Finite Group Databasebeta

← C2×#13071008 #14912054

Subgroups — C2×#13071008 #14912054

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D11C211yesmaximal, characteristic
2#13071008C2116yesmaximal, direct product factor
3C2×#10622264C212yesmaximal, complemented
4C2×#10622263C212yesmaximal, complemented
5C2×#10622277C212yesmaximal
6C2×#10622280C212yesmaximal
7C2×C4×Dic11⋊C4C212yesmaximal, complemented
8C2×C4×(C2×D11)⋊C4C212yesmaximal
9C2×#10622545C211yesmaximal, characteristic, complemented
10C2×C11×#376C211yesmaximal, characteristic, complemented
11C23×C4×D11C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C42×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2214yes—
17C22×Dic11⋊C4C2214yes—
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×C42×D11C4116yescomplemented
23C2×C42×D11C2218yes—
24C11×#376C2218yescomplemented
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C4×(C2×D11)⋊C4C22116yes—
32#10622545C2218yescomplemented
33C4×Dic11⋊C4C22116yescomplemented
34#10622280C22116yes—
35#10622277C22116yes—
36#10622264C22116yescomplemented
37#10622263C22116yescomplemented
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×C11—28no—
57C2×C42×C11C2×C418yes—
58C2×C42×C11C2318yes—
59C2×C42×C11C2314yes—
60C2×(C2×D11)⋊C4—216no—
61C2×(C2×D11)⋊C4C23116yes—
62C2×Dic11⋊C4—216no—
63C2×Dic11⋊C4C23116yes—
64C2×C4×Dic11—28no—
65C2×C4×Dic11C2×C418yes—
66C2×C4×Dic11C2×C418yes—
67C2×C4×Dic11C2×C418yes—
68C2×C4×Dic11C2318yes—
69C2×C4×Dic11C2314yes—
70C2×C4×Dic11C2314yes—
71C2×C4×Dic11C2314yes—
72C42×D11C2×C4164yescomplemented
73C11×#95C2318yes—
74C11×#95C2318yes—
75C11⋊#95C23116yes—
76C11⋊#95C2318yes—
77C11⋊#95C23116yes—
78C11⋊#95C2318yes—
79C2×#2283—111nomaximal, Sylow
80C24×C11C2411yescharacteristic
81C23×D11—24no—
82C23×D11—24no—
83C23×D11C22×C414yes—
84C23×D11#4118yes—
85C23×D11C2412yes—
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×C11#4118yes—
95C22×C4×C11C2418yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2412yes—
98C22×C4×C11C2412yes—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—28no—
102C22×Dic11—28no—
103C22×Dic11—28no—
104C22×Dic11C22×C414yes—
105C22×Dic11C22×C414yes—
106C22×Dic11C22×C414yes—
107C22×Dic11#4118yes—
108C22×Dic11C2418yes—
109C22×Dic11C2412yes—
110C22×Dic11C2412yes—
111C22×Dic11C2412yes—
112C2×C4×D11—232no—
113C2×C4×D11—216no—
114C2×C4×D11—232no—
115C2×C4×D11—216no—
116C2×C4×D11—232no—
117C2×C4×D11—216no—
118C2×C4×D11C22×C4116yes—
119C2×C4×D11C22×C4116yes—
120C2×C4×D11C22×C4116yes—
121C42×C11—216no—
122C42×C11C22×C4116yes—
123(C2×D11)⋊C4—232no—
124Dic11⋊C4—232no—
125C4×Dic11—216no—
126C4×Dic11C22×C4116yes—
127C4×Dic11C22×C4116yes—
128C4×Dic11C22×C4116yes—
129C23×C42—111no—
130#2283—1116no—
131C2×#383—112no—
132C2×#382—112no—
133C2×#381—112no—
134C2×#380—112no—
135C2×C4×C4⋊C4—112no—
136C2×C4×C22⋊C4—112no—
137C2×#376—111no—
138C2×#376D1111yescharacteristic, complemented
139C23×C11C23×C412yes—
140C23×C11C2×#4114yes—
