Finite Group Databasebeta

← C11×#10054 #14587247

Subgroups — C11×#10054 #14587247

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#492C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C11×#2541C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic, complemented
5C2×C11×#331C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—22no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#121—22no—
13C2×C4×D4×C11C2211yescharacteristic
14C11×#492—22no—
15C11×#492—22no—
16C11×#476—22no—
17C11×#476—22no—
18C2×C11×#106—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102—21no—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#392—22no—
24C11×#390—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#331—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—24no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D412yes—
35C23×C4×C11—21no—
36C2×C11×SD16—28no—
37C2×C11×SD16—48no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D412yescomplemented
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—42no—
50C11×#127—42no—
51C11×#121—44no—
52C11×#121—44no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D412yes—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—21no—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C11×#106—24no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yescomplemented
70C11×#102—24no—
71C4×C8×C11—21no—
72C4×C8×C11D412yescomplemented
73C11×#95—21no—
74#10054C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—21no—
76C24×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—44no—
79C2×Q8×C11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—22no—
82C2×D4×C11—21no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—44no—
88C2×D4×C11—48no—
89C2×D4×C11—48no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—84no—
101C2×D4×C11SD1612yescomplemented
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C11×SD16—416no—
113C2×C8×C11—24no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—42no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4SD1614yescomplemented
128C11×C22⋊C4—48no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C2×#492C2×C1111yescharacteristic, complemented
138C2×#476C2×C1111yescharacteristic, complemented
139#2541C2×C1111yescharacteristic
140#1987C2×C1111yescharacteristic, complemented
141C2×#331C2×C1111yescharacteristic, complemented
142C2×D4⋊C8C2×C1111yescharacteristic, complemented
143#1279C2×C1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—44no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—44no—
154C23×C11#12011yescharacteristic
155Q8×C11—44no—
156Q8×C11—82no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—44no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—82no—
163D4×C11—816no—
164D4×C11—81no—
165D4×C11—81no—
166D4×C11—82no—
167D4×C11—81no—
168D4×C11—81no—
169D4×C11—81no—
170D4×C11—81no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—82no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12711yescharacteristic
188C2×C4×C11C2×SD1611yescharacteristic
189C2×C4×C11C2×SD1612yes—
190C2×C4×C11#13511yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)12yes—
193C2×C4×C11#13711yescharacteristic
194C8×C11—24no—
195C8×C11—42no—
196C8×C11—81no—
197C22×SD16—22no—
198C2×C4⋊Q8C22×C1111yescharacteristic
199C2×#127—21no—
200C2×#127C22×C1111yescharacteristic
201C2×#121—22no—
202C2×C4×D4C22×C1111yescharacteristic
203#492—22no—
204#492—22no—
205#476—22no—
206#476—22no—
207C2×#106—21no—
208C2×C4⋊C8C22×C1111yescharacteristic
209C2×C4⋊C8C22×C1111yescharacteristic
210C2×#102—21no—
211C2×C4×C8C22×C1111yescharacteristic
212#392—22no—
213#390—21no—
214C4×C4⋊C4C22×C1111yescharacteristic
215#340—22no—
216#331—22no—
217D4⋊C8—22no—
218C22×C11—44no—
219C22×C11—42no—
220C22×C11—82no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—84no—
224C22×C11—84no—
225C22×C11—82no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11#39211yescharacteristic
229C22×C11#45011yescharacteristic
230C22×C11#45012yes—
231C22×C11#45211yescharacteristic
232C22×C11#45312yes—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—44no—
236C4×C11—82no—
237C4×C11—81no—
238C4×C11#44811yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#46012yes—
241C4×C11#46511yescharacteristic
242C4×C11#46811yescharacteristic
243C4×C11#49211yescharacteristic
244C4×C11#49611yescharacteristic
245C22×Q8—21no—
246C22×D4—24no—
