Finite Group Databasebeta

← C11×#10246 #14587439

Subgroups — C11×#10246 #14587439

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C11×#2541C211yesmaximal, characteristic
4C11×#1545C211yesmaximal, characteristic, complemented
5C11×#1503C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#127—21no—
10C2×C11×#127C2211yescharacteristic
11C2×C11×#121—22no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#492—21no—
14C11×#486—21no—
15C11×#478—22no—
16C11×#476—21no—
17C11×#474—21no—
18C11×#460—22no—
19C11×#450—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#428—21no—
23C11×#423C2211yescharacteristic
24C11×#418—21no—
25C11×#392—22no—
26C11×#390—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#331—22no—
29C11×#328—22no—
30C11×D4⋊C8—22no—
31C22×D4×C11—24no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C22×D4×C11D412yes—
36C23×C4×C11—21no—
37C2×C11×SD16—24no—
38C2×C11×M16—21no—
39C11×C4⋊Q8D411yescharacteristic, complemented
40C11×C4⋊Q8D411yescharacteristic, complemented
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—42no—
46C11×#127—42no—
47C11×#125—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C11×#121—48no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C11×#117—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C11×#107—22no—
65C11×#106—22no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yescomplemented
69C11×C4⋊C8D412yescomplemented
70C11×#102—22no—
71C11×#102—22no—
72C11×#102—24no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77C11×#95D412yes—
78#10246C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—21no—
80C24×C11—22no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—44no—
91C2×D4×C11—48no—
92C2×D4×C11—48no—
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—82no—
102C2×D4×C11—84no—
103C2×D4×C11SD1612yescomplemented
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—44no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C11×SD16—84no—
113C11×M16—41no—
114C11×M16—41no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—41no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C22⋊C4—48no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138#3208C2×C1111yescharacteristic, complemented
139#3077C2×C1111yescharacteristic, complemented
140#2541C2×C1111yescharacteristic
141#1545C2×C1111yescharacteristic, complemented
142#1503C2×C1111yescharacteristic, complemented
143#1478C2×C1111yescharacteristic, complemented
144#1303C2×C1111yescharacteristic, complemented
145C23×C11—22no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—44no—
149C23×C11—44no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11#12011yescharacteristic
156Q8×C11—42no—
157Q8×C11—81no—
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—41no—
161D4×C11—44no—
162D4×C11—41no—
163D4×C11—82no—
164D4×C11—82no—
165D4×C11—82no—
166D4×C11—816no—
167D4×C11—81no—
168D4×C11—81no—
169D4×C11—81no—
170D4×C11—81no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—82no—
181C2×C4×C11—82no—
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×C11#13511yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11#13711yescharacteristic
192C8×C11—42no—
193C8×C11—42no—
194C8×C11—81no—
195#533C22×C1111yescharacteristic
196C2×#127—21no—
197C2×#127C22×C1111yescharacteristic
198C2×#121—22no—
199C2×C4×D4C22×C1111yescharacteristic
200#492—21no—
201#486—21no—
202#478—22no—
203#476—21no—
204#474—21no—
205#460—22no—
206#450—22no—
207#431C22×C1111yescharacteristic
208#431C22×C1111yescharacteristic
209#428—21no—
210#423C22×C1111yescharacteristic
211#418—21no—
212#392—22no—
213#390—21no—
214C4×C4⋊C4C22×C1111yescharacteristic
215#331—22no—
216#328—22no—
217D4⋊C8—22no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—84no—
224C22×C11—84no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11#39211yescharacteristic
231C22×C11#45011yescharacteristic
232C22×C11#45211yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—44no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11#44811yescharacteristic
241C4×C11#44911yescharacteristic
242C4×C11#45312yes—
243C4×C11#46511yescharacteristic
244C4×C11#46811yescharacteristic
245C22×D4—24no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4D4×C1111yescharacteristic
