Finite Group Databasebeta

← C2×#13071013 #14912059

Subgroups — C2×#13071013 #14912059

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D11C211yesmaximal, characteristic
2#13071013C2116yesmaximal, direct product factor
3C2×#10622550C211yesmaximal, characteristic, complemented
4C2×#10622263C212yesmaximal, complemented
5C2×#10622277C212yesmaximal
6C2×#10622280C212yesmaximal
7C2×#10622262C212yesmaximal, complemented
8C2×#10622279C212yesmaximal
9C2×#10622261C212yesmaximal, complemented
10C2×C11×#383C211yesmaximal, characteristic, complemented
11C23×C4×D11C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2214yes—
16C22×Dic11⋊C4C2214yes—
17C22×C4×Dic11C2214yes—
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×C42×D11C4116yescomplemented
22C2×C42×D11C2218yes—
23C11×#383C2218yescomplemented
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622550C2218yescomplemented
32#10622280C22116yes—
33#10622279C22116yes—
34#10622277C22116yes—
35#10622263C22116yescomplemented
36#10622262C22116yescomplemented
37#10622261C22116yescomplemented
38C24×D11C2311yescharacteristic
39C23×C4×C11C2314yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2314yes—
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C22×C4×D11—28no—
48C22×C4×D11—28no—
49C22×C4×D11—28no—
50C22×C4×D11C2×C418yes—
51C22×C4×D11C2×C418yes—
52C22×C4×D11C2×C418yes—
53C22×C4×D11C2314yes—
54C22×C4×D11C2314yes—
55C22×C4×D11C2314yes—
56C2×C42×C11C2×C418yes—
57C2×C42×C11C2314yes—
58C2×(C2×D11)⋊C4—216no—
59C2×(C2×D11)⋊C4C23116yes—
60C2×Dic11⋊C4—216no—
61C2×Dic11⋊C4C23116yes—
62C2×C4×Dic11—216no—
63C2×C4×Dic11C2×C418yes—
64C2×C4×Dic11C2×C418yes—
65C2×C4×Dic11C2×C418yes—
66C2×C4×Dic11C23116yes—
67C2×C4×Dic11C2314yes—
68C2×C4×Dic11C2314yes—
69C2×C4×Dic11C2314yes—
70C42×D11C2×C4164yescomplemented
71C11×#95C2318yes—
72C11×#95C2318yes—
73C11×#95C2318yes—
74C11⋊#95C23116yes—
75C11⋊#95C2318yes—
76C11⋊#95C2318yes—
77C11⋊#95C2318yes—
78C2×#2283—111nomaximal, Sylow
79C24×C11C2411yescharacteristic
80C23×D11—24no—
81C23×D11—24no—
82C23×D11C22×C414yes—
83C23×D11#4118yes—
84C23×D11C2412yes—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—28no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11C22×C414yes—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C2418yes—
95C22×C4×C11C2412yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2412yes—
98C22×Dic11—24no—
99C22×Dic11—28no—
100C22×Dic11—28no—
101C22×Dic11—28no—
102C22×Dic11C22×C414yes—
103C22×Dic11C22×C414yes—
104C22×Dic11C22×C414yes—
105C22×Dic11#4118yes—
106C22×Dic11#4118yes—
107C22×Dic11C2418yes—
108C22×Dic11C2412yes—
109C22×Dic11C2412yes—
110C22×Dic11C2412yes—
111C2×C4×D11—232no—
112C2×C4×D11—232no—
113C2×C4×D11—216no—
114C2×C4×D11—216no—
115C2×C4×D11—232no—
116C2×C4×D11—216no—
117C2×C4×D11C22×C4116yes—
118C2×C4×D11C22×C4116yes—
119C2×C4×D11C22×C4116yes—
120C42×C11C22×C4116yes—
121(C2×D11)⋊C4—232no—
122Dic11⋊C4—232no—
123C4×Dic11—232no—
124C4×Dic11C22×C4116yes—
125C4×Dic11C22×C4116yes—
126C4×Dic11C22×C4116yes—
127C23×C42—111no—
128#2283—1116no—
