Finite Group Databasebeta

← C11×#33738 #14610931

Subgroups — C11×#33738 #14610931

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3170C211yesmaximal, characteristic, complemented
2C11×#3168C211yesmaximal, characteristic
3C11×#2255C211yesmaximal, characteristic, complemented
4C11×#2251C211yesmaximal, characteristic, complemented
5C11×#2245C211yesmaximal, characteristic, complemented
6C11×#2243C211yesmaximal, characteristic, complemented
7C11×#2220C212yesmaximal
8C11×#2219C212yesmaximal, complemented
9C4×C11×Q32C212yesmaximal, complemented
10C4×C11×SD32C212yesmaximal, complemented
11C4×C11×M32C211yesmaximal, characteristic, complemented
12C11×#533—21no—
13C11×#529—21no—
14C2×C11×Q32C2212yes—
15C2×C11×SD32C2212yes—
16C2×C11×M32C2212yes—
17C11×#500C2211yescharacteristic
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20C11×#494C2211yescharacteristic
21C11×#488—21no—
22C11×#487—21no—
23C11×#467—21no—
24C11×#467C2211yescharacteristic
25C11×#467C2212yes—
26C11×#466C2211yescharacteristic
27C11×#465—21no—
28C4×C11×Q16—21no—
29C4×C11×Q16C2211yescharacteristic
30C4×C11×Q16C2212yes—
31C4×C11×SD16—21no—
32C4×C11×D8C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C11×#367C2212yes—
35C11×#366C2212yes—
36C11×#358C2212yes—
37C11×#358C2212yes—
38C11×#358C2212yes—
39C11×#357C2212yes—
40C11×#346C2211yescharacteristic
41C11×#346C2211yescharacteristic
42C4×C11×C16C2212yes—
43C2×C11×Q16—21no—
44C2×C11×Q16C2312yes—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×#126—41no—
53C11×#125—21no—
54C11×#125—41no—
55C11×#124—21no—
56C11×#123—41no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—41no—
60C11×#121—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—22no—
63C4×Q8×C11—41no—
64C4×D4×C11—21no—
65C4×D4×C11—41no—
66C11×#117—41no—
67C11×#117—41no—
68C2×C42×C11D411yescharacteristic
69C11×Q32—24no—
70C11×SD32—24no—
71C11×M32—24no—
72C2×C11×C16C2312yes—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2311yescharacteristic
76C11×#107C2311yescharacteristic
77C11×#107C2312yes—
78C11×#106—21no—
79C11×#103—21no—
80C11×#103—22no—
81C11×#103—21no—
82C11×#103—22no—
83C11×#102—21no—
84C11×#102—21no—
85C4×C8×C11D411yescharacteristic
86C4×C8×C11D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#33738C1111yesmaximal, characteristic, direct product factor, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—41no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11D811yescharacteristic
97C22×C4×C11D811yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×Q16—22no—
100C11×Q16—22no—
101C11×Q16—22no—
102C11×Q16—42no—
103C11×SD16—42no—
104C11×D8—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2411yescharacteristic
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11—41no—
130C42×C11—42no—
131C42×C11D811yescharacteristic
132C42×C11D811yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C11×C16—22no—
136C11×C16#4114yes—
137#3170C2×C1111yescharacteristic, complemented
138#3168C2×C1111yescharacteristic
139#2255C2×C1111yescharacteristic, complemented
140#2251C2×C1111yescharacteristic, complemented
141#2245C2×C1111yescharacteristic, complemented
142#2243C2×C1111yescharacteristic, complemented
143#2220C2×C1112yes—
144#2219C2×C1112yescomplemented
145C4×Q32C2×C1112yescomplemented
146C4×SD32C2×C1112yescomplemented
147C4×M32C2×C1111yescharacteristic, complemented
148C23×C11—41no—
149C23×C11C2×D811yescharacteristic
150Q8×C11—42no—
151Q8×C11—41no—
152Q8×C11—41no—
153Q8×C11—42no—
154Q8×C11—82no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—82no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—82no—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C8×C11—21no—
175C8×C11—21no—
176C8×C11#13512yes—
177C8×C11C2×#4112yes—
178#533—21no—
179#529—21no—
180C2×Q32C22×C1112yes—
181C2×SD32C22×C1112yes—
182C2×M32C22×C1112yes—
183#500C22×C1111yescharacteristic
184#499C22×C1111yescharacteristic
185#495C22×C1111yescharacteristic
186#494C22×C1111yescharacteristic
187#488—21no—
188#487—21no—
189#467—21no—
190#467C22×C1111yescharacteristic
191#467C22×C1112yes—
192#466C22×C1111yescharacteristic
193#465—21no—
194C4×Q16—21no—
195C4×Q16C22×C1111yescharacteristic
196C4×Q16C22×C1112yes—
