Finite Group Databasebeta

← C11×#22183 #14599376

Subgroups — C11×#22183 #14599376

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C4×C11×C22⋊Q8C212yesmaximal
3C11×#1927C212yesmaximal, complemented
4C11×#1918C212yesmaximal, complemented
5C11×#1892C212yesmaximal
6C11×#1878C212yesmaximal, complemented
7C11×#1865C212yesmaximal, complemented
8C11×#1807C211yesmaximal, characteristic
9C2×C11×#336C211yesmaximal, characteristic
10C22×C11×Q16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C4×Q8×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C11×#467C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C11×#391C2212yes—
24C11×#389C2212yes—
25C11×#387—22no—
26C11×#385—22no—
27C11×#380C2212yes—
28C4×C11×C4⋊C4—22no—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C22⋊C4—22no—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×Q8×C11C2312yes—
37C23×C4×C11D412yes—
38C23×C4×C11C2311yescharacteristic
39C2×C11×Q16—41no—
40C2×C11×Q16—41no—
41C2×C11×Q16C2×C414yescomplemented
42C22×C8×C11—22no—
43C22×C8×C11—41no—
44C22×C8×C11—41no—
45C22×C8×C11—41no—
46C22×C8×C11—41no—
47C22×C8×C11C2×C414yes—
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8C2×C418yes—
53C4×Q8×C11—42no—
54C4×Q8×C11—42no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11—41no—
66C2×C42×C11—41no—
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D411yescharacteristic
69C2×C42×C11C2312yes—
70C11×#107C2×C414yescomplemented
71C11×#106—41no—
72C11×#106—41no—
73C11×#103—42no—
74C11×#103—42no—
75C11×#103C2×C418yescomplemented
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81#22183C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11C22×C414yes—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—42no—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11#4112yes—
105C22×C4×C11C2411yescharacteristic
106C11×Q16—44no—
107C2×C8×C11—22no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—44no—
115C2×C8×C11—44no—
116C2×C8×C11C22×C412yes—
117C2×C8×C11C22×C412yes—
118C11×C4⋊C4—28no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4C22×C414yes—
127C11×C22⋊C4—28no—
128C11×C22⋊C4—44no—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11—44no—
134C42×C11—44no—
135C2×#467C2×C1111yescharacteristic
136C4×C22⋊Q8C2×C1112yes—
137#1927C2×C1112yescomplemented
138#1918C2×C1112yescomplemented
139#1892C2×C1112yes—
140#1878C2×C1112yescomplemented
141#1865C2×C1112yescomplemented
142#1807C2×C1111yescharacteristic
143C2×#336C2×C1111yescharacteristic
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—22no—
147C23×C11C4×D412yes—
148C23×C11#13714yes—
149C23×C11C22×D411yescharacteristic
150Q8×C11—24no—
151Q8×C11—24no—
152Q8×C11—42no—
153Q8×C11—42no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—48no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11C4×D412yes—
179C2×C4×C11#13514yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×C4×C11H(5,𝔽2)11yescharacteristic
184C2×C4×C11H(5,𝔽2)11yescharacteristic
185C2×C4×C112−1+411yescharacteristic
186C8×C11—22no—
187C8×C11—22no—
188C8×C11—42no—
189C22×Q16C22×C1111yescharacteristic
190C23×C8C22×C1111yescharacteristic
191C23×C8C22×C1111yescharacteristic
192C2×C22⋊Q8C22×C1112yes—
193C2×C4×Q8C22×C1112yes—
194C22×C42C22×C1111yescharacteristic
195#467C4×C1118yescomplemented
196C2×#107C22×C1111yescharacteristic
197C2×#106C22×C1111yescharacteristic
198C2×#106C22×C1111yescharacteristic
199C2×#103C22×C1112yes—
200C2×#103C22×C1112yes—
201C2×#103C22×C1112yes—
202#391C22×C1112yes—
203#389C22×C1112yes—
204#387—22no—
205#385—22no—
206#380C22×C1112yes—
207C4×C4⋊C4—22no—
208C4×C4⋊C4C22×C1112yes—
209C4×C22⋊C4—22no—
210#340C22×C1112yes—
211#340C22×C1112yes—
212#340C22×C1112yes—
213#336C22×C1112yes—
214#336C22×C1112yes—
215C22×C11—22no—
216C22×C11—24no—
217C22×C11—22no—
218C22×C11—24no—
219C22×C11#44114yes—
220C22×C11C2×C4×D411yescharacteristic
221C22×C11#53411yescharacteristic
222C22×C11#53711yescharacteristic
223C22×C11C2×#13512yes—
224C22×C11C2×#13712yes—
225C4×C11—22no—
