Finite Group Databasebeta

← C11×#34643 #14611836

Subgroups — C11×#34643 #14611836

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C212yesmaximal, complemented
2C11×#2664C214yesmaximal, complemented
3C11×#2663C214yesmaximal, complemented
4C11×#2662C214yesmaximal, complemented
5C11×#2661C214yesmaximal, complemented
6C11×#2399C211yesmaximal, characteristic, complemented
7C11×#2398C212yesmaximal, complemented
8C11×#2397C211yesmaximal, characteristic, complemented
9C11×#2392C214yesmaximal, complemented
10C11×#2293C214yesmaximal, complemented
11C4×C11×#117C211yesmaximal, characteristic, complemented
12C11×#529—216no—
13C2×C11×#126C2214yes—
14C2×C11×#125C2212yes—
15C2×C11×#124C2212yes—
16C2×C11×#123C2214yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×#121C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C4×D4×C11C2214yes—
21C2×C4×D4×C11C2214yes—
22C2×C4×D4×C11C2212yes—
23C2×C11×#117C2212yes—
24C2×C11×#117C2214yes—
25C22×C42×C11C2211yescharacteristic
26C11×#400C2214yes—
27C11×#399C2214yes—
28C11×#398C2214yes—
29C11×#398C2214yes—
30C11×#397C2214yes—
31C11×#397C2214yes—
32C11×#396C2218yes—
33C11×#395C2214yes—
34C11×#394C2218yes—
35C11×#394C2214yes—
36C11×#394C2214yes—
37C11×#393C2214yes—
38C11×#392C2214yes—
39C11×#392C2214yes—
40C11×#390C2218yes—
41C11×#389C2218yes—
42C11×#388C2218yes—
43C11×#388C2218yes—
44C4×C11×C4⋊C4C2214yes—
45C4×C11×C4⋊C4C2214yes—
46C4×C11×C22⋊C4C2218yes—
47C4×C11×C22⋊C4C2214yes—
48C11×#376C2211yescharacteristic
49C11×#376C2211yescharacteristic
50C43×C11C2212yes—
51C22×Q8×C11C2312yes—
52C22×D4×C11C2314yes—
53C22×D4×C11C2312yes—
54C22×D4×C11C2314yes—
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C11×#126—216no—
59C11×#125—28no—
60C11×#124—28no—
61C11×#123—216no—
62C11×C22⋊Q8—28no—
63C11×#121—28no—
64C4×Q8×C11—28no—
65C4×D4×C11—216no—
66C4×D4×C11—28no—
67C4×D4×C11—216no—
68C11×#117—216no—
69C11×#117—28no—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2318yes—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C11×C22⋊C4C2318yes—
88C2×C42×C11D418yescomplemented
89C2×C42×C11C2312yes—
90C2×C42×C11C2314yes—
91C2×C42×C11C2318yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2312yes—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11×#95C2318yes—
99C11×#95C2318yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102#34643C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11C2414yes—
104C24×C11C2411yescharacteristic
105C2×Q8×C11—24no—
106C2×Q8×C11—44no—
107C2×D4×C11—28no—
108C2×D4×C11—24no—
109C2×D4×C11—28no—
110C2×D4×C11—48no—
111C2×D4×C11—44no—
112C2×D4×C11—48no—
113C22×C4×C11—24no—
114C22×C4×C11—28no—
115C22×C4×C11—216no—
116C22×C4×C11—44no—
117C22×C4×C11C2×D414yes—
118C22×C4×C11C2×D418yes—
119C22×C4×C11C2414yes—
120C22×C4×C11C2414yes—
121C22×C4×C11C2414yes—
122C22×C4×C11C2414yes—
123C22×C4×C11C2412yes—
124C22×C4×C11C2412yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2414yes—
127C22×C4×C11C2411yescharacteristic
128C11×C4⋊C4—28no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—48no—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—28no—
140C11×C22⋊C4—28no—
141C11×C22⋊C4—28no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—216no—
144C11×C22⋊C4—48no—
145C11×C22⋊C4—48no—
146C42×C11—28no—
147C42×C11—24no—
148C42×C11—48no—
149C42×C11C2×D414yes—
150C42×C11C2×D414yes—
