Finite Group Databasebeta

← C11×#10273 #14587466

Subgroups — C11×#10273 #14587466

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#498C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C2×C11×#462C211yesmaximal, characteristic
4C11×#1984C211yesmaximal, characteristic
5C2×C11×#333C211yesmaximal, characteristic
6C2×C11×#332C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C22×C11×Q16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#498—22no—
13C11×#498—22no—
14C11×#477—22no—
15C11×#477—22no—
16C11×#462—22no—
17C11×#462—22no—
18C2×C11×#107—21no—
19C2×C11×#106—22no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103—21no—
24C2×C11×#103—21no—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#336—22no—
27C11×#333—22no—
28C11×#332—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic
32C2×C11×Q16—24no—
33C2×C11×Q16—42no—
34C2×C11×Q16—42no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11D412yes—
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⋊Q8D412yes—
46C11×C4⋊Q8D412yes—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×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⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C11×#107—24no—
60C11×#106—28no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×#103—24no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71#10273C1111yesmaximal, characteristic, direct product factor, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—82no—
86C2×Q8×C11SD1612yes—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C11×Q16—48no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—42no—
105C2×C8×C11Q1614yescomplemented
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C2×#498C2×C1111yescharacteristic
125C2×#477C2×C1111yescharacteristic
126C2×#462C2×C1111yescharacteristic
127#1984C2×C1111yescharacteristic
128C2×#333C2×C1111yescharacteristic
129C2×#332C2×C1111yescharacteristic
130#1277C2×C1111yescharacteristic
131C23×C11#12111yescharacteristic
132Q8×C11—22no—
133Q8×C11—22no—
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—82no—
139Q8×C11—82no—
140Q8×C11—81no—
141Q8×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11—82no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11C2×Q1612yes—
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C2×C4×C11#13712yes—
165C8×C11—24no—
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—81no—
169C22×Q16—21no—
170C2×C4⋊Q8C22×C1111yescharacteristic
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×C4×Q8C22×C1111yescharacteristic
173#498—22no—
174#498—22no—
175#477—22no—
176#477—22no—
177#462—22no—
178#462—22no—
179C2×#107—21no—
180C2×#106—22no—
181C2×C4⋊C8C22×C1111yescharacteristic
182C2×C4⋊C8C22×C1111yescharacteristic
183C2×C4⋊C8C22×C1111yescharacteristic
184C2×#103—21no—
185C2×#103—21no—
186C2×C4×C8C22×C1111yescharacteristic
187#336—22no—
188#333—22no—
189#332—22no—
190C22×C11#39211yescharacteristic
191C22×C11#46212yes—
192C22×C11#46511yescharacteristic
193C22×C11#46811yescharacteristic
194C22×C11#47112yes—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11—82no—
199C4×C11—81no—
200C4×C11—82no—
201C4×C11#44811yescharacteristic
202C4×C11#44911yescharacteristic
203C4×C11#45011yescharacteristic
204C4×C11#45112yes—
205C4×C11#45211yescharacteristic
206C4×C11#49411yescharacteristic
207C4×C11#49711yescharacteristic
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8D4×C1111yescharacteristic
211C2×Q16—24no—
212C2×Q16—42no—
213C2×Q16—42no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8D4×C1112yes—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8D4×C1112yes—
225C4⋊Q8D4×C1112yes—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4D4×C1111yescharacteristic
236C2×C42—21no—
237C2×C42C23×C1111yescharacteristic
238#107—24no—
239#106—28no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8D4×C1112yes—
245C4⋊C8D4×C1112yes—
246#103—24no—
247#103—24no—
248C4×C8—21no—
249C4×C8—21no—
250C2×C11#167212yes—
251C2×C11#169212yes—
252C2×C11#200011yescharacteristic
253C2×C11#201611yescharacteristic
254C2×C11#201911yescharacteristic
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—82no—
269C2×Q8C11×SD1612yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C11×#4111yescharacteristic
277Q16—48no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—42no—
288C2×C8C11×Q1614yescomplemented
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C42—41no—
302C42—41no—
303C42C2×D4×C1111yescharacteristic
304C42C2×D4×C1111yescharacteristic
305C42C2×D4×C1111yescharacteristic
306C42C2×D4×C1111yescharacteristic
307C11#1027311yescharacteristic, direct product factor, Sylow
308C23C11×#12111yescharacteristic
309Q8—22no—
310Q8—22no—
311Q8—41no—
312Q8—41no—
313Q8—42no—
314Q8—42no—
315Q8—82no—
316Q8—82no—
317Q8—81no—
318Q8—81no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4C11×#12011yescharacteristic
331C2×C4C11×#12011yescharacteristic
332C2×C4C11×#12011yescharacteristic
333C2×C4C11×#12111yescharacteristic
334C2×C4C11×#12111yescharacteristic
335C2×C4C11×#12711yescharacteristic
336C2×C4C2×C11×SD1611yescharacteristic
337C2×C4C2×C11×Q1612yes—
338C2×C4C11×#13511yescharacteristic
339C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
340C2×C4C11×#13712yes—
341C2×C4C11×#13711yescharacteristic
342C8—24no—
343C8—42no—
344C8—42no—
345C8—81no—
346C22C11×#39211yescharacteristic
347C22C11×#46212yes—
348C22C11×#46511yescharacteristic
349C22C11×#46811yescharacteristic
350C22C11×#47112yes—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—82no—
355C4—81no—
356C4—82no—
357C4C11×#44811yescharacteristic
358C4C11×#44911yescharacteristic
359C4C11×#45011yescharacteristic
360C4C11×#45112yes—
361C4C11×#45211yescharacteristic
362C4C11×#49411yescharacteristic
363C4C11×#49711yescharacteristic
364C2C11×#167212yes—
365C2C11×#169212yes—
366C2C11×#200011yescharacteristic
367C2C11×#201611yescharacteristic
368C2C11×#201911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#121
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
71. #10273C11direct (N × H)
105. C2×C8×C11Q16semidirect
288. C2×C8C11×Q16semidirect
307. C11#10273direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C2×C11×#4772
C2×C11×#4622
C11×#19842
C2×C11×#3332
C2×C11×#3322
C11×#12772
#1027311