Finite Group Databasebeta

← C11×#22227 #14599420

Subgroups — C11×#22227 #14599420

Order 2816.

774 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
1C2×C11×#488C211yesmaximal, characteristic
2C11×#2330C211yesmaximal, characteristic, complemented
3C11×#2326C211yesmaximal, characteristic
4C11×#1992C211yesmaximal, characteristic, complemented
5C11×#1959C211yesmaximal, characteristic
6C11×#1927C212yesmaximal, complemented
7C11×#1926C212yesmaximal
8C11×#1865C212yesmaximal, complemented
9C11×#1864C212yesmaximal
10C11×#1844C211yesmaximal, characteristic, complemented
11C11×#1746C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C2×C11×#124C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#488C418yescomplemented
17C2×C11×#106C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×#103C2212yes—
20C2×C11×#103C2212yes—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389—22no—
28C11×#389C2212yes—
29C11×#388—22no—
30C11×#387—22no—
31C11×#385—22no—
32C11×#384C2211yescharacteristic
33C11×#384C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C11×#376C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#336C2212yes—
39C11×#336C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C11×#125—22no—
46C11×#125C2×C414yescomplemented
47C11×#124—22no—
48C11×#124C2×C414yes—
49C4×Q8×C11—42no—
50C4×D4×C11—42no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—21no—
64C2×C42×C11—22no—
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C11×#106—42no—
69C11×#106—42no—
70C11×#103—42no—
71C11×#103C2×C418yescomplemented
72C11×#102—42no—
73C11×#102C2×C418yes—
74C11×#97—22no—
75C4×C8×C11C2×C414yescomplemented
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95D412yes—
80C11×#95D412yes—
81#22227C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11C22×C412yes—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11C22×C412yes—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—42no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2411yescharacteristic
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11C22×C414yes—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—82no—
117C11×C4⋊C4—82no—
118C11×C4⋊C4—82no—
119C11×C4⋊C4C22×C414yes—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—82no—
123C42×C11—22no—
124C42×C11—22no—
125C42×C11—42no—
126C42×C11—82no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129C2×#488C2×C1111yescharacteristic
130#2330C2×C1111yescharacteristic, complemented
131#2326C2×C1111yescharacteristic
132#1992C2×C1111yescharacteristic, complemented
133#1959C2×C1111yescharacteristic
134#1927C2×C1112yescomplemented
135#1926C2×C1112yes—
136#1865C2×C1112yescomplemented
137#1864C2×C1112yes—
138#1844C2×C1111yescharacteristic, complemented
139#1746C2×C1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11C22×D411yescharacteristic
146Q8×C11—24no—
147Q8×C11—42no—
148D4×C11—24no—
149D4×C11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—84no—
173C2×C4×C11C4×D414yes—
174C2×C4×C11C23×C411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11H(5,𝔽2)12yes—
177C2×C4×C112−1+412yes—
178C8×C11—24no—
179C8×C11—42no—
180C2×#125C22×C1111yescharacteristic
181C2×#124C22×C1111yescharacteristic
182C2×C4×Q8C22×C1111yescharacteristic
183C2×C4×D4C22×C1111yescharacteristic
184#488C4×C1118yescomplemented
185C2×#106C22×C1112yes—
186C2×#106C22×C1112yes—
187C2×#103C22×C1112yes—
188C2×#103C22×C1112yes—
189C2×#102C22×C1112yes—
190C2×#102C22×C1112yes—
191C2×#97C22×C1111yescharacteristic
192C2×C4×C8C22×C1111yescharacteristic
193#391C22×C1111yescharacteristic
194#390C22×C1111yescharacteristic
195#389—22no—
196#389C22×C1112yes—
197#388—22no—
198#387—22no—
199#385—22no—
200#384C22×C1111yescharacteristic
201#384C22×C1111yescharacteristic
202C4×C4⋊C4C22×C1112yes—
203#376C22×C1111yescharacteristic
204#340C22×C1112yes—
205#340C22×C1112yes—
206#336C22×C1112yes—
207#336C22×C1112yes—
208C22×C11—42no—