249C22×D4D4×C1112yes—
250C23×C4—21no—
251C2×SD16—24no—
252C2×M16—21no—
253C4⋊Q8D4×C1111yescharacteristic, complemented
254C4⋊Q8D4×C1111yescharacteristic, complemented
255#127—21no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127—42no—
260#127—42no—
261#125—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264#121—48no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C1111yescharacteristic
274C2×C22⋊C4—24no—
275C2×C22⋊C4—21no—
276C2×C42—21no—
277C2×C42C23×C1111yescharacteristic
278#107—22no—
279#106—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8D4×C1112yescomplemented
283C4⋊C8D4×C1112yescomplemented
284#102—22no—
285#102—22no—
286#102—24no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C4×C8—21no—
290C4×C8—21no—
291#95D4×C1112yes—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11—162no—
296C2×C11#200011yescharacteristic
297C2×C11#200211yescharacteristic
298C2×C11#200811yescharacteristic
299C24—21no—
300C24—22no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×D4—21no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—44no—
311C2×D4—48no—
312C2×D4—48no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—82no—
322C2×D4—84no—
323C2×D4C11×SD1612yescomplemented
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—44no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C2×D4×C1111yescharacteristic
330C22×C4C2×D4×C1111yescharacteristic
331C22×C4C2×D4×C1111yescharacteristic
332SD16—84no—
333M16—41no—
334M16—41no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—41no—
338C4⋊C4—24no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C22⋊C4—48no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—41no—
352C42—41no—
353C42—41no—
354C42C2×D4×C1111yescharacteristic
355C42C2×D4×C1111yescharacteristic
356C42C2×D4×C1111yescharacteristic
357C42C11×#4111yescharacteristic
358C11#1024611yescharacteristic, direct product factor, Sylow
359C23—22no—
360C23—42no—
361C23—42no—
362C23—44no—
363C23—44no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23C11×#12011yescharacteristic
370Q8—42no—
371Q8—81no—
372D4—22no—
373D4—22no—
374D4—41no—
375D4—44no—
376D4—41no—
377D4—82no—
378D4—82no—
379D4—82no—
380D4—816no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4C11×#12011yescharacteristic
397C2×C4C11×#12011yescharacteristic
398C2×C4C11×#12111yescharacteristic
399C2×C4C11×#12111yescharacteristic
400C2×C4C11×#12111yescharacteristic
401C2×C4C11×#12711yescharacteristic
402C2×C4C2×C11×SD1611yescharacteristic
403C2×C4C11×#13511yescharacteristic
404C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
405C2×C4C11×#13711yescharacteristic
406C8—42no—
407C8—42no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—42no—
413C22—82no—
414C22—84no—
415C22—84no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22C11×#39211yescharacteristic
422C22C11×#45011yescharacteristic
423C22C11×#45211yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—44no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4C11×#44811yescharacteristic
432C4C11×#44911yescharacteristic
433C4C11×#45312yes—
434C4C11×#46511yescharacteristic
435C4C11×#46811yescharacteristic
436C2—21no—
437C2—21no—
438C2—82no—
439C2—162no—
440C2C11×#200011yescharacteristic
441C2C11×#200211yescharacteristic
442C2C11×#200811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2541C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3208C2semidirect
2. C11×#3077C2semidirect
4. C11×#1545C2semidirect
5. C11×#1503C2semidirect
6. C11×#1478C2semidirect
7. C11×#1303C2semidirect
39. C11×C4⋊Q8D4semidirect
40. C11×C4⋊Q8D4semidirect
68. C11×C4⋊C8D4semidirect
69. C11×C4⋊C8D4semidirect
78. #10246C11direct (N × H)
103. C2×D4×C11SD16semidirect
138. #3208C2×C11semidirect
139. #3077C2×C11semidirect
141. #1545C2×C11semidirect
142. #1503C2×C11semidirect
143. #1478C2×C11semidirect
144. #1303C2×C11semidirect
253. C4⋊Q8D4×C11semidirect
254. C4⋊Q8D4×C11semidirect
282. C4⋊C8D4×C11semidirect
283. C4⋊C8D4×C11semidirect
323. C2×D4C11×SD16semidirect
358. C11#10246direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32082
C11×#30772
C11×#25412
C11×#15452
C11×#15032
C11×#14782
C11×#13032
#1024611