151C42×C11C2×D418yes—
152C42×C11#4118yes—
153C2×#529C2×C1112yescomplemented
154#2664C2×C1114yescomplemented
155#2663C2×C1114yescomplemented
156#2662C2×C1114yescomplemented
157#2661C2×C1114yescomplemented
158#2399C2×C1111yescharacteristic, complemented
159#2398C2×C1112yescomplemented
160#2397C2×C1111yescharacteristic, complemented
161#2392C2×C1114yescomplemented
162#2293C2×C1114yescomplemented
163C4×#117C2×C1111yescharacteristic, complemented
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—24no—
167C23×C11—28no—
168C23×C11—24no—
169C23×C11—28no—
170C23×C11—24no—
171C23×C11C22×D412yes—
172C23×C11C2511yescharacteristic
173Q8×C11—48no—
174D4×C11—48no—
175D4×C11—416no—
176D4×C11—416no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—28no—
180C2×C4×C11—24no—
181C2×C4×C11—28no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—28no—
187C2×C4×C11—28no—
188C2×C4×C11—24no—
189C2×C4×C11—28no—
190C2×C4×C11—24no—
191C2×C4×C11—48no—
192C2×C4×C11—416no—
193C2×C4×C11C22×D412yes—
194C2×C4×C11C22×D414yes—
195C2×C4×C11C22×D414yes—
196C2×C4×C11C22×D412yes—
197C2×C4×C11C2×#4118yes—
198C2×C4×C11C2×#4114yes—
199#529—216no—
200C2×#126C22×C1114yes—
201C2×#125C22×C1112yes—
202C2×#124C22×C1112yes—
203C2×#123C22×C1114yes—
204C2×C22⋊Q8C22×C1112yes—
205C2×#121C22×C1112yes—
206C2×C4×Q8C22×C1112yes—
207C2×C4×D4C22×C1114yes—
208C2×C4×D4C22×C1114yes—
209C2×C4×D4C22×C1112yes—
210C2×#117C22×C1112yes—
211C2×#117C22×C1114yes—
212C22×C42C22×C1111yescharacteristic
213#400C22×C1114yes—
214#399C22×C1114yes—
215#398C22×C1114yes—
216#398C22×C1114yes—
217#397C22×C1114yes—
218#397C22×C1114yes—
219#396C22×C1118yes—
220#395C22×C1114yes—
221#394C22×C1118yes—
222#394C22×C1114yes—
223#394C22×C1114yes—
224#393C22×C1114yes—
225#392C22×C1114yes—
226#392C22×C1114yes—
227#390C22×C1118yes—
228#389C22×C1118yes—
229#388C22×C1118yes—
230#388C22×C1118yes—
231C4×C4⋊C4C22×C1114yes—
232C4×C4⋊C4C22×C1114yes—
233C4×C22⋊C4C22×C1118yes—
234C4×C22⋊C4C22×C1114yes—
235#376C22×C1111yescharacteristic
236#376C22×C1111yescharacteristic
237C43C22×C1112yes—
238C22×C11—22no—
239C22×C11—24no—
240C22×C11—44no—
241C22×C11—44no—
242C22×C11—44no—
243C22×C11—44no—
244C22×C11—48no—
245C22×C11—48no—
246C22×C11C23×D411yescharacteristic
247C22×C11C22×#4112yes—
248C22×C11#58514yes—
249C4×C11—22no—
250C4×C11—24no—
251C4×C11—24no—
252C4×C11—28no—
253C4×C11—44no—
254C4×C11—44no—
255C4×C11—44no—
256C4×C11—44no—
257C4×C11#53214yes—
258C22×Q8C23×C1112yes—
259C22×D4C23×C1114yes—
260C22×D4C23×C1112yes—
261C22×D4C23×C1114yes—
262C23×C4C23×C1114yes—
263C23×C4C23×C1111yescharacteristic
264C23×C4C23×C1112yes—
265#126—216no—
266#125—28no—
267#124—28no—
268#123—216no—
269C22⋊Q8—28no—
270#121—28no—
271C4×Q8—28no—
272C4×D4—216no—
273C4×D4—28no—
274C4×D4—216no—
275#117—216no—
276#117—28no—
277C2×C4⋊C4C23×C1114yes—
278C2×C4⋊C4C23×C1114yes—
279C2×C4⋊C4C23×C1114yes—
280C2×C4⋊C4C23×C1112yes—
281C2×C4⋊C4C23×C1114yes—
282C2×C4⋊C4C23×C1114yes—
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1114yes—
285C2×C4⋊C4C23×C1118yes—
286C2×C22⋊C4C23×C1114yes—
287C2×C22⋊C4C23×C1114yes—
288C2×C22⋊C4C23×C1114yes—
289C2×C22⋊C4C23×C1114yes—
290C2×C22⋊C4C23×C1114yes—
291C2×C22⋊C4C23×C1114yes—
292C2×C22⋊C4C23×C1118yes—
293C2×C22⋊C4C23×C1118yes—
294C2×C22⋊C4C23×C1118yes—
295C2×C42D4×C1118yescomplemented
296C2×C42C23×C1114yes—
