Finite Group Databasebeta

← C11×#33691 #14610884

Subgroups — C11×#33691 #14610884

Order 2816.

524 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×#3173C211yesmaximal, characteristic, complemented
2C11×#2955C211yesmaximal, characteristic, complemented
3C11×#2239C211yesmaximal, characteristic, complemented
4C11×#2238C211yesmaximal, characteristic, complemented
5C11×#2230C212yesmaximal, complemented
6C11×#2212C212yesmaximal, complemented
7C11×#2191C211yesmaximal, characteristic, complemented
8C11×#2190C211yesmaximal, characteristic
9C11×AGL(1,ℤ/16)C212yesmaximal, complemented
10C11×#2180C212yesmaximal, complemented
11C11×#2166C211yesmaximal, characteristic, complemented
12C11×#575C2211yescharacteristic
13C2×C11×#131—21no—
14C11×#542—21no—
15C11×#510C2212yes—
16C11×#509C2212yes—
17C11×#498C2211yescharacteristic, complemented
18C11×#495C2211yescharacteristic, complemented
19C11×#489—21no—
20C11×#470C2211yescharacteristic
21C11×#469C2211yescharacteristic
22C11×#465—21no—
23C11×#444—21no—
24C11×#444C2212yes—
25C11×#443—21no—
26C11×#443C2212yes—
27C11×#442C2211yescharacteristic, complemented
28C11×#441C2211yescharacteristic, complemented
29C4×C11×SD16—21no—
30C11×#430C2211yescharacteristic
31C11×#421—21no—
32C11×#405C2211yescharacteristic
33C11×#365C2212yescomplemented
34C11×#365C2212yescomplemented
35C11×#364C2212yescomplemented
36C11×#362C2212yescomplemented
37C11×#361C2212yescomplemented
38C11×#360C2212yes—
39C11×#360C2212yes—
40C11×#349C2211yescharacteristic
41C11×#349C2211yescharacteristic
42C11×#347C2212yescomplemented
43C2×C11×#41—21no—
44C11×#137—22no—
45C11×AGL(1,ℤ/8)—22no—
46C11×#135—21no—
47C11×#135C2312yes—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C11×#131—22no—
52C11×#131—22no—
53C11×#131—41no—
54C11×#131—41no—
55C2×C11×M16—21no—
56C2×C11×M16—41no—
57C2×C11×M16C2311yescharacteristic
58C22×C8×C11—41no—
59C22×C8×C11D411yescharacteristic
60C11×C4⋊Q8—21no—
61C11×#126—41no—
62C11×#124—21no—
63C11×#124—41no—
64C11×#123—41no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—41no—
67C11×#121—21no—
68C4×Q8×C11—21no—
69C4×D4×C11—21no—
70C11×#117D411yescharacteristic
71C11×Q32—22no—
72C11×SD32—22no—
73C11×SD32—22no—
74C11×D16—22no—
75C11×M32C2312yes—
76C11×M32C2312yes—
77C11×#108—21no—
78C11×#108C2312yes—
79C11×#106—21no—
80C11×#106C2311yescharacteristic
81C11×#106C2311yescharacteristic
82C11×#104—22no—
83C11×#104—22no—
84C11×#103—21no—
85C11×#103—21no—
86C11×#102—21no—
87C11×#102—21no—
88C11×#97D411yescharacteristic
89C11×#97C2311yescharacteristic
90C4×C8×C11D411yescharacteristic
91C4×C8×C11C2311yescharacteristic
92#33691C1111yesmaximal, characteristic, direct product factor, Sylow
93C11×#41—22no—
94C11×#41—22no—
95C11×#41—41no—
96C11×#41—41no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—41no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C11×Q16—21no—
108C11×Q16—22no—
109C11×Q16#4112yes—
110C11×SD16—22no—
111C11×SD16—22no—
112C11×SD16—41no—
113C11×SD16—41no—
114C11×D8—21no—
115C11×D8—22no—
116C11×D8#4112yes—
117C11×M16—22no—
118C11×M16—22no—
119C11×M16—41no—
120C11×M16—42no—
121C11×M16—42no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—41no—
125C2×C8×C11—42no—
126C2×C8×C11—42no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—21no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C11×C16—22no—
