Finite Group Databasebeta

← C11×#13336 #14590529

Subgroups — C11×#13336 #14590529

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#509C211yesmaximal, characteristic, complemented
2C22×C11×D16C211yesmaximal, characteristic, complemented
3C11×#3155C211yesmaximal, characteristic, complemented
4C2×C11×#361C211yesmaximal, characteristic, complemented
5C2×C11×#359C211yesmaximal, characteristic, complemented
6C11×#1978C211yesmaximal, characteristic, complemented
7C11×#1379C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C2×C11×#135C2211yescharacteristic
10C22×C11×D8C2211yescharacteristic
11C22×C11×D8C2211yescharacteristic
12C11×#535—21no—
13C11×#509—22no—
14C11×#509—22no—
15C2×C11×SD32—21no—
16C2×C11×D16—22no—
17C2×C11×D16—21no—
18C2×C11×D16—22no—
19C2×C11×D16—22no—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C11×#496—22no—
23C11×#495—21no—
24C11×#493—21no—
25C2×C11×#108C2211yescharacteristic
26C11×#418—21no—
27C2×C11×#100—21no—
28C11×#405C2211yescharacteristic
29C11×#361—22no—
30C11×#359—22no—
31C2×C11×#41—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C11×AGL(1,ℤ/8)—42no—
35C11×AGL(1,ℤ/8)—42no—
36C11×#135—21no—
37C11×#135—21no—
38C11×#135—21no—
39C11×#135—21no—
40C2×C11×Q16D411yescharacteristic
41C2×C11×SD16—22no—
42C2×C11×SD16—21no—
43C2×C11×D8—22no—
44C2×C11×D8—21no—
45C2×C11×D8—21no—
46C2×C11×D8—21no—
47C2×C11×D8—21no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C2×C11×D8—21no—
51C2×C11×D8—21no—
52C2×C11×D8—21no—
53C2×C11×D8—21no—
54C2×C11×D8D411yescharacteristic
55C2×C11×D8D412yes—
56C2×C11×D8D412yescomplemented
57C2×C11×M16—21no—
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#127—22no—
61C11×#124—22no—
62C11×#121—42no—
63C11×#120—42no—
64C11×#117D411yescharacteristic
65C11×SD32—24no—
66C11×D16—28no—
67C11×D16—24no—
68C11×M32—21no—
69C11×M32D412yescomplemented
70C2×C11×C16—21no—
71C2×C11×C16—21no—
72C2×C11×C16—21no—
73C2×C11×C16D412yescomplemented
74C11×#108—21no—
75C11×#108—21no—
76C11×#102—42no—
77C11×#100—42no—
78C11×#97—21no—
79C4×C8×C11—21no—
80#13336C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—41no—
82C24×C11—41no—
83C11×#41—41no—
84C11×#41—41no—
85C11×#41—41no—
86C11×#41—41no—
87C2×Q8×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—44no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C11×Q16—21no—
106C11×Q16—21no—
107C11×SD16—44no—
108C11×SD16—41no—
109C11×SD16—41no—
110C11×D8—22no—
111C11×D8—22no—
112C11×D8—21no—
113C11×D8—22no—
114C11×D8—22no—
115C11×D8—21no—
116C11×D8—44no—
117C11×D8—41no—
118C11×D8—41no—
119C11×D8—41no—
120C11×D8—41no—
121C11×M16—21no—
122C11×M16—41no—
123C11×M16—41no—
124C11×M16D812yes—
125C2×C8×C11—21no—
126C2×C8×C11—41no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11#4111yescharacteristic
133C11×C4⋊C4D812yes—
134C11×C22⋊C4—21no—
135C11×C22⋊C4—44no—
136C42×C11—21no—
137C11×C16—22no—
138C11×C16—22no—
139C2×#509C2×C1111yescharacteristic, complemented
140C22×D16C2×C1111yescharacteristic, complemented
141#3155C2×C1111yescharacteristic, complemented
142C2×#361C2×C1111yescharacteristic, complemented
143C2×#359C2×C1111yescharacteristic, complemented
144#1978C2×C1111yescharacteristic, complemented
145#1379C2×C1111yescharacteristic, complemented
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—162no—
154C23×C11—162no—
155C23×C11AGL(1,ℤ/8)11yescharacteristic
156Q8×C11—41no—
157Q8×C11—41no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—42no—
163D4×C11—42no—
164D4×C11—81no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168D4×C11—81no—
169D4×C11—81no—
170D4×C11—164no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12711yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C8×C11—22no—
182C8×C11—81no—
183C8×C11#12011yescharacteristic
184C8×C11#12011yescharacteristic
185C8×C11#12111yescharacteristic
186C8×C11#12111yescharacteristic
187C2×AGL(1,ℤ/8)—21no—
188C2×#135C22×C1111yescharacteristic
189C22×D8C22×C1111yescharacteristic
190C22×D8C22×C1111yescharacteristic
191#535—21no—
192#509—22no—
193#509—22no—
194C2×SD32—21no—
195C2×D16—22no—
196C2×D16—21no—
197C2×D16—22no—
198C2×D16—22no—
199C2×M32C22×C1111yescharacteristic
200C22×C16C22×C1111yescharacteristic
201#496—22no—
202#495—21no—
203#493—21no—
204C2×#108C22×C1111yescharacteristic
205#418—21no—
206C2×#100—21no—
207#405C22×C1111yescharacteristic
208#361—22no—
209#359—22no—
210C22×C11—22no—
