Finite Group Databasebeta

← C11×#33702 #14610895

Subgroups — C11×#33702 #14610895

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3164C211yesmaximal, characteristic, complemented
2C11×#3155C211yesmaximal, characteristic
3C11×#2244C212yesmaximal, complemented
4C11×#2243C212yesmaximal, complemented
5C11×#2242C212yesmaximal, complemented
6C11×#2240C212yesmaximal, complemented
7C11×#2140C211yesmaximal, characteristic, complemented
8C11×#2139C211yesmaximal, characteristic, complemented
9C11×#2138C211yesmaximal, characteristic, complemented
10C2×C11×#357C211yesmaximal, characteristic, complemented
11C11×#2108C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C11×#544—21no—
16C11×#535—21no—
17C2×C11×M32C2211yescharacteristic
18C22×C11×C16C2211yescharacteristic
19C11×#501—22no—
20C11×#500C2212yescomplemented
21C11×#499C2212yescomplemented
22C11×#496—22no—
23C11×#495C2212yes—
24C11×#493C2212yes—
25C11×#428—21no—
26C11×#427C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C11×#358C2211yescharacteristic, complemented
30C11×#358C2211yescharacteristic, complemented
31C11×#358C2212yescomplemented
32C11×#357C2212yes—
33C11×#357C2212yes—
34C11×#357C2212yes—
35C11×#357C2212yes—
36C11×#357C2211yescharacteristic, complemented
37C11×#357C2211yescharacteristic, complemented
38C11×#357C2212yescomplemented
39C11×#346C2212yescomplemented
40C4×C11×C16C2212yescomplemented
41C2×C11×#41—21no—
42C22×D4×C11—21no—
43C11×AGL(1,ℤ/8)—44no—
44C11×#135—22no—
45C11×#135—22no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—22no—
48C2×C11×SD16—21no—
49C2×C11×D8—22no—
50C2×C11×D8—21no—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C2×C11×D8C2311yescharacteristic
54C2×C11×D8C2312yes—
55C2×C11×M16D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—41no—
59C11×#127—22no—
60C11×#125—22no—
61C11×#125—41no—
62C11×#124—22no—
63C11×C22⋊Q8—42no—
64C11×#121—41no—
65C11×#121—41no—
66C11×#120—42no—
67C11×#117—21no—
68C11×#117D411yescharacteristic
69C2×C11×C4⋊C4—21no—
70C11×M32—22no—
71C2×C11×C16—22no—
72C2×C11×C16C2311yescharacteristic
73C2×C11×C16C2311yescharacteristic
74C2×C11×C16C2312yes—
75C11×#107—22no—
76C11×#107—21no—
77C11×#107C2311yescharacteristic
78C11×#107C2312yes—
79C11×#107C2311yescharacteristic
80C11×#106—22no—
81C11×#106—21no—
82C11×#97D412yes—
83C4×C8×C11C2312yes—
84#33702C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—41no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×Q8×C11—42no—
90C2×D4×C11—22no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C11×Q16—21no—
102C11×Q16—21no—
103C11×SD16—42no—
104C11×SD16—44no—
105C11×D8—22no—
106C11×D8—22no—
107C11×D8—21no—
108C11×D8—21no—
109C11×D8—42no—
110C11×D8—44no—
111C11×M16SD1614yes—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D412yes—
114C2×C8×C11#4112yes—
115C2×C8×C11#4112yes—
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4D811yescharacteristic
125C11×C4⋊C4D811yescharacteristic
126C11×C22⋊C4—41no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4D812yes—
130C42×C11—41no—
131C42×C11C2×D412yes—
132C11×C16—21no—
133C11×C16—21no—
134C11×C16—22no—
135#3164C2×C1111yescharacteristic, complemented
136#3155C2×C1111yescharacteristic
137#2244C2×C1112yescomplemented
138#2243C2×C1112yescomplemented
139#2242C2×C1112yescomplemented
