Finite Group Databasebeta

← C11×#33665 #14610858

Subgroups — C11×#33665 #14610858

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic, complemented
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C11×#2236C211yesmaximal, characteristic, complemented
4C11×#2233C211yesmaximal, characteristic, complemented
5C11×#2228C212yesmaximal, complemented
6C11×#2210C212yesmaximal, complemented
7C11×#2187C211yesmaximal, characteristic, complemented
8C11×#2184C211yesmaximal, characteristic
9C4×C11×SD32C212yesmaximal, complemented
10C4×C11×D16C212yesmaximal, complemented
11C11×#2162C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C11×#529—21no—
14C2×C4×D4×C11—21no—
15C2×C11×SD32C2212yes—
16C2×C11×D16C2212yes—
17C11×#499C2211yescharacteristic, complemented
18C11×#495C2211yescharacteristic, complemented
19C11×#488—21no—
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22C11×#465—21no—
23C4×C11×Q16C2211yescharacteristic, complemented
24C4×C11×SD16—21no—
25C4×C11×D8—21no—
26C4×C11×D8—21no—
27C4×C11×D8C2212yes—
28C4×C11×D8C2212yes—
29C4×C11×D8C2211yescharacteristic, complemented
30C2×C11×#107C2211yescharacteristic
31C2×C11×#102—21no—
32C2×C4×C8×C11C2211yescharacteristic
33C11×#367C2212yescomplemented
34C11×#366C2212yescomplemented
35C11×C4⋊C16C2212yescomplemented
36C11×#358C2212yescomplemented
37C11×#357C2212yes—
38C11×#357C2212yes—
39C11×#357C2212yescomplemented
40C11×C22⋊C16C2211yescharacteristic
41C11×C22⋊C16C2211yescharacteristic
42C4×C11×C16C2212yescomplemented
43C22×D4×C11—21no—
44C23×C4×C11—41no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8—24no—
48C2×C11×D8—21no—
49C2×C11×D8C2311yescharacteristic
50C2×C11×D8C2312yes—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×#126—41no—
54C11×#125—21no—
55C11×#124—21no—
56C11×#123—41no—
57C11×C22⋊Q8—21no—
58C11×#121—21no—
59C4×Q8×C11—21no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—21no—
63C4×D4×C11—41no—
64C4×D4×C11—41no—
65C4×D4×C11—41no—
66C11×#117—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C22⋊C4—41no—
69C2×C42×C11D411yescharacteristic
70C11×SD32—24no—
71C11×D16—24no—
72C2×C11×C16C2312yes—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2311yescharacteristic
76C11×#107C2311yescharacteristic
77C11×#107C2312yes—
78C11×#106—21no—
79C11×#103—21no—
80C11×#103—21no—
81C11×#102—22no—
82C11×#102—22no—
83C11×#102—21no—
84C11×#102—21no—
85C4×C8×C11D411yescharacteristic
86C4×C8×C11D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#33665C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—41no—
91C2×Q8×C11—21no—
92C2×D4×C11—24no—
93C2×D4×C11—22no—
94C2×D4×C11—21no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—42no—
100C22×C4×C11—41no—
101C22×C4×C11—42no—
102C22×C4×C11—84no—
103C22×C4×C11D811yescharacteristic
104C22×C4×C11D811yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C11×Q16—22no—
107C11×SD16—42no—
108C11×D8—24no—
109C11×D8—22no—
110C11×D8—22no—
111C11×D8#4114yes—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2411yescharacteristic
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11D811yescharacteristic
135C42×C11D811yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C11×C16—22no—
139C11×C16—22no—
140#3168C2×C1111yescharacteristic, complemented
141C2×C4×D8C2×C1111yescharacteristic, complemented
