Finite Group Databasebeta

← C11×#10502 #14587695

Subgroups — C11×#10502 #14587695

Order 2816.

412 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic
2C11×#1997C211yesmaximal, characteristic, complemented
3C11×#1987C211yesmaximal, characteristic, complemented
4C11×#1980C211yesmaximal, characteristic
5C11×#1565C211yesmaximal, characteristic, complemented
6C11×#1547C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#498—21no—
11C11×#486—21no—
12C11×#481—22no—
13C11×#476—21no—
14C11×#476—21no—
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#104—21no—
19C2×C11×#104—21no—
20C4×C11×M16C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#343—21no—
23C11×#343—21no—
24C11×#340—22no—
25C11×#335—21no—
26C11×#334—21no—
27C11×#332—21no—
28C11×#331—21no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C2×C11×M16—21no—
32C2×C11×M16D411yescharacteristic
33C2×C11×M16D411yescharacteristic
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D412yes—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C11×#106—22no—
52C11×#106—22no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D411yescharacteristic
58C11×C4⋊C8D411yescharacteristic
59C11×#104—42no—
60C11×#104—42no—
61C11×#102—22no—
62C11×#102—22no—
63C11×C22⋊C8—21no—
64C11×#97—21no—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67C11×#95—21no—
68#10502C1111yesmaximal, characteristic, direct product factor, Sylow
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C2×Q8×C11—21no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—82no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×M16—21no—
88C11×M16—21no—
89C11×M16—21no—
90C11×M16—41no—
91C11×M16—41no—
92C11×M16SD1612yes—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11—42no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11#4111yescharacteristic
116#3227C2×C1111yescharacteristic
117#1997C2×C1111yescharacteristic, complemented
118#1987C2×C1111yescharacteristic, complemented
119#1980C2×C1111yescharacteristic
120#1565C2×C1111yescharacteristic, complemented
121#1547C2×C1111yescharacteristic
122#1303C2×C1111yescharacteristic, complemented
123C23×C11—41no—
124C23×C11#12111yescharacteristic
125Q8×C11—41no—
126Q8×C11—41no—
127Q8×C11—82no—
128Q8×C11—82no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—41no—
132D4×C11—41no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12411yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C8×C11—22no—
158C8×C11—41no—
159C8×C11—41no—
160C8×C11—41no—
161C8×C11—81no—
162C8×C11—81no—
163#532C22×C1111yescharacteristic
164C2×C4⋊Q8C22×C1111yescharacteristic
165#498—21no—
166#486—21no—
167#481—22no—
168#476—21no—
169#476—21no—
170#431C22×C1111yescharacteristic
171#423C22×C1111yescharacteristic
172C2×C4⋊C8C22×C1111yescharacteristic
173C2×#104—21no—
174C2×#104—21no—
175C4×M16C22×C1111yescharacteristic
176C4×C4⋊C4C22×C1111yescharacteristic
177#343—21no—
178#343—21no—
179#340—22no—
180#335—21no—
181#334—21no—
182#332—21no—
183#331—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11#39411yescharacteristic
190C22×C11#46011yescharacteristic
191C22×C11#46411yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—82no—
196C4×C11—82no—
197C4×C11—81no—
198C4×C11#45411yescharacteristic
199C4×C11#45611yescharacteristic
200C4×C11#46111yescharacteristic
201C4×C11#46311yescharacteristic
202C4×C11#46511yescharacteristic
203C4×C11#46811yescharacteristic
204C2×#41—21no—
205C22×Q8—21no—
206C2×M16—21no—
207C2×M16D4×C1111yescharacteristic
208C2×M16D4×C1111yescharacteristic
209C22×C8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8D4×C1111yescharacteristic
215#127D4×C1111yescharacteristic
216#124—21no—
217#121—21no—
218#121—21no—
219C4×D4—21no—
220C4×D4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C1112yes—
224C2×C42—21no—
225C2×C42C23×C1111yescharacteristic
226#106—22no—
227#106—22no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8D4×C1111yescharacteristic
233C4⋊C8D4×C1111yescharacteristic
234#104—42no—
235#104—42no—
236#102—22no—
237#102—22no—
238C22⋊C8—21no—
239#97—21no—
240C4×C8—21no—
241C4×C8—21no—
242#95—21no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—161no—
246C2×C11#203811yescharacteristic
247C2×C11#204811yescharacteristic
248C2×C11#205511yescharacteristic
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—82no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C1111yescharacteristic
265C22×C4C2×D4×C1111yescharacteristic
266C22×C4C11×#4111yescharacteristic
267M16—21no—
268M16—21no—
269M16—21no—
270M16—41no—
271M16—41no—
272M16C11×SD1612yes—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—42no—
278C2×C8—41no—
279C2×C8—41no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—41no—
291C42—41no—
292C42C2×D4×C1111yescharacteristic
293C42C2×D4×C1111yescharacteristic
294C42C11×#4111yescharacteristic
295C42C11×#4111yescharacteristic
296C11#1050211yescharacteristic, direct product factor, Sylow
297C23—41no—
298C23C11×#12111yescharacteristic
299Q8—41no—
300Q8—41no—
301Q8—82no—
302Q8—82no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4C11×#12011yescharacteristic
322C2×C4C11×#12111yescharacteristic
323C2×C4C11×#12111yescharacteristic
324C2×C4C11×#12311yescharacteristic
325C2×C4C11×#12311yescharacteristic
326C2×C4C11×#12411yescharacteristic
327C2×C4C2×C11×SD1611yescharacteristic
328C2×C4C11×#13511yescharacteristic
329C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
330C2×C4C11×#13711yescharacteristic
331C8—22no—
332C8—41no—
333C8—41no—
334C8—41no—
335C8—81no—
336C8—81no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C11×#39411yescharacteristic
343C22C11×#46011yescharacteristic
344C22C11×#46411yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—82no—
350C4—81no—
351C4C11×#45411yescharacteristic
352C4C11×#45611yescharacteristic
353C4C11×#46111yescharacteristic
354C4C11×#46311yescharacteristic
355C4C11×#46511yescharacteristic
356C4C11×#46811yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C11×#203811yescharacteristic
361C2C11×#204811yescharacteristic
362C2C11×#205511yescharacteristic
subgroupG/H
center, socleC22×C11#394
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
2. C11×#1997C2semidirect
3. C11×#1987C2semidirect
5. C11×#1565C2semidirect
7. C11×#1303C2semidirect
68. #10502C11direct (N × H)
117. #1997C2×C11semidirect
118. #1987C2×C11semidirect
120. #1565C2×C11semidirect
122. #1303C2×C11semidirect
296. C11#10502direct (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×#19972
C11×#19872
C11×#19802
C11×#15652
C11×#15472
C11×#13032
#1050211