Finite Group Databasebeta

← C11×#33756 #14610949

Subgroups — C11×#33756 #14610949

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3050C211yesmaximal, characteristic
2C2×C11×#467C211yesmaximal, characteristic, complemented
3C11×#2237C212yesmaximal, complemented
4C11×#2235C211yesmaximal, characteristic, complemented
5C11×#2232C211yesmaximal, characteristic, complemented
6C11×#2217C212yesmaximal, complemented
7C11×#2216C212yesmaximal, complemented
8C11×#2189C212yesmaximal, complemented
9C11×#2188C211yesmaximal, characteristic, complemented
10C11×#2185C211yesmaximal, characteristic, complemented
11C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C11×#525—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×Q32C2212yescomplemented
18C2×C11×SD32C2212yescomplemented
19C22×C11×C16C2212yes—
20C11×#467—21no—
21C11×#467—21no—
22C11×#467C2211yescharacteristic
23C11×#467C2212yes—
24C11×#467C2211yescharacteristic
25C11×#467C2212yes—
26C11×#466C2211yescharacteristic
27C11×#466C2211yescharacteristic
28C11×#465—21no—
29C11×#465—21no—
30C11×#427C2211yescharacteristic
31C2×C11×#107C2211yescharacteristic
32C11×#416—21no—
33C2×C11×#103—21no—
34C11×#367C2212yescomplemented
35C11×#366C2212yescomplemented
36C11×#358C2212yescomplemented
37C11×#358C2212yescomplemented
38C11×#358C2212yescomplemented
39C11×#357C2212yescomplemented
40C11×C22⋊C16C2211yescharacteristic
41C11×C22⋊C16C2211yescharacteristic
42C11×C22⋊C16C2212yes—
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C23×C4×C11D411yescharacteristic
46C11×#135—42no—
47C2×C11×Q16—21no—
48C2×C11×Q16—42no—
49C2×C11×Q16C2312yes—
50C2×C11×Q16C2311yescharacteristic
51C2×C11×SD16—21no—
52C2×C11×D8C2311yescharacteristic
53C22×C8×C11—42no—
54C22×C8×C11D411yescharacteristic
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#123—41no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—41no—
66C11×C22⋊Q8—41no—
67C11×#121—21no—
68C11×#121—21no—
69C11×#120—41no—
70C4×D4×C11—41no—
71C4×D4×C11—41no—
72C11×#117—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C22⋊C4—41no—
76C11×Q32—42no—
77C11×SD32—42no—
78C2×C11×C16—42no—
79C2×C11×C16C2312yes—
80C2×C11×C16C2312yes—
81C11×#107—21no—
82C11×#107C2312yes—
83C11×#107C2311yescharacteristic
84C11×#107C2311yescharacteristic
85C11×#106—21no—
86C11×#103—22no—
87C11×#103—22no—
88C11×#103—21no—
89C11×#103—21no—
90C11×#102—21no—
91C11×#102—21no—
92#33756C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11D811yescharacteristic
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—41no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11D811yescharacteristic
111C22×C4×C11D811yescharacteristic
112C22×C4×C11D811yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C11×Q16—22no—
117C11×Q16—22no—
118C11×Q16—22no—
119C11×Q16—42no—
120C11×SD16—42no—
121C11×D8—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11—41no—
148C11×C16—22no—
149C11×C16—22no—
150#3050C2×C1111yescharacteristic
151C2×#467C2×C1111yescharacteristic, complemented
152#2237C2×C1112yescomplemented
153#2235C2×C1111yescharacteristic, complemented
154#2232C2×C1111yescharacteristic, complemented
155#2217C2×C1112yescomplemented
156#2216C2×C1112yescomplemented
157#2189C2×C1112yescomplemented
158#2188C2×C1111yescharacteristic, complemented
159#2185C2×C1111yescharacteristic, complemented
160C2×C22⋊C16C2×C1111yescharacteristic, complemented
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11C2×D811yescharacteristic
166C23×C11C2×D811yescharacteristic
167C23×C11C2×D811yescharacteristic
168Q8×C11—41no—
169Q8×C11—42no—
170Q8×C11—42no—
171Q8×C11—41no—
172Q8×C11—82no—
173D4×C11—41no—
174D4×C11—41no—
175D4×C11—82no—
176D4×C11—82no—
177D4×C11—82no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—82no—
193C2×C4×C11—82no—
194C2×C4×C11—82no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C8×C11—21no—
200C8×C11—21no—
201C8×C11—21no—
202C8×C11H(5,𝔽2)12yes—
203C2×#135C22×C1111yescharacteristic
204C22×Q16C22×C1111yescharacteristic
205C23×C8C22×C1111yescharacteristic
206#525—21no—
207C2×C22⋊Q8—21no—
208C2×Q32C22×C1112yescomplemented
209C2×SD32C22×C1112yescomplemented
210C22×C16C22×C1112yes—
211#467—21no—
212#467—21no—
213#467C22×C1111yescharacteristic
214#467C22×C1112yes—
215#467C22×C1111yescharacteristic
216#467C22×C1112yes—
217#466C22×C1111yescharacteristic
218#466C22×C1111yescharacteristic
219#465—21no—
220#465—21no—
221#427C22×C1111yescharacteristic
222C2×#107C22×C1111yescharacteristic
223#416—21no—
224C2×#103—21no—
225#367C22×C1112yescomplemented
226#366C22×C1112yescomplemented
227#358C22×C1112yescomplemented
228#358C22×C1112yescomplemented
229#358C22×C1112yescomplemented
230#357C22×C1112yescomplemented