211C22×C11—82no—
212C22×C11—84no—
213C22×C11—81no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—162no—
217C22×C11—162no—
218C22×C11—162no—
219C22×C11—162no—
220C22×C11—162no—
221C22×C11#44711yescharacteristic
222C22×C11#45911yescharacteristic
223C22×C11#49611yescharacteristic
224C4×C11—42no—
225C4×C11—81no—
226C4×C11#39211yescharacteristic
227C4×C11#44711yescharacteristic
228C4×C11#45911yescharacteristic
229C4×C11#49311yescharacteristic
230C2×#41—21no—
231C22×D4—21no—
232C22×D4—21no—
233AGL(1,ℤ/8)—42no—
234AGL(1,ℤ/8)—42no—
235#135—21no—
236#135—21no—
237#135—21no—
238#135—21no—
239C2×Q16D4×C1111yescharacteristic
240C2×SD16—22no—
241C2×SD16—21no—
242C2×D8—22no—
243C2×D8—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8D4×C1112yes—
254C2×D8D4×C1111yescharacteristic
255C2×D8D4×C1112yescomplemented
256C2×M16—21no—
257C2×M16D4×C1111yescharacteristic
258C22×C8C23×C1111yescharacteristic
259#127—22no—
260#124—22no—
261#121—42no—
262#120—42no—
263#117D4×C1111yescharacteristic
264SD32—24no—
265D16—28no—
266D16—24no—
267M32—21no—
268M32D4×C1112yescomplemented
269C2×C16—21no—
270C2×C16—21no—
271C2×C16—21no—
272C2×C16D4×C1112yescomplemented
273#108—21no—
274#108—21no—
275#102—42no—
276#100—42no—
277#97—21no—
278C4×C8—21no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—161no—
282C2×C11—162no—
283C2×C11—162no—
284C2×C11#201111yescharacteristic
285C2×C11#219212yes—
286C24—41no—
287C24—41no—
288#41—41no—
289#41—41no—
290#41—41no—
291#41—41no—
292C2×Q8—21no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—44no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C22×C4—41no—
309C22×C4C2×D4×C1111yescharacteristic
310Q16—21no—
311Q16—21no—
312SD16—44no—
313SD16—41no—
314SD16—41no—
315D8—22no—
316D8—22no—
317D8—21no—
318D8—22no—
319D8—22no—
320D8—21no—
321D8—44no—
322D8—41no—
323D8—41no—
324D8—41no—
325D8—41no—
326M16—21no—
327M16—41no—
328M16—41no—
329M16C11×D812yes—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8C2×D4×C1111yescharacteristic
333C2×C8C2×D4×C1111yescharacteristic
334C2×C8C2×D4×C1111yescharacteristic
335C2×C8C2×D4×C1111yescharacteristic
336C2×C8C2×D4×C1111yescharacteristic
337C2×C8C11×#4111yescharacteristic
338C4⋊C4C11×D812yes—
339C22⋊C4—21no—
340C22⋊C4—44no—
341C42—21no—
342C16—22no—
343C16—22no—
344C11#1333611yescharacteristic, direct product factor, Sylow
345C23—42no—
346C23—41no—
347C23—42no—
348C23—81no—
349C23—81no—
350C23—81no—
351C23—81no—
352C23—162no—
353C23—162no—
354C23C11×AGL(1,ℤ/8)11yescharacteristic
355Q8—41no—
356Q8—41no—
357D4—42no—
358D4—42no—
359D4—41no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—164no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4C11×#12011yescharacteristic
375C2×C4C11×#12111yescharacteristic
376C2×C4C11×#12711yescharacteristic
377C2×C4C2×C11×D811yescharacteristic
378C2×C4C2×C11×D811yescharacteristic
379C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
380C8—22no—
381C8—81no—
382C8C11×#12011yescharacteristic
383C8C11×#12011yescharacteristic
384C8C11×#12111yescharacteristic
385C8C11×#12111yescharacteristic
386C22—22no—
387C22—82no—
388C22—84no—
389C22—81no—
390C22—82no—
391C22—82no—
392C22—162no—
393C22—162no—
394C22—162no—
395C22—162no—
396C22—162no—
397C22C11×#44711yescharacteristic
398C22C11×#45911yescharacteristic
399C22C11×#49611yescharacteristic
400C4—42no—
401C4—81no—
402C4C11×#39211yescharacteristic
403C4C11×#44711yescharacteristic
404C4C11×#45911yescharacteristic
405C4C11×#49311yescharacteristic
406C2—21no—
407C2—21no—
408C2—162no—
409C2—161no—
410C2—162no—
411C2C11×#201111yescharacteristic
412C2C11×#219212yes—
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#509C2semidirect
2. C22×C11×D16C2semidirect
3. C11×#3155C2semidirect
4. C2×C11×#361C2semidirect
5. C2×C11×#359C2semidirect
6. C11×#1978C2semidirect
7. C11×#1379C2semidirect
56. C2×C11×D8D4semidirect
69. C11×M32D4semidirect
73. C2×C11×C16D4semidirect
80. #13336C11direct (N × H)
139. C2×#509C2×C11semidirect
140. C22×D16C2×C11semidirect
141. #3155C2×C11semidirect
142. C2×#361C2×C11semidirect
143. C2×#359C2×C11semidirect
144. #1978C2×C11semidirect
145. #1379C2×C11semidirect
255. C2×D8D4×C11semidirect
268. M32D4×C11semidirect
272. C2×C16D4×C11semidirect
344. C11#13336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5092
C22×C11×D162
C11×#31552
C2×C11×#3612
C2×C11×#3592
C11×#19782
C11×#13792
#1333611