297C2×C42C23×C1112yes—
298C2×C42C23×C1118yes—
299C2×C42C23×C1111yescharacteristic
300C2×C42C23×C1111yescharacteristic
301C2×C42C23×C1112yes—
302C2×C42C23×C1112yes—
303#95C23×C1114yes—
304#95C23×C1114yes—
305#95C23×C1118yes—
306#95C23×C1118yes—
307#95C23×C1114yes—
308#95C23×C1114yes—
309C2×C11—42no—
310C2×C11—84no—
311C2×C11C2×#53211yescharacteristic
312C2×C11#344912yes—
313C2×C11#345514yes—
314C24C24×C1114yes—
315C24C24×C1111yescharacteristic
316C2×Q8—24no—
317C2×Q8—44no—
318C2×D4—28no—
319C2×D4—24no—
320C2×D4—28no—
321C2×D4—48no—
322C2×D4—44no—
323C2×D4—48no—
324C22×C4—24no—
325C22×C4—28no—
326C22×C4—216no—
327C22×C4—44no—
328C22×C4C2×D4×C1114yes—
329C22×C4C2×D4×C1118yes—
330C22×C4C24×C1114yes—
331C22×C4C24×C1114yes—
332C22×C4C24×C1114yes—
333C22×C4C24×C1114yes—
334C22×C4C24×C1112yes—
335C22×C4C24×C1112yes—
336C22×C4C24×C1111yescharacteristic
337C22×C4C24×C1114yes—
338C22×C4C24×C1111yescharacteristic
339C4⋊C4—28no—
340C4⋊C4—28no—
341C4⋊C4—24no—
342C4⋊C4—28no—
343C4⋊C4—24no—
344C4⋊C4—28no—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—48no—
348C22⋊C4—28no—
349C22⋊C4—28no—
350C22⋊C4—28no—
351C22⋊C4—28no—
352C22⋊C4—28no—
353C22⋊C4—28no—
354C22⋊C4—216no—
355C22⋊C4—48no—
356C22⋊C4—48no—
357C42—28no—
358C42—24no—
359C42—48no—
360C42C2×D4×C1114yes—
361C42C2×D4×C1114yes—
362C42C2×D4×C1118yes—
363C42C11×#4118yes—
364C11#3464311yescharacteristic, direct product factor, Sylow
365C23—22no—
366C23—24no—
367C23—24no—
368C23—28no—
369C23—24no—
370C23—28no—
371C23—24no—
372C23C22×D4×C1112yes—
373C23C25×C1111yescharacteristic
374Q8—48no—
375D4—48no—
376D4—416no—
377D4—416no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—28no—
381C2×C4—24no—
382C2×C4—28no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—28no—
388C2×C4—28no—
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—48no—
393C2×C4—416no—
394C2×C4C22×D4×C1112yes—
395C2×C4C22×D4×C1114yes—
396C2×C4C22×D4×C1114yes—
397C2×C4C22×D4×C1112yes—
398C2×C4C2×C11×#4118yes—
399C2×C4C2×C11×#4114yes—
400C22—22no—
401C22—24no—
402C22—44no—
403C22—44no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—48no—
408C22C23×D4×C1111yescharacteristic
409C22C22×C11×#4112yes—
410C22C11×#58514yes—
411C4—22no—
412C4—24no—
413C4—24no—
414C4—28no—
415C4—44no—
416C4—44no—
417C4—44no—
418C4—44no—
419C4C11×#53214yes—
420C2—42no—
421C2—84no—
422C2C2×C11×#53211yescharacteristic
423C2C11×#344912yes—
424C2C11×#345514yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#529C2semidirect
2. C11×#2664C2semidirect
3. C11×#2663C2semidirect
4. C11×#2662C2semidirect
5. C11×#2661C2semidirect
6. C11×#2399C2semidirect
7. C11×#2398C2semidirect
8. C11×#2397C2semidirect
9. C11×#2392C2semidirect
10. C11×#2293C2semidirect
11. C4×C11×#117C2semidirect
88. C2×C42×C11D4semidirect
102. #34643C11direct (N × H)
153. C2×#529C2×C11semidirect
154. #2664C2×C11semidirect
155. #2663C2×C11semidirect
156. #2662C2×C11semidirect
157. #2661C2×C11semidirect
158. #2399C2×C11semidirect
159. #2398C2×C11semidirect
160. #2397C2×C11semidirect
161. #2392C2×C11semidirect
162. #2293C2×C11semidirect
163. C4×#117C2×C11semidirect
295. C2×C42D4×C11semidirect
364. C11#34643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C11×#26642
C11×#26632
C11×#26622
C11×#26612
C11×#23992
C11×#23982
C11×#23972
C11×#23922
C11×#22932
C4×C11×#1172
#3464311