Finite Group Databasebeta

← C11×#33754 #14610947

Subgroups — C11×#33754 #14610947

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3050C211yesmaximal, characteristic, complemented
2C2×C11×#466C211yesmaximal, characteristic, complemented
3C11×#2236C211yesmaximal, characteristic, complemented
4C11×#2234C212yesmaximal, complemented
5C11×#2233C211yesmaximal, characteristic, complemented
6C11×#2217C212yesmaximal, complemented
7C11×#2215C212yesmaximal, complemented
8C11×#2187C211yesmaximal, characteristic, complemented
9C11×#2186C212yesmaximal, complemented
10C11×#2184C211yesmaximal, characteristic, complemented
11C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic, complemented
13C22×C11×D8C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C11×#525—21no—
16C2×C11×#121—21no—
17C2×C11×SD32C2212yescomplemented
18C2×C11×D16C2212yescomplemented
19C22×C11×C16C2212yescomplemented
20C11×#467C2211yescharacteristic
21C11×#467C2211yescharacteristic, complemented
22C11×#466—21no—
23C11×#466—21no—
24C11×#466C2211yescharacteristic
25C11×#466C2212yes—
26C11×#466C2212yes—
27C11×#466C2211yescharacteristic, complemented
28C11×#465—21no—
29C11×#465—21no—
30C11×#427C2211yescharacteristic, complemented
31C2×C11×#107C2211yescharacteristic
32C11×#416—21no—
33C2×C11×#102—21no—
34C11×#367C2212yescomplemented
35C11×#366C2212yescomplemented
36C11×#358C2212yescomplemented
37C11×#357C2212yescomplemented
38C11×#357C2212yescomplemented
39C11×#357C2212yescomplemented
40C11×C22⋊C16C2211yescharacteristic
41C11×C22⋊C16C2211yescharacteristic
42C11×C22⋊C16C2212yescomplemented
43C2×C11×#41—21no—
44C22×D4×C11—21no—
45C22×D4×C11—41no—
46C23×C4×C11D411yescharacteristic
47C11×#135—42no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8—21no—
51C2×C11×D8—42no—
52C2×C11×D8C2311yescharacteristic
53C2×C11×D8C2312yes—
54C22×C8×C11—42no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#123—41no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×#121—22no—
65C11×#121—22no—
66C11×#121—21no—
67C11×#121—21no—
68C11×#121—41no—
69C11×#121—41no—
70C11×#120—41no—
71C4×D4×C11—41no—
72C4×D4×C11—41no—
73C11×#117—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C22⋊C4—41no—
76C11×SD32—42no—
77C11×D16—42no—
78C2×C11×C16—42no—
79C2×C11×C16C2312yes—
80C2×C11×C16C2312yes—
81C11×#107—21no—
82C11×#107C2311yescharacteristic
83C11×#107C2311yescharacteristic
84C11×#107C2312yes—
85C11×#106—21no—
86C11×#103—21no—
87C11×#103—21no—
88C11×#102—22no—
89C11×#102—22no—
90C11×#102—21no—
91C11×#102—21no—
92#33754C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—41no—
94C24×C11D811yescharacteristic
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—21no—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—41no—
108C2×D4×C11—84no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11D811yescharacteristic
114C22×C4×C11D811yescharacteristic
115C22×C4×C11D811yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C11×Q16—22no—
120C11×SD16—42no—
121C11×D8—22no—
122C11×D8—22no—
123C11×D8—22no—
124C11×D8—42no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—42no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11—41no—
149C11×C16—22no—
150C11×C16—22no—
151#3050C2×C1111yescharacteristic, complemented
152C2×#466C2×C1111yescharacteristic, complemented
153#2236C2×C1111yescharacteristic, complemented
154#2234C2×C1112yescomplemented
155#2233C2×C1111yescharacteristic, complemented
156#2217C2×C1112yescomplemented
157#2215C2×C1112yescomplemented
