Finite Group Databasebeta

← C11×#10053 #14587246

Subgroups — C11×#10053 #14587246

Order 2816.

634 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×#486C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#486—22no—
13C11×#486—22no—
14C11×#460—22no—
15C11×#460—22no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—21no—
19C2×C11×#102—22no—
20C2×C11×#102—22no—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#400—22no—
23C11×#391—21no—
24C11×#391—22no—
25C11×#382—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#332—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C2×C11×SD16—24no—
35C2×C11×SD16—42no—
36C2×C11×SD16—42no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127D412yes—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#102—24no—
65C11×#102—28no—
66C11×#102—44no—
67C4×C8×C11—21no—
68C4×C8×C11D412yes—
69C11×#95—24no—
70C11×#95—24no—
71C11×#95—21no—
72#10053C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—41no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11SD1612yes—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—44no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×SD16—48no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11—42no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130C2×#486C2×C1111yescharacteristic
131C2×#460C2×C1111yescharacteristic
132#2568C2×C1111yescharacteristic, complemented
133#1982C2×C1111yescharacteristic
134C2×#332C2×C1111yescharacteristic, complemented
135C2×Q8⋊C8C2×C1111yescharacteristic, complemented
136#1279C2×C1111yescharacteristic, complemented
137C23×C11—42no—
138C23×C11—81no—
139C23×C11—81no—
140C23×C11—82no—
141C23×C11—82no—
142C23×C11#12011yescharacteristic
143Q8×C11—22no—
144Q8×C11—22no—
145Q8×C11—41no—
146Q8×C11—41no—
147Q8×C11—82no—
148Q8×C11—81no—
149Q8×C11—81no—
150D4×C11—44no—
151D4×C11—42no—
152D4×C11—42no—
153D4×C11—44no—
154D4×C11—82no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—44no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12711yescharacteristic
176C2×C4×C11C2×SD1611yescharacteristic
177C2×C4×C11#13511yescharacteristic
178C2×C4×C11#13512yes—
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11#13711yescharacteristic
182C8×C11—42no—
183C8×C11—42no—
184C8×C11—81no—
185C22×SD16—21no—
186C2×C4⋊Q8C22×C1111yescharacteristic
187C2×#127C22×C1111yescharacteristic
188C2×C4×Q8C22×C1111yescharacteristic
189#486—22no—
190#486—22no—
191#460—22no—
192#460—22no—
193C2×C4⋊C8C22×C1111yescharacteristic
194C2×C4⋊C8C22×C1111yescharacteristic
195C2×#102—22no—
196C2×#102—21no—
197C2×#102—22no—
198C2×C4×C8C22×C1111yescharacteristic
199#400—22no—
200#391—21no—
201#391—22no—
202#382—21no—
203C4×C4⋊C4C22×C1111yescharacteristic
204#332—22no—
205Q8⋊C8—22no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—162no—
210C22×C11—162no—
211C22×C11#39211yescharacteristic
212C22×C11#44811yescharacteristic
213C22×C11#44912yes—
214C22×C11#44911yescharacteristic
215C22×C11#45412yes—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—82no—
220C4×C11—81no—
221C4×C11—82no—
222C4×C11#45011yescharacteristic
223C4×C11#45211yescharacteristic
224C4×C11#46312yes—
225C4×C11#46511yescharacteristic
226C4×C11#46811yescharacteristic
227C4×C11#49511yescharacteristic
228C4×C11#49611yescharacteristic
229C22×Q8—21no—
230C22×Q8D4×C1111yescharacteristic
231C22×D4—21no—
232C22×D4—21no—
233C22×D4—21no—
234C2×SD16—24no—
235C2×SD16—42no—
236C2×SD16—42no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244#127—21no—
245#127—21no—
246#127—21no—
247#127D4×C1112yes—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4D4×C1111yescharacteristic
255C2×C4⋊C4D4×C1112yes—
256C2×C4⋊C4D4×C1112yes—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42C23×C1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8D4×C1112yes—
264#102—24no—
265#102—28no—
266#102—44no—
267C4×C8—21no—
268C4×C8D4×C1112yes—
269#95—24no—
270#95—24no—
271#95—21no—
272C2×C11—162no—
273C2×C11#162612yes—
274C2×C11#162812yes—
275C2×C11#200011yescharacteristic
276C2×C11#200311yescharacteristic
277C2×C11#201211yescharacteristic
278C24—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8C11×SD1612yes—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—44no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4C2×D4×C1111yescharacteristic
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C2×D4×C1111yescharacteristic
309SD16—48no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—42no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42C2×D4×C1111yescharacteristic
332C42C2×D4×C1111yescharacteristic
333C42C2×D4×C1111yescharacteristic
334C42C11×#4111yescharacteristic
335C11#1005311yescharacteristic, direct product factor, Sylow
336C23—42no—
337C23—81no—
338C23—81no—
339C23—82no—
340C23—82no—
341C23C11×#12011yescharacteristic
342Q8—22no—
343Q8—22no—
344Q8—41no—
345Q8—41no—
346Q8—81no—
347Q8—81no—
348Q8—82no—
349D4—44no—
350D4—42no—
351D4—42no—
352D4—44no—
353D4—82no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4C11×#12011yescharacteristic
370C2×C4C11×#12011yescharacteristic
371C2×C4C11×#12111yescharacteristic
372C2×C4C11×#12111yescharacteristic
373C2×C4C11×#12111yescharacteristic
374C2×C4C11×#12711yescharacteristic
375C2×C4C2×C11×SD1611yescharacteristic
376C2×C4C11×#13512yes—
377C2×C4C11×#13511yescharacteristic
378C2×C4C11×AGL(1,ℤ/8)12yes—
379C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
380C2×C4C11×#13711yescharacteristic
381C8—42no—
382C8—42no—
383C8—81no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22—162no—
388C22—162no—
389C22C11×#39211yescharacteristic
390C22C11×#44811yescharacteristic
391C22C11×#44912yes—
392C22C11×#44911yescharacteristic
393C22C11×#45412yes—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—82no—
398C4—81no—
399C4—82no—
400C4C11×#45011yescharacteristic
401C4C11×#45211yescharacteristic
402C4C11×#46312yes—
403C4C11×#46511yescharacteristic
404C4C11×#46811yescharacteristic
405C4C11×#49511yescharacteristic
406C4C11×#49611yescharacteristic
407C2—162no—
408C2C11×#162612yes—
409C2C11×#162812yes—
410C2C11×#200011yescharacteristic
411C2C11×#200311yescharacteristic
412C2C11×#201211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2568C2semidirect
5. C2×C11×#332C2semidirect
6. C2×C11×Q8⋊C8C2semidirect
7. C11×#1279C2semidirect
72. #10053C11direct (N × H)
132. #2568C2×C11semidirect
134. C2×#332C2×C11semidirect
135. C2×Q8⋊C8C2×C11semidirect
136. #1279C2×C11semidirect
335. C11#10053direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C2×C11×#4602
C11×#25682
C11×#19822
C2×C11×#3322
C2×C11×Q8⋊C82
C11×#12792
#1005311