141C23×C11C2×#4114yes—
142C23×C11C2×#4114yes—
143C23×C11C2511yescharacteristic
144C22×D11—28no—
145C22×D11—28no—
146C22×D11—232no—
147C22×D11—24no—
148C22×D11—24no—
149C22×D11#117116yes—
150C22×D11C23×C414yes—
151C22×D11C2×#4118yes—
152C2×C4×C11—28no—
153C2×C4×C11—28no—
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×C11#117116yes—
161C2×C4×C11C23×C414yes—
162C2×C4×C11C23×C414yes—
163C2×C4×C11C23×C414yes—
164C2×C4×C11C2×#4118yes—
165C2×Dic11—28no—
166C2×Dic11—28no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—28no—
170C2×Dic11—28no—
171C2×Dic11—28no—
172C2×Dic11—416no—
173C2×Dic11#117116yes—
174C2×Dic11C23×C414yes—
175C2×Dic11C23×C414yes—
176C2×Dic11C23×C414yes—
177C2×Dic11C2×#4118yes—
178C4×D11—232no—
179C4×D11—232no—
180C4×D11—232no—
181C24×C4—111no—
182C24×C4—111no—
183C24×C4—111no—
184C22×C4⋊C4—114no—
185C22×C22⋊C4—114no—
186C22×C42—111no—
187C22×C42—111no—
188C22×C42—111no—
189C22×C42—118no—
190C22×C42—1116no—
191C22×C42—112no—
192C22×C42C2×D1112yes—
193C22×C42C2×D1111yescharacteristic
194#383—1116no—
195#382—1116no—
196#381—1116no—
197#380—1116no—
198C4×C4⋊C4—1116no—
199C4×C22⋊C4—1116no—
200#376—118no—
201#376C2×D1118yescomplemented
202C2×#95—112no—
203C2×#95—112no—
204C2×#95—114no—
205C2×#95—114no—
206C2×#95C2×D1112yes—
207C2×#95C2×D1112yes—
208C22×C11C2×#11714yes—
209C22×C11C2×#11714yes—
210C22×C11C2×#11714yes—
211C22×C11#529116yes—
212C22×C11C24×C411yescharacteristic
213C22×C11C22×#4112yes—
214C22×C11C22×#4112yes—
215C22×C11C22×#4112yes—
216C2×D11—24no—
217C2×D11—24no—
218C2×D11—216no—
219C2×D11—232no—
220C2×D11C2×#11718yes—
221C4×C11—24no—
222C4×C11—24no—
223C4×C11—48no—
224C4×C11C2×#11718yes—
225Dic11—24no—
226Dic11—24no—
227Dic11—48no—
228Dic11C2×#11718yes—
229C25—111no—
230C23×C4—111no—
231C23×C4—111no—
232C23×C4—111no—
233C23×C4—118no—
234C23×C4—118no—
235C23×C4—118no—
236C23×C4—114no—
237C23×C4—114no—
238C23×C4—114no—
239C23×C4—114no—
240C23×C4—228no—
241C23×C4—228no—
242C23×C4—228no—
243C23×C4C22×D1114yes—
244C23×C4C22×D1111yescharacteristic
245C23×C4C22×D1111yescharacteristic
246C23×C4C22×D1111yescharacteristic
247C2×C4⋊C4—1116no—
248C2×C4⋊C4—2216no—
249C2×C22⋊C4—1116no—
250C2×C22⋊C4—2216no—
251C2×C42—28no—
252C2×C42—118no—
253C2×C42—118no—
254C2×C42—118no—
255C2×C42—114no—
256C2×C42—114no—
257C2×C42—114no—
258C2×C42—1164no—
259C2×C42—118no—
260C2×C42—228no—
261C2×C42C4×D1118yes—
262C2×C42C22×D1118yes—
263C2×C42C22×D1114yes—
264#95—118no—
265#95—118no—
266#95—1116no—
267#95—1116no—
268#95C22×D1118yes—
269#95C22×D1118yes—
270C2×C11#228318yescomplemented
271C2×C11C22×#11711yescharacteristic
272C2×C11C22×#11711yescharacteristic
273C2×C11C22×#11711yescharacteristic
274C2×C11C2×#52914yes—
275D11—28no—
276C24—114no—
277C24—118no—
278C24—112no—
279C24—224no—
280C24—224no—
281C24C23×D1111yescharacteristic
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—28no—
285C22×C4—28no—
286C22×C4—28no—
287C22×C4—114no—
288C22×C4—118no—
