Finite Group Databasebeta

← C2×#13071010 #14912056

Subgroups — C2×#13071010 #14912056

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic11C211yesmaximal, characteristic
2#13071010C2116yesmaximal, direct product factor
3C2×#10622264C212yesmaximal, complemented
4C2×#10622263C212yesmaximal, complemented
5C2×#10622556C212yesmaximal
6C2×#10622555C212yesmaximal
7C2×C4×Dic11⋊C4C212yesmaximal, complemented
8C2×C4×C22⋊Dic11C211yesmaximal, characteristic
9C2×#10622545C212yesmaximal, complemented
10C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C42×C11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×Dic11⋊C4C2214yes—
18C22×C4×Dic11C4116yescomplemented
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2218yes—
25C4×C11×C22⋊C4C2218yes—
26C2×C11×#95C2212yes—
27C4×C22⋊Dic11C2218yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2214yes—
32#10622556C22116yes—
33#10622555C22116yes—
34#10622545C22116yescomplemented
35C4×Dic11⋊C4C22116yescomplemented
36#10622264C22116yescomplemented
37#10622263C22116yescomplemented
38C25×C11C2311yescharacteristic
39C23×C4×C11—28no—
40C23×C4×C11C2×C418yes—
41C23×C4×C11C2314yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2314yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—28no—
46C23×Dic11—28no—
47C23×Dic11C2×C418yes—
48C23×Dic11C2×C418yes—
49C23×Dic11C2314yes—
50C23×Dic11C2314yes—
51C23×Dic11C2314yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C2×C11×C22⋊C4—28no—
57C2×C11×C22⋊C4C2318yes—
58C2×C42×C11—28no—
59C2×C42×C11C2318yes—
60C2×C22⋊Dic11—28no—
61C2×C22⋊Dic11C2318yes—
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×Dic11C2×C418yes—
69C2×C4×Dic11C2×C4164yescomplemented
70C2×C4×Dic11C2318yes—
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2314yes—
75C11×#95C2318yes—
76C11⋊#95C2318yes—
77C11⋊#95C23116yes—
78C11⋊#95C23116yes—
79C11⋊#95C23116yes—
80C2×#2283—111nomaximal, Sylow
81C24×C11—24no—
82C24×C11—24no—
83C24×C11C22×C414yes—
84C24×C11#4118yes—
85C24×C11C2412yes—
86C24×C11C2411yescharacteristic
87C22×C4×C11—24no—
88C22×C4×C11—232no—
89C22×C4×C11—216no—
90C22×C4×C11—28no—
91C22×C4×C11—28no—
92C22×C4×C11—28no—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C22×C4116yes—
95C22×C4×C11C22×C414yes—
96C22×C4×C11#4118yes—
97C22×C4×C11C2418yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2412yes—
100C22×Dic11—232no—
101C22×Dic11—216no—
102C22×Dic11—232no—
103C22×Dic11—216no—
104C22×Dic11—24no—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11—28no—
108C22×Dic11—28no—
109C22×Dic11—28no—
110C22×Dic11C22×C414yes—
111C22×Dic11C22×C414yes—
112C22×Dic11C22×C414yes—
113C22×Dic11C22×C4116yes—
114C22×Dic11C22×C4116yes—
115C22×Dic11C22×C414yes—
116C22×Dic11#4118yes—
117C22×Dic11C2418yes—
118C22×Dic11C2412yes—
119C22×Dic11C2412yes—
120C22×Dic11C2412yes—
121C22×Dic11C2412yes—
122C11×C22⋊C4—216no—
123C42×C11—216no—
124C22⋊Dic11—216no—
125Dic11⋊C4—232no—
126C4×Dic11—216no—
127C4×Dic11C22×C4116yes—
128C4×Dic11C22×C4116yes—
129C4×Dic11C22×C4116yes—
130C4×Dic11C22×C4116yes—