129C2×#383—111no—
130C2×#383D1111yescharacteristic, complemented
131C2×#382—112no—
132C2×#381—112no—
133C2×#380—112no—
134C2×C4×C4⋊C4—112no—
135C2×C4×C22⋊C4—112no—
136C2×#376—112no—
137C23×C11C23×C412yes—
138C23×C11C2×#4114yes—
139C23×C11C2×#4114yes—
140C23×C11C2×#4114yes—
141C23×C11C2511yescharacteristic
142C22×D11—28no—
143C22×D11—28no—
144C22×D11—232no—
145C22×D11—24no—
146C22×D11—24no—
147C22×D11#117116yes—
148C22×D11C23×C414yes—
149C22×D11C2×#4118yes—
150C2×C4×C11—28no—
151C2×C4×C11—28no—
152C2×C4×C11—28no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—28no—
157C2×C4×C11—28no—
158C2×C4×C11—28no—
159C2×C4×C11—416no—
160C2×C4×C11C23×C414yes—
161C2×C4×C11C23×C414yes—
162C2×C4×C11C23×C414yes—
163C2×Dic11—28no—
164C2×Dic11—24no—
165C2×Dic11—28no—
166C2×Dic11—28no—
167C2×Dic11—28no—
168C2×Dic11—416no—
169C2×Dic11#117116yes—
170C2×Dic11#117116yes—
171C2×Dic11C23×C414yes—
172C2×Dic11C23×C414yes—
173C2×Dic11C23×C414yes—
174C2×Dic11C2×#4118yes—
175C2×Dic11C2×#4118yes—
176C4×D11—232no—
177C4×D11—232no—
178C4×D11—232no—
179C24×C4—111no—
180C24×C4—111no—
181C24×C4—111no—
182C22×C4⋊C4—114no—
183C22×C22⋊C4—114no—
184C22×C42—111no—
185C22×C42—111no—
186C22×C42—111no—
187C22×C42—118no—
188C22×C42—1116no—
189C22×C42—114no—
190C22×C42C2×D1111yescharacteristic
191#383—118no—
192#383C2×D1118yescomplemented
193#382—1116no—
194#381—1116no—
195#380—1116no—
196C4×C4⋊C4—1116no—
197C4×C22⋊C4—1116no—
198#376—1116no—
199C2×#95—112no—
200C2×#95—114no—
201C2×#95—112no—
202C2×#95—112no—
203C2×#95C2×D1112yes—
204C2×#95C2×D1112yes—
205C2×#95C2×D1112yes—
206C22×C11C2×#11714yes—
207C22×C11C2×#11714yes—
208C22×C11C2×#11714yes—
209C22×C11#529116yes—
210C22×C11C24×C411yescharacteristic
211C22×C11C22×#4112yes—
212C22×C11C22×#4112yes—
213C22×C11C22×#4112yes—
214C2×D11—24no—
215C2×D11—24no—
216C2×D11—216no—
217C2×D11—232no—
218C2×D11C2×#11718yes—
219C4×C11—24no—
220C4×C11—24no—
221C4×C11—24no—
222C4×C11—48no—
223Dic11—24no—
224Dic11—48no—
225Dic11C2×#11718yes—
226Dic11C2×#11718yes—
227C25—111no—
228C23×C4—111no—
229C23×C4—111no—
230C23×C4—111no—
231C23×C4—118no—
232C23×C4—118no—
233C23×C4—118no—
234C23×C4—114no—
235C23×C4—114no—
236C23×C4—114no—
237C23×C4—114no—
238C23×C4—228no—
239C23×C4—228no—
240C23×C4—228no—
241C23×C4C22×D1114yes—
242C23×C4C22×D1111yescharacteristic
243C23×C4C22×D1111yescharacteristic
244C23×C4C22×D1111yescharacteristic
245C2×C4⋊C4—1116no—
246C2×C4⋊C4—2216no—
247C2×C22⋊C4—1116no—
248C2×C22⋊C4—2216no—
249C2×C42—118no—
250C2×C42—118no—
251C2×C42—118no—
252C2×C42—114no—
253C2×C42—114no—
254C2×C42—114no—
255C2×C42—1164no—
256C2×C42—1116no—
257C2×C42—2216no—
258C2×C42C4×D1118yes—
259C2×C42C22×D1114yes—
260#95—118no—
261#95—1116no—
262#95—118no—
263#95—118no—
264#95C22×D1118yes—
265#95C22×D1118yes—
266#95C22×D1118yes—
267C2×C11#228318yescomplemented
268C2×C11C22×#11711yescharacteristic
269C2×C11C22×#11711yescharacteristic
270C2×C11C22×#11711yescharacteristic
271C2×C11C2×#52914yes—
272D11—28no—
273C24—114no—
274C24—118no—
275C24—112no—
276C24—224no—
277C24—224no—