289C22×C4—112no—
290C22×C4—114no—
291C22×C4—114no—
292C22×C4—112no—
293C22×C4—112no—
294C22×C4—1116no—
295C22×C4—1116no—
296C22×C4—1116no—
297C22×C4—118no—
298C22×C4—2232no—
299C22×C4—2216no—
300C22×C4—2232no—
301C22×C4—2216no—
302C22×C4—224no—
303C22×C4—224no—
304C22×C4—2232no—
305C22×C4—2216no—
306C22×C4—228no—
307C22×C4—228no—
308C22×C4—228no—
309C22×C4C2×C4×D1114yes—
310C22×C4C2×C4×D1114yes—
311C22×C4C2×C4×D1114yes—
312C22×C4#433918yes—
313C22×C4C23×D1118yes—
314C22×C4C23×D1112yes—
315C22×C4C23×D1112yes—
316C22×C4C23×D1112yes—
317C4⋊C4—2232no—
318C22⋊C4—2232no—
319C42—216no—
320C42—1116no—
321C42—1116no—
322C42—1116no—
323C42—2216no—
324C42C2×C4×D11116yes—
325C11C2×#228311yescharacteristic, complemented, Sylow
326C23—1116no—
327C23—114no—
328C23—118no—
329C23—228no—
330C23—228no—
331C23—2232no—
332C23—224no—
333C23—224no—
334C23C22×C4×D1112yes—
335C23C2×#433914yes—
336C23#41×D1114yes—
337C23#41×D1114yes—
338C23C24×D1111yescharacteristic
339C2×C4—28no—
340C2×C4—28no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—28no—
344C2×C4—28no—
345C2×C4—28no—
346C2×C4—416no—
347C2×C4—1116no—
348C2×C4—114no—
349C2×C4—118no—
350C2×C4—114no—
351C2×C4—114no—
352C2×C4—2232no—
353C2×C4—2232no—
354C2×C4—228no—
355C2×C4—228no—
356C2×C4—224no—
357C2×C4—224no—
358C2×C4—2232no—
359C2×C4—228no—
360C2×C4—228no—
361C2×C4—228no—
362C2×C4—4416no—
363C2×C4#66925116yes—
364C2×C4C22×C4×D1114yes—
365C2×C4C22×C4×D1114yes—
366C2×C4C22×C4×D1114yes—
367C2×C4C2×#433918yes—
368C22—118no—
369C22—2216no—
370C22—2232no—
371C22—224no—
372C22—224no—
373C22C2×#6692514yes—
374C22D11×#11714yes—
375C22D11×#11714yes—
376C22#10623059116yes—
377C22C23×C4×D1111yescharacteristic
378C22C22×#433912yes—
379C22C2×#41×D1112yes—
380C22C2×#41×D1112yes—
381C4—24no—
382C4—24no—
383C4—48no—
384C4—118no—
385C4—224no—
386C4—224no—
387C4—448no—
388C4C2×#6692518yes—
389C2—228no—
390C2#1307100818yesdirect product factor
391C2C2×D11×#11711yescharacteristic
392C2C2×D11×#11711yescharacteristic
393C2C22×#6692511yescharacteristic
394C2C2×#1062305914yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#376C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#376D11
hypocenterC11C2×#2283
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
2. #13071008C2direct (N × H)
3. C2×#10622264C2semidirect
4. C2×#10622263C2semidirect
7. C2×C4×Dic11⋊C4C2semidirect
9. C2×#10622545C2semidirect
10. C2×C11×#376C2semidirect
22. C2×C42×D11C4semidirect
24. C11×#376C22semidirect
32. #10622545C22semidirect
33. C4×Dic11⋊C4C22semidirect
36. #10622264C22semidirect
37. #10622263C22semidirect
72. C42×D11C2×C4semidirect
138. C2×#376D11semidirect
201. #376C2×D11semidirect
270. C2×C11#2283semidirect
325. C11C2×#2283semidirect
390. C2#13071008direct (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
#130710082
C2×#106222642
C2×#106222632
C2×#106222772
C2×#106222802
C2×C4×Dic11⋊C42
C2×C4×(C2×D11)⋊C42
C2×#106225452
C2×C11×#3762
C2×#228311