226C4×C11—24no—
227C4×C11—44no—
228C4×C11—42no—
229C4×C11—44no—
230C4×C11—82no—
231C4×C11—82no—
232C4×C11#51811yescharacteristic
233C4×C11#52011yescharacteristic
234C4×C11#53811yescharacteristic
235C4×C11#53911yescharacteristic
236C22×Q8C23×C1112yes—
237C23×C4D4×C1112yes—
238C23×C4C23×C1111yescharacteristic
239C2×Q16—41no—
240C2×Q16—41no—
241C2×Q16C2×C4×C1114yescomplemented
242C22×C8—22no—
243C22×C8—41no—
244C22×C8—41no—
245C22×C8—41no—
246C22×C8—41no—
247C22×C8C2×C4×C1114yes—
248C22×C8C23×C1112yes—
249C22×C8C23×C1111yescharacteristic
250C22×C8C23×C1111yescharacteristic
251C22⋊Q8—24no—
252C22⋊Q8C2×C4×C1118yes—
253C4×Q8—42no—
254C4×Q8—42no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4C23×C1112yes—
259C2×C4⋊C4C23×C1112yes—
260C2×C4⋊C4C23×C1112yes—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C42—22no—
264C2×C42—22no—
265C2×C42—41no—
266C2×C42—41no—
267C2×C42D4×C1111yescharacteristic
268C2×C42D4×C1111yescharacteristic
269C2×C42C23×C1112yes—
270#107C2×C4×C1114yescomplemented
271#106—41no—
272#106—41no—
273#103—42no—
274#103—42no—
275#103C2×C4×C1118yescomplemented
276#95—22no—
277#95—22no—
278#95—22no—
279#95—22no—
280#95—22no—
281C2×C11—24no—
282C2×C11#232511yescharacteristic
283C2×C11C4×#13511yescharacteristic
284C2×C11C2×#44111yescharacteristic
285C2×C11#319012yes—
286C2×C11#324812yes—
287C24C2×D4×C1111yescharacteristic
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8C22×C4×C1114yes—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—42no—
305C22×C4C22×C4×C1112yes—
306C22×C4C2×D4×C1112yes—
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C2×D4×C1112yes—
309C22×C4C11×#4112yes—
310C22×C4C24×C1111yescharacteristic
311Q16—44no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—44no—
320C2×C8—44no—
321C2×C8C22×C4×C1112yes—
322C2×C8C22×C4×C1112yes—
323C4⋊C4—28no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—44no—
330C4⋊C4—44no—
331C4⋊C4C22×C4×C1114yes—
332C22⋊C4—28no—
333C22⋊C4—44no—
334C42—22no—
335C42—22no—
336C42—41no—
337C42—41no—
338C42—44no—
339C42—44no—
340C11#2218311yescharacteristic, direct product factor, Sylow
341C23—21no—
342C23—21no—
343C23—22no—
344C23C4×D4×C1112yes—
345C23C11×#13714yes—
346C23C22×D4×C1111yescharacteristic
347Q8—24no—
348Q8—24no—
349Q8—42no—
350Q8—42no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—48no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4C4×D4×C1112yes—
376C2×C4C11×#13514yes—
377C2×C4C23×C4×C1111yescharacteristic
378C2×C4C2×C11×#4111yescharacteristic
379C2×C4C11×H(5,𝔽2)11yescharacteristic
380C2×C4C11×H(5,𝔽2)11yescharacteristic
381C2×C4C11×H(5,𝔽2)11yescharacteristic
382C2×C4C11×2−1+411yescharacteristic
383C8—22no—
384C8—22no—
385C8—42no—
386C22—24no—
387C22—22no—
388C22—24no—
389C22—22no—
390C22C11×#44114yes—
391C22C2×C4×D4×C1111yescharacteristic
392C22C11×#53411yescharacteristic
393C22C11×#53711yescharacteristic
394C22C2×C11×#13512yes—
395C22C2×C11×#13712yes—
396C4—24no—
397C4—22no—
398C4—42no—
399C4—44no—
400C4—44no—
401C4—82no—
402C4—82no—
403C4C11×#51811yescharacteristic
404C4C11×#52011yescharacteristic
405C4C11×#53811yescharacteristic
406C4C11×#53911yescharacteristic
407C2—24no—
408C2C11×#232511yescharacteristic
409C2C4×C11×#13511yescharacteristic
410C2C2×C11×#44111yescharacteristic
411C2C11×#319012yes—
412C2C11×#324812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1927C2semidirect
4. C11×#1918C2semidirect
6. C11×#1878C2semidirect
7. C11×#1865C2semidirect
16. C11×#467C4semidirect
41. C2×C11×Q16C2×C4semidirect
70. C11×#107C2×C4semidirect
75. C11×#103C2×C4semidirect
81. #22183C11direct (N × H)
137. #1927C2×C11semidirect
138. #1918C2×C11semidirect
140. #1878C2×C11semidirect
141. #1865C2×C11semidirect
195. #467C4×C11semidirect
241. C2×Q16C2×C4×C11semidirect
270. #107C2×C4×C11semidirect
275. #103C2×C4×C11semidirect
340. C11#22183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C4×C11×C22⋊Q82
C11×#19272
C11×#19182
C11×#18922
C11×#18782
C11×#18652
C11×#18072
C2×C11×#3362
#2218311