Finite Group Databasebeta

← C2×#13076796 #14960149

Subgroups — C2×#13076796 #14960149

Order 2816.

1718 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076796C2116yesmaximal, direct product factor
2C2×C11⋊#401C212yesmaximal
3C2×#10622273C212yesmaximal
4C2×#10622272C212yesmaximal
5C2×#10622599C211yesmaximal, characteristic
6C2×#10622597C212yesmaximal
7C2×#10622592C212yesmaximal
8C2×#10622587C211yesmaximal, characteristic
9C2×#10622594C212yesmaximal
10C2×C11×#398C211yesmaximal, characteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic11C2212yes—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C11×#398C2218yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33#10622599C2218yes—
34#10622597C22116yes—
35#10622594C22116yes—
36#10622592C22116yes—
37#10622587C2218yes—
38C11⋊#401C22116yes—
39#10622273C22116yes—
40#10622272C22116yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C22×Dic22—24no—
51C22×Dic22—42no—
52C22×Dic22—42no—
53C22×Dic22C2314yes—
54C2×C11×C4⋊C4—28no—
55C2×C11×C4⋊C4—42no—
56C2×C11×C4⋊C4—42no—
57C2×C11×C4⋊C4C2318yes—
58C2×C11×C4⋊C4C2314yes—
59C2×C11×C4⋊C4C2314yes—
60C2×C4⋊Dic11—44no—
61C2×C4⋊Dic11—42no—
62C2×C4⋊Dic11C2318yes—
63C2×C4⋊Dic11C2314yes—
64C2×Dic11⋊C4—44no—
65C2×Dic11⋊C4—44no—
66C2×Dic11⋊C4C2318yes—
67C2×Dic11⋊C4C2318yes—
68C2×C4×Dic11—42no—
69C2×C4×Dic11C2314yes—
70C11×#95C2318yes—
71C11×#95C2314yes—
72C11⋊#95C2314yes—
73C11⋊#95C2318yes—
74C11⋊#95C2318yes—
75C11⋊#95C2318yes—
76C11⋊#95C2318yes—
77C11⋊#95C2318yes—
78C11⋊#95C2318yes—
79C11⋊#95C2318yes—
80C11⋊#95C2318yes—
81C11⋊#95C2318yes—
82C2×#2833—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11#4114yes—
97C22×C4×C11C2414yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2412yes—
100C22×C4×C11C2414yes—
101C22×C4×C11C2412yes—
102C22×Dic11—24no—
103C22×Dic11—24no—
104C22×Dic11—24no—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—28no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11C2414yes—
114C22×Dic11C2414yes—
115C22×Dic11C2414yes—
116C22×Dic11C2414yes—
117C2×Dic22—28no—
118C2×Dic22—44no—
119C2×Dic22—44no—
120C2×Dic22—416no—
121C11×C4⋊C4—216no—
122C11×C4⋊C4—44no—
123C11×C4⋊C4—44no—
124C4⋊Dic11—48no—
125C4⋊Dic11—44no—
126Dic11⋊C4—48no—
127Dic11⋊C4—48no—
128C4×Dic11—44no—
129#2833—1116no—
130C2×#401—112no—
131C2×#400—112no—
132C2×#400—112no—
133C2×#400—111no—
134C2×#398—112no—
135C2×#398D1111yescharacteristic
136C2×#395—112no—
137C2×#391—111no—
138C2×#387—112no—
139C23×C11C2×#4112yes—
140C23×C11H(5,𝔽2)12yes—
141C23×C11H(5,𝔽2)12yes—
142C23×C112−1+414yes—
143C23×C112−1+414yes—
144C23×C11C2511yescharacteristic
145C2×C4×C11—28no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—48no—
159C2×C4×C11—48no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11C2×#4114yes—
163C2×Dic11—24no—
164C2×Dic11—24no—
165C2×Dic11—24no—
166C2×Dic11—24no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—24no—
170C2×Dic11—28no—
171C2×Dic11—24no—
172C2×Dic11—24no—
173C2×Dic11—24no—
174C2×Dic11—48no—
175C2×Dic11—48no—
176C2×Dic11—48no—
177C2×Dic11—48no—
178Dic22—416no—
179C23×Q8—111no—
180C22×C4⋊C4—112no—
181C22×C4⋊C4—112no—
182C22×C4⋊C4—112no—
183C22×C4⋊C4—111no—
184C22×C4⋊C4C2×D1112yes—
185C22×C4⋊C4C2×D1111yescharacteristic
186C22×C4⋊C4C2×D1111yescharacteristic
187C22×C42—111no—
188#401—1116no—
189#400—118no—
190#400—1116no—
191#400—1116no—
192#398—1116no—
193#398C2×D1118yes—
194#395—1116no—
195#391—118no—
196#387—1116no—
197C2×#95—112no—
198C2×#95—112no—
199C2×#95—112no—
200C2×#95—112no—
201C2×#95—112no—
202C2×#95—112no—
203C2×#95—111no—
204C2×#95—112no—
205C2×#95—112no—
206C2×#95—112no—
207C2×#95C2×D1112yes—
208C2×#95C2×D1111yescharacteristic
209C22×C11#53814yes—
210C22×C11#54118yes—
211C22×C11#56314yes—
