Finite Group Databasebeta

← C11×#9159 #14586352

Subgroups — C11×#9159 #14586352

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3116C211yesmaximal, characteristic
2C11×#2970C211yesmaximal, characteristic
3C11×#1759C211yesmaximal, characteristic
4C11×#1526C211yesmaximal, characteristic, complemented
5C11×#1506C211yesmaximal, characteristic, complemented
6C11×#1300C211yesmaximal, characteristic, complemented
7C11×#1291C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C4×C11×#41C2211yescharacteristic
10C11×#485—21no—
11C11×#477C411yescharacteristic, complemented
12C11×#476C411yescharacteristic, complemented
13C11×#462C411yescharacteristic, complemented
14C11×#461C411yescharacteristic, complemented
15C11×#452—21no—
16C11×#446—21no—
17C11×#441—21no—
18C11×#440—21no—
19C11×#435—22no—
20C8×D4×C11—21no—
21C11×#432—21no—
22C11×#432C2211yescharacteristic
23C11×#432C2211yescharacteristic
24C2×C11×#104—21no—
25C4×C11×M16C2211yescharacteristic
26C4×C11×M16C2211yescharacteristic
27C2×C11×#97—21no—
28C11×#376C2211yescharacteristic
29C11×#339—21no—
30C11×#330—21no—
31C11×#330—21no—
32C11×#328—22no—
33C2×C11×#41D411yescharacteristic
34C2×C11×Q16—21no—
35C2×C11×SD16—21no—
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C22×C8×C11—22no—
39C11×C4⋊Q8C2×C411yescharacteristic
40C11×C4⋊Q8C2×C411yescharacteristic
41C11×#125—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11C2×C411yescharacteristic
47C4×Q8×C11D411yescharacteristic
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11C2×C411yescharacteristic
51C4×D4×C11D411yescharacteristic
52C11×#117—21no—
53C11×#117—21no—
54C11×#117D411yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—21no—
59C11×#106—21no—
60C11×C4⋊C8—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8C2×C411yescharacteristic
63C11×C4⋊C8C2×C411yescharacteristic
64C11×#104—24no—
65C11×#103—21no—
66C11×#103—21no—
67C11×#103—21no—
68C11×#102—21no—
69C11×C22⋊C8—22no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8D412yes—
72C11×#97—22no—
73C11×#97—21no—
74C11×#97—21no—
75C11×#97—21no—
76C11×#97D411yescharacteristic
77C11×#97D411yescharacteristic
78C4×C8×C11—21no—
79C4×C8×C11—21no—
80C11×#95—21no—
81C11×#95—21no—
82#9159C1111yesmaximal, characteristic, direct product factor, Sylow
83C11×#41—22no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11C22⋊C411yescharacteristic
88C2×D4×C11—21no—
89C2×D4×C11C22⋊C411yescharacteristic
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C11×Q16—42no—
98C11×SD16—42no—
99C11×M16—22no—
100C11×M16—41no—
101C11×M16—42no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—22no—
107C2×C8×C11—44no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4C22⋊C411yescharacteristic
118C11×C4⋊C4C22⋊C411yescharacteristic
119C11×C22⋊C4—21no—
120C11×C22⋊C4—21no—
121C11×C22⋊C4—21no—
122C11×C22⋊C4—41no—
123C42×C11—21no—
124C42×C11—21no—
125C42×C11—21no—
126C42×C11—22no—
127C42×C11—41no—
128C42×C11—41no—
129C42×C11C22×C411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133#3116C2×C1111yescharacteristic
134#2970C2×C1111yescharacteristic
135#1759C2×C1111yescharacteristic
136#1526C2×C1111yescharacteristic, complemented
137#1506C2×C1111yescharacteristic, complemented
138#1300C2×C1111yescharacteristic, complemented
139#1291C2×C1111yescharacteristic, complemented
140C23×C11—21no—
141C23×C11#12111yescharacteristic
142Q8×C11—21no—
143Q8×C11—21no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—81no—
147D4×C11—21no—
148D4×C11—42no—
149D4×C11#10412yes—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11C4×D411yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C8×C11—22no—
172C8×C11—42no—
173C8×C11—41no—
174C8×C11—42no—
175C8×C11—41no—
176C8×C11—41no—
177#533C22×C1111yescharacteristic
178C4×#41C22×C1111yescharacteristic
179#485—21no—
180#477C4×C1111yescharacteristic, complemented
181#476C4×C1111yescharacteristic, complemented
182#462C4×C1111yescharacteristic, complemented
183#461C4×C1111yescharacteristic, complemented
184#452—21no—
185#446—21no—
186#441—21no—
187#440—21no—
188#435—22no—