131C23×C42—111no—
132#2283—1116no—
133C2×#383—112no—
134C2×#382—112no—
135C2×#381—112no—
136C2×#380—112no—
137C2×C4×C4⋊C4—112no—
138C2×C4×C22⋊C4—111no—
139C2×C4×C22⋊C4D1111yescharacteristic
140C2×#376—112no—
141C23×C11—28no—
142C23×C11—28no—
143C23×C11—232no—
144C23×C11—24no—
145C23×C11—24no—
146C23×C11#117116yes—
147C23×C11C23×C414yes—
148C23×C11C23×C412yes—
149C23×C11C2×#4118yes—
150C23×C11C2×#4114yes—
151C23×C11C2×#4114yes—
152C23×C11C2×#4114yes—
153C23×C11C2511yescharacteristic
154C2×C4×C11—28no—
155C2×C4×C11—24no—
156C2×C4×C11—232no—
157C2×C4×C11—28no—
158C2×C4×C11—28no—
159C2×C4×C11—28no—
160C2×C4×C11—416no—
161C2×C4×C11#117116yes—
162C2×C4×C11C23×C414yes—
163C2×C4×C11C23×C414yes—
164C2×C4×C11C2×#4118yes—
165C2×Dic11—232no—
166C2×Dic11—28no—
167C2×Dic11—28no—
168C2×Dic11—28no—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11—24no—
172C2×Dic11—232no—
173C2×Dic11—28no—
174C2×Dic11—28no—
175C2×Dic11—28no—
176C2×Dic11—416no—
177C2×Dic11#117116yes—
178C2×Dic11C23×C414yes—
179C2×Dic11C23×C414yes—
180C2×Dic11C23×C414yes—
181C2×Dic11C23×C414yes—
182C2×Dic11C2×#4118yes—
183C24×C4—111no—
184C24×C4—111no—
185C24×C4C2×D1111yescharacteristic
186C22×C4⋊C4—114no—
187C22×C22⋊C4—112no—
188C22×C22⋊C4C2×D1112yes—
189C22×C42—111no—
190C22×C42—111no—
191C22×C42—118no—
192C22×C42—111no—
193C22×C42—111no—
194C22×C42—1116no—
195C22×C42—112no—
196C22×C42C2×D1112yes—
197#383—1116no—
198#382—1116no—
199#381—1116no—
200#380—1116no—
201C4×C4⋊C4—1116no—
202C4×C22⋊C4—118no—
203C4×C22⋊C4C2×D1118yes—
204#376—1116no—
205C2×#95—114no—
206C2×#95—114no—
207C2×#95—112no—
208C2×#95—114no—
209C2×#95C2×D1112yes—
210C22×C11—24no—
211C22×C11—24no—
212C22×C11—216no—
213C22×C11—232no—
214C22×C11C2×#11718yes—
215C22×C11C2×#11714yes—
216C22×C11C2×#11714yes—
217C22×C11C2×#11714yes—
218C22×C11#529116yes—
219C22×C11C24×C411yescharacteristic
220C22×C11C22×#4112yes—
221C22×C11C22×#4112yes—
222C22×C11C22×#4112yes—
223C4×C11—24no—
224C4×C11—48no—
225C4×C11C2×#11718yes—
226Dic11—24no—
227Dic11—24no—
228Dic11—24no—
229Dic11—48no—
230Dic11C2×#11718yes—
231C25C22×D1111yescharacteristic
232C23×C4—28no—
233C23×C4—111no—
234C23×C4—118no—
235C23×C4—118no—
236C23×C4—111no—
237C23×C4—111no—
238C23×C4—111no—
239C23×C4—114no—
240C23×C4—114no—
241C23×C4—114no—
242C23×C4—228no—
243C23×C4—228no—
244C23×C4C4×D1118yes—
245C23×C4C22×D1114yes—
246C23×C4C22×D1111yescharacteristic
247C23×C4C22×D1114yes—
248C23×C4C22×D1111yescharacteristic
249C2×C4⋊C4—1116no—
250C2×C4⋊C4—2216no—
251C2×C22⋊C4—28no—
252C2×C22⋊C4—118no—
253C2×C22⋊C4—228no—
254C2×C22⋊C4C22×D1118yes—
255C2×C42—28no—
256C2×C42—118no—
257C2×C42—118no—
258C2×C42—118no—
259C2×C42—118no—
260C2×C42—1164no—
261C2×C42—114no—
262C2×C42—114no—
263C2×C42—114no—
264C2×C42—114no—
265C2×C42—118no—
266C2×C42—228no—
267C2×C42C22×D1118yes—
268#95—1116no—
269#95—1116no—
270#95—118no—
271#95—1116no—
272#95C22×D1118yes—
273C2×C11—28no—
274C2×C11#228318yescomplemented
275C2×C11C22×#11711yescharacteristic
276C2×C11C22×#11711yescharacteristic
277C2×C11C22×#11711yescharacteristic
