Finite Group Databasebeta

← C11×#10261 #14587454

Subgroups — C11×#10261 #14587454

Order 2816.

678 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
1C2×C11×#486C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4C11×#1954C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×#331C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C22×C11×D8—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#486—22no—
14C11×#486—22no—
15C11×#461—22no—
16C11×#461—22no—
17C11×#459—22no—
18C11×#459—22no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103—21no—
23C2×C11×#102—22no—
24C2×C11×#102—21no—
25C2×C11×C22⋊C8—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#332—22no—
28C11×#331—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×SD16—24no—
36C2×C11×SD16—42no—
37C2×C11×SD16—42no—
38C2×C11×D8—24no—
39C2×C11×D8—42no—
40C2×C11×D8—42no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C22×C8×C11—21no—
44C22×C8×C11D412yes—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8D412yes—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127D412yes—
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×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C11×#102—24no—
70C11×#102—28no—
71C11×C22⋊C8—44no—
72C4×C8×C11—21no—
73C4×C8×C11—21no—
74#10261C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—21no—
76C24×C11—41no—
77C2×Q8×C11—22no—
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—21no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—42no—
100C2×D4×C11—82no—
101C2×D4×C11D812yes—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C11×SD16—48no—
112C11×D8—48no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C2×C8×C11—41no—
123C2×C8×C11—42no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C2×#486C2×C1111yescharacteristic, complemented
137C2×#461C2×C1111yescharacteristic, complemented
138C2×#459C2×C1111yescharacteristic
139#1954C2×C1111yescharacteristic, complemented
140C2×#332C2×C1111yescharacteristic, complemented
141C2×#331C2×C1111yescharacteristic, complemented
142#1277C2×C1111yescharacteristic, complemented
143C23×C11—22no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—82no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—82no—
153C23×C11#12111yescharacteristic
154Q8×C11—42no—
155Q8×C11—42no—
156Q8×C11—81no—
157Q8×C11—81no—
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—42no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—42no—
164D4×C11—44no—
165D4×C11—82no—
166D4×C11—82no—
167D4×C11—81no—
168D4×C11—81no—
169D4×C11—81no—
170D4×C11—81no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—82no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12711yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11#13511yescharacteristic
188C2×C4×C11#13512yes—
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C8×C11—42no—
193C8×C11—42no—
194C8×C11—42no—
195C8×C11—81no—
196C22×SD16—21no—
197C22×D8—21no—
198C2×C4⋊Q8C22×C1111yescharacteristic
199C2×#127C22×C1111yescharacteristic
200C2×C4×D4C22×C1111yescharacteristic
201#486—22no—
202#486—22no—
203#461—22no—
204#461—22no—
205#459—22no—
206#459—22no—
207C2×C4⋊C8C22×C1111yescharacteristic
208C2×C4⋊C8C22×C1111yescharacteristic
209C2×C4⋊C8C22×C1111yescharacteristic
210C2×#103—21no—
211C2×#102—22no—
212C2×#102—21no—
213C2×C22⋊C8—22no—
214C2×C4×C8C22×C1111yescharacteristic
215#332—22no—
216#331—22no—
217C22×C11—44no—
218C22×C11—42no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11—162no—
226C22×C11—162no—
227C22×C11#39211yescharacteristic
228C22×C11#46312yes—
229C22×C11#46611yescharacteristic
230C22×C11#46911yescharacteristic
231C22×C11#47112yes—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—82no—
235C4×C11—81no—
236C4×C11#44711yescharacteristic
237C4×C11#44711yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#44912yes—