140#2240C2×C1112yescomplemented
141#2140C2×C1111yescharacteristic, complemented
142#2139C2×C1111yescharacteristic, complemented
143#2138C2×C1111yescharacteristic, complemented
144C2×#357C2×C1111yescharacteristic, complemented
145#2108C2×C1111yescharacteristic, complemented
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—82no—
149C23×C11—161no—
150C23×C11—161no—
151C23×C11C2×D811yescharacteristic
152Q8×C11—41no—
153Q8×C11—41no—
154Q8×C11—162no—
155D4×C11—42no—
156D4×C11—41no—
157D4×C11—41no—
158D4×C11—42no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—162no—
162D4×C11—162no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—82no—
168C2×C4×C11—161no—
169C2×C4×C11#12412yes—
170C2×C4×C11C2×D812yes—
171C2×C4×C11C2×D812yes—
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×SD1612yes—
174C2×C4×C11C22×D411yescharacteristic
175C8×C11#12412yes—
176C8×C11C2×SD1614yes—
177C8×C11C2×#4111yescharacteristic
178C8×C11C2×#4111yescharacteristic
179C2×AGL(1,ℤ/8)—21no—
180C2×#135C22×C1111yescharacteristic
181C22×D8C22×C1111yescharacteristic
182#544—21no—
183#535—21no—
184C2×M32C22×C1111yescharacteristic
185C22×C16C22×C1111yescharacteristic
186#501—22no—
187#500C22×C1112yescomplemented
188#499C22×C1112yescomplemented
189#496—22no—
190#495C22×C1112yes—
191#493C22×C1112yes—
192#428—21no—
193#427C22×C1111yescharacteristic
194C2×#107C22×C1111yescharacteristic
195#405C22×C1111yescharacteristic
196#358C22×C1111yescharacteristic, complemented
197#358C22×C1111yescharacteristic, complemented
198#358C22×C1112yescomplemented
199#357C22×C1112yes—
200#357C22×C1112yes—
201#357C22×C1112yes—
202#357C22×C1112yes—
203#357C22×C1111yescharacteristic, complemented
204#357C22×C1111yescharacteristic, complemented
205#357C22×C1112yescomplemented
206#346C22×C1112yescomplemented
207C4×C16C22×C1112yescomplemented
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—81no—
211C22×C11—82no—
212C22×C11—81no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—82no—
216C22×C11—164no—
217C22×C11#48612yes—
218C22×C11C22×D811yescharacteristic
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—81no—
222C4×C11—82no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11#48612yes—
226C4×C11C2×#12411yescharacteristic
227C4×C11C22×SD1611yescharacteristic
228C2×#41—21no—
229C22×D4—21no—
230AGL(1,ℤ/8)—44no—
231#135—22no—
232#135—22no—
233C2×Q16C23×C1111yescharacteristic
234C2×SD16—21no—
235C2×SD16—22no—
236C2×D8—21no—
237C2×D8—22no—
238C2×D8—22no—
239C2×D8—22no—
240C2×D8C23×C1112yes—
241C2×D8C23×C1111yescharacteristic
242C2×M16D4×C1111yescharacteristic
243C22×C8C23×C1111yescharacteristic
244C4⋊Q8—22no—
245C4⋊Q8—41no—
246#127—22no—
247#125—22no—
248#125—41no—
249#124—22no—
250C22⋊Q8—42no—
251#121—41no—
252#121—41no—
253#120—42no—
254#117—21no—
255#117D4×C1111yescharacteristic
256C2×C4⋊C4—21no—
257M32—22no—
258C2×C16—22no—
259C2×C16C23×C1111yescharacteristic
260C2×C16C23×C1112yes—
261C2×C16C23×C1111yescharacteristic
262#107—21no—
263#107—22no—
264#107C23×C1112yes—
265#107C23×C1111yescharacteristic
266#107C23×C1111yescharacteristic
267#106—21no—
268#106—22no—
269#97D4×C1112yes—
270C4×C8C23×C1112yes—
271C2×C11—22no—
272C2×C11—161no—
273C2×C11—162no—
274C2×C11C2×#48611yescharacteristic
275C2×C11#341511yescharacteristic
276C2×C11#341611yescharacteristic
