Finite Group Databasebeta

← C11×#10286 #14587479

Subgroups — C11×#10286 #14587479

Order 2816.

542 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×#3227C211yesmaximal, characteristic
2C11×#3226C211yesmaximal, characteristic
3C11×#2862C211yesmaximal, characteristic, complemented
4C11×#1962C211yesmaximal, characteristic
5C11×#1549C211yesmaximal, characteristic, complemented
6C11×#1546C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C11×#500—21no—
12C11×#498—21no—
13C11×#486—21no—
14C11×#486—21no—
15C11×#481—22no—
16C11×#480—22no—
17C11×#476—22no—
18C11×#474—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C2×C11×#104—22no—
23C11×#391—22no—
24C11×#391—22no—
25C11×#382—22no—
26C43×C11C2211yescharacteristic
27C11×#332—22no—
28C11×#332—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C2×C11×M16—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×#127D411yescharacteristic
43C11×#124—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C4⋊C4D412yes—
52C2×C42×C11—21no—
53C2×C42×C11—21no—
54C2×C42×C11D412yes—
55C2×C42×C11C2311yescharacteristic
56C11×#107—24no—
57C11×#106—24no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×C4⋊C8D412yes—
62C11×#104—44no—
63C11×#102—24no—
64C11×#102—24no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C11×#95—28no—
70#10286C1111yesmaximal, characteristic, direct product factor, Sylow
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—21no—
74C2×Q8×C11—44no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—24no—
109C42×C11—22no—
110C42×C11—22no—
111C42×C11—42no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116#3227C2×C1111yescharacteristic
117#3226C2×C1111yescharacteristic
118#2862C2×C1111yescharacteristic, complemented
119#1962C2×C1111yescharacteristic
120#1549C2×C1111yescharacteristic, complemented
121#1546C2×C1111yescharacteristic, complemented
122#1276C2×C1111yescharacteristic, complemented
123C23×C11—41no—
124C23×C11#12011yescharacteristic
125Q8×C11—42no—
126Q8×C11—82no—
127Q8×C11—82no—
128Q8×C11—82no—
129Q8×C11—81no—
130Q8×C11—81no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—82no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—44no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—44no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11#13512yes—
154C2×C4×C11AGL(1,ℤ/8)12yes—
155C8×C11—42no—
156C8×C11—42no—
157C8×C11—81no—
158#532C22×C1111yescharacteristic
159C2×C4⋊Q8C22×C1111yescharacteristic
160C2×C4⋊Q8C22×C1111yescharacteristic
161#500—21no—
162#498—21no—
163#486—21no—
164#486—21no—
165#481—22no—
166#480—22no—
167#476—22no—
168#474—22no—
169#431C22×C1111yescharacteristic
170#431C22×C1111yescharacteristic
171#423C22×C1111yescharacteristic
172C2×#104—22no—
173#391—22no—
174#391—22no—
175#382—22no—
176C43C22×C1111yescharacteristic
177#332—22no—
178#332—22no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#39211yescharacteristic
185C22×C11#44912yes—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—44no—
189C4×C11—82no—
190C4×C11—82no—
191C4×C11—81no—
192C4×C11#45412yes—
193C4×C11#45612yes—
194C4×C11#46312yes—
195C4×C11#49511yescharacteristic
196C4×C11#49611yescharacteristic
197C2×#41—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C2×M16—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8D4×C1111yescharacteristic
210#127D4×C1111yescharacteristic
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4×C1112yes—
219C2×C4⋊C4D4×C1112yes—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42D4×C1112yes—
223C2×C42C23×C1111yescharacteristic
224#107—24no—
225#106—24no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8D4×C1112yes—
229C4⋊C8D4×C1112yes—
230#104—44no—
231#102—24no—
232#102—24no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C4×C8—21no—
236C4×C8—21no—
237#95—28no—
238C2×C11—22no—
239C2×C11—161no—
240C2×C11#200311yescharacteristic
241C2×C11#200511yescharacteristic
242C2×C11#201211yescharacteristic
243#41—42no—
244#41—42no—
245C2×Q8—21no—
246C2×Q8—44no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264M16—42no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42—24no—
281C42—22no—
282C42—22no—
283C42—42no—
284C42C2×D4×C1111yescharacteristic
285C42C2×D4×C1111yescharacteristic
286C42C2×D4×C1111yescharacteristic
287C42C11×#4111yescharacteristic
288C11#1028611yescharacteristic, direct product factor, Sylow
289C23—41no—
290C23C11×#12011yescharacteristic
291Q8—42no—
292Q8—82no—
293Q8—81no—
294Q8—81no—
295Q8—82no—
296Q8—82no—
297D4—42no—
298D4—42no—
299D4—42no—
300D4—82no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—44no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4C11×#12011yescharacteristic
314C2×C4C11×#12011yescharacteristic
315C2×C4C11×#12111yescharacteristic
316C2×C4C11×#12111yescharacteristic
317C2×C4C11×#12111yescharacteristic
318C2×C4C11×#12711yescharacteristic
319C2×C4C11×#13512yes—
320C2×C4C11×AGL(1,ℤ/8)12yes—
321C8—42no—
322C8—42no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22C11×#39211yescharacteristic
330C22C11×#44912yes—
331C4—21no—
332C4—21no—
333C4—44no—
334C4—82no—
335C4—82no—
336C4—81no—
337C4C11×#45412yes—
338C4C11×#45612yes—
339C4C11×#46312yes—
340C4C11×#49511yescharacteristic
341C4C11×#49611yescharacteristic
342C2—22no—
343C2—161no—
344C2C11×#200311yescharacteristic
345C2C11×#200511yescharacteristic
346C2C11×#201211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
3. C11×#2862C2semidirect
5. C11×#1549C2semidirect
6. C11×#1546C2semidirect
7. C11×#1276C2semidirect
70. #10286C11direct (N × H)
118. #2862C2×C11semidirect
120. #1549C2×C11semidirect
121. #1546C2×C11semidirect
122. #1276C2×C11semidirect
288. C11#10286direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C11×#32262
C11×#28622
C11×#19622
C11×#15492
C11×#15462
C11×#12762
#1028611