Finite Group Databasebeta

← C11×#10151 #14587344

Subgroups — C11×#10151 #14587344

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3229C211yesmaximal, characteristic, complemented
2C11×#3138C211yesmaximal, characteristic
3C2×C11×#486C211yesmaximal, characteristic
4C11×#1966C211yesmaximal, characteristic, complemented
5C11×#1545C211yesmaximal, characteristic
6C11×#1493C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C11×#498—21no—
12C11×#490—22no—
13C11×#487—21no—
14C11×#486—21no—
15C11×#486—21no—
16C11×#486—22no—
17C11×#486—22no—
18C11×#483—22no—
19C11×#475—22no—
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C11×#418—22no—
23C2×C11×#102—22no—
24C2×C11×#101—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#331—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127D412yes—
46C11×#125—21no—
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×C42×C11C2311yescharacteristic
55C11×#106—24no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×#103—24no—
60C11×#102—24no—
61C11×#102—24no—
62C11×#102—28no—
63C11×#101—44no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11D412yes—
70#10151C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—41no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—44no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—82no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×M16—22no—
93C11×M16—22no—
94C11×M16—42no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—42no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116#3229C2×C1111yescharacteristic, complemented
117#3138C2×C1111yescharacteristic
118C2×#486C2×C1111yescharacteristic
119#1966C2×C1111yescharacteristic, complemented
120#1545C2×C1111yescharacteristic
121#1493C2×C1111yescharacteristic, complemented
122#1278C2×C1111yescharacteristic, complemented
123C23×C11—42no—
124C23×C11—82no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11#12111yescharacteristic
128Q8×C11—42no—
129Q8×C11—42no—
130Q8×C11—82no—
131Q8×C11—81no—
132Q8×C11—81no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—81no—
139D4×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
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×C11#13512yes—
153C2×C4×C11AGL(1,ℤ/8)12yes—
154C8×C11—42no—
155C8×C11—42no—
156C8×C11—42no—
157C8×C11—81no—
158#533C22×C1111yescharacteristic
159C2×C4⋊Q8C22×C1111yescharacteristic
160C2×#127C22×C1111yescharacteristic
161#498—21no—
162#490—22no—
163#487—21no—
164#486—21no—
165#486—21no—
166#486—22no—
167#486—22no—
168#483—22no—
169#475—22no—
170#431C22×C1111yescharacteristic
171#423C22×C1111yescharacteristic
172#418—22no—
173C2×#102—22no—
174C2×#101—22no—
175C4×M16C22×C1111yescharacteristic
176C2×C4×C8C22×C1111yescharacteristic
177#331—22no—
178Q8⋊C8—22no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—164no—
185C22×C11#39211yescharacteristic
186C22×C11#46312yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—82no—
191C4×C11—81no—
192C4×C11#44912yes—
193C4×C11#45412yes—
194C4×C11#47112yes—
195C4×C11#49511yescharacteristic
196C4×C11#49611yescharacteristic
197C22×Q8—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C2×M16—21no—
202C2×M16D4×C1112yes—
203C22×C8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8D4×C1111yescharacteristic
209C4⋊Q8D4×C1111yescharacteristic
210#127—21no—
211#127—21no—
212#127—21no—
213#127D4×C1112yes—
214#125—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219#117—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4D4×C1112yes—
222C2×C42C23×C1111yescharacteristic
223#106—24no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8D4×C1112yes—
227#103—24no—
228#102—28no—
229#102—24no—
230#102—24no—
231#101—44no—
232C22⋊C8—21no—
233#97—21no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8—21no—
237C4×C8D4×C1112yes—
238C2×C11—22no—
239C2×C11—162no—
240C2×C11#200311yescharacteristic
241C2×C11#201211yescharacteristic
242C2×C11#201911yescharacteristic
243C24—41no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—44no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—82no—
260C22×C4—22no—
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C11×#4111yescharacteristic
264M16—22no—
265M16—22no—
266M16—42no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—42no—
271C2×C8—41no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C42—41no—
284C42C2×D4×C1111yescharacteristic
285C42C2×D4×C1111yescharacteristic
286C42C2×D4×C1111yescharacteristic
287C42C2×D4×C1111yescharacteristic
288C11#1015111yescharacteristic, direct product factor, Sylow
289C23—42no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23C11×#12111yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—81no—
297Q8—81no—
298Q8—82no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—81no—
303D4—81no—
304D4—82no—
305D4—82no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4C11×#12011yescharacteristic
313C2×C4C11×#12011yescharacteristic
314C2×C4C11×#12011yescharacteristic
315C2×C4C11×#12111yescharacteristic
316C2×C4C11×#12111yescharacteristic
317C2×C4C11×#12711yescharacteristic
318C2×C4C11×#13512yes—
319C2×C4C11×AGL(1,ℤ/8)12yes—
320C8—42no—
321C8—42no—
322C8—42no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22C11×#39211yescharacteristic
331C22C11×#46312yes—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—82no—
336C4—81no—
337C4C11×#44912yes—
338C4C11×#45412yes—
339C4C11×#47112yes—
340C4C11×#49511yescharacteristic
341C4C11×#49611yescharacteristic
342C2—22no—
343C2—162no—
344C2C11×#200311yescharacteristic
345C2C11×#201211yescharacteristic
346C2C11×#201911yescharacteristic
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×#3229C2semidirect
4. C11×#1966C2semidirect
6. C11×#1493C2semidirect
7. C11×#1278C2semidirect
70. #10151C11direct (N × H)
116. #3229C2×C11semidirect
119. #1966C2×C11semidirect
121. #1493C2×C11semidirect
122. #1278C2×C11semidirect
288. C11#10151direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#31382
C2×C11×#4862
C11×#19662
C11×#15452
C11×#14932
C11×#12782
#1015111