277C24—41no—
278#41—42no—
279#41—42no—
280C2×Q8—21no—
281C2×Q8—42no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—42no—
286C2×D4—41no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4C2×D4×C1111yescharacteristic
293Q16—21no—
294Q16—21no—
295SD16—42no—
296SD16—44no—
297D8—22no—
298D8—22no—
299D8—21no—
300D8—21no—
301D8—42no—
302D8—44no—
303M16C11×SD1614yes—
304C2×C8C2×D4×C1111yescharacteristic
305C2×C8C2×D4×C1112yes—
306C2×C8C11×#4112yes—
307C2×C8C11×#4112yes—
308C2×C8C24×C1111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4C11×D811yescharacteristic
317C4⋊C4C11×D811yescharacteristic
318C22⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4C11×D812yes—
322C42—41no—
323C42C2×D4×C1112yes—
324C16—21no—
325C16—21no—
326C16—22no—
327C11#3370211yescharacteristic, direct product factor, Sylow
328C23—42no—
329C23—41no—
330C23—82no—
331C23—161no—
332C23—161no—
333C23C2×C11×D811yescharacteristic
334Q8—41no—
335Q8—41no—
336Q8—162no—
337D4—42no—
338D4—41no—
339D4—41no—
340D4—42no—
341D4—82no—
342D4—82no—
343D4—162no—
344D4—162no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—161no—
351C2×C4C11×#12412yes—
352C2×C4C2×C11×D812yes—
353C2×C4C2×C11×D812yes—
354C2×C4C2×C11×D811yescharacteristic
355C2×C4C2×C11×SD1612yes—
356C2×C4C22×D4×C1111yescharacteristic
357C8C11×#12412yes—
358C8C2×C11×SD1614yes—
359C8C2×C11×#4111yescharacteristic
360C8C2×C11×#4111yescharacteristic
361C22—21no—
362C22—21no—
363C22—81no—
364C22—82no—
365C22—81no—
366C22—82no—
367C22—81no—
368C22—82no—
369C22—164no—
370C22C11×#48612yes—
371C22C22×C11×D811yescharacteristic
372C4—22no—
373C4—22no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4C11×#48612yes—
379C4C2×C11×#12411yescharacteristic
380C4C22×C11×SD1611yescharacteristic
381C2—22no—
382C2—162no—
383C2—161no—
384C2C2×C11×#48611yescharacteristic
385C2C11×#341511yescharacteristic
386C2C11×#341611yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#3155C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3164C2semidirect
3. C11×#2244C2semidirect
4. C11×#2243C2semidirect
5. C11×#2242C2semidirect
6. C11×#2240C2semidirect
7. C11×#2140C2semidirect
8. C11×#2139C2semidirect
9. C11×#2138C2semidirect
10. C2×C11×#357C2semidirect
11. C11×#2108C2semidirect
20. C11×#500C22semidirect
21. C11×#499C22semidirect
29. C11×#358C22semidirect
30. C11×#358C22semidirect
31. C11×#358C22semidirect
36. C11×#357C22semidirect
37. C11×#357C22semidirect
38. C11×#357C22semidirect
39. C11×#346C22semidirect
40. C4×C11×C16C22semidirect
84. #33702C11direct (N × H)
135. #3164C2×C11semidirect
137. #2244C2×C11semidirect
138. #2243C2×C11semidirect
139. #2242C2×C11semidirect
140. #2240C2×C11semidirect
141. #2140C2×C11semidirect
142. #2139C2×C11semidirect
143. #2138C2×C11semidirect
144. C2×#357C2×C11semidirect
145. #2108C2×C11semidirect
187. #500C22×C11semidirect
188. #499C22×C11semidirect
196. #358C22×C11semidirect
197. #358C22×C11semidirect
198. #358C22×C11semidirect
203. #357C22×C11semidirect
204. #357C22×C11semidirect
205. #357C22×C11semidirect
206. #346C22×C11semidirect
207. C4×C16C22×C11semidirect
327. C11#33702direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31642
C11×#31552
C11×#22442
C11×#22432
C11×#22422
C11×#22402
C11×#21402
C11×#21392
C11×#21382
C2×C11×#3572
C11×#21082
#3370211