Finite Group Databasebeta

← C11×#22182 #14599375

Subgroups — C11×#22182 #14599375

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 436 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×#1928C212yesmaximal, complemented
4C11×#1921C212yesmaximal, complemented
5C11×#1892C212yesmaximal
6C11×#1878C212yesmaximal, complemented
7C11×#1863C212yesmaximal, complemented
8C11×#1808C211yesmaximal, 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×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
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×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C2×C11×Q16—41no—
41C2×C11×Q16—41no—
42C2×C11×Q16C2×C414yescomplemented
43C22×C8×C11—22no—
44C22×C8×C11—41no—
45C22×C8×C11—41no—
46C22×C8×C11—41no—
47C22×C8×C11—41no—
48C22×C8×C11C2×C414yes—
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8C2×C418yes—
54C4×Q8×C11—42no—
55C4×Q8×C11—42no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—41no—
67C2×C42×C11—41no—
68C2×C42×C11D412yes—
69C2×C42×C11C2312yes—
70C11×#107—41no—
71C11×#107—41no—
72C11×#107C2×C414yescomplemented
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#22182C1111yesmaximal, 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—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11Q1614yescomplemented
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C11×Q16—44no—
110C2×C8×C11—22no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—44no—
118C2×C8×C11—44no—
119C2×C8×C11C22×C412yes—
120C2×C8×C11C22×C412yes—
121C11×C4⋊C4—28no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4C22×C414yes—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—44no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—42no—
135C42×C11—44no—
136C42×C11—44no—
137C2×#467C2×C1111yescharacteristic
138C4×C22⋊Q8C2×C1112yes—
139#1928C2×C1112yescomplemented
140#1921C2×C1112yescomplemented
141#1892C2×C1112yes—
142#1878C2×C1112yescomplemented
143#1863C2×C1112yescomplemented
144#1808C2×C1111yescharacteristic
145C2×#336C2×C1111yescharacteristic
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11C4×D412yes—
151C23×C11C2×Q1612yes—
152C23×C11#13512yes—
153C23×C11C22×D411yescharacteristic
154Q8×C11—24no—
155Q8×C11—24no—
156Q8×C11—42no—
157Q8×C11—42no—
158C2×C4×C11—22no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11C4×D412yes—
184C2×C4×C11C2×Q1614yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C2×C4×C11H(5,𝔽2)11yescharacteristic
189C2×C4×C11H(5,𝔽2)11yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C8×C11—22no—
192C8×C11—22no—
193C8×C11—42no—
194C22×Q16C22×C1111yescharacteristic
195C23×C8C22×C1111yescharacteristic
196C23×C8C22×C1111yescharacteristic
197C2×C22⋊Q8C22×C1112yes—
198C2×C4×Q8C22×C1112yes—
199C22×C42C22×C1111yescharacteristic
200#467C4×C1118yescomplemented
201C2×#107C22×C1111yescharacteristic
202C2×#107C22×C1111yescharacteristic
203C2×#107C22×C1111yescharacteristic
204C2×#103C22×C1112yes—
205C2×#103C22×C1112yes—
206C2×#103C22×C1112yes—
207#391C22×C1112yes—
208#389C22×C1112yes—
209#387—22no—
210#385—22no—
211#380C22×C1112yes—
212C4×C4⋊C4—22no—
213C4×C4⋊C4C22×C1112yes—
214C4×C22⋊C4—22no—
215#340C22×C1112yes—
216#340C22×C1112yes—
217#340C22×C1112yes—
218#336C22×C1112yes—
219#336C22×C1112yes—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11C4×Q1614yes—
227C22×C11C2×C4×D411yescharacteristic
228C22×C11#53411yescharacteristic
229C22×C11#53711yescharacteristic
230C22×C11C22×Q1611yescharacteristic
231C22×C11C2×#13511yescharacteristic
232C22×C11#57511yescharacteristic
233C22×C11#57511yescharacteristic
234C4×C11—22no—
235C4×C11—24no—
236C4×C11—44no—
237C4×C11—42no—
238C4×C11—44no—
239C4×C11—82no—
240C4×C11—82no—
241C4×C11#51811yescharacteristic
242C4×C11#52011yescharacteristic
243C4×C11#53811yescharacteristic
244C4×C11#53911yescharacteristic
245C22×Q8C23×C1112yes—
246C23×C4D4×C1111yescharacteristic
247C23×C4D4×C1111yescharacteristic
