Finite Group Databasebeta

← C11×#10266 #14587459

Subgroups — C11×#10266 #14587459

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#492C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, 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—22no—
9C22×C11×D8—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#492—22no—
14C11×#492—22no—
15C11×#474—22no—
16C11×#474—22no—
17C11×#459—22no—
18C11×#459—22no—
19C2×C11×#107—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102—21no—
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—28no—
36C2×C11×SD16—44no—
37C2×C11×SD16—44no—
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×#107—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#102—24no—
70C11×#102—24no—
71C11×C22⋊C8—44no—
72C4×C8×C11—21no—
73C4×C8×C11—21no—
74#10266C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—21no—
76C24×C11—41no—
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C2×D4×C11—82no—
99C2×D4×C11SD1612yescomplemented
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C11×SD16—416no—
110C11×D8—48no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C2×C8×C11—42no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11D814yescomplemented
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C2×#492C2×C1111yescharacteristic, complemented
135C2×#474C2×C1111yescharacteristic, complemented
136C2×#459C2×C1111yescharacteristic
137#1954C2×C1111yescharacteristic, complemented
138C2×#332C2×C1111yescharacteristic, complemented
139C2×#331C2×C1111yescharacteristic, complemented
140#1277C2×C1111yescharacteristic, complemented
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—82no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—82no—
151C23×C11#12111yescharacteristic
152Q8×C11—44no—
153Q8×C11—81no—
154Q8×C11—81no—
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—44no—
158D4×C11—41no—
159D4×C11—42no—
160D4×C11—41no—
161D4×C11—42no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—81no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11—82no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12711yescharacteristic
182C2×C4×C11C2×D812yes—
183C2×C4×C11C2×SD1611yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11AGL(1,ℤ/8)12yes—
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11#13711yescharacteristic
188C8×C11—24no—
189C8×C11—42no—
190C8×C11—42no—
191C8×C11—81no—
192C22×SD16—22no—
193C22×D8—21no—
194C2×C4⋊Q8C22×C1111yescharacteristic
195C2×#127C22×C1111yescharacteristic
196C2×C4×D4C22×C1111yescharacteristic
197#492—22no—
198#492—22no—
199#474—22no—
200#474—22no—
201#459—22no—
202#459—22no—
203C2×#107—21no—
204C2×C4⋊C8C22×C1111yescharacteristic
205C2×C4⋊C8C22×C1111yescharacteristic
206C2×C4⋊C8C22×C1111yescharacteristic
207C2×#102—21no—
208C2×#102—21no—
209C2×C22⋊C8—22no—
210C2×C4×C8C22×C1111yescharacteristic
211#332—22no—
212#331—22no—
213C22×C11—44no—
214C22×C11—42no—
215C22×C11—82no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—162no—
222C22×C11—162no—
223C22×C11#39211yescharacteristic
224C22×C11#45912yes—
225C22×C11#46511yescharacteristic
226C22×C11#46811yescharacteristic
227C22×C11#47112yes—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—81no—
231C4×C11—82no—
232C4×C11#44712yes—
233C4×C11#44811yescharacteristic
234C4×C11#44911yescharacteristic
235C4×C11#45011yescharacteristic
236C4×C11#45211yescharacteristic
237C4×C11#49311yescharacteristic
238C4×C11#49611yescharacteristic
239C22×Q8—21no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4D4×C1111yescharacteristic
244C23×C4—21no—
245C2×SD16—28no—
246C2×SD16—44no—
247C2×SD16—44no—
