Finite Group Databasebeta

← C11×#10277 #14587470

Subgroups — C11×#10277 #14587470

Order 2816.

510 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
1C2×C11×#487C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C2×C11×#475C211yesmaximal, characteristic
4C11×#1984C211yesmaximal, characteristic
5C2×C11×#333C211yesmaximal, characteristic
6C2×C11×#332C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#487—22no—
12C11×#487—22no—
13C11×#477—22no—
14C11×#477—22no—
15C11×#475—22no—
16C11×#475—22no—
17C2×C11×#107—21no—
18C2×C11×#106—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103—21no—
23C2×C11×#103—21no—
24C2×C11×#103—22no—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#336—22no—
27C11×#333—22no—
28C11×#332—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11D412yes—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D412yes—
43C11×C4⋊Q8D412yes—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C11×#107—24no—
57C11×#106—24no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C4⋊C8D412yes—
64C11×#103—24no—
65C11×#103—24no—
66C11×#103—28no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69#10277C1111yesmaximal, characteristic, direct product factor, Sylow
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×Q8×C11—82no—
82C2×Q8×C11Q1612yes—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—42no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11—41no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C2×#487C2×C1111yescharacteristic
120C2×#477C2×C1111yescharacteristic
121C2×#475C2×C1111yescharacteristic
122#1984C2×C1111yescharacteristic
123C2×#333C2×C1111yescharacteristic
124C2×#332C2×C1111yescharacteristic
125#1277C2×C1111yescharacteristic
126C23×C11#12111yescharacteristic
127Q8×C11—22no—
128Q8×C11—22no—
129Q8×C11—41no—
130Q8×C11—41no—
131Q8×C11—44no—
132Q8×C11—82no—
133Q8×C11—82no—
134Q8×C11—81no—
135Q8×C11—81no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11—82no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×C4×C11C2×Q1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11#13512yes—
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×C4×C11#13712yes—
158C8×C11—42no—
159C8×C11—42no—
160C8×C11—42no—
161C8×C11—81no—
162C2×C4⋊Q8C22×C1111yescharacteristic
163C2×C4⋊Q8C22×C1111yescharacteristic
164C2×C4×Q8C22×C1111yescharacteristic
165#487—22no—
166#487—22no—
167#477—22no—
168#477—22no—
169#475—22no—
170#475—22no—
171C2×#107—21no—
172C2×#106—21no—
173C2×C4⋊C8C22×C1111yescharacteristic
174C2×C4⋊C8C22×C1111yescharacteristic
175C2×C4⋊C8C22×C1111yescharacteristic
176C2×#103—21no—
177C2×#103—21no—
178C2×#103—22no—
179C2×C4×C8C22×C1111yescharacteristic
180#336—22no—
181#333—22no—
182#332—22no—
183C22×C11#39211yescharacteristic
184C22×C11#46412yes—
185C22×C11#46711yescharacteristic
186C22×C11#47011yescharacteristic
187C22×C11#47112yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—82no—
192C4×C11—81no—
193C4×C11—82no—
194C4×C11#45111yescharacteristic
195C4×C11#45111yescharacteristic
196C4×C11#45211yescharacteristic
197C4×C11#45211yescharacteristic
198C4×C11#45212yes—
199C4×C11#49511yescharacteristic
200C4×C11#49711yescharacteristic
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8D4×C1111yescharacteristic
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8D4×C1112yes—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8D4×C1112yes—
215C4⋊Q8D4×C1112yes—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4D4×C1111yescharacteristic
226C2×C42—21no—
227C2×C42C23×C1111yescharacteristic
228#107—24no—
229#106—24no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8D4×C1112yes—
235C4⋊C8D4×C1112yes—
236#103—24no—
237#103—24no—
238#103—28no—
239C4×C8—21no—
240C4×C8—21no—
241C2×C11#168412yes—
242C2×C11#170412yes—
243C2×C11#200111yescharacteristic
244C2×C11#201511yescharacteristic
245C2×C11#201911yescharacteristic
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—82no—
258C2×Q8C11×Q1612yes—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265C22×C4C11×#4111yescharacteristic
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—42no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C42—41no—
290C42—41no—
291C42C2×D4×C1111yescharacteristic
292C42C2×D4×C1111yescharacteristic
293C42C2×D4×C1111yescharacteristic
294C42C2×D4×C1111yescharacteristic
295C11#1027711yescharacteristic, direct product factor, Sylow
296C23C11×#12111yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—44no—
302Q8—82no—
303Q8—82no—
304Q8—81no—
305Q8—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4C11×#12011yescharacteristic
317C2×C4C11×#12011yescharacteristic
318C2×C4C11×#12011yescharacteristic
319C2×C4C11×#12111yescharacteristic
320C2×C4C11×#12111yescharacteristic
321C2×C4C11×#12711yescharacteristic
322C2×C4C2×C11×Q1611yescharacteristic
323C2×C4C11×#13512yes—
324C2×C4C11×#13511yescharacteristic
325C2×C4C11×#13712yes—
326C2×C4C11×#13711yescharacteristic
327C2×C4C11×#13711yescharacteristic
328C8—42no—
329C8—42no—
330C8—42no—
331C8—81no—
332C22C11×#39211yescharacteristic
333C22C11×#46412yes—
334C22C11×#46711yescharacteristic
335C22C11×#47011yescharacteristic
336C22C11×#47112yes—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—82no—
341C4—81no—
342C4—82no—
343C4C11×#45111yescharacteristic
344C4C11×#45111yescharacteristic
345C4C11×#45211yescharacteristic
346C4C11×#45211yescharacteristic
347C4C11×#45212yes—
348C4C11×#49511yescharacteristic
349C4C11×#49711yescharacteristic
350C2C11×#168412yes—
351C2C11×#170412yes—
352C2C11×#200111yescharacteristic
353C2C11×#201511yescharacteristic
354C2C11×#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
69. #10277C11direct (N × H)
295. C11#10277direct (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×#4772
C2×C11×#4752
C11×#19842
C2×C11×#3332
C2×C11×#3322
C11×#12772
#1027711