158#2187C2×C1111yescharacteristic, complemented
159#2186C2×C1112yescomplemented
160#2184C2×C1111yescharacteristic, complemented
161C2×C22⋊C16C2×C1111yescharacteristic, complemented
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—82no—
168C23×C11—82no—
169C23×C11—82no—
170C23×C11C2×D811yescharacteristic
171C23×C11C2×D811yescharacteristic
172C23×C11C2×D811yescharacteristic
173Q8×C11—41no—
174Q8×C11—41no—
175D4×C11—42no—
176D4×C11—41no—
177D4×C11—42no—
178D4×C11—41no—
179D4×C11—82no—
180D4×C11—84no—
181D4×C11—82no—
182D4×C11—82no—
183D4×C11—82no—
184D4×C11—84no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—82no—
199C2×C4×C11—82no—
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C8×C11—21no—
205C8×C11—21no—
206C8×C11—21no—
207C8×C11H(5,𝔽2)12yes—
208C2×#135C22×C1111yescharacteristic, complemented
209C22×D8C22×C1111yescharacteristic
210C23×C8C22×C1111yescharacteristic
211#525—21no—
212C2×#121—21no—
213C2×SD32C22×C1112yescomplemented
214C2×D16C22×C1112yescomplemented
215C22×C16C22×C1112yescomplemented
216#467C22×C1111yescharacteristic
217#467C22×C1111yescharacteristic, complemented
218#466—21no—
219#466—21no—
220#466C22×C1111yescharacteristic
221#466C22×C1112yes—
222#466C22×C1112yes—
223#466C22×C1111yescharacteristic, complemented
224#465—21no—
225#465—21no—
226#427C22×C1111yescharacteristic, complemented
227C2×#107C22×C1111yescharacteristic
228#416—21no—
229C2×#102—21no—
230#367C22×C1112yescomplemented
231#366C22×C1112yescomplemented
232#358C22×C1112yescomplemented
233#357C22×C1112yescomplemented
234#357C22×C1112yescomplemented
235#357C22×C1112yescomplemented
236C22⋊C16C22×C1111yescharacteristic
237C22⋊C16C22×C1111yescharacteristic
238C22⋊C16C22×C1112yescomplemented
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—44no—
247C22×C11—81no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—82no—
253C22×C11—164no—
254C22×C11#50812yes—
255C22×C11#50912yes—
256C22×C11C22×D811yescharacteristic
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11—81no—
263C4×C11—81no—
264C4×C11#53411yescharacteristic
265C4×C11#57511yescharacteristic
266C2×#41—21no—
267C22×D4—21no—
268C22×D4—41no—
269C23×C4D4×C1111yescharacteristic
270#135—42no—
271C2×Q16C23×C1111yescharacteristic
272C2×SD16—21no—
273C2×D8—21no—
274C2×D8—42no—
275C2×D8C23×C1112yes—
276C2×D8C23×C1111yescharacteristic
277C22×C8—42no—
278C22×C8D4×C1111yescharacteristic
279C22×C8D4×C1111yescharacteristic
280C22×C8D4×C1111yescharacteristic
281C22×C8C23×C1111yescharacteristic
282C22×C8C23×C1111yescharacteristic
283C22×C8C23×C1111yescharacteristic
284#123—41no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287#121—22no—
288#121—22no—
289#121—21no—
290#121—21no—
291#121—41no—
292#121—41no—
293#120—41no—
294C4×D4—41no—
295C4×D4—41no—
296#117—21no—
297C2×C4⋊C4—21no—
298C2×C22⋊C4—41no—
299SD32—42no—
300D16—42no—
301C2×C16—42no—
302C2×C16C23×C1112yes—
303C2×C16C23×C1112yes—
304#107—21no—
305#107C23×C1111yescharacteristic
306#107C23×C1111yescharacteristic
307#107C23×C1112yes—
308#106—21no—
309#103—21no—
310#103—21no—
311#102—22no—
312#102—22no—
313#102—21no—
314#102—21no—
315C2×C11—22no—
316C2×C11—22no—
317C2×C11—41no—
318C2×C11—161no—
319C2×C11—162no—
320C2×C11#318611yescharacteristic
321C2×C11C2×#50811yescharacteristic
322C2×C11C2×#50911yescharacteristic
323C24—41no—
324C24C11×D811yescharacteristic
325#41—42no—
326#41—42no—
327C2×Q8—21no—
328C2×D4—22no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—84no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4C11×D811yescharacteristic
