Finite Group Databasebeta

← C11×#10057 #14587250

Subgroups — C11×#10057 #14587250

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#494C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C11×#2567C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic
5C2×C11×#333C211yesmaximal, characteristic
6C2×C11×Q8⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C22×C11×Q16—22no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#494—22no—
13C11×#494—22no—
14C11×#477—22no—
15C11×#477—22no—
16C2×C11×#107—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#395—22no—
22C11×#391—21no—
23C11×#389—22no—
24C11×#384—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#333—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×Q8×C11D412yes—
32C2×C11×Q16—28no—
33C2×C11×Q16—48no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D412yes—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#107—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66C4×C8×C11—21no—
67C4×C8×C11D412yes—
68C11×#95—24no—
69C11×#95—21no—
70#10057C1111yesmaximal, characteristic, direct product factor, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—44no—
80C2×Q8×C11—44no—
81C2×Q8×C11—41no—
82C2×Q8×C11Q1612yescomplemented
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C11×Q16—416no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—42no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—84no—
113C11×C4⋊C4Q1614yescomplemented
114C42×C11—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C2×#494C2×C1111yescharacteristic
123C2×#477C2×C1111yescharacteristic
124#2567C2×C1111yescharacteristic
125#1987C2×C1111yescharacteristic
126C2×#333C2×C1111yescharacteristic
127C2×Q8⋊C8C2×C1111yescharacteristic
128#1279C2×C1111yescharacteristic
129C23×C11#12011yescharacteristic
130Q8×C11—22no—
131Q8×C11—22no—
132Q8×C11—44no—
133Q8×C11—44no—
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—82no—
137Q8×C11—82no—
138C2×C4×C11—22no—
139C2×C4×C11—24no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—44no—
150C2×C4×C11—82no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11C2×Q1611yescharacteristic
158C2×C4×C11C2×Q1612yes—
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×C4×C11#13712yes—
163C8×C11—24no—
164C8×C11—42no—
165C8×C11—81no—
166C22×Q16—22no—
167C2×C4⋊Q8C22×C1111yescharacteristic
168C2×C4⋊Q8C22×C1111yescharacteristic
169C2×C4×Q8C22×C1111yescharacteristic
170#494—22no—
171#494—22no—
172#477—22no—
173#477—22no—
174C2×#107—21no—
175C2×C4⋊C8C22×C1111yescharacteristic
176C2×C4⋊C8C22×C1111yescharacteristic
177C2×#103—21no—
178C2×C4×C8C22×C1111yescharacteristic
179#395—22no—
180#391—21no—
181#389—22no—
182#384—21no—
183C4×C4⋊C4C22×C1111yescharacteristic
184#340—22no—
185#333—22no—
186Q8⋊C8—22no—
187C22×C11#39211yescharacteristic
188C22×C11#45112yes—
189C22×C11#45111yescharacteristic
190C22×C11#45211yescharacteristic
191C22×C11#45312yes—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—44no—
195C4×C11—42no—
196C4×C11—81no—
197C4×C11—82no—
198C4×C11—82no—
199C4×C11#45111yescharacteristic
200C4×C11#45211yescharacteristic
201C4×C11#46212yes—
202C4×C11#46711yescharacteristic
203C4×C11#47011yescharacteristic
204C4×C11#49411yescharacteristic
205C4×C11#49711yescharacteristic
206C22×Q8—21no—
207C22×Q8D4×C1111yescharacteristic
208C22×Q8D4×C1112yes—
209C2×Q16—28no—
210C2×Q16—48no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8D4×C1112yes—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4D4×C1111yescharacteristic
233C2×C4⋊C4D4×C1112yes—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42C23×C1111yescharacteristic
237#107—24no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8D4×C1112yes—
242#103—24no—
243C4×C8—21no—
244C4×C8D4×C1112yes—
245#95—24no—
246#95—21no—
247C2×C11#163212yes—
248C2×C11#163312yes—
249C2×C11#200111yescharacteristic
250C2×C11#200211yescharacteristic
251C2×C11#201611yescharacteristic
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—22no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—44no—
261C2×Q8—44no—
262C2×Q8—41no—
263C2×Q8C11×Q1612yescomplemented
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C2×D4×C1111yescharacteristic
271C22×C4C2×D4×C1111yescharacteristic
272Q16—416no—
273C2×C8—24no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—42no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—84no—
294C4⋊C4C11×Q1614yescomplemented
295C42—41no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42C2×D4×C1111yescharacteristic
300C42C2×D4×C1111yescharacteristic
301C42C2×D4×C1111yescharacteristic
302C42C11×#4111yescharacteristic
303C11#1005711yescharacteristic, direct product factor, Sylow
304C23C11×#12011yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—44no—
308Q8—44no—
309Q8—41no—
310Q8—41no—
311Q8—82no—
312Q8—82no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—82no—
326C2×C4C11×#12011yescharacteristic
327C2×C4C11×#12011yescharacteristic
328C2×C4C11×#12111yescharacteristic
329C2×C4C11×#12111yescharacteristic
330C2×C4C11×#12111yescharacteristic
331C2×C4C11×#12711yescharacteristic
332C2×C4C2×C11×Q1612yes—
333C2×C4C2×C11×Q1611yescharacteristic
334C2×C4C11×#13511yescharacteristic
335C2×C4C11×#13712yes—
336C2×C4C11×#13711yescharacteristic
337C2×C4C11×#13711yescharacteristic
338C8—24no—
339C8—42no—
340C8—81no—
341C22C11×#39211yescharacteristic
342C22C11×#45112yes—
343C22C11×#45111yescharacteristic
344C22C11×#45211yescharacteristic
345C22C11×#45312yes—
346C4—21no—
347C4—21no—
348C4—44no—
349C4—42no—
350C4—82no—
351C4—81no—
352C4—82no—
353C4C11×#45111yescharacteristic
354C4C11×#45211yescharacteristic
355C4C11×#46212yes—
356C4C11×#46711yescharacteristic
357C4C11×#47011yescharacteristic
358C4C11×#49411yescharacteristic
359C4C11×#49711yescharacteristic
360C2C11×#163212yes—
361C2C11×#163312yes—
362C2C11×#200111yescharacteristic
363C2C11×#200211yescharacteristic
364C2C11×#201611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
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
70. #10057C11direct (N × H)
82. C2×Q8×C11Q16semidirect
113. C11×C4⋊C4Q16semidirect
263. C2×Q8C11×Q16semidirect
294. C4⋊C4C11×Q16semidirect
303. C11#10057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4942
C2×C11×#4772
C11×#25672
C11×#19872
C2×C11×#3332
C2×C11×Q8⋊C82
C11×#12792
#1005711