Finite Group Databasebeta

← C11×#13381 #14590574

Subgroups — C11×#13381 #14590574

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C2×C11×#367C211yesmaximal, characteristic, complemented
3C2×C11×#357C211yesmaximal, characteristic, complemented
4C2×C11×#357C211yesmaximal, characteristic, complemented
5C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
6C11×#1808C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C2×C11×#121—21no—
11C22×C11×C16C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#466—22no—
14C11×#466—22no—
15C2×C11×#107C2211yescharacteristic
16C2×C11×#107C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#102—21no—
19C11×#380—21no—
20C11×#367—22no—
21C11×#357—22no—
22C11×#357—22no—
23C11×C22⋊C16—22no—
24C11×#340—21no—
25C22×D4×C11—21no—
26C22×D4×C11—41no—
27C23×C4×C11D411yescharacteristic
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8D412yes—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C22×C8×C11D411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C11×#121—24no—
43C11×#121—42no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
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×C16D412yescomplemented
55C11×#107—21no—
56C11×#107—21no—
57C11×#107—21no—
58C11×#107—21no—
59C11×#107—21no—
60C11×#107D412yes—
61C11×#102—24no—
62C11×#95—41no—
63#13381C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—41no—
65C24×C11D811yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—44no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—82no—
74C2×D4×C11—82no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11D811yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C11×D8—22no—
87C11×D8—22no—
88C11×D8—41no—
89C11×D8—41no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—44no—
110C11×C22⋊C4—82no—
111C11×C16—22no—
112C11×C16—41no—
113C2×#466C2×C1111yescharacteristic
114C2×#367C2×C1111yescharacteristic, complemented
115C2×#357C2×C1111yescharacteristic, complemented
116C2×#357C2×C1111yescharacteristic, complemented
117C2×C22⋊C16C2×C1111yescharacteristic, complemented
118#1808C2×C1111yescharacteristic, complemented
119#1380C2×C1111yescharacteristic, complemented
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—42no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11SD3212yes—
134C23×C11C2×D811yescharacteristic
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—88no—
138D4×C11—81no—
139D4×C11—81no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C8×C11—41no—
163C8×C11#12111yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12311yescharacteristic
166C8×C11#12411yescharacteristic
167C22×D8C22×C1111yescharacteristic
168C23×C8C22×C1111yescharacteristic
169C2×#121—21no—
170C22×C16C22×C1111yescharacteristic
171C22×C16C22×C1111yescharacteristic
172#466—22no—
173#466—22no—
174C2×#107C22×C1111yescharacteristic
175C2×#107C22×C1111yescharacteristic
176C2×#107C22×C1111yescharacteristic
177C2×#102—21no—
178#380—21no—
179#367—22no—
180#357—22no—
181#357—22no—
182C22⋊C16—22no—
183#340—21no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—161no—
195C22×C11—161no—
196C22×C11—161no—
197C22×C11—161no—
198C22×C11#44711yescharacteristic
199C22×C11#46611yescharacteristic
200C22×C11#48011yescharacteristic
201C22×C11C2×SD3211yescharacteristic
202C22×C11#50811yescharacteristic
203C22×C11#50911yescharacteristic
204C22×C11#50911yescharacteristic
205C4×C11—41no—
206C4×C11—82no—
207C4×C11—161no—
208C4×C11—161no—
209C4×C11#39411yescharacteristic
210C4×C11#45211yescharacteristic
211C4×C11#46811yescharacteristic
212C4×C11#48211yescharacteristic
213C22×D4—21no—
214C22×D4—41no—
215C23×C4D4×C1111yescharacteristic
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8D4×C1112yes—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8D4×C1111yescharacteristic
229C22×C8C23×C1111yescharacteristic
230#121—24no—
231#121—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4—41no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16D4×C1112yescomplemented
243#107—21no—
244#107—21no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D4×C1112yes—
249#102—24no—
250#95—41no—
251C2×C11—42no—
252C2×C11—162no—
253C2×C11#203311yescharacteristic
254C2×C11#218611yescharacteristic
255C2×C11#218711yescharacteristic
256C2×C11#221711yescharacteristic
257C2×C11#221811yescharacteristic
258C2×C11#223311yescharacteristic
259C2×C11#223411yescharacteristic
260C24—41no—
261C24C11×D811yescharacteristic
262C2×D4—22no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—82no—
270C2×D4—82no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C11×D811yescharacteristic
281C22×C4C2×D4×C1111yescharacteristic
282D8—22no—
283D8—22no—
284D8—41no—
285D8—41no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8C2×D4×C1111yescharacteristic
294C2×C8C2×D4×C1111yescharacteristic
295C2×C8C2×D4×C1111yescharacteristic
296C2×C8C11×#4111yescharacteristic
297C2×C8C11×#4111yescharacteristic
298C2×C8C11×#4111yescharacteristic
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—44no—
306C22⋊C4—82no—
307C16—22no—
308C16—41no—
309C11#1338111yescharacteristic, direct product factor, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23C11×SD3212yes—
324C23C2×C11×D811yescharacteristic
325D4—42no—
326D4—42no—
327D4—88no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C11×#12011yescharacteristic
347C2×C4C11×#12111yescharacteristic
348C2×C4C11×#12311yescharacteristic
349C2×C4C11×#13511yescharacteristic
350C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
351C2×C4C11×#13711yescharacteristic
352C8—41no—
353C8C11×#12111yescharacteristic
354C8C11×#12111yescharacteristic
355C8C11×#12311yescharacteristic
356C8C11×#12411yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22C11×#44711yescharacteristic
372C22C11×#46611yescharacteristic
373C22C11×#48011yescharacteristic
374C22C2×C11×SD3211yescharacteristic
375C22C11×#50811yescharacteristic
376C22C11×#50911yescharacteristic
377C22C11×#50911yescharacteristic
378C4—41no—
379C4—82no—
380C4—161no—
381C4—161no—
382C4C11×#39411yescharacteristic
383C4C11×#45211yescharacteristic
384C4C11×#46811yescharacteristic
385C4C11×#48211yescharacteristic
386C2—42no—
387C2—162no—
388C2C11×#203311yescharacteristic
389C2C11×#218611yescharacteristic
390C2C11×#218711yescharacteristic
391C2C11×#221711yescharacteristic
392C2C11×#221811yescharacteristic
393C2C11×#223311yescharacteristic
394C2C11×#223411yescharacteristic
subgroupG/H
center, socleC23×C11C2×D8
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#466C2
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×#367C2semidirect
3. C2×C11×#357C2semidirect
4. C2×C11×#357C2semidirect
5. C2×C11×C22⋊C16C2semidirect
6. C11×#1808C2semidirect
7. C11×#1380C2semidirect
54. C2×C11×C16D4semidirect
63. #13381C11direct (N × H)
114. C2×#367C2×C11semidirect
115. C2×#357C2×C11semidirect
116. C2×#357C2×C11semidirect
117. C2×C22⋊C16C2×C11semidirect
118. #1808C2×C11semidirect
119. #1380C2×C11semidirect
242. C2×C16D4×C11semidirect
309. C11#13381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C2×C11×#3672
C2×C11×#3572
C2×C11×C22⋊C162
C11×#18082
C11×#13802
#1338111