Finite Group Databasebeta

← C11×#13383 #14590576

Subgroups — C11×#13383 #14590576

Order 2816.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C11×#366C211yesmaximal, characteristic, complemented
3C2×C11×#358C211yesmaximal, characteristic, complemented
4C2×C11×#358C211yesmaximal, characteristic, complemented
5C2×C11×C22⋊C16C211yesmaximal, characteristic
6C11×#1808C211yesmaximal, characteristic
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C2×C11×C22⋊Q8—21no—
11C22×C11×C16C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#467—22no—
14C11×#467—22no—
15C2×C11×#107C2211yescharacteristic
16C2×C11×#107C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#103—21no—
19C11×#380—21no—
20C11×#366—22no—
21C11×#358—22no—
22C11×#358—22no—
23C11×C22⋊C16—22no—
24C11×#340—21no—
25C22×Q8×C11—21no—
26C23×C4×C11D411yescharacteristic
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16D412yes—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—42no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—41no—
47C2×C11×C22⋊C4—41no—
48C2×C11×C22⋊C4—41no—
49C2×C11×C16—21no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16D412yes—
55C11×#107—21no—
56C11×#107—21no—
57C11×#107—21no—
58C11×#107—21no—
59C11×#107—21no—
60C11×#107D412yes—
61C11×#103—24no—
62C11×#95—41no—
63#13383C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11D811yescharacteristic
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11D811yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C11×Q16—22no—
84C11×Q16—22no—
85C11×Q16—41no—
86C11×Q16—41no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—44no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—44no—
108C11×C22⋊C4—82no—
109C11×C16—22no—
110C11×C16—41no—
111C2×#467C2×C1111yescharacteristic
112C2×#366C2×C1111yescharacteristic, complemented
113C2×#358C2×C1111yescharacteristic, complemented
114C2×#358C2×C1111yescharacteristic, complemented
115C2×C22⋊C16C2×C1111yescharacteristic
116#1808C2×C1111yescharacteristic
117#1380C2×C1111yescharacteristic, complemented
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11Q3212yes—
125C23×C11C2×D811yescharacteristic
126Q8×C11—42no—
127Q8×C11—42no—
128Q8×C11—81no—
129Q8×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C8×C11—41no—
156C8×C11#12111yescharacteristic
157C8×C11#12111yescharacteristic
158C8×C11#12311yescharacteristic
159C8×C11#12411yescharacteristic
160C22×Q16C22×C1111yescharacteristic
161C23×C8C22×C1111yescharacteristic
162C2×C22⋊Q8—21no—
163C22×C16C22×C1111yescharacteristic
164C22×C16C22×C1111yescharacteristic
165#467—22no—
166#467—22no—
167C2×#107C22×C1111yescharacteristic
168C2×#107C22×C1111yescharacteristic
169C2×#107C22×C1111yescharacteristic
170C2×#103—21no—
171#380—21no—
172#366—22no—
173#358—22no—
174#358—22no—
175C22⋊C16—22no—
176#340—21no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11#44711yescharacteristic
185C22×C11#46611yescharacteristic
186C22×C11#48011yescharacteristic
187C22×C11C2×Q3211yescharacteristic
188C22×C11#50811yescharacteristic
189C22×C11#50911yescharacteristic
190C22×C11#51011yescharacteristic
191C4×C11—41no—
192C4×C11—82no—
193C4×C11—82no—
194C4×C11—161no—
195C4×C11—161no—
196C4×C11#39411yescharacteristic
197C4×C11#45211yescharacteristic
198C4×C11#46811yescharacteristic
199C4×C11#48211yescharacteristic
200C22×Q8—21no—
201C23×C4D4×C1111yescharacteristic
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16D4×C1112yes—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8D4×C1111yescharacteristic
215C22×C8C23×C1111yescharacteristic
216C22⋊Q8—24no—
217C22⋊Q8—42no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—41no—
222C2×C22⋊C4—41no—
223C2×C22⋊C4—41no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16—21no—
229C2×C16D4×C1112yes—
230#107—21no—
231#107—21no—
232#107—21no—
233#107—21no—
234#107—21no—
235#107D4×C1112yes—
236#103—24no—
237#95—41no—
238C2×C11—42no—
239C2×C11#203311yescharacteristic
240C2×C11#218611yescharacteristic
241C2×C11#218811yescharacteristic
242C2×C11#221611yescharacteristic
243C2×C11#222011yescharacteristic
244C2×C11#223611yescharacteristic
245C2×C11#223711yescharacteristic
246C24C11×D811yescharacteristic
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4C11×D811yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8C2×D4×C1111yescharacteristic
277C2×C8C2×D4×C1111yescharacteristic
278C2×C8C2×D4×C1111yescharacteristic
279C2×C8C11×#4111yescharacteristic
280C2×C8C11×#4111yescharacteristic
281C2×C8C11×#4111yescharacteristic
282C4⋊C4—22no—
283C4⋊C4—44no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—44no—
290C22⋊C4—82no—
291C16—22no—
292C16—41no—
293C11#1338311yescharacteristic, direct product factor, Sylow
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23C11×Q3212yes—
301C23C2×C11×D811yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4C11×#12011yescharacteristic
326C2×C4C11×#12111yescharacteristic
327C2×C4C11×#12311yescharacteristic
328C2×C4C11×#13511yescharacteristic
329C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
330C2×C4C11×#13711yescharacteristic
331C8—41no—
332C8C11×#12111yescharacteristic
333C8C11×#12111yescharacteristic
334C8C11×#12311yescharacteristic
335C8C11×#12411yescharacteristic
336C22—22no—
337C22—22no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22C11×#44711yescharacteristic
344C22C11×#46611yescharacteristic
345C22C11×#48011yescharacteristic
346C22C2×C11×Q3211yescharacteristic
347C22C11×#50811yescharacteristic
348C22C11×#50911yescharacteristic
349C22C11×#51011yescharacteristic
350C4—41no—
351C4—82no—
352C4—82no—
353C4—161no—
354C4—161no—
355C4C11×#39411yescharacteristic
356C4C11×#45211yescharacteristic
357C4C11×#46811yescharacteristic
358C4C11×#48211yescharacteristic
359C2—42no—
360C2C11×#203311yescharacteristic
361C2C11×#218611yescharacteristic
362C2C11×#218811yescharacteristic
363C2C11×#221611yescharacteristic
364C2C11×#222011yescharacteristic
365C2C11×#223611yescharacteristic
366C2C11×#223711yescharacteristic
subgroupG/H
center, socleC23×C11C2×D8
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC24×C11D8
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#366C2semidirect
3. C2×C11×#358C2semidirect
4. C2×C11×#358C2semidirect
7. C11×#1380C2semidirect
63. #13383C11direct (N × H)
112. C2×#366C2×C11semidirect
113. C2×#358C2×C11semidirect
114. C2×#358C2×C11semidirect
117. #1380C2×C11semidirect
293. C11#13383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C11×#3662
C2×C11×#3582
C2×C11×C22⋊C162
C11×#18082
C11×#13802
#1338311