Finite Group Databasebeta

← C2×#13081626 #15634707

Subgroups — C2×#13081626 #15634707

Order 2816.

2086 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C212yesmaximal, complemented
2#13081626C2116yesmaximal, direct product factor
3C2×#10622804C212yesmaximal, complemented
4C2×#10622308C211yesmaximal, characteristic
5C2×#10622640C212yesmaximal, complemented
6C2×#10622432C214yesmaximal, complemented
7C2×C8×Dic22C211yesmaximal, characteristic, complemented
8C2×#10622485C212yesmaximal, complemented
9C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
10C22×C11×Q16C2211yescharacteristic
11C2×C4×Q8×C11C2212yes—
12C2×#67000C2214yes—
13C22×#4325C2214yes—
14C22×D88C2212yes—
15C22×D88C2212yes—
16#10623116—28no—
17#10623116C22116yescomplemented
18C2×#66947—24no—
19C2×#66946C2214yes—
20C2×#66928—22no—
21C2×#66927C2212yes—
22C2×C4×D44—22no—
23C2×C4×Dic22C2211yescharacteristic
24C4×C11×Q16C2218yescomplemented
25C2×C11×#107C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28#10622804C22116yescomplemented
29C2×Dic11⋊C8C2212yes—
30C2×C8×Dic11C2212yes—
31#10622640C22116yescomplemented
32C2×#66873C2214yes—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34#10622485C22116yescomplemented
35#10622432C22132yescomplemented
36#10622308C2218yes—
37C8×Dic22C2218yescomplemented
38C22×Q8×C11C2312yes—
39C22×D44—22no—
40C22×D44—22no—
41C22×D44C2314yes—
42C22×C4×D11—24no—
43C22×Dic22D411yescharacteristic
44C2×C11×Q16—24no—
45C2×C11×Q16C2314yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C4×Q8×C11—24no—
49C4×Q8×C11C2318yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2312yes—
52C2×C42×C11—22no—
53C2×C42×C11C2311yescharacteristic
54#67000—28no—
55#67000C23116yes—
56C2×#4325—48no—
57C2×#4325C23116yes—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×Dic11⋊C4D412yes—
63C2×C4×Dic11C2312yes—
64C22×C11⋊C8C2312yes—
65C2×D88—28no—
66C2×D88—44no—
67C2×D88C2318yes—
68C2×D88C2318yes—
69#66947—232no—
70#66946—28no—
71#66946C23116yes—
72#66928—216no—
73#66927—24no—
74#66927C2318yes—
75C4×D44—216no—
76C4×Dic22D414yes—
77C4×Dic22C2314yes—
78C11×#107C2314yes—
79C11×#103C2318yes—
80C4×C8×C11C2314yes—
81Dic11⋊C8C2318yes—
82C8×Dic11C2318yes—
83#66873C23116yes—
84C4⋊(C11⋊C8)C2314yes—
85C2×#3396—111nomaximal, Sylow
86C23×D11—24no—
87C2×Q8×C11—22no—
88C2×Q8×C11—24no—
89C2×Q8×C11—24no—
90C2×Q8×C11C2414yes—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11C2×D412yes—
97C22×Dic11C2×D412yes—
98C2×D44—28no—
99C2×D44—24no—
100C2×D44—28no—
101C2×D44—28no—
102C2×D44—28no—
103C2×D44—48no—
104C2×D44—84no—
105C2×D44C2418yes—
106C2×C4×D11—216no—
107C2×C4×D11—88no—
108C2×Dic22—24no—
109C2×Dic22C2×D414yes—
110C11×Q16—28no—
111C2×C8×C11—22no—
112C2×C8×C11#4114yes—
113C2×C8×C11C2412yes—
114C2×C8×C11C2412yes—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4C2414yes—
118C42×C11—28no—
119C42×C11C2×D412yes—
120C42×C11C2412yes—
121#4325—416no—
122(C2×D11)⋊C4—216no—