278C2×C11C2×#52914yes—
279C24—24no—
280C24—24no—
281C24C2×C4×D1114yes—
282C24#433918yes—
283C24C23×D1112yes—
284C24C23×D1111yescharacteristic
285C22×C4—24no—
286C22×C4—232no—
287C22×C4—216no—
288C22×C4—28no—
289C22×C4—28no—
290C22×C4—28no—
291C22×C4—114no—
292C22×C4—118no—
293C22×C4—112no—
294C22×C4—1116no—
295C22×C4—1116no—
296C22×C4—114no—
297C22×C4—114no—
298C22×C4—114no—
299C22×C4—112no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—118no—
303C22×C4—2232no—
304C22×C4—2216no—
305C22×C4—2232no—
306C22×C4—2216no—
307C22×C4—224no—
308C22×C4—224no—
309C22×C4—224no—
310C22×C4—228no—
311C22×C4—228no—
312C22×C4—228no—
313C22×C4C2×C4×D1114yes—
314C22×C4C2×C4×D11116yes—
315C22×C4C2×C4×D1114yes—
316C22×C4#434118yes—
317C22×C4C23×D1118yes—
318C22×C4C23×D1112yes—
319C22×C4C23×D1112yes—
320C4⋊C4—2232no—
321C22⋊C4—216no—
322C22⋊C4—2216no—
323C42—216no—
324C42—1116no—
325C42—1116no—
326C42—1116no—
327C42—1116no—
328C42—2216no—
329C11C2×#228311yescharacteristic, complemented, Sylow
330C23—28no—
331C23—28no—
332C23—232no—
333C23—24no—
334C23—24no—
335C23#66925116yes—
336C23C22×C4×D1114yes—
337C23C22×C4×D1112yes—
338C23C2×#433918yes—
339C23C2×#433914yes—
340C23C2×#434114yes—
341C23#41×D1114yes—
342C23C24×D1111yescharacteristic
343C2×C4—28no—
344C2×C4—24no—
345C2×C4—232no—
346C2×C4—28no—
347C2×C4—28no—
348C2×C4—28no—
349C2×C4—416no—
350C2×C4—1116no—
351C2×C4—114no—
352C2×C4—118no—
353C2×C4—114no—
354C2×C4—114no—
355C2×C4—114no—
356C2×C4—2232no—
357C2×C4—2232no—
358C2×C4—228no—
359C2×C4—228no—
360C2×C4—228no—
361C2×C4—224no—
362C2×C4—224no—
363C2×C4—224no—
364C2×C4—228no—
365C2×C4—228no—
366C2×C4—228no—
367C2×C4—4416no—
368C2×C4#66930116yes—
369C2×C4C22×C4×D1114yes—
370C2×C4C22×C4×D1114yes—
371C2×C4C2×#434118yes—
372C22—216no—
373C22—232no—
374C22—24no—
375C22—24no—
376C22C2×#6692518yes—
377C22C2×#6692514yes—
378C22C2×#6693014yes—
379C22D11×#11714yes—
380C22#10623069116yes—
381C22C23×C4×D1111yescharacteristic
382C22C22×#433912yes—
383C22C22×#434112yes—
384C22C2×#41×D1112yes—
385C4—24no—
386C4—48no—
387C4—118no—
388C4—224no—
389C4—224no—
390C4—224no—
391C4—448no—
392C4C2×#6693018yes—
393C2—28no—
394C2#1307101018yesdirect product factor
395C2C2×D11×#11711yescharacteristic
396C2C22×#6693011yescharacteristic
397C2C22×#6692511yescharacteristic
398C2C2×#1062306914yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2283
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071010C2direct (N × H)
3. C2×#10622264C2semidirect
4. C2×#10622263C2semidirect
7. C2×C4×Dic11⋊C4C2semidirect
9. C2×#10622545C2semidirect
18. C22×C4×Dic11C4semidirect
34. #10622545C22semidirect
35. C4×Dic11⋊C4C22semidirect
36. #10622264C22semidirect
37. #10622263C22semidirect
69. C2×C4×Dic11C2×C4semidirect
274. C2×C11#2283semidirect
329. C11C2×#2283semidirect
394. C2#13071010direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
#130710102
C2×#106222642
C2×#106222632
C2×#106225562
C2×#106225552
C2×C4×Dic11⋊C42
C2×C4×C22⋊Dic112
C2×#106225452
C2×C4×C11×C22⋊C42
C2×#228311