278C24C23×D1111yescharacteristic
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—28no—
283C22×C4—28no—
284C22×C4—28no—
285C22×C4—114no—
286C22×C4—114no—
287C22×C4—118no—
288C22×C4—118no—
289C22×C4—112no—
290C22×C4—112no—
291C22×C4—114no—
292C22×C4—112no—
293C22×C4—1116no—
294C22×C4—1116no—
295C22×C4—1116no—
296C22×C4—118no—
297C22×C4—2232no—
298C22×C4—2232no—
299C22×C4—2216no—
300C22×C4—2216no—
301C22×C4—2232no—
302C22×C4—2216no—
303C22×C4—224no—
304C22×C4—228no—
305C22×C4—228no—
306C22×C4—228no—
307C22×C4C2×C4×D1114yes—
308C22×C4C2×C4×D1114yes—
309C22×C4C2×C4×D1114yes—
310C22×C4C23×D1118yes—
311C22×C4C23×D1112yes—
312C22×C4C23×D1112yes—
313C22×C4C23×D1112yes—
314C4⋊C4—2232no—
315C22⋊C4—2232no—
316C42—1116no—
317C42—1116no—
318C42—1116no—
319C42—2232no—
320C42C2×C4×D11116yes—
321C11C2×#228311yescharacteristic, complemented, Sylow
322C23—1116no—
323C23—114no—
324C23—118no—
325C23—2232no—
326C23—228no—
327C23—228no—
328C23—224no—
329C23—224no—
330C23C22×C4×D1112yes—
331C23#41×D1114yes—
332C23#41×D1114yes—
333C23#41×D1114yes—
334C23C24×D1111yescharacteristic
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—28no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—28no—
342C2×C4—28no—
343C2×C4—28no—
344C2×C4—416no—
345C2×C4—1116no—
346C2×C4—1116no—
347C2×C4—114no—
348C2×C4—114no—
349C2×C4—118no—
350C2×C4—118no—
351C2×C4—114no—
352C2×C4—2232no—
353C2×C4—2232no—
354C2×C4—2232no—
355C2×C4—228no—
356C2×C4—224no—
357C2×C4—228no—
358C2×C4—228no—
359C2×C4—228no—
360C2×C4—4416no—
361C2×C4C22×C4×D1114yes—
362C2×C4C22×C4×D1114yes—
363C2×C4C22×C4×D1114yes—
364C22—118no—
365C22—2216no—
366C22—2232no—
367C22—224no—
368C22—224no—
369C22D11×#11714yes—
370C22D11×#11714yes—
371C22D11×#11714yes—
372C22#10623237116yes—
373C22C23×C4×D1111yescharacteristic
374C22C2×#41×D1112yes—
375C22C2×#41×D1112yes—
376C22C2×#41×D1112yes—
377C4—24no—
378C4—24no—
379C4—24no—
380C4—48no—
381C4—118no—
382C4—118no—
383C4—224no—
384C4—448no—
385C2—228no—
386C2#1307101318yesdirect product factor
387C2C2×D11×#11711yescharacteristic
388C2C2×D11×#11711yescharacteristic
389C2C2×D11×#11711yescharacteristic
390C2C2×#1062323714yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#383C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#383D11
hypocenterC11C2×#2283
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. #13071013C2direct (N × H)
3. C2×#10622550C2semidirect
4. C2×#10622263C2semidirect
7. C2×#10622262C2semidirect
9. C2×#10622261C2semidirect
10. C2×C11×#383C2semidirect
21. C2×C42×D11C4semidirect
23. C11×#383C22semidirect
31. #10622550C22semidirect
35. #10622263C22semidirect
36. #10622262C22semidirect
37. #10622261C22semidirect
70. C42×D11C2×C4semidirect
130. C2×#383D11semidirect
192. #383C2×D11semidirect
267. C2×C11#2283semidirect
321. C11C2×#2283semidirect
386. C2#13071013direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42×D112
#130710132
C2×#106225502
C2×#106222632
C2×#106222772
C2×#106222802
C2×#106222622
C2×#106222792
C2×#106222612
C2×C11×#3832
C2×#228311