123(C2×D11)⋊C4—216no—
124(C2×D11)⋊C4—216no—
125C4⋊Dic11C2×D414yes—
126Dic11⋊C4C2×D418yes—
127C4×Dic11C2×D414yes—
128C4×Dic11C2414yes—
129C2×C11⋊C8—24no—
130C2×C11⋊C8C2414yes—
131D88—216no—
132D88—48no—
133C2×#559—112no—
134#3396—1116no—
135C2×#495—112no—
136C2×#493—111no—
137C2×#460—112no—
138C2×#463—114no—
139C2×C8×Q8—111no—
140C2×C4×Q16D1111yescharacteristic, complemented
141C2×C4×D8—112no—
142C23×C11C22×D411yescharacteristic
143C22×D11—28no—
144C22×D11—48no—
145C22×D11—48no—
146C22×D11—48no—
147Q8×C11—24no—
148Q8×C11—24no—
149Q8×C11—44no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11#13514yes—
156C2×C4×C11C22×D412yes—
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C22×D412yes—
159C2×C4×C11C2×#4112yes—
160C2×C4×C11H(5,𝔽2)12yes—
161C2×C4×C11C2511yescharacteristic
162C2×Dic11—24no—
163C2×Dic11—24no—
164C2×Dic11C22×D414yes—
165C2×Dic11C22×D414yes—
166D44—28no—
167D44—28no—
168D44—48no—
169D44—416no—
170D44—88no—
171C4×D11—816no—
172Dic22—28no—
173C8×C11—22no—
174C8×C11C2×#4114yes—
175C11⋊C8—24no—
176C22×Q16C2×D1111yescharacteristic
177C22×SD16—114no—
178C22×D8—112no—
179C22×D8—112no—
180#559—1116no—
181#559—228no—
182C2×#127—112no—
183C2×#124—114no—
184C2×#124—222no—
185C2×#123—224no—
186C2×C4×Q8—111no—
187C2×C4×Q8C2×D1112yes—
188C2×C4×D4—114no—
189C2×C4×D4—222no—
190#495—1116no—
191#493—118no—
192#463—1132no—
193#460—1116no—
194C8×Q8—118no—
195C4×Q16C2×D1118yescomplemented
196C4×D8—1116no—
197C2×#107C2×D1111yescharacteristic
198C2×C4⋊C8—112no—
199C2×C4⋊C8—111no—
200C2×#103C2×D1112yes—
201C2×#102—114no—
202C2×C4×C8—112no—
203C2×C4×C8C2×D1111yescharacteristic
204C22×C11#55012yes—
205C22×C11C2×#13512yes—
206C22×C11#57612yes—
207C22×C11C23×D411yescharacteristic
208C2×D11—48no—
209C2×D11—48no—
210C2×D11—48no—
211C2×D11—816no—
212C4×C11—22no—
213C4×C11—44no—
214C4×C11—44no—
215C4×C11#55012yes—
216C4×C11C2×#13514yes—
217C4×C11C22×#4111yescharacteristic
218C4×C11C2×H(5,𝔽2)11yescharacteristic
219Dic11—24no—
220Dic11—24no—
221C22×Q8—111no—
222C22×Q8C22×D1112yes—
223C22×D4—114no—
224C22×D4—222no—
225C22×D4—222no—
226C23×C4—224no—
227C2×Q16—24no—
228C2×Q16C22×D1114yes—
229C2×SD16—1116no—
230C2×SD16—448no—
231C2×D8—118no—
232C2×D8—118no—
233C2×D8—228no—
234C2×D8—444no—
235C22×C8—112no—
236C22×C8C22×D1111yescharacteristic
237C22×C8C22×D1111yescharacteristic
238#127—118no—
239#127—224no—
240#124—1116no—
241#124—2216no—
242#124—228no—
243#123—2232no—
244C4×Q8—24no—
245C4×Q8—114no—
246C4×Q8—114no—
247C4×Q8C22×D1118yes—
248C4×D4—1116no—
249C4×D4—2216no—
250C4×D4—228no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4C22×D1112yes—
255C2×C22⋊C4—224no—
256C2×C22⋊C4—224no—
257C2×C22⋊C4—224no—
258C2×C42—22no—
259C2×C42—112no—
260C2×C42C22×D1111yescharacteristic
261#107C22×D1114yes—
262C4⋊C8—118no—
263C4⋊C8—114no—
264#103C22×D1118yes—
265#102—1116no—
266C4×C8—118no—
267C4×C8C22×D1114yes—
268C2×C11#339614yescomplemented