197C4×SD16—21no—
198C4×D8C22×C1111yescharacteristic
199C2×C4×C8C22×C1111yescharacteristic
200#367C22×C1112yes—
201#366C22×C1112yes—
202#358C22×C1112yes—
203#358C22×C1112yes—
204#358C22×C1112yes—
205#357C22×C1112yes—
206#346C22×C1111yescharacteristic
207#346C22×C1111yescharacteristic
208C4×C16C22×C1112yes—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11C22×D811yescharacteristic
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11—82no—
223C4×C11—81no—
224C4×C11—82no—
225C4×C11#51012yes—
226C4×C11#53211yescharacteristic
227C4×C11C2×#13511yescharacteristic
228C2×Q16—21no—
229C2×Q16C23×C1112yes—
230C2×Q16C23×C1111yescharacteristic
231C2×SD16—21no—
232C2×D8C23×C1111yescharacteristic
233C22×C8D4×C1111yescharacteristic
234C22×C8C23×C1111yescharacteristic
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237#126—41no—
238#125—21no—
239#125—41no—
240#124—21no—
241#123—41no—
242C22⋊Q8—21no—
243C22⋊Q8—22no—
244C22⋊Q8—41no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—22no—
248C4×Q8—41no—
249C4×D4—21no—
250C4×D4—41no—
251#117—41no—
252#117—41no—
253C2×C42D4×C1111yescharacteristic
254Q32—24no—
255SD32—24no—
256M32—24no—
257C2×C16C23×C1112yes—
258C2×C16C23×C1112yes—
259#107—21no—
260#107C23×C1112yes—
261#107C23×C1111yescharacteristic
262#107C23×C1111yescharacteristic
263#106—21no—
264#103—21no—
265#103—22no—
266#103—21no—
267#103—22no—
268#102—21no—
269#102—21no—
270C4×C8D4×C1111yescharacteristic
271C4×C8D4×C1111yescharacteristic
272C4×C8C23×C1111yescharacteristic
273C4×C8C23×C1111yescharacteristic
274C2×C11—41no—
275C2×C11—161no—
276C2×C11#316911yescharacteristic
277C2×C11C2×#51011yescharacteristic
278C2×C11#341411yescharacteristic
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4C11×D811yescharacteristic
286C22×C4C11×D811yescharacteristic
287C22×C4C2×D4×C1111yescharacteristic
288Q16—22no—
289Q16—22no—
290Q16—22no—
291Q16—42no—
292SD16—42no—
293D8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×D4×C1111yescharacteristic
297C2×C8C2×D4×C1111yescharacteristic
298C2×C8C2×D4×C1111yescharacteristic
299C2×C8C24×C1111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—42no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C42—41no—
319C42—42no—
320C42C11×D811yescharacteristic
321C42C11×D811yescharacteristic
322C42C2×D4×C1111yescharacteristic
323C42C2×D4×C1111yescharacteristic
324C16—22no—
325C16C11×#4114yes—
326C11#3373811yescharacteristic, direct product factor, Sylow
327C23—41no—
328C23C2×C11×D811yescharacteristic
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—42no—
333Q8—82no—
334D4—41no—
335D4—41no—
336D4—82no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—82no—
347C2×C4C2×C11×D811yescharacteristic
348C2×C4C2×C11×D811yescharacteristic
349C2×C4C2×C11×D811yescharacteristic
350C2×C4C2×C11×D811yescharacteristic
351C2×C4C2×C11×D811yescharacteristic
352C2×C4C22×D4×C1111yescharacteristic
353C8—21no—
354C8—21no—
355C8C11×#13512yes—
356C8C2×C11×#4112yes—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22C22×C11×D811yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—82no—
371C4—81no—
372C4—82no—
373C4C11×#51012yes—
374C4C11×#53211yescharacteristic
375C4C2×C11×#13511yescharacteristic
376C2—41no—
377C2—161no—
378C2C11×#316911yescharacteristic
379C2C2×C11×#51011yescharacteristic
380C2C11×#341411yescharacteristic
subgroupG/H
centerC2×C4×C11C2×D8
commutator, Frattini, cosocleC2×C8C24×C11
socleC22×C11C22×D8
prime radicalC11×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3170C2semidirect
3. C11×#2255C2semidirect
4. C11×#2251C2semidirect
5. C11×#2245C2semidirect
6. C11×#2243C2semidirect
8. C11×#2219C2semidirect
9. C4×C11×Q32C2semidirect
10. C4×C11×SD32C2semidirect
11. C4×C11×M32C2semidirect
89. #33738C11direct (N × H)
137. #3170C2×C11semidirect
139. #2255C2×C11semidirect
140. #2251C2×C11semidirect
141. #2245C2×C11semidirect
142. #2243C2×C11semidirect
144. #2219C2×C11semidirect
145. C4×Q32C2×C11semidirect
146. C4×SD32C2×C11semidirect
147. C4×M32C2×C11semidirect
326. C11#33738direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31702
C11×#31682
C11×#22552
C11×#22512
C11×#22452
C11×#22432
C11×#22202
C11×#22192
C4×C11×Q322
C4×C11×SD322
C4×C11×M322
#3373811