241C4×C11#49511yescharacteristic
242C4×C11#49611yescharacteristic
243C22×Q8—21no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4D4×C1111yescharacteristic
248C23×C4—21no—
249C2×SD16—24no—
250C2×SD16—42no—
251C2×SD16—42no—
252C2×D8—24no—
253C2×D8—42no—
254C2×D8—42no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8D4×C1112yes—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8D4×C1112yes—
263#127—21no—
264#127—21no—
265#127—21no—
266#127D4×C1112yes—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C1111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C42C23×C1111yescharacteristic
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8D4×C1112yes—
281C4⋊C8D4×C1112yes—
282#103—24no—
283#102—24no—
284#102—28no—
285C22⋊C8—44no—
286C4×C8—21no—
287C4×C8—21no—
288C2×C11—82no—
289C2×C11—162no—
290C2×C11#168112yes—
291C2×C11#170112yes—
292C2×C11#199911yescharacteristic
293C2×C11#201211yescharacteristic
294C2×C11#201911yescharacteristic
295C24—21no—
296C24—41no—
297C2×Q8—22no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4—82no—
321C2×D4C11×D812yes—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C2×D4×C1111yescharacteristic
329C22×C4C2×D4×C1111yescharacteristic
330C22×C4C11×#4111yescharacteristic
331SD16—48no—
332D8—48no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—42no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42C2×D4×C1111yescharacteristic
353C42C2×D4×C1111yescharacteristic
354C42C2×D4×C1111yescharacteristic
355C42C2×D4×C1111yescharacteristic
356C11#1026111yescharacteristic, direct product factor, Sylow
357C23—22no—
358C23—41no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23—42no—
363C23—82no—
364C23—81no—
365C23—81no—
366C23—82no—
367C23C11×#12111yescharacteristic
368Q8—42no—
369Q8—42no—
370Q8—81no—
371Q8—81no—
372D4—22no—
373D4—22no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—42no—
378D4—44no—
379D4—82no—
380D4—82no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4C11×#12011yescharacteristic
395C2×C4C11×#12011yescharacteristic
396C2×C4C11×#12011yescharacteristic
397C2×C4C11×#12111yescharacteristic
398C2×C4C11×#12111yescharacteristic
399C2×C4C11×#12711yescharacteristic
400C2×C4C2×C11×D811yescharacteristic
401C2×C4C11×#13512yes—
402C2×C4C11×#13511yescharacteristic
403C2×C4C11×AGL(1,ℤ/8)12yes—
404C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
405C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
406C8—42no—
407C8—42no—
408C8—42no—
409C8—81no—
410C22—44no—
411C22—42no—
412C22—82no—
413C22—81no—
414C22—81no—
415C22—82no—
416C22—82no—
417C22—82no—
418C22—162no—
419C22—162no—
420C22C11×#39211yescharacteristic
421C22C11×#46312yes—
422C22C11×#46611yescharacteristic
423C22C11×#46911yescharacteristic
424C22C11×#47112yes—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—81no—
429C4C11×#44711yescharacteristic
430C4C11×#44711yescharacteristic
431C4C11×#44911yescharacteristic
432C4C11×#44911yescharacteristic
433C4C11×#44912yes—
434C4C11×#49511yescharacteristic
435C4C11×#49611yescharacteristic
436C2—82no—
437C2—162no—
438C2C11×#168112yes—
439C2C11×#170112yes—
440C2C11×#199911yescharacteristic
441C2C11×#201211yescharacteristic
442C2C11×#201911yescharacteristic
subgroupG/H
center, socleC23×C11#121
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
2. C2×C11×#461C2semidirect
4. C11×#1954C2semidirect
5. C2×C11×#332C2semidirect
6. C2×C11×#331C2semidirect
7. C11×#1277C2semidirect
74. #10261C11direct (N × H)
136. C2×#486C2×C11semidirect
137. C2×#461C2×C11semidirect
139. #1954C2×C11semidirect
140. C2×#332C2×C11semidirect
141. C2×#331C2×C11semidirect
142. #1277C2×C11semidirect
356. C11#10261direct (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×#4612
C2×C11×#4592
C11×#19542
C2×C11×#3322
C2×C11×#3312
C11×#12772
#1026111