Finite Group Databasebeta

← C11×#10064 #14587257

Subgroups — C11×#10064 #14587257

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#487C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic
4C11×#1988C211yesmaximal, characteristic, complemented
5C2×C11×#333C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#487—22no—
13C11×#487—22no—
14C11×#461—22no—
15C11×#461—22no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—22no—
19C2×C11×#103—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#393—22no—
22C11×#390—21no—
23C11×#382—21no—
24C11×#380—22no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#333—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×C11×SD16—24no—
34C2×C11×SD16—42no—
35C2×C11×SD16—42no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8D412yes—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—24no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66C11×#103—28no—
67C4×C8×C11—21no—
68C4×C8×C11D412yes—
69C11×#95—24no—
70C11×#95—21no—
71#10064C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—44no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11SD1612yes—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×SD16—48no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—42no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—42no—
106C2×C8×C11—41no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—84no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128C2×#487C2×C1111yescharacteristic, complemented
129C2×#461C2×C1111yescharacteristic
130#2563C2×C1111yescharacteristic
131#1988C2×C1111yescharacteristic, complemented
132C2×#333C2×C1111yescharacteristic, complemented
133C2×D4⋊C8C2×C1111yescharacteristic
134#1279C2×C1111yescharacteristic, complemented
135C23×C11—22no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11#12011yescharacteristic
141Q8×C11—44no—
142Q8×C11—42no—
143Q8×C11—42no—
144Q8×C11—82no—
145Q8×C11—81no—
146Q8×C11—81no—
147D4×C11—22no—
148D4×C11—22no—
149D4×C11—41no—
150D4×C11—41no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—82no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12711yescharacteristic
171C2×C4×C11C2×SD1611yescharacteristic
172C2×C4×C11#13511yescharacteristic
173C2×C4×C11#13512yes—
174C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C11#13711yescharacteristic
176C2×C4×C11#13712yes—
177C8×C11—42no—
178C8×C11—42no—
179C8×C11—81no—
180C22×SD16—21no—
181C2×C4⋊Q8C22×C1111yescharacteristic
182C2×C4⋊Q8C22×C1111yescharacteristic
183C2×C4×D4C22×C1111yescharacteristic
184#487—22no—
185#487—22no—
186#461—22no—
187#461—22no—
188C2×C4⋊C8C22×C1111yescharacteristic
189C2×C4⋊C8C22×C1111yescharacteristic
190C2×#103—22no—
191C2×#103—21no—
192C2×C4×C8C22×C1111yescharacteristic
193#393—22no—
194#390—21no—
195#382—21no—
196#380—22no—
197C4×C4⋊C4C22×C1111yescharacteristic
198#340—22no—
199#333—22no—
200D4⋊C8—22no—
201C22×C11—44no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#39211yescharacteristic
207C22×C11#44811yescharacteristic
208C22×C11#44911yescharacteristic
209C22×C11#45212yes—
210C22×C11#45512yes—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—82no—
214C4×C11—82no—
215C4×C11—82no—
216C4×C11—81no—
217C4×C11#45011yescharacteristic
218C4×C11#45211yescharacteristic
219C4×C11#46412yes—
220C4×C11#46511yescharacteristic
221C4×C11#46811yescharacteristic
222C4×C11#49511yescharacteristic
223C4×C11#49711yescharacteristic
224C22×Q8—21no—
225C22×Q8D4×C1112yes—
226C22×D4D4×C1111yescharacteristic
227C23×C4—21no—
228C2×SD16—24no—
229C2×SD16—42no—
230C2×SD16—42no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C1112yes—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C1111yescharacteristic
251C2×C4⋊C4D4×C1112yes—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—24no—
254C2×C42—21no—
255C2×C42C23×C1111yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C1112yes—
260#103—24no—
261#103—28no—
262C4×C8—21no—
263C4×C8D4×C1112yes—
264#95—24no—
265#95—21no—
266C2×C11—82no—
267C2×C11#164312yes—
268C2×C11#164612yes—
269C2×C11#200011yescharacteristic
270C2×C11#200411yescharacteristic
271C2×C11#201511yescharacteristic
272C24—21no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—44no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4C11×SD1612yes—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C2×D4×C1111yescharacteristic
299SD16—48no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—42no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—84no—
322C42—41no—
323C42—41no—
324C42C2×D4×C1111yescharacteristic
325C42C2×D4×C1111yescharacteristic
326C42C2×D4×C1111yescharacteristic
327C42C11×#4111yescharacteristic
328C11#1006411yescharacteristic, direct product factor, Sylow
329C23—22no—
330C23—41no—
331C23—41no—
332C23—42no—
333C23—42no—
334C23C11×#12011yescharacteristic
335Q8—44no—
336Q8—42no—
337Q8—42no—
338Q8—82no—
339Q8—81no—
340Q8—81no—
341D4—22no—
342D4—22no—
343D4—41no—
344D4—41no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—82no—
359C2×C4C11×#12011yescharacteristic
360C2×C4C11×#12011yescharacteristic
361C2×C4C11×#12111yescharacteristic
362C2×C4C11×#12111yescharacteristic
363C2×C4C11×#12111yescharacteristic
364C2×C4C11×#12711yescharacteristic
365C2×C4C2×C11×SD1611yescharacteristic
366C2×C4C11×#13512yes—
367C2×C4C11×#13511yescharacteristic
368C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
369C2×C4C11×#13712yes—
370C2×C4C11×#13711yescharacteristic
371C8—42no—
372C8—42no—
373C8—81no—
374C22—44no—
375C22—42no—
376C22—82no—
377C22—81no—
378C22—81no—
379C22C11×#39211yescharacteristic
380C22C11×#44811yescharacteristic
381C22C11×#44911yescharacteristic
382C22C11×#45212yes—
383C22C11×#45512yes—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—82no—
388C4—82no—
389C4—81no—
390C4C11×#45011yescharacteristic
391C4C11×#45211yescharacteristic
392C4C11×#46412yes—
393C4C11×#46511yescharacteristic
394C4C11×#46811yescharacteristic
395C4C11×#49511yescharacteristic
396C4C11×#49711yescharacteristic
397C2—82no—
398C2C11×#164312yes—
399C2C11×#164612yes—
400C2C11×#200011yescharacteristic
401C2C11×#200411yescharacteristic
402C2C11×#201511yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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×#487C2semidirect
4. C11×#1988C2semidirect
5. C2×C11×#333C2semidirect
7. C11×#1279C2semidirect
71. #10064C11direct (N × H)
128. C2×#487C2×C11semidirect
131. #1988C2×C11semidirect
132. C2×#333C2×C11semidirect
134. #1279C2×C11semidirect
328. C11#10064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4872
C2×C11×#4612
C11×#25632
C11×#19882
C2×C11×#3332
C2×C11×D4⋊C82
C11×#12792
#1006411