Finite Group Databasebeta

← C11×#33690 #14610883

Subgroups — C11×#33690 #14610883

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3183C211yesmaximal, characteristic, complemented
2C11×#2956C211yesmaximal, characteristic, complemented
3C11×#2239C211yesmaximal, characteristic, complemented
4C11×#2238C211yesmaximal, characteristic, complemented
5C11×#2231C212yesmaximal, complemented
6C11×#2212C212yesmaximal, complemented
7C11×#2191C211yesmaximal, characteristic, complemented
8C11×#2190C211yesmaximal, characteristic
9C11×AGL(1,ℤ/16)C212yesmaximal, complemented
10C11×#2180C212yesmaximal, complemented
11C11×#2165C211yesmaximal, characteristic, complemented
12C11×#575C2211yescharacteristic
13C11×#568—21no—
14C11×#529—21no—
15C11×#510C2212yes—
16C11×#509C2212yes—
17C11×#499C2211yescharacteristic, complemented
18C11×#495C2211yescharacteristic, complemented
19C11×#488—21no—
20C11×#470C2211yescharacteristic
21C11×#469C2211yescharacteristic
22C11×#468—21no—
23C11×#444—21no—
24C11×#444C2212yes—
25C11×#443—21no—
26C11×#443C2212yes—
27C11×#442C2211yescharacteristic, complemented
28C11×#441C2211yescharacteristic, complemented
29C11×#440—21no—
30C11×#430C2211yescharacteristic
31C2×C11×#104—21no—
32C4×C11×M16C2211yescharacteristic
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—42no—
54C2×C11×M16—21no—
55C2×C11×M16—42no—
56C2×C11×M16D411yescharacteristic
57C2×C11×M16C2311yescharacteristic
58C11×#126—41no—
59C11×#125—21no—
60C11×#124—21no—
61C11×#123—41no—
62C11×C22⋊Q8—21no—
63C11×#121—21no—
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—41no—
67C11×#117—41no—
68C2×C42×C11D411yescharacteristic
69C11×Q32—22no—
70C11×SD32—22no—
71C11×SD32—22no—
72C11×D16—22no—
73C11×M32C2312yes—
74C11×M32C2312yes—
75C11×#108—21no—
76C11×#108C2312yes—
77C11×#107—21no—
78C11×#106C2311yescharacteristic
79C11×#106C2311yescharacteristic
80C11×#104—22no—
81C11×#104—22no—
82C11×#103—21no—
83C11×#103—21no—
84C11×#102—21no—
85C11×#102—21no—
86C11×#97D411yescharacteristic
87C11×#97C2311yescharacteristic
88C4×C8×C11D411yescharacteristic
89C4×C8×C11C2311yescharacteristic
90#33690C1111yesmaximal, characteristic, direct product factor, Sylow
91C11×#41—22no—
92C11×#41—22no—
93C11×#41—41no—
94C11×#41—41no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C11×Q16—21no—
106C11×Q16—22no—
107C11×Q16#4112yes—
108C11×SD16—22no—
109C11×SD16—22no—
110C11×SD16—42no—
111C11×D8—21no—
112C11×D8—22no—
113C11×D8#4112yes—
114C11×M16—22no—
115C11×M16—22no—
116C11×M16—22no—
117C11×M16—41no—
118C11×M16—42no—
119C11×M16—42no—
120C2×C8×C11—41no—
121C2×C8×C11—42no—
122C2×C8×C11—42no—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2411yescharacteristic
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11—21no—
139C42×C11—41no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C11×C16—22no—
143C11×C16—22no—
144#3183C2×C1111yescharacteristic, complemented
145#2956C2×C1111yescharacteristic, complemented
146#2239C2×C1111yescharacteristic, complemented
147#2238C2×C1111yescharacteristic, complemented
148#2231C2×C1112yescomplemented
149#2212C2×C1112yescomplemented
150#2191C2×C1111yescharacteristic, complemented
151#2190C2×C1111yescharacteristic
152AGL(1,ℤ/16)C2×C1112yescomplemented
153#2180C2×C1112yescomplemented
154#2165C2×C1111yescharacteristic, complemented
155C23×C11—41no—
156C23×C11—41no—
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158Q8×C11—22no—
159Q8×C11—41no—
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—22no—
163D4×C11—41no—
164D4×C11—42no—
165D4×C11—42no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—82no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—81no—
180C2×C4×C11—82no—
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C8×C11—21no—
184C8×C11—21no—
185C8×C11—42no—
186C8×C11AGL(1,ℤ/8)12yes—
187C8×C11C2×#4112yes—
188#575C22×C1111yescharacteristic
189#568—21no—
190#529—21no—
191#510C22×C1112yes—
192#509C22×C1112yes—
193#499C22×C1111yescharacteristic, complemented
194#495C22×C1111yescharacteristic, complemented
195#488—21no—
196#470C22×C1111yescharacteristic
197#469C22×C1111yescharacteristic
198#468—21no—
199#444—21no—
200#444C22×C1112yes—
201#443—21no—
202#443C22×C1112yes—
203#442C22×C1111yescharacteristic, complemented
204#441C22×C1111yescharacteristic, complemented
205#440—21no—
206#430C22×C1111yescharacteristic
207C2×#104—21no—
208C4×M16C22×C1111yescharacteristic
209#365C22×C1112yescomplemented
