4—448no—
252C2×C42—118no—
253C2×C42—228no—
254C2×C42D4418yes—
255C2×C42C22×D1114yes—
256#95—1116no—
257#95C22×D1118yes—
258#95C22×D1118yes—
259#95C22×D1118yes—
260C2×C11#263218yescomplemented
261C2×C11C2×#52511yescharacteristic
262C2×C11C2×#53511yescharacteristic
263C2×C11C2×#53611yescharacteristic
264C2×C11C2×#54214yes—
265D11—84no—
266C24—114no—
267C24—224no—
268C24—228no—
269C24—228no—
270C24—228no—
271C24C23×D1111yescharacteristic
272C2×Q8—2216no—
273C2×Q8—2232no—
274C2×Q8—228no—
275C2×Q8—228no—
276C2×Q8—448no—
277C2×Q8—4416no—
278C2×D4—228no—
279C2×D4—448no—
280C2×D4—4416no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—28no—
285C22×C4—28no—
286C22×C4—28no—
287C22×C4—118no—
288C22×C4—114no—
289C22×C4—114no—
290C22×C4—114no—
291C22×C4—224no—
292C22×C4—224no—
293C22×C4—224no—
294C22×C4—224no—
295C22×C4—228no—
296C22×C4—228no—
297C22×C4C2×D4414yes—
298C22×C4C2×D4414yes—
299C22×C4C2×D4414yes—
300C22×C4C23×D1118yes—
301C22×C4C23×D1112yes—
302C22×C4C23×D1112yes—
303C22×C4C23×D1112yes—
304C4⋊C4—2216no—
305C4⋊C4—228no—
306C4⋊C4—4416no—
307C22⋊C4—2232no—
308C22⋊C4—2216no—
309C22⋊C4—2216no—
310C22⋊C4—4416no—
311C42—2216no—
312C42C2×D44116yes—
313C11C2×#263211yescharacteristic, complemented, Sylow
314C23—224no—
315C23—228no—
316C23—228no—
317C23—228no—
318C23—4432no—
319C23—448no—
320C23—448no—
321C23—448no—
322C23C22×D4412yes—
323C23#41×D1114yes—
324C23#6704214yes—
325C23#6704314yes—
326C23C24×D1111yescharacteristic
327Q8—2232no—
328Q8—4416no—
329D4—4416no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—28no—
338C2×C4—28no—
339C2×C4—416no—
340C2×C4—118no—
341C2×C4—2216no—
342C2×C4—224no—
343C2×C4—224no—
344C2×C4—224no—
345C2×C4—224no—
346C2×C4—228no—
347C2×C4—228no—
348C2×C4—448no—
349C2×C4—448no—
350C2×C4C22×D4414yes—
351C2×C4C22×D4414yes—
352C2×C4C22×D4414yes—
353C22—444no—
354C22—444no—
355C22—444no—
356C22—4416no—
357C22—8816no—
358C22#1062305514yes—
359C22#1062305614yes—
360C22#1062305714yes—
361C22#10623241116yes—
362C22C23×D4411yescharacteristic
363C22C2×#41×D1112yes—
364C22C2×#6704212yes—
365C22C2×#6704312yes—
366C4—24no—
367C4—24no—
368C4—24no—
369C4—48no—
370C4—228no—
371C4—444no—
372C4—444no—
373C2—884no—
374C2#1307447918yesdirect product factor
375C2C2×#1062305511yescharacteristic
376C2C2×#1062305611yescharacteristic
377C2C2×#1062305711yescharacteristic
378C2C2×#1062324114yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#383C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#383D11
hypocenterC11C2×#2632
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13074479C2direct (N × H)
4. C2×#10622290C2semidirect
5. C2×#10622269C2semidirect
7. C2×#10622286C2semidirect
8. C2×#10622283C2semidirect
9. C2×C11×#383C2semidirect
25. C2×C4×Dic22C22semidirect
26. C11×#383C22semidirect
31. #10622290C22semidirect
32. #10622286C22semidirect
34. #10622283C22semidirect
35. #10622269C22semidirect
133. C2×#383D11semidirect
194. #383C2×D11semidirect
260. C2×C11#2632semidirect
313. C11C2×#2632semidirect
374. C2#13074479direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
C22×C4×Dic222
#130744792
C2×#106222902
C2×#106222692
C2×#106222852
C2×#106222862
C2×#106222832
C2×C11×#3832
C2×#263211