248C23×C4C23×C1111yescharacteristic
249C2×Q16—41no—
250C2×Q16—41no—
251C2×Q16C2×C4×C1114yescomplemented
252C22×C8—22no—
253C22×C8—41no—
254C22×C8—41no—
255C22×C8—41no—
256C22×C8—41no—
257C22×C8C2×C4×C1114yes—
258C22×C8C23×C1112yes—
259C22×C8C23×C1111yescharacteristic
260C22×C8C23×C1111yescharacteristic
261C22⋊Q8—24no—
262C22⋊Q8C2×C4×C1118yes—
263C4×Q8—42no—
264C4×Q8—42no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4C23×C1112yes—
269C2×C4⋊C4C23×C1112yes—
270C2×C4⋊C4C23×C1112yes—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—41no—
276C2×C42—41no—
277C2×C42D4×C1112yes—
278C2×C42C23×C1112yes—
279#107—41no—
280#107—41no—
281#107C2×C4×C1114yescomplemented
282#103—42no—
283#103—42no—
284#103C2×C4×C1118yescomplemented
285#95—22no—
286#95—22no—
287#95—22no—
288#95—22no—
289#95—22no—
290C2×C11—24no—
291C2×C11#232511yescharacteristic
292C2×C11C2×C4×Q1611yescharacteristic
293C2×C11#294311yescharacteristic
294C2×C11#318911yescharacteristic
295C2×C11#319111yescharacteristic
296C2×C11#324911yescharacteristic
297C2×C11#325011yescharacteristic
298C24C2×D4×C1111yescharacteristic
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8C22×C4×C1114yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C11×Q1614yescomplemented
319C22×C4C22×C4×C1112yes—
320C22×C4C2×D4×C1112yes—
321C22×C4C2×D4×C1111yescharacteristic
322C22×C4C2×D4×C1112yes—
323C22×C4C11×#4112yes—
324C22×C4C24×C1111yescharacteristic
325Q16—44no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—44no—
334C2×C8—44no—
335C2×C8C22×C4×C1112yes—
336C2×C8C22×C4×C1112yes—
337C4⋊C4—28no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—44no—
344C4⋊C4—44no—
345C4⋊C4C22×C4×C1114yes—
346C22⋊C4—28no—
347C22⋊C4—44no—
348C42—22no—
349C42—22no—
350C42—42no—
351C42—44no—
352C42—44no—
353C11#2218211yescharacteristic, direct product factor, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23C4×D4×C1112yes—
359C23C2×C11×Q1612yes—
360C23C11×#13512yes—
361C23C22×D4×C1111yescharacteristic
362Q8—24no—
363Q8—24no—
364Q8—42no—
365Q8—42no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4C4×D4×C1112yes—
392C2×C4C2×C11×Q1614yes—
393C2×C4C23×C4×C1111yescharacteristic
394C2×C4C2×C11×#4111yescharacteristic
395C2×C4C11×H(5,𝔽2)11yescharacteristic
396C2×C4C11×H(5,𝔽2)11yescharacteristic
397C2×C4C11×H(5,𝔽2)11yescharacteristic
398C2×C4C11×2−1+411yescharacteristic
399C8—22no—
400C8—22no—
401C8—42no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22C4×C11×Q1614yes—
409C22C2×C4×D4×C1111yescharacteristic
410C22C11×#53411yescharacteristic
411C22C11×#53711yescharacteristic
412C22C22×C11×Q1611yescharacteristic
413C22C2×C11×#13511yescharacteristic
414C22C11×#57511yescharacteristic
415C22C11×#57511yescharacteristic
416C4—24no—
417C4—22no—
418C4—42no—
419C4—44no—
420C4—44no—
421C4—82no—
422C4—82no—
423C4C11×#51811yescharacteristic
424C4C11×#52011yescharacteristic
425C4C11×#53811yescharacteristic
426C4C11×#53911yescharacteristic
427C2—24no—
428C2C11×#232511yescharacteristic
429C2C2×C4×C11×Q1611yescharacteristic
430C2C11×#294311yescharacteristic
431C2C11×#318911yescharacteristic
432C2C11×#319111yescharacteristic
433C2C11×#324911yescharacteristic
434C2C11×#325011yescharacteristic
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×#1928C2semidirect
4. C11×#1921C2semidirect
6. C11×#1878C2semidirect
7. C11×#1863C2semidirect
16. C11×#467C4semidirect
42. C2×C11×Q16C2×C4semidirect
72. C11×#107C2×C4semidirect
75. C11×#103C2×C4semidirect
81. #22182C11direct (N × H)
102. C22×C4×C11Q16semidirect
139. #1928C2×C11semidirect
140. #1921C2×C11semidirect
142. #1878C2×C11semidirect
143. #1863C2×C11semidirect
200. #467C4×C11semidirect
251. C2×Q16C2×C4×C11semidirect
281. #107C2×C4×C11semidirect
284. #103C2×C4×C11semidirect
318. C22×C4C11×Q16semidirect
353. C11#22182direct (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×#19282
C11×#19212
C11×#18922
C11×#18782
C11×#18632
C11×#18082
C2×C11×#3362
#2218211