231C22⋊C16C22×C1111yescharacteristic
232C22⋊C16C22×C1111yescharacteristic
233C22⋊C16C22×C1112yes—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—44no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11#50812yes—
246C22×C11#51012yes—
247C22×C11C22×D811yescharacteristic
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—82no—
252C4×C11—81no—
253C4×C11—81no—
254C4×C11—81no—
255C4×C11—82no—
256C4×C11#53411yescharacteristic
257C4×C11#57511yescharacteristic
258C2×#41—21no—
259C22×Q8—21no—
260C23×C4D4×C1111yescharacteristic
261#135—42no—
262C2×Q16—21no—
263C2×Q16—42no—
264C2×Q16C23×C1112yes—
265C2×Q16C23×C1111yescharacteristic
266C2×SD16—21no—
267C2×D8C23×C1111yescharacteristic
268C22×C8—42no—
269C22×C8D4×C1111yescharacteristic
270C22×C8D4×C1111yescharacteristic
271C22×C8D4×C1111yescharacteristic
272C22×C8C23×C1111yescharacteristic
273C22×C8C23×C1111yescharacteristic
274C22×C8C23×C1111yescharacteristic
275#123—41no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8—41no—
281C22⋊Q8—41no—
282#121—21no—
283#121—21no—
284#120—41no—
285C4×D4—41no—
286C4×D4—41no—
287#117—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—41no—
290C2×C22⋊C4—41no—
291Q32—42no—
292SD32—42no—
293C2×C16—42no—
294C2×C16C23×C1112yes—
295C2×C16C23×C1112yes—
296#107—21no—
297#107C23×C1112yes—
298#107C23×C1111yescharacteristic
299#107C23×C1111yescharacteristic
300#106—21no—
301#103—22no—
302#103—22no—
303#103—21no—
304#103—21no—
305#102—21no—
306#102—21no—
307C2×C11—22no—
308C2×C11—22no—
309C2×C11—41no—
310C2×C11—161no—
311C2×C11#318611yescharacteristic
312C2×C11C2×#50811yescharacteristic
313C2×C11C2×#51011yescharacteristic
314C24C11×D811yescharacteristic
315#41—42no—
316#41—42no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—42no—
320C2×Q8—42no—
321C2×Q8—41no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C11×D811yescharacteristic
332C22×C4C11×D811yescharacteristic
333C22×C4C11×D811yescharacteristic
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C2×D4×C1111yescharacteristic
337Q16—22no—
338Q16—22no—
339Q16—22no—
340Q16—42no—
341SD16—42no—
342D8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8C2×D4×C1111yescharacteristic
350C2×C8C2×D4×C1111yescharacteristic
351C2×C8C2×D4×C1111yescharacteristic
352C2×C8C24×C1111yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—41no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—41no—
369C16—22no—
370C16—22no—
371C11#3375611yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—22no—
374C23—41no—
375C23—41no—
376C23C2×C11×D811yescharacteristic
377C23C2×C11×D811yescharacteristic
378C23C2×C11×D811yescharacteristic
379Q8—41no—
380Q8—42no—
381Q8—42no—
382Q8—41no—
383Q8—82no—
384D4—41no—
385D4—41no—
386D4—82no—
387D4—82no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4C2×C11×D811yescharacteristic
407C2×C4C2×C11×D811yescharacteristic
408C2×C4C2×C11×D811yescharacteristic
409C2×C4C22×D4×C1111yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8C11×H(5,𝔽2)12yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—44no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22C11×#50812yes—
426C22C11×#51012yes—
427C22C22×C11×D811yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—82no—
436C4C11×#53411yescharacteristic
437C4C11×#57511yescharacteristic
438C2—22no—
439C2—22no—
440C2—41no—
441C2—161no—
442C2C11×#318611yescharacteristic
443C2C2×C11×#50811yescharacteristic
444C2C2×C11×#51011yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#467C2semidirect
3. C11×#2237C2semidirect
4. C11×#2235C2semidirect
5. C11×#2232C2semidirect
6. C11×#2217C2semidirect
7. C11×#2216C2semidirect
8. C11×#2189C2semidirect
9. C11×#2188C2semidirect
10. C11×#2185C2semidirect
11. C2×C11×C22⋊C16C2semidirect
17. C2×C11×Q32C22semidirect
18. C2×C11×SD32C22semidirect
34. C11×#367C22semidirect
35. C11×#366C22semidirect
36. C11×#358C22semidirect
37. C11×#358C22semidirect
38. C11×#358C22semidirect
39. C11×#357C22semidirect
92. #33756C11direct (N × H)
151. C2×#467C2×C11semidirect
152. #2237C2×C11semidirect
153. #2235C2×C11semidirect
154. #2232C2×C11semidirect
155. #2217C2×C11semidirect
156. #2216C2×C11semidirect
157. #2189C2×C11semidirect
158. #2188C2×C11semidirect
159. #2185C2×C11semidirect
160. C2×C22⋊C16C2×C11semidirect
208. C2×Q32C22×C11semidirect
209. C2×SD32C22×C11semidirect
225. #367C22×C11semidirect
226. #366C22×C11semidirect
227. #358C22×C11semidirect
228. #358C22×C11semidirect
229. #358C22×C11semidirect
230. #357C22×C11semidirect
371. C11#33756direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30502
C2×C11×#4672
C11×#22372
C11×#22352
C11×#22322
C11×#22172
C11×#22162
C11×#21892
C11×#21882
C11×#21852
C2×C11×C22⋊C162
#3375611