142#2236C2×C1111yescharacteristic, complemented
143#2233C2×C1111yescharacteristic, complemented
144#2228C2×C1112yescomplemented
145#2210C2×C1112yescomplemented
146#2187C2×C1111yescharacteristic, complemented
147#2184C2×C1111yescharacteristic
148C4×SD32C2×C1112yescomplemented
149C4×D16C2×C1112yescomplemented
150#2162C2×C1111yescharacteristic, complemented
151C23×C11—44no—
152C23×C11—42no—
153C23×C11—41no—
154C23×C11—82no—
155C23×C11—82no—
156C23×C11C2×D811yescharacteristic
157Q8×C11—41no—
158Q8×C11—41no—
159D4×C11—24no—
160D4×C11—44no—
161D4×C11—41no—
162D4×C11—42no—
163D4×C11—41no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—84no—
174C2×C4×C11—82no—
175C2×C4×C11—82no—
176C2×C4×C11—84no—
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C8×C11—21no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11C2×#4112yes—
187C22×D8C22×C1111yescharacteristic
188#529—21no—
189C2×C4×D4—21no—
190C2×SD32C22×C1112yes—
191C2×D16C22×C1112yes—
192#499C22×C1111yescharacteristic, complemented
193#495C22×C1111yescharacteristic, complemented
194#488—21no—
195#467C22×C1111yescharacteristic
196#466C22×C1111yescharacteristic
197#465—21no—
198C4×Q16C22×C1111yescharacteristic, complemented
199C4×SD16—21no—
200C4×D8—21no—
201C4×D8—21no—
202C4×D8C22×C1112yes—
203C4×D8C22×C1112yes—
204C4×D8C22×C1111yescharacteristic, complemented
205C2×#107C22×C1111yescharacteristic
206C2×#102—21no—
207C2×C4×C8C22×C1111yescharacteristic
208#367C22×C1112yescomplemented
209#366C22×C1112yescomplemented
210C4⋊C16C22×C1112yescomplemented
211#358C22×C1112yescomplemented
212#357C22×C1112yes—
213#357C22×C1112yes—
214#357C22×C1112yescomplemented
215C22⋊C16C22×C1111yescharacteristic
216C22⋊C16C22×C1111yescharacteristic
217C4×C16C22×C1112yescomplemented
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—88no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11#50812yes—
228C22×C11C22×D811yescharacteristic
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11—82no—
237C4×C11#50912yes—
238C4×C11#52511yescharacteristic
239C4×C11#57511yescharacteristic
240C22×D4—21no—
241C23×C4—41no—
242C2×Q16C23×C1111yescharacteristic
243C2×SD16—21no—
244C2×D8—24no—
245C2×D8—21no—
246C2×D8C23×C1111yescharacteristic
247C2×D8C23×C1112yes—
248C22×C8D4×C1111yescharacteristic
249C22×C8C23×C1111yescharacteristic
250#126—41no—
251#125—21no—
252#124—21no—
253#123—41no—
254C22⋊Q8—21no—
255#121—21no—
256C4×Q8—21no—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—21no—
260C4×D4—41no—
261C4×D4—41no—
262C4×D4—41no—
263#117—41no—
264C2×C4⋊C4—21no—
265C2×C22⋊C4—41no—
266C2×C42D4×C1111yescharacteristic
267SD32—24no—
268D16—24no—
269C2×C16C23×C1112yes—
270C2×C16C23×C1112yes—
271#107—21no—
272#107C23×C1111yescharacteristic
273#107C23×C1111yescharacteristic
274#107C23×C1112yes—
275#106—21no—
276#103—21no—
277#103—21no—
278#102—22no—
279#102—22no—
280#102—21no—
281#102—21no—
282C4×C8D4×C1111yescharacteristic
283C4×C8D4×C1111yescharacteristic
284C4×C8C23×C1111yescharacteristic
285C4×C8C23×C1111yescharacteristic
286C2×C11—22no—
287C2×C11—84no—
288C2×C11—161no—
289C2×C11#310011yescharacteristic
290C2×C11C2×#50811yescharacteristic
291C2×C11C2×#50911yescharacteristic
292C24—41no—
293C2×Q8—21no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—21no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—84no—