212C22×C11#56314yes—
213C22×C11#56318yes—
214C22×C11C22×#4111yescharacteristic
215C22×C11C2×H(5,𝔽2)11yescharacteristic
216C22×C11C2×H(5,𝔽2)11yescharacteristic
217C22×C11C2×2−1+412yes—
218C22×C11C2×2−1+412yes—
219C4×C11—24no—
220C4×C11—44no—
221C4×C11—44no—
222C4×C11—42no—
223C4×C11—42no—
224Dic11—44no—
225Dic11—44no—
226Dic11—44no—
227Dic11—44no—
228C22×Q8—114no—
229C22×Q8—224no—
230C22×Q8—442no—
231C22×Q8—442no—
232C23×C4—112no—
233C23×C4—112no—
234C23×C4—112no—
235C23×C4—112no—
236C23×C4C22×D1112yes—
237C23×C4C22×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C23×C4C22×D1112yes—
240C23×C4C22×D1111yescharacteristic
241C2×C4⋊C4—28no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—118no—
245C2×C4⋊C4—118no—
246C2×C4⋊C4—118no—
247C2×C4⋊C4—114no—
248C2×C4⋊C4—444no—
249C2×C4⋊C4—444no—
250C2×C4⋊C4—442no—
251C2×C4⋊C4—444no—
252C2×C4⋊C4C22×D1118yes—
253C2×C4⋊C4C22×D1114yes—
254C2×C4⋊C4C22×D1114yes—
255C2×C42—114no—
256C2×C42—442no—
257#95—118no—
258#95—118no—
259#95—118no—
260#95—118no—
261#95—118no—
262#95—118no—
263#95—118no—
264#95—118no—
265#95—118no—
266#95—114no—
267#95C22×D1118yes—
268#95C22×D1114yes—
269C2×C11#283318yescomplemented
270C2×C11C2×#53811yescharacteristic
271C2×C11C2×#54112yes—
272C2×C11C2×#56311yescharacteristic
273C2×C11C2×#56311yescharacteristic
274C2×C11C2×#56312yes—
275C24C23×D1111yescharacteristic
276C2×Q8—228no—
277C2×Q8—444no—
278C2×Q8—444no—
279C2×Q8—4416no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—114no—
293C22×C4—114no—
294C22×C4—114no—
295C22×C4—114no—
296C22×C4—224no—
297C22×C4—224no—
298C22×C4—224no—
299C22×C4—228no—
300C22×C4—224no—
301C22×C4—224no—
302C22×C4—224no—
303C22×C4—224no—
304C22×C4—224no—
305C22×C4—224no—
306C22×C4—224no—
307C22×C4#434114yes—
308C22×C4C23×D1114yes—
309C22×C4C23×D1112yes—
310C22×C4C23×D1112yes—
311C22×C4C23×D1114yes—
312C22×C4C23×D1112yes—
313C4⋊C4—216no—
314C4⋊C4—44no—
315C4⋊C4—44no—
316C4⋊C4—448no—
317C4⋊C4—448no—
318C4⋊C4—444no—
319C4⋊C4—448no—
320C42—444no—
321C11C2×#283311yescharacteristic, complemented, Sylow
322C23C2×#434112yes—
323C23#6703712yes—
324C23#6704014yes—
325C23#6704212yes—
326C23#6704314yes—
327C23C24×D1111yescharacteristic
328Q8—4416no—
329C2×C4—28no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—48no—
343C2×C4—48no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—224no—
347C2×C4—224no—
348C2×C4—224no—
349C2×C4—228no—
350C2×C4—224no—
351C2×C4—224no—
352C2×C4—224no—
353C2×C4—224no—
354C2×C4—224no—
355C2×C4—224no—
356C2×C4—224no—
357C2×C4—448no—
358C2×C4—448no—
359C2×C4—448no—
360C2×C4—448no—
361C2×C4C2×#434114yes—
362C22#1062314814yes—
363C22#1062315618yes—
364C22#1062318214yes—
365C22#1062323018yes—
366C22#1062326614yes—
367C22C22×#434111yescharacteristic
368C22C2×#6703711yescharacteristic
369C22C2×#6704012yes—
370C22C2×#6704211yescharacteristic
371C22C2×#6704312yes—
372C4—24no—
373C4—44no—
374C4—42no—
375C4—42no—
376C4—44no—
377C4—444no—
378C4—444no—
379C4—444no—
380C4—444no—
381C2#1307679618yesdirect product factor
382C2C2×#1062314811yescharacteristic
383C2C2×#1062315612yes—
384C2C2×#1062326611yescharacteristic
385C2C2×#1062318211yescharacteristic
386C2C2×#1062323012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socle, prime radicalC24×C11C24
hypercenterC2×#398D11
hypocenterC11C2×#2833
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #13076796C2direct (N × H)
269. C2×C11#2833semidirect
321. C11C2×#2833semidirect
381. C2#13076796direct (N × H)

Maximal subgroups

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

subgroupindex
#130767962
C2×C11⋊#4012
C2×#106222732
C2×#106222722
C2×#106225992
C2×#106225972
C2×#106225922
C2×#106225872
C2×#106225942
C2×C11×#3982
C2×#283311