210#365C22×C1112yescomplemented
211#364C22×C1112yescomplemented
212#362C22×C1112yescomplemented
213#361C22×C1112yescomplemented
214#360C22×C1112yes—
215#360C22×C1112yes—
216#349C22×C1111yescharacteristic
217#349C22×C1111yescharacteristic
218#347C22×C1112yescomplemented
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—42no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—161no—
226C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C11—21no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—42no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11#52511yescharacteristic
235C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
236C2×#41—21no—
237#137—22no—
238AGL(1,ℤ/8)—22no—
239#135—21no—
240#135C23×C1112yes—
241C2×Q16C23×C1111yescharacteristic
242C2×SD16—21no—
243C2×D8C23×C1111yescharacteristic
244#131—22no—
245#131—22no—
246#131—42no—
247C2×M16—21no—
248C2×M16—42no—
249C2×M16D4×C1111yescharacteristic
250C2×M16C23×C1111yescharacteristic
251#126—41no—
252#125—21no—
253#124—21no—
254#123—41no—
255C22⋊Q8—21no—
256#121—21no—
257C4×Q8—21no—
258C4×D4—21no—
259C4×D4—41no—
260#117—41no—
261C2×C42D4×C1111yescharacteristic
262Q32—22no—
263SD32—22no—
264SD32—22no—
265D16—22no—
266M32C23×C1112yes—
267M32C23×C1112yes—
268#108—21no—
269#108C23×C1112yes—
270#107—21no—
271#106C23×C1111yescharacteristic
272#106C23×C1111yescharacteristic
273#104—22no—
274#104—22no—
275#103—21no—
276#103—21no—
277#102—21no—
278#102—21no—
279#97D4×C1111yescharacteristic
280#97C23×C1111yescharacteristic
281C4×C8D4×C1111yescharacteristic
282C4×C8C23×C1111yescharacteristic
283C2×C11—21no—
284C2×C11—41no—
285C2×C11—82no—
286C2×C11—161no—
287C2×C11#310911yescharacteristic
288#41—22no—
289#41—22no—
290#41—41no—
291#41—41no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C1111yescharacteristic
302Q16—21no—
303Q16—22no—
304Q16C11×#4112yes—
305SD16—22no—
306SD16—22no—
307SD16—42no—
308D8—21no—
309D8—22no—
310D8C11×#4112yes—
311M16—22no—
312M16—22no—
313M16—22no—
314M16—42no—
315M16—41no—
316M16—42no—
317C2×C8—42no—
318C2×C8—41no—
319C2×C8—42no—
320C2×C8C2×D4×C1111yescharacteristic
321C2×C8C2×D4×C1111yescharacteristic
322C2×C8C2×D4×C1111yescharacteristic
323C2×C8C24×C1111yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42—21no—
336C42—41no—
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C16—22no—
340C16—22no—
341C11#3369011yescharacteristic, direct product factor, Sylow
342C23—41no—
343C23—41no—
344C23C11×AGL(1,ℤ/8)11yescharacteristic
345Q8—22no—
346Q8—41no—
347Q8—41no—
348Q8—41no—
349D4—22no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—82no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
369C2×C4C22×D4×C1111yescharacteristic
370C8—21no—
371C8—21no—
372C8—42no—
373C8C11×AGL(1,ℤ/8)12yes—
374C8C2×C11×#4112yes—
375C22—21no—
376C22—41no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—161no—
382C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
383C4—21no—
384C4—41no—
385C4—41no—
386C4—42no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4C11×#52511yescharacteristic
391C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
392C2—21no—
393C2—41no—
394C2—82no—
395C2—161no—
396C2C11×#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 ◁ C4×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3183C2semidirect
2. C11×#2956C2semidirect
3. C11×#2239C2semidirect
4. C11×#2238C2semidirect
5. C11×#2231C2semidirect
6. C11×#2212C2semidirect
7. C11×#2191C2semidirect
9. C11×AGL(1,ℤ/16)C2semidirect
10. C11×#2180C2semidirect
11. C11×#2165C2semidirect
17. C11×#499C22semidirect
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
90. #33690C11direct (N × H)
144. #3183C2×C11semidirect
145. #2956C2×C11semidirect
146. #2239C2×C11semidirect
147. #2238C2×C11semidirect
148. #2231C2×C11semidirect
149. #2212C2×C11semidirect
150. #2191C2×C11semidirect
152. AGL(1,ℤ/16)C2×C11semidirect
153. #2180C2×C11semidirect
154. #2165C2×C11semidirect
193. #499C22×C11semidirect
194. #495C22×C11semidirect
203. #442C22×C11semidirect
204. #441C22×C11semidirect
209. #365C22×C11semidirect
210. #365C22×C11semidirect
211. #364C22×C11semidirect
212. #362C22×C11semidirect
213. #361C22×C11semidirect
218. #347C22×C11semidirect
341. C11#33690direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31832
C11×#29562
C11×#22392
C11×#22382
C11×#22312
C11×#22122
C11×#21912
C11×#21902
C11×AGL(1,ℤ/16)2
C11×#21802
C11×#21652
#3369011