269C2×C11C2×#55011yescharacteristic
270C2×C11C22×#13511yescharacteristic
271C2×C11C2×#57611yescharacteristic
272D11—88no—
273C24—224no—
274C2×Q8—22no—
275C2×Q8—24no—
276C2×Q8—24no—
277C2×Q8—114no—
278C2×Q8—224no—
279C2×Q8C23×D1114yes—
280C2×D4—118no—
281C2×D4—228no—
282C2×D4—228no—
283C2×D4—224no—
284C2×D4—228no—
285C2×D4—228no—
286C2×D4—448no—
287C2×D4—884no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—112no—
291C22×C4—112no—
292C22×C4—2216no—
293C22×C4—888no—
294C22×C4D4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296C22×C4C23×D1111yescharacteristic
297Q16—28no—
298SD16—4416no—
299D8—2216no—
300D8—448no—
301C2×C8—22no—
302C2×C8—114no—
303C2×C8—224no—
304C2×C8#433914yes—
305C2×C8C23×D1112yes—
306C2×C8C23×D1112yes—
307C4⋊C4—28no—
308C4⋊C4—22no—
309C4⋊C4—114no—
310C4⋊C4—118no—
311C4⋊C4C23×D1114yes—
312C22⋊C4—2216no—
313C22⋊C4—2216no—
314C22⋊C4—2216no—
315C42—28no—
316C42—114no—
317C42—114no—
318C42D4×D1112yes—
319C42C23×D1112yes—
320C11C2×#339611yescharacteristic, complemented, Sylow
321C23—228no—
322C23—448no—
323C23—448no—
324C23—448no—
325C23C2×D4×D1111yescharacteristic
326Q8—24no—
327Q8—24no—
328Q8—44no—
329Q8—228no—
330D4—228no—
331D4—228no—
332D4—4416no—
333D4—448no—
334D4—888no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—114no—
341C2×C4—114no—
342C2×C4—224no—
343C2×C4—224no—
344C2×C4—8816no—
345C2×C4#6697214yes—
346C2×C4C2×#433912yes—
347C2×C4C2×D4×D1112yes—
348C2×C4C2×D4×D1112yes—
349C2×C4C2×D4×D1111yescharacteristic
350C2×C4#6704212yes—
351C2×C4C24×D1111yescharacteristic
352C8—22no—
353C8—224no—
354C8C2×#433914yes—
355C22—448no—
356C22—448no—
357C22—448no—
358C22—8816no—
359C22#1062308412yes—
360C22C2×#6697212yes—
361C22#1062330012yes—
362C22C22×D4×D1111yescharacteristic
363C4—22no—
364C4—44no—
365C4—44no—
366C4—224no—
367C4—224no—
368C4#1062308412yes—
369C4C2×#6697214yes—
370C4C22×#433911yescharacteristic
371C4C2×#6704211yescharacteristic
372C2—888no—
373C2#1308162614yesdirect product factor
374C2C2×#1062308411yescharacteristic
375C2C22×#6697211yescharacteristic
376C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC2×#10622308C2
hypercenterC2×C4×Q16D11
hypocenterC11C2×#3396
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. #13081626C2direct (N × H)
3. C2×#10622804C2semidirect
5. C2×#10622640C2semidirect
6. C2×#10622432C2semidirect
7. C2×C8×Dic22C2semidirect
8. C2×#10622485C2semidirect
9. C2×C4×C11×Q16C2semidirect
17. #10623116C22semidirect
24. C4×C11×Q16C22semidirect
28. #10622804C22semidirect
31. #10622640C22semidirect
34. #10622485C22semidirect
35. #10622432C22semidirect
37. C8×Dic22C22semidirect
140. C2×C4×Q16D11semidirect
195. C4×Q16C2×D11semidirect
268. C2×C11#3396semidirect
320. C11C2×#3396semidirect
373. C2#13081626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130816262
C2×#106228042
C2×#106223082
C2×#106226402
C2×#106224322
C2×C8×Dic222
C2×#106224852
C2×C4×C11×Q162
C2×#339611