147C11×C16—22no—
148#3173C2×C1111yescharacteristic, complemented
149#2955C2×C1111yescharacteristic, complemented
150#2239C2×C1111yescharacteristic, complemented
151#2238C2×C1111yescharacteristic, complemented
152#2230C2×C1112yescomplemented
153#2212C2×C1112yescomplemented
154#2191C2×C1111yescharacteristic, complemented
155#2190C2×C1111yescharacteristic
156AGL(1,ℤ/16)C2×C1112yescomplemented
157#2180C2×C1112yescomplemented
158#2166C2×C1111yescharacteristic, complemented
159C23×C11—41no—
160C23×C11—41no—
161C23×C11AGL(1,ℤ/8)11yescharacteristic
162Q8×C11—22no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—41no—
166Q8×C11—161no—
167D4×C11—22no—
168D4×C11—41no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—161no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—161no—
185C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—42no—
190C8×C11AGL(1,ℤ/8)11yescharacteristic
191C8×C11AGL(1,ℤ/8)11yescharacteristic
192C8×C11C2×#4112yes—
193#575C22×C1111yescharacteristic
194C2×#131—21no—
195#542—21no—
196#510C22×C1112yes—
197#509C22×C1112yes—
198#498C22×C1111yescharacteristic, complemented
199#495C22×C1111yescharacteristic, complemented
200#489—21no—
201#470C22×C1111yescharacteristic
202#469C22×C1111yescharacteristic
203#465—21no—
204#444—21no—
205#444C22×C1112yes—
206#443—21no—
207#443C22×C1112yes—
208#442C22×C1111yescharacteristic, complemented
209#441C22×C1111yescharacteristic, complemented
210C4×SD16—21no—
211#430C22×C1111yescharacteristic
212#421—21no—
213#405C22×C1111yescharacteristic
214#365C22×C1112yescomplemented
215#365C22×C1112yescomplemented
216#364C22×C1112yescomplemented
217#362C22×C1112yescomplemented
218#361C22×C1112yescomplemented
219#360C22×C1112yes—
220#360C22×C1112yes—
221#349C22×C1111yescharacteristic
222#349C22×C1111yescharacteristic
223#347C22×C1112yescomplemented
224C22×C11—21no—
225C22×C11—41no—
226C22×C11—42no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—82no—
230C22×C11—81no—
231C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C11—21no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—42no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11#52511yescharacteristic
240C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
241C2×#41—21no—
242#137—22no—
243AGL(1,ℤ/8)—22no—
244#135—21no—
245#135C23×C1112yes—
246C2×Q16C23×C1111yescharacteristic
247C2×SD16—21no—
248C2×D8C23×C1111yescharacteristic
249#131—22no—
250#131—22no—
251#131—41no—
252#131—41no—
253C2×M16—21no—
254C2×M16—41no—
255C2×M16C23×C1111yescharacteristic
256C22×C8—41no—
257C22×C8D4×C1111yescharacteristic
258C4⋊Q8—21no—
259#126—41no—
260#124—21no—
261#124—41no—
262#123—41no—
263C22⋊Q8—21no—
264C22⋊Q8—41no—
265#121—21no—
266C4×Q8—21no—
267C4×D4—21no—
268#117D4×C1111yescharacteristic
269Q32—22no—
270SD32—22no—
271SD32—22no—
272D16—22no—
273M32C23×C1112yes—
274M32C23×C1112yes—
275#108—21no—
276#108C23×C1112yes—
277#106—21no—
278#106C23×C1111yescharacteristic
279#106C23×C1111yescharacteristic
280#104—22no—
281#104—22no—
282#103—21no—
283#103—21no—
284#102—21no—
285#102—21no—
286#97D4×C1111yescharacteristic
287#97C23×C1111yescharacteristic
288C4×C8D4×C1111yescharacteristic
289C4×C8C23×C1111yescharacteristic
290C2×C11—21no—
291C2×C11—41no—
292C2×C11—82no—
293C2×C11—161no—