248C2×D8—24no—
249C2×D8—42no—
250C2×D8—42no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8D4×C1112yes—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8D4×C1112yes—
259#127—21no—
260#127—21no—
261#127—21no—
262#127D4×C1112yes—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C1111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C42C23×C1111yescharacteristic
272#107—24no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8D4×C1112yes—
278C4⋊C8D4×C1112yes—
279#102—24no—
280#102—24no—
281C22⋊C8—44no—
282C4×C8—21no—
283C4×C8—21no—
284C2×C11—82no—
285C2×C11—162no—
286C2×C11#166512yes—
287C2×C11#168512yes—
288C2×C11#200011yescharacteristic
289C2×C11#201111yescharacteristic
290C2×C11#201911yescharacteristic
291C24—21no—
292C24—41no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—41no—
314C2×D4—82no—
315C2×D4C11×SD1612yescomplemented
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4C2×D4×C1111yescharacteristic
323C22×C4C2×D4×C1111yescharacteristic
324C22×C4C11×#4111yescharacteristic
325SD16—416no—
326D8—48no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—42no—
337C2×C8C11×D814yescomplemented
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42C2×D4×C1111yescharacteristic
347C42C2×D4×C1111yescharacteristic
348C42C2×D4×C1111yescharacteristic
349C42C2×D4×C1111yescharacteristic
350C11#1026611yescharacteristic, direct product factor, Sylow
351C23—22no—
352C23—41no—
353C23—42no—
354C23—41no—
355C23—42no—
356C23—42no—
357C23—82no—
358C23—81no—
359C23—81no—
360C23—82no—
361C23C11×#12111yescharacteristic
362Q8—44no—
363Q8—81no—
364Q8—81no—
365D4—22no—
366D4—22no—
367D4—44no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—42no—
372D4—82no—
373D4—82no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4C11×#12011yescharacteristic
387C2×C4C11×#12011yescharacteristic
388C2×C4C11×#12011yescharacteristic
389C2×C4C11×#12111yescharacteristic
390C2×C4C11×#12111yescharacteristic
391C2×C4C11×#12711yescharacteristic
392C2×C4C2×C11×D812yes—
393C2×C4C2×C11×SD1611yescharacteristic
394C2×C4C11×#13511yescharacteristic
395C2×C4C11×AGL(1,ℤ/8)12yes—
396C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
397C2×C4C11×#13711yescharacteristic
398C8—24no—
399C8—42no—
400C8—42no—
401C8—81no—
402C22—44no—
403C22—42no—
404C22—82no—
405C22—81no—
406C22—81no—
407C22—82no—
408C22—82no—
409C22—82no—
410C22—162no—
411C22—162no—
412C22C11×#39211yescharacteristic
413C22C11×#45912yes—
414C22C11×#46511yescharacteristic
415C22C11×#46811yescharacteristic
416C22C11×#47112yes—
417C4—21no—
418C4—21no—
419C4—81no—
420C4—82no—
421C4C11×#44712yes—
422C4C11×#44811yescharacteristic
423C4C11×#44911yescharacteristic
424C4C11×#45011yescharacteristic
425C4C11×#45211yescharacteristic
426C4C11×#49311yescharacteristic
427C4C11×#49611yescharacteristic
428C2—82no—
429C2—162no—
430C2C11×#166512yes—
431C2C11×#168512yes—
432C2C11×#200011yescharacteristic
433C2C11×#201111yescharacteristic
434C2C11×#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×#492C2semidirect
2. C2×C11×#474C2semidirect
4. C11×#1954C2semidirect
5. C2×C11×#332C2semidirect
6. C2×C11×#331C2semidirect
7. C11×#1277C2semidirect
74. #10266C11direct (N × H)
99. C2×D4×C11SD16semidirect
121. C2×C8×C11D8semidirect
134. C2×#492C2×C11semidirect
135. C2×#474C2×C11semidirect
137. #1954C2×C11semidirect
138. C2×#332C2×C11semidirect
139. C2×#331C2×C11semidirect
140. #1277C2×C11semidirect
315. C2×D4C11×SD16semidirect
337. C2×C8C11×D8semidirect
350. C11#10266direct (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×#4742
C2×C11×#4592
C11×#19542
C2×C11×#3322
C2×C11×#3312
C11×#12772
#1026611