Finite Group Databasebeta

← C11×#10050 #14587243

Subgroups — C11×#10050 #14587243

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic, complemented
2C2×C11×#459C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—21no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#486—22no—
14C11×#486—22no—
15C11×#459—22no—
16C11×#459—22no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102—21no—
20C2×C11×#102—22no—
21C2×C11×#102—22no—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#397—22no—
24C11×#391—21no—
25C11×#380—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×C11×D8—24no—
36C2×C11×D8—42no—
37C2×C11×D8—42no—
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⋊Q8—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127D412yes—
49C11×#124—42no—
50C11×#124—42no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#102—24no—
68C11×#102—28no—
69C11×#102—44no—
70C4×C8×C11—21no—
71C4×C8×C11D412yes—
72C11×#95—24no—
73C11×#95—21no—
74#10050C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—21no—
76C24×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—44no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11D812yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
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×D8—48no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—42no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—42no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
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×#486C2×C1111yescharacteristic, complemented
138C2×#459C2×C1111yescharacteristic
139#2547C2×C1111yescharacteristic, complemented
140#1982C2×C1111yescharacteristic, complemented
141C2×#332C2×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—81no—
151C23×C11—81no—
152C23×C11—82no—
153C23×C11—82no—
154C23×C11#12011yescharacteristic
155Q8×C11—81no—
156Q8×C11—81no—
157Q8×C11—81no—
158Q8×C11—81no—
159D4×C11—22no—
160D4×C11—22no—
161D4×C11—44no—
162D4×C11—42no—
163D4×C11—41no—
164D4×C11—42no—
165D4×C11—44no—
166D4×C11—41no—
167D4×C11—82no—
168D4×C11—81no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—81no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—82no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11#13511yescharacteristic
192C2×C4×C11#13512yes—
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C8×C11—42no—
197C8×C11—42no—
198C8×C11—81no—
199C22×D8—21no—
200C2×C4⋊Q8C22×C1111yescharacteristic
201C2×#127C22×C1111yescharacteristic
202C2×#124—21no—
203C2×C4×D4C22×C1111yescharacteristic
204#486—22no—
205#486—22no—
206#459—22no—
207#459—22no—
208C2×C4⋊C8C22×C1111yescharacteristic
209C2×C4⋊C8C22×C1111yescharacteristic
210C2×#102—22no—
211C2×#102—21no—
212C2×#102—22no—
213C2×C4×C8C22×C1111yescharacteristic
214#397—22no—
215#391—21no—
216#380—22no—
217C4×C4⋊C4C22×C1111yescharacteristic
218#332—22no—
219D4⋊C8—22no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—82no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—162no—
229C22×C11—162no—
230C22×C11#39211yescharacteristic
231C22×C11#44711yescharacteristic
232C22×C11#44912yes—
233C22×C11#44911yescharacteristic
234C22×C11#45412yes—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—82no—
238C4×C11—82no—
239C4×C11—81no—
240C4×C11#44711yescharacteristic
241C4×C11#44911yescharacteristic
242C4×C11#46312yes—
243C4×C11#46611yescharacteristic
244C4×C11#46911yescharacteristic
245C4×C11#49511yescharacteristic
246C4×C11#49611yescharacteristic
247C22×Q8—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4D4×C1111yescharacteristic
252C23×C4—21no—
253C2×D8—24no—
254C2×D8—42no—
255C2×D8—42no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263#127—21no—
264#127—21no—
265#127—21no—
266#127D4×C1112yes—
267#124—42no—
268#124—42no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C1111yescharacteristic
275C2×C4⋊C4D4×C1112yes—
276C2×C4⋊C4D4×C1112yes—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—21no—
279C2×C42—21no—
280C2×C42C23×C1111yescharacteristic
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8D4×C1112yes—
285#102—24no—
286#102—28no—
287#102—44no—
288C4×C8—21no—
289C4×C8D4×C1112yes—
290#95—24no—
291#95—21no—
292C2×C11—82no—
293C2×C11—162no—
294C2×C11#162512yes—
295C2×C11#162812yes—
296C2×C11#199911yescharacteristic
297C2×C11#200311yescharacteristic
298C2×C11#201211yescharacteristic
299C24—21no—
300C24—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×D4—21no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—44no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—42no—
321C2×D4—41no—
322C2×D4—42no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C11×D812yes—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4C2×D4×C1111yescharacteristic
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1111yescharacteristic
336D8—48no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—42no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C22⋊C4—48no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—41no—
356C42—41no—
357C42C2×D4×C1111yescharacteristic
358C42C2×D4×C1111yescharacteristic
359C42C2×D4×C1111yescharacteristic
360C42C11×#4111yescharacteristic
361C11#1005011yescharacteristic, direct product factor, Sylow
362C23—22no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—81no—
369C23—81no—
370C23—82no—
371C23—82no—
372C23C11×#12011yescharacteristic
373Q8—81no—
374Q8—81no—
375Q8—81no—
376Q8—81no—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—42no—
381D4—41no—
382D4—42no—
383D4—44no—
384D4—41no—
385D4—82no—
386D4—81no—
387D4—81no—
388D4—81no—
389D4—81no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—82no—
402C2×C4C11×#12011yescharacteristic
403C2×C4C11×#12011yescharacteristic
404C2×C4C11×#12111yescharacteristic
405C2×C4C11×#12111yescharacteristic
406C2×C4C11×#12111yescharacteristic
407C2×C4C11×#12711yescharacteristic
408C2×C4C2×C11×D811yescharacteristic
409C2×C4C11×#13512yes—
410C2×C4C11×#13511yescharacteristic
411C2×C4C11×AGL(1,ℤ/8)12yes—
412C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
413C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
414C8—42no—
415C8—42no—
416C8—81no—
417C22—44no—
418C22—42no—
419C22—82no—
420C22—81no—
421C22—81no—
422C22—82no—
423C22—82no—
424C22—82no—
425C22—162no—
426C22—162no—
427C22C11×#39211yescharacteristic
428C22C11×#44711yescharacteristic
429C22C11×#44912yes—
430C22C11×#44911yescharacteristic
431C22C11×#45412yes—
432C4—21no—
433C4—21no—
434C4—82no—
435C4—82no—
436C4—81no—
437C4C11×#44711yescharacteristic
438C4C11×#44911yescharacteristic
439C4C11×#46312yes—
440C4C11×#46611yescharacteristic
441C4C11×#46911yescharacteristic
442C4C11×#49511yescharacteristic
443C4C11×#49611yescharacteristic
444C2—82no—
445C2—162no—
446C2C11×#162512yes—
447C2C11×#162812yes—
448C2C11×#199911yescharacteristic
449C2C11×#200311yescharacteristic
450C2C11×#201211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#459C2
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×#486C2semidirect
3. C11×#2547C2semidirect
4. C11×#1982C2semidirect
5. C2×C11×#332C2semidirect
6. C2×C11×D4⋊C8C2semidirect
7. C11×#1279C2semidirect
74. #10050C11direct (N × H)
137. C2×#486C2×C11semidirect
139. #2547C2×C11semidirect
140. #1982C2×C11semidirect
141. C2×#332C2×C11semidirect
142. C2×D4⋊C8C2×C11semidirect
143. #1279C2×C11semidirect
361. C11#10050direct (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×#4592
C11×#25472
C11×#19822
C2×C11×#3322
C2×C11×D4⋊C82
C11×#12792
#1005011