305C22×C4C11×D811yescharacteristic
306C22×C4C11×D811yescharacteristic
307C22×C4C2×D4×C1111yescharacteristic
308Q16—22no—
309SD16—42no—
310D8—24no—
311D8—22no—
312D8—22no—
313D8C11×#4114yes—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8C2×D4×C1111yescharacteristic
317C2×C8C2×D4×C1111yescharacteristic
318C2×C8C2×D4×C1111yescharacteristic
319C2×C8C24×C1111yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42—41no—
336C42C11×D811yescharacteristic
337C42C11×D811yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C2×D4×C1111yescharacteristic
340C16—22no—
341C16—22no—
342C11#3366511yescharacteristic, direct product factor, Sylow
343C23—44no—
344C23—42no—
345C23—41no—
346C23—82no—
347C23—82no—
348C23C2×C11×D811yescharacteristic
349Q8—41no—
350Q8—41no—
351D4—24no—
352D4—44no—
353D4—41no—
354D4—42no—
355D4—41no—
356D4—82no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—84no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—84no—
369C2×C4C2×C11×D811yescharacteristic
370C2×C4C2×C11×D811yescharacteristic
371C2×C4C2×C11×D811yescharacteristic
372C2×C4C2×C11×D811yescharacteristic
373C2×C4C2×C11×D811yescharacteristic
374C2×C4C22×D4×C1111yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8C2×C11×#4112yes—
379C22—21no—
380C22—21no—
381C22—44no—
382C22—88no—
383C22—82no—
384C22—82no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22C11×#50812yes—
389C22C22×C11×D811yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—82no—
396C4—81no—
397C4—81no—
398C4C11×#50912yes—
399C4C11×#52511yescharacteristic
400C4C11×#57511yescharacteristic
401C2—22no—
402C2—84no—
403C2—161no—
404C2C11×#310011yescharacteristic
405C2C2×C11×#50811yescharacteristic
406C2C2×C11×#50911yescharacteristic
subgroupG/H
centerC2×C4×C11C2×D8
commutator, Frattini, cosocleC2×C8C24×C11
socleC22×C11C22×D8
prime radicalC11×#2184C2
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×#3168C2semidirect
2. C2×C4×C11×D8C2semidirect
3. C11×#2236C2semidirect
4. C11×#2233C2semidirect
5. C11×#2228C2semidirect
6. C11×#2210C2semidirect
7. C11×#2187C2semidirect
9. C4×C11×SD32C2semidirect
10. C4×C11×D16C2semidirect
11. C11×#2162C2semidirect
17. C11×#499C22semidirect
18. C11×#495C22semidirect
23. C4×C11×Q16C22semidirect
29. C4×C11×D8C22semidirect
33. C11×#367C22semidirect
34. C11×#366C22semidirect
35. C11×C4⋊C16C22semidirect
36. C11×#358C22semidirect
39. C11×#357C22semidirect
42. C4×C11×C16C22semidirect
89. #33665C11direct (N × H)
140. #3168C2×C11semidirect
141. C2×C4×D8C2×C11semidirect
142. #2236C2×C11semidirect
143. #2233C2×C11semidirect
144. #2228C2×C11semidirect
145. #2210C2×C11semidirect
146. #2187C2×C11semidirect
148. C4×SD32C2×C11semidirect
149. C4×D16C2×C11semidirect
150. #2162C2×C11semidirect
192. #499C22×C11semidirect
193. #495C22×C11semidirect
198. C4×Q16C22×C11semidirect
204. C4×D8C22×C11semidirect
208. #367C22×C11semidirect
209. #366C22×C11semidirect
210. C4⋊C16C22×C11semidirect
211. #358C22×C11semidirect
214. #357C22×C11semidirect
217. C4×C16C22×C11semidirect
342. C11#33665direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31682
C2×C4×C11×D82
C11×#22362
C11×#22332
C11×#22282
C11×#22102
C11×#21872
C11×#21842
C4×C11×SD322
C4×C11×D162
C11×#21622
#3366511