Finite Group Databasebeta

← C11×#10292 #14587485

Subgroups — C11×#10292 #14587485

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic
3C11×#2858C211yesmaximal, characteristic
4C11×#1994C211yesmaximal, characteristic, complemented
5C11×#1549C211yesmaximal, characteristic, complemented
6C11×#1545C211yesmaximal, characteristic
7C11×#1276C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—22no—
12C11×#500—21no—
13C11×#492—21no—
14C11×#487—21no—
15C11×#486—21no—
16C11×#484—22no—
17C11×#477—22no—
18C11×#460—22no—
19C11×#450—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#390—22no—
24C11×#390—22no—
25C43×C11C2211yescharacteristic
26C11×#339—22no—
27C11×#332—22no—
28C11×#331—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×C11×SD16—24no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#125—21no—
46C11×#124—48no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C22⋊C4—28no—
55C2×C42×C11—21no—
56C2×C42×C11—21no—
57C2×C42×C11D412yes—
58C2×C42×C11C2311yescharacteristic
59C11×#107—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C4⋊C8D412yes—
64C11×#103—24no—
65C11×#102—24no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70#10292C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—44no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C11×SD16—84no—
93C11×M16—42no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—416no—
108C11×C22⋊C4—41no—
109C42×C11—24no—
110C42×C11—22no—
111C42×C11—22no—
112C42×C11—42no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118#3230C2×C1111yescharacteristic, complemented
119#3208C2×C1111yescharacteristic
120#2858C2×C1111yescharacteristic
121#1994C2×C1111yescharacteristic, complemented
122#1549C2×C1111yescharacteristic, complemented
123#1545C2×C1111yescharacteristic
124#1276C2×C1111yescharacteristic, complemented
125C23×C11—44no—
126C23×C11—44no—
127C23×C11—42no—
128C23×C11—44no—
129C23×C11#12011yescharacteristic
130Q8×C11—42no—
131Q8×C11—42no—
132Q8×C11—82no—
133Q8×C11—82no—
134D4×C11—44no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—81no—
140D4×C11—81no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—44no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12711yescharacteristic
156C2×C4×C11#13512yes—
157C2×C4×C11#13712yes—
158C8×C11—42no—
159C8×C11—42no—
160C8×C11—81no—
161#533C22×C1111yescharacteristic
162C2×C4⋊Q8C22×C1111yescharacteristic
163C2×#127C22×C1111yescharacteristic
164C2×#124—22no—
165#500—21no—
166#492—21no—
167#487—21no—
168#486—21no—
169#484—22no—
170#477—22no—
171#460—22no—
172#450—22no—
173#431C22×C1111yescharacteristic
174#431C22×C1111yescharacteristic
175#423C22×C1111yescharacteristic
176#390—22no—
177#390—22no—
178C43C22×C1111yescharacteristic
179#339—22no—
180#332—22no—
181#331—22no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—88no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11#39211yescharacteristic
189C22×C11#45212yes—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—44no—
193C4×C11—82no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11#45312yes—
197C4×C11#45412yes—
198C4×C11#46412yes—
199C4×C11#49511yescharacteristic
200C4×C11#49711yescharacteristic
201C22×Q8—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4D4×C1112yes—
205C2×SD16—24no—
206C2×M16—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8D4×C1111yescharacteristic
212C4⋊Q8D4×C1111yescharacteristic
213#127—21no—
214#127—21no—
215#127—21no—
216#127—21no—
217#125—21no—
218#124—48no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4D4×C1112yes—
226C2×C22⋊C4—28no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42D4×C1112yes—
230C2×C42C23×C1111yescharacteristic
231#107—24no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8D4×C1112yes—
235C4⋊C8D4×C1112yes—
236#103—24no—
237#102—24no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240C4×C8—21no—
241C4×C8—21no—
242C2×C11—22no—
243C2×C11—162no—
244C2×C11#200211yescharacteristic
245C2×C11#200311yescharacteristic
246C2×C11#201511yescharacteristic
247C24—22no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—44no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—42no—
262C2×D4—42no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4C2×D4×C1111yescharacteristic
266C22×C4C2×D4×C1111yescharacteristic
267C22×C4C2×D4×C1111yescharacteristic
268SD16—84no—
269M16—42no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—41no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—416no—
284C22⋊C4—41no—
285C42—24no—
286C42—22no—
287C42—22no—
288C42—42no—
289C42—41no—
290C42C2×D4×C1111yescharacteristic
291C42C2×D4×C1111yescharacteristic
292C42C2×D4×C1111yescharacteristic
293C42C11×#4111yescharacteristic
294C11#1029211yescharacteristic, direct product factor, Sylow
295C23—44no—
296C23—44no—
297C23—42no—
298C23—44no—
299C23C11×#12011yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—82no—
303Q8—82no—
304D4—44no—
305D4—82no—
306D4—82no—
307D4—81no—
308D4—81no—
309D4—82no—
310D4—82no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4C11×#12011yescharacteristic
321C2×C4C11×#12011yescharacteristic
322C2×C4C11×#12111yescharacteristic
323C2×C4C11×#12111yescharacteristic
324C2×C4C11×#12111yescharacteristic
325C2×C4C11×#12711yescharacteristic
326C2×C4C11×#13512yes—
327C2×C4C11×#13712yes—
328C8—42no—
329C8—42no—
330C8—81no—
331C22—21no—
332C22—21no—
333C22—88no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22C11×#39211yescharacteristic
338C22C11×#45212yes—
339C4—21no—
340C4—21no—
341C4—44no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4C11×#45312yes—
346C4C11×#45412yes—
347C4C11×#46412yes—
348C4C11×#49511yescharacteristic
349C4C11×#49711yescharacteristic
350C2—22no—
351C2—162no—
352C2C11×#200211yescharacteristic
353C2C11×#200311yescharacteristic
354C2C11×#201511yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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×#3230C2semidirect
4. C11×#1994C2semidirect
5. C11×#1549C2semidirect
7. C11×#1276C2semidirect
70. #10292C11direct (N × H)
118. #3230C2×C11semidirect
121. #1994C2×C11semidirect
122. #1549C2×C11semidirect
124. #1276C2×C11semidirect
294. C11#10292direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#32082
C11×#28582
C11×#19942
C11×#15492
C11×#15452
C11×#12762
#1029211