294C2×C11#310911yescharacteristic
295#41—22no—
296#41—22no—
297#41—41no—
298#41—41no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—41no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4C2×D4×C1111yescharacteristic
309Q16—21no—
310Q16—22no—
311Q16C11×#4112yes—
312SD16—22no—
313SD16—22no—
314SD16—41no—
315SD16—41no—
316D8—21no—
317D8—22no—
318D8C11×#4112yes—
319M16—22no—
320M16—22no—
321M16—42no—
322M16—41no—
323M16—42no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—42no—
327C2×C8—41no—
328C2×C8—42no—
329C2×C8C2×D4×C1111yescharacteristic
330C2×C8C2×D4×C1111yescharacteristic
331C2×C8C2×D4×C1111yescharacteristic
332C2×C8C24×C1111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C22⋊C4—21no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C42—41no—
346C42C2×D4×C1111yescharacteristic
347C42C2×D4×C1111yescharacteristic
348C16—22no—
349C16—22no—
350C11#3369111yescharacteristic, direct product factor, Sylow
351C23—41no—
352C23—41no—
353C23C11×AGL(1,ℤ/8)11yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—41no—
357Q8—41no—
358Q8—161no—
359D4—22no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—41no—
364D4—41no—
365D4—161no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—161no—
377C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
378C2×C4C22×D4×C1111yescharacteristic
379C8—21no—
380C8—21no—
381C8—42no—
382C8C11×AGL(1,ℤ/8)11yescharacteristic
383C8C11×AGL(1,ℤ/8)11yescharacteristic
384C8C2×C11×#4112yes—
385C22—21no—
386C22—41no—
387C22—42no—
388C22—81no—
389C22—81no—
390C22—82no—
391C22—81no—
392C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—42no—
397C4—81no—
398C4—81no—
399C4—81no—
400C4C11×#52511yescharacteristic
401C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
402C2—21no—
403C2—41no—
404C2—82no—
405C2—161no—
406C2C11×#310911yescharacteristic
subgroupG/H
center, socleC2×C11#3109
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#2190C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3173C2semidirect
2. C11×#2955C2semidirect
3. C11×#2239C2semidirect
4. C11×#2238C2semidirect
5. C11×#2230C2semidirect
6. C11×#2212C2semidirect
7. C11×#2191C2semidirect
9. C11×AGL(1,ℤ/16)C2semidirect
10. C11×#2180C2semidirect
11. C11×#2166C2semidirect
17. C11×#498C22semidirect
18. C11×#495C22semidirect
27. C11×#442C22semidirect
28. C11×#441C22semidirect
33. C11×#365C22semidirect
34. C11×#365C22semidirect
35. C11×#364C22semidirect
36. C11×#362C22semidirect
37. C11×#361C22semidirect
42. C11×#347C22semidirect
92. #33691C11direct (N × H)
148. #3173C2×C11semidirect
149. #2955C2×C11semidirect
150. #2239C2×C11semidirect
151. #2238C2×C11semidirect
152. #2230C2×C11semidirect
153. #2212C2×C11semidirect
154. #2191C2×C11semidirect
156. AGL(1,ℤ/16)C2×C11semidirect
157. #2180C2×C11semidirect
158. #2166C2×C11semidirect
198. #498C22×C11semidirect
199. #495C22×C11semidirect
208. #442C22×C11semidirect
209. #441C22×C11semidirect
214. #365C22×C11semidirect
215. #365C22×C11semidirect
216. #364C22×C11semidirect
217. #362C22×C11semidirect
218. #361C22×C11semidirect
223. #347C22×C11semidirect
350. C11#33691direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31732
C11×#29552
C11×#22392
C11×#22382
C11×#22302
C11×#22122
C11×#21912
C11×#21902
C11×AGL(1,ℤ/16)2
C11×#21802
C11×#21662
#3369111