247C22×D4—21no—
248C22×D4—21no—
249C22×D4D4×C1111yescharacteristic
250C22×D4D4×C1112yes—
251C23×C4—21no—
252C2×SD16—28no—
253C2×SD16—48no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8D4×C1112yescomplemented
261#127—21no—
262#127—21no—
263#127—21no—
264#127—21no—
265#127—42no—
266#127—42no—
267#121—44no—
268#121—44no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4D4×C1111yescharacteristic
276C2×C4⋊C4D4×C1112yes—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—21no—
279C2×C42—21no—
280C2×C42C23×C1111yescharacteristic
281#106—24no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8D4×C1112yescomplemented
286#102—24no—
287C4×C8—21no—
288C4×C8D4×C1112yescomplemented
289#95—21no—
290C2×C11—82no—
291C2×C11—162no—
292C2×C11#162912yes—
293C2×C11#163112yes—
294C2×C11#200011yescharacteristic
295C2×C11#200211yescharacteristic
296C2×C11#201411yescharacteristic
297C24—21no—
298C24—22no—
299C2×Q8—22no—
300C2×Q8—44no—
301C2×Q8—41no—
302C2×D4—21no—
303C2×D4—22no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—44no—
310C2×D4—48no—
311C2×D4—48no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—42no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—84no—
323C2×D4C11×SD1612yescomplemented
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4C2×D4×C1111yescharacteristic
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1111yescharacteristic
334SD16—416no—
335C2×C8—24no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—42no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4C11×SD1614yescomplemented
350C22⋊C4—48no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42—41no—
354C42—41no—
355C42C2×D4×C1111yescharacteristic
356C42C2×D4×C1111yescharacteristic
357C42C2×D4×C1111yescharacteristic
358C42C11×#4111yescharacteristic
359C11#1005411yescharacteristic, direct product factor, Sylow
360C23—22no—
361C23—41no—
362C23—42no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—44no—
367C23—42no—
368C23—42no—
369C23—44no—
370C23C11×#12011yescharacteristic
371Q8—44no—
372Q8—82no—
373D4—22no—
374D4—22no—
375D4—44no—
376D4—41no—
377D4—41no—
378D4—82no—
379D4—816no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—82no—
385D4—81no—
386D4—81no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—82no—
398C2×C4C11×#12011yescharacteristic
399C2×C4C11×#12011yescharacteristic
400C2×C4C11×#12111yescharacteristic
401C2×C4C11×#12111yescharacteristic
402C2×C4C11×#12111yescharacteristic
403C2×C4C11×#12711yescharacteristic
404C2×C4C2×C11×SD1612yes—
405C2×C4C2×C11×SD1611yescharacteristic
406C2×C4C11×#13511yescharacteristic
407C2×C4C11×AGL(1,ℤ/8)12yes—
408C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
409C2×C4C11×#13711yescharacteristic
410C8—24no—
411C8—42no—
412C8—81no—
413C22—44no—
414C22—42no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—84no—
419C22—84no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22C11×#39211yescharacteristic
424C22C11×#45011yescharacteristic
425C22C11×#45012yes—
426C22C11×#45211yescharacteristic
427C22C11×#45312yes—
428C4—21no—
429C4—21no—
430C4—44no—
431C4—82no—
432C4—81no—
433C4C11×#44811yescharacteristic
434C4C11×#44911yescharacteristic
435C4C11×#46012yes—
436C4C11×#46511yescharacteristic
437C4C11×#46811yescharacteristic
438C4C11×#49211yescharacteristic
439C4C11×#49611yescharacteristic
440C2—82no—
441C2—162no—
442C2C11×#162912yes—
443C2C11×#163112yes—
444C2C11×#200011yescharacteristic
445C2C11×#200211yescharacteristic
446C2C11×#201411yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2541C2
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
1. C2×C11×#492C2semidirect
2. C2×C11×#476C2semidirect
4. C11×#1987C2semidirect
5. C2×C11×#331C2semidirect
6. C2×C11×D4⋊C8C2semidirect
7. C11×#1279C2semidirect
44. C11×C4⋊Q8D4semidirect
69. C11×C4⋊C8D4semidirect
72. C4×C8×C11D4semidirect
74. #10054C11direct (N × H)
101. C2×D4×C11SD16semidirect
127. C11×C4⋊C4SD16semidirect
137. C2×#492C2×C11semidirect
138. C2×#476C2×C11semidirect
140. #1987C2×C11semidirect
141. C2×#331C2×C11semidirect
142. C2×D4⋊C8C2×C11semidirect
143. #1279C2×C11semidirect
260. C4⋊Q8D4×C11semidirect
285. C4⋊C8D4×C11semidirect
288. C4×C8D4×C11semidirect
323. C2×D4C11×SD16semidirect
349. C4⋊C4C11×SD16semidirect
359. C11#10054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4922
C2×C11×#4762
C11×#25412
C11×#19872
C2×C11×#3312
C2×C11×D4⋊C82
C11×#12792
#1005411