189C8×D4—21no—
190#432—21no—
191#432C22×C1111yescharacteristic
192#432C22×C1111yescharacteristic
193C2×#104—21no—
194C4×M16C22×C1111yescharacteristic
195C4×M16C22×C1111yescharacteristic
196C2×#97—21no—
197#376C22×C1111yescharacteristic
198#339—21no—
199#330—21no—
200#330—21no—
201#328—22no—
202C22×C11—21no—
203C22×C11—22no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11#38611yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—82no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11C2×#10411yescharacteristic
221C4×C11#42111yescharacteristic
222C2×#41D4×C1111yescharacteristic
223C2×Q16—21no—
224C2×SD16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C22×C8—22no—
228C4⋊Q8C2×C4×C1111yescharacteristic
229C4⋊Q8C2×C4×C1111yescharacteristic
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8C2×C4×C1111yescharacteristic
236C4×Q8D4×C1111yescharacteristic
237C4×D4—21no—
238C4×D4—21no—
239C4×D4C2×C4×C1111yescharacteristic
240C4×D4D4×C1111yescharacteristic
241#117—21no—
242#117—21no—
243#117D4×C1111yescharacteristic
244C2×C42—21no—
245C2×C42—21no—
246C2×C42C23×C1111yescharacteristic
247#107—21no—
248#106—21no—
249C4⋊C8—22no—
250C4⋊C8—21no—
251C4⋊C8C2×C4×C1111yescharacteristic
252C4⋊C8C2×C4×C1111yescharacteristic
253#104—24no—
254#103—21no—
255#103—21no—
256#103—21no—
257#102—21no—
258C22⋊C8—22no—
259C22⋊C8—21no—
260C22⋊C8D4×C1112yes—
261#97—22no—
262#97—21no—
263#97—21no—
264#97—21no—
265#97D4×C1111yescharacteristic
266#97D4×C1111yescharacteristic
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270#95—21no—
271C2×C11—41no—
272C2×C11—42no—
273C2×C11#187111yescharacteristic
274C2×C11#190211yescharacteristic
275C2×C11#190611yescharacteristic
276#41—22no—
277#41—41no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8C11×C22⋊C411yescharacteristic
281C2×D4—21no—
282C2×D4C11×C22⋊C411yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4C2×D4×C1111yescharacteristic
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C11×#4111yescharacteristic
290Q16—42no—
291SD16—42no—
292M16—22no—
293M16—42no—
294M16—41no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—44no—
301C2×C8—41no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4C11×C22⋊C411yescharacteristic
311C4⋊C4C11×C22⋊C411yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—41no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—22no—
320C42—41no—
321C42—41no—
322C42C22×C4×C1111yescharacteristic
323C42C2×D4×C1111yescharacteristic
324C42C2×D4×C1111yescharacteristic
325C42C11×#4111yescharacteristic
326C11#915911yescharacteristic, direct product factor, Sylow
327C23—21no—
328C23C11×#12111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—41no—
332Q8—41no—
333Q8—81no—
334D4—21no—
335D4—42no—
336D4C11×#10412yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4C2×C11×C22⋊C411yescharacteristic
353C2×C4C4×D4×C1111yescharacteristic
354C2×C4C4×D4×C1111yescharacteristic
355C2×C4C11×#12011yescharacteristic
356C2×C4C11×#12111yescharacteristic
357C2×C4C11×#12311yescharacteristic
358C8—22no—
359C8—42no—
360C8—41no—
361C8—42no—
362C8—41no—
363C8—41no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22C11×#38611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—82no—
380C4—81no—
381C4—81no—
382C4C2×C11×#10411yescharacteristic
383C4C11×#42111yescharacteristic
384C2—41no—
385C2—42no—
386C2C11×#187111yescharacteristic
387C2C11×#190211yescharacteristic
388C2C11×#190611yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1526C2semidirect
5. C11×#1506C2semidirect
6. C11×#1300C2semidirect
7. C11×#1291C2semidirect
11. C11×#477C4semidirect
12. C11×#476C4semidirect
13. C11×#462C4semidirect
14. C11×#461C4semidirect
82. #9159C11direct (N × H)
136. #1526C2×C11semidirect
137. #1506C2×C11semidirect
138. #1300C2×C11semidirect
139. #1291C2×C11semidirect
180. #477C4×C11semidirect
181. #476C4×C11semidirect
182. #462C4×C11semidirect
183. #461C4×C11semidirect
326. C11#9159direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31162
C11×#29702
C11×#17592
C11×#15262
C11×#15062
C11×#13002
C11×#12912
#915911