209C22×C11—44no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—82no—
213C22×C11C2×C4×D411yescharacteristic
214C22×C11#53511yescharacteristic
215C22×C11#53611yescharacteristic
216C22×C11#57712yes—
217C22×C11#57712yes—
218C4×C11—24no—
219C4×C11—42no—
220C4×C11—44no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—42no—
224C4×C11—82no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11#52012yes—
228C4×C11#54212yes—
229C22×Q8C23×C1111yescharacteristic
230C22×D4C23×C1111yescharacteristic
231C23×C4—21no—
232C22×C8C23×C1112yes—
233C22×C8C23×C1112yes—
234#125—22no—
235#125C2×C4×C1114yescomplemented
236#124—22no—
237#124C2×C4×C1114yes—
238C4×Q8—42no—
239C4×D4—42no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4C23×C1111yescharacteristic
246C2×C4⋊C4C23×C1111yescharacteristic
247C2×C4⋊C4C23×C1112yes—
248C2×C4⋊C4C23×C1112yes—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—22no—
252C2×C42—21no—
253C2×C42—22no—
254C2×C42C23×C1111yescharacteristic
255C2×C42C23×C1111yescharacteristic
256C2×C42C23×C1111yescharacteristic
257#106—42no—
258#106—42no—
259#103—42no—
260#103C2×C4×C1118yescomplemented
261#102—42no—
262#102C2×C4×C1118yes—
263#97—22no—
264C4×C8C2×C4×C1114yescomplemented
265#95—22no—
266#95—22no—
267#95—22no—
268#95D4×C1112yes—
269#95D4×C1112yes—
270C2×C11—82no—
271C2×C11#232611yescharacteristic
272C2×C11#295212yes—
273C2×C11#322111yescharacteristic
274C2×C11#322211yescharacteristic
275C2×C11#324412yes—
276C24—21no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8C22×C4×C1112yes—
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4C22×C4×C1112yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—82no—
292C22×C4C2×D4×C1112yes—
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295C22×C4C2×D4×C1112yes—
296C22×C4C24×C1111yescharacteristic
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8C22×C4×C1114yes—
303C4⋊C4—28no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—42no—
310C4⋊C4—82no—
311C4⋊C4—82no—
312C4⋊C4—82no—
313C4⋊C4C22×C4×C1114yes—
314C22⋊C4—28no—
315C22⋊C4—42no—
316C22⋊C4—82no—
317C42—22no—
318C42—22no—
319C42—42no—
320C42—82no—
321C42C22×C4×C1112yes—
322C42C11×#4112yes—
323C11#2222711yescharacteristic, direct product factor, Sylow
324C23—22no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23C22×D4×C1111yescharacteristic
330Q8—24no—
331Q8—42no—
332D4—24no—
333D4—42no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—84no—
357C2×C4C4×D4×C1114yes—
358C2×C4C23×C4×C1111yescharacteristic
359C2×C4C2×C11×#4111yescharacteristic
360C2×C4C11×H(5,𝔽2)12yes—
361C2×C4C11×2−1+412yes—
362C8—24no—
363C8—42no—
364C22—44no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—82no—
369C22C2×C4×D4×C1111yescharacteristic
370C22C11×#53511yescharacteristic
371C22C11×#53611yescharacteristic
372C22C11×#57712yes—
373C22C11×#57712yes—
374C4—24no—
375C4—44no—
376C4—41no—
377C4—41no—
378C4—42no—
379C4—42no—
380C4—82no—
381C4—81no—
382C4—81no—
383C4C11×#52012yes—
384C4C11×#54212yes—
385C2—82no—
386C2C11×#232611yescharacteristic
387C2C11×#295212yes—
388C2C11×#322111yescharacteristic
389C2C11×#322211yescharacteristic
390C2C11×#324412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2330C2semidirect
4. C11×#1992C2semidirect
6. C11×#1927C2semidirect
8. C11×#1865C2semidirect
10. C11×#1844C2semidirect
11. C11×#1746C2semidirect
16. C11×#488C4semidirect
46. C11×#125C2×C4semidirect
71. C11×#103C2×C4semidirect
75. C4×C8×C11C2×C4semidirect
81. #22227C11direct (N × H)
130. #2330C2×C11semidirect
132. #1992C2×C11semidirect
134. #1927C2×C11semidirect
136. #1865C2×C11semidirect
138. #1844C2×C11semidirect
139. #1746C2×C11semidirect
184. #488C4×C11semidirect
235. #125C2×C4×C11semidirect
260. #103C2×C4×C11semidirect
264. C4×C8C2×C4×C11semidirect
323. C11#22227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4882
C11×#23302
C11×#23262
C11×#19922
C11×#19592
C11×#19272
C11×#19262
C11×#18652
C11×#18642
C11×#18442
C11×#17462
#2222711