344C22×C4C11×D811yescharacteristic
345C22×C4C11×D811yescharacteristic
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1111yescharacteristic
349Q16—22no—
350SD16—42no—
351D8—22no—
352D8—22no—
353D8—22no—
354D8—42no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8C2×D4×C1111yescharacteristic
362C2×C8C2×D4×C1111yescharacteristic
363C2×C8C2×D4×C1111yescharacteristic
364C2×C8C24×C1111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C42—41no—
379C16—22no—
380C16—22no—
381C11#3375411yescharacteristic, direct product factor, Sylow
382C23—22no—
383C23—22no—
384C23—41no—
385C23—41no—
386C23—42no—
387C23—82no—
388C23—82no—
389C23—82no—
390C23C2×C11×D811yescharacteristic
391C23C2×C11×D811yescharacteristic
392C23C2×C11×D811yescharacteristic
393Q8—41no—
394Q8—41no—
395D4—42no—
396D4—41no—
397D4—42no—
398D4—41no—
399D4—82no—
400D4—84no—
401D4—82no—
402D4—82no—
403D4—82no—
404D4—84no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4C2×C11×D811yescharacteristic
421C2×C4C2×C11×D811yescharacteristic
422C2×C4C2×C11×D811yescharacteristic
423C2×C4C22×D4×C1111yescharacteristic
424C8—21no—
425C8—21no—
426C8—21no—
427C8C11×H(5,𝔽2)12yes—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—44no—
436C22—81no—
437C22—82no—
438C22—82no—
439C22—81no—
440C22—81no—
441C22—82no—
442C22—164no—
443C22C11×#50812yes—
444C22C11×#50912yes—
445C22C22×C11×D811yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—81no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4C11×#53411yescharacteristic
454C4C11×#57511yescharacteristic
455C2—22no—
456C2—22no—
457C2—41no—
458C2—162no—
459C2—161no—
460C2C11×#318611yescharacteristic
461C2C2×C11×#50811yescharacteristic
462C2C2×C11×#50911yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
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
1. C11×#3050C2semidirect
2. C2×C11×#466C2semidirect
3. C11×#2236C2semidirect
4. C11×#2234C2semidirect
5. C11×#2233C2semidirect
6. C11×#2217C2semidirect
7. C11×#2215C2semidirect
8. C11×#2187C2semidirect
9. C11×#2186C2semidirect
10. C11×#2184C2semidirect
11. C2×C11×C22⋊C16C2semidirect
12. C2×C11×#135C22semidirect
17. C2×C11×SD32C22semidirect
18. C2×C11×D16C22semidirect
19. C22×C11×C16C22semidirect
21. C11×#467C22semidirect
27. C11×#466C22semidirect
30. C11×#427C22semidirect
34. C11×#367C22semidirect
35. C11×#366C22semidirect
36. C11×#358C22semidirect
37. C11×#357C22semidirect
38. C11×#357C22semidirect
39. C11×#357C22semidirect
42. C11×C22⋊C16C22semidirect
92. #33754C11direct (N × H)
151. #3050C2×C11semidirect
152. C2×#466C2×C11semidirect
153. #2236C2×C11semidirect
154. #2234C2×C11semidirect
155. #2233C2×C11semidirect
156. #2217C2×C11semidirect
157. #2215C2×C11semidirect
158. #2187C2×C11semidirect
159. #2186C2×C11semidirect
160. #2184C2×C11semidirect
161. C2×C22⋊C16C2×C11semidirect
208. C2×#135C22×C11semidirect
213. C2×SD32C22×C11semidirect
214. C2×D16C22×C11semidirect
215. C22×C16C22×C11semidirect
217. #467C22×C11semidirect
223. #466C22×C11semidirect
226. #427C22×C11semidirect
230. #367C22×C11semidirect
231. #366C22×C11semidirect
232. #358C22×C11semidirect
233. #357C22×C11semidirect
234. #357C22×C11semidirect
235. #357C22×C11semidirect
238. C22⋊C16C22×C11semidirect
381. C11#33754direct (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×#4662
C11×#22362
C11×#22342
C11×#22332
C11×#22172
C11×#22152
C11×#21872
C11×#21862
C11×#21842
C2×C11×C22⋊C162
#3375411