Finite Group Databasebeta

← C11×#13040 #14590233

Subgroups — C11×#13040 #14590233

Order 2816.

508 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×#509C211yesmaximal, characteristic
2C2×C11×#444C211yesmaximal, characteristic, complemented
3C2×C11×#361C211yesmaximal, characteristic, complemented
4C2×C11×#360C211yesmaximal, characteristic, complemented
5C11×#1972C211yesmaximal, characteristic, complemented
6C11×#1383C211yesmaximal, characteristic, complemented
7C11×#1375C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C22×C11×D8C2211yescharacteristic
10C2×C11×#131—21no—
11C11×#509—22no—
12C11×#509—22no—
13C2×C11×SD32C412yescomplemented
14C2×C11×D16C412yescomplemented
15C2×C11×M32C2211yescharacteristic
16C2×C11×M32C2211yescharacteristic
17C11×#444—22no—
18C11×#444—22no—
19C2×C11×#108C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#104—21no—
22C2×C11×#102—21no—
23C2×C11×#97C2211yescharacteristic
24C11×#390—21no—
25C11×#361—22no—
26C11×#360—22no—
27C2×C11×#41—21no—
28C22×D4×C11—21no—
29C11×#135—21no—
30C11×#135—21no—
31C11×#135D412yes—
32C11×#135D412yes—
33C2×C11×Q16C2×C411yescharacteristic
34C2×C11×SD16—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8—21no—
40C2×C11×D8C2×C412yes—
41C2×C11×D8C2×C411yescharacteristic
42C11×#131—24no—
43C11×#131—42no—
44C2×C11×M16—21no—
45C2×C11×M16—41no—
46C22×C8×C11—41no—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4—21no—
50C2×C11×C22⋊C4—42no—
51C2×C42×C11D411yescharacteristic
52C11×SD32—24no—
53C11×D16—24no—
54C11×M32—21no—
55C11×M32—21no—
56C11×M32—21no—
57C11×M32—21no—
58C2×C11×C16—21no—
59C2×C11×C16C2×C412yes—
60C11×#108—21no—
61C11×#108D412yes—
62C11×#106—21no—
63C11×#106—21no—
64C11×#104—24no—
65C11×#102—42no—
66C11×#97—21no—
67C11×#97—21no—
68#13040C1111yesmaximal, characteristic, direct product factor, Sylow
69C24×C11—41no—
70C11×#41—22no—
71C11×#41—22no—
72C11×#41—41no—
73C11×#41—41no—
74C2×Q8×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—22no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C11×Q16—21no—
88C11×Q16C22⋊C412yescomplemented
89C11×SD16—22no—
90C11×SD16—22no—
91C11×D8—21no—
92C11×D8—22no—
93C11×D8—22no—
94C11×D8—41no—
95C11×D8—41no—
96C11×D8C22⋊C412yescomplemented
97C11×M16—22no—
98C11×M16—44no—
99C11×M16—41no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—44no—
103C2×C8×C11—41no—
104C2×C8×C11D812yes—
105C2×C8×C11C22×C411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—84no—
114C42×C11—21no—
115C42×C11—21no—
116C11×C16—22no—
117C11×C16—41no—
118C2×#509C2×C1111yescharacteristic
119C2×#444C2×C1111yescharacteristic, complemented
120C2×#361C2×C1111yescharacteristic, complemented
121C2×#360C2×C1111yescharacteristic, complemented
122#1972C2×C1111yescharacteristic, complemented
123#1383C2×C1111yescharacteristic, complemented
124#1375C2×C1111yescharacteristic, complemented
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—82no—
128C23×C11—82no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11AGL(1,ℤ/8)11yescharacteristic
132Q8×C11—22no—
133Q8×C11—41no—
134D4×C11—22no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—41no—
139D4×C11—42no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—82no—
148C2×C4×C11—81no—
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C8×C11—22no—
156C8×C11—42no—
157C8×C11C2×C22⋊C411yescharacteristic
158C8×C11C4×D411yescharacteristic
159C8×C11#12111yescharacteristic
160C8×C11#12311yescharacteristic
161C2×#135C22×C1111yescharacteristic
162C22×D8C22×C1111yescharacteristic
163C2×#131—21no—
164#509—22no—
165#509—22no—
166C2×SD32C4×C1112yescomplemented
167C2×D16C4×C1112yescomplemented
168C2×M32C22×C1111yescharacteristic
169C2×M32C22×C1111yescharacteristic
170#444—22no—
171#444—22no—
172C2×#108C22×C1111yescharacteristic
173C2×#106C22×C1111yescharacteristic
174C2×#104—21no—
175C2×#102—21no—
176C2×#97C22×C1111yescharacteristic
177#390—21no—
178#361—22no—
179#360—22no—
180C22×C11—22no—
181C22×C11—42no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—84no—
185C22×C11—162no—
186C22×C11—161no—
187C22×C11—161no—
188C22×C11#44211yescharacteristic
189C22×C11#44911yescharacteristic
190C22×C11#45911yescharacteristic
191C4×C11—42no—
192C4×C11—81no—
193C4×C11—161no—
194C4×C11#38611yescharacteristic
195C4×C11C4×D811yescharacteristic
196C4×C11#44711yescharacteristic
197C4×C11#46311yescharacteristic
198C2×#41—21no—
199C22×D4—21no—
200#135—21no—
201#135—21no—
202#135D4×C1112yes—
203#135D4×C1112yes—
204C2×Q16C2×C4×C1111yescharacteristic
205C2×SD16—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8C2×C4×C1112yes—
212C2×D8C2×C4×C1111yescharacteristic
213#131—24no—
214#131—42no—
215C2×M16—21no—
216C2×M16—41no—
217C22×C8—41no—
218C22×C8D4×C1111yescharacteristic
219C22×C8C23×C1111yescharacteristic
220C2×C4⋊C4—21no—
221C2×C22⋊C4—42no—
222C2×C42D4×C1111yescharacteristic
223SD32—24no—
224D16—24no—
225M32—21no—
226M32—21no—
227M32—21no—
228M32—21no—
229C2×C16—21no—
230C2×C16C2×C4×C1112yes—
231#108—21no—
232#108D4×C1112yes—
233#106—21no—
234#106—21no—
235#104—24no—
236#102—42no—
237#97—21no—
238#97—21no—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11—82no—
242C2×C11—162no—
243C2×C11#187911yescharacteristic
244C2×C11AGL(1,ℤ/16)12yes—
245C24—41no—
246#41—22no—
247#41—22no—
248#41—41no—
249#41—41no—
250C2×Q8—21no—
251C2×D4—21no—
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C2×D4×C1111yescharacteristic
263Q16—21no—
264Q16C11×C22⋊C412yescomplemented
265SD16—22no—
266SD16—22no—
267D8—22no—
268D8—21no—
269D8—22no—
270D8—41no—
271D8—41no—
272D8C11×C22⋊C412yescomplemented
273M16—22no—
274M16—44no—
275M16—41no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—44no—
279C2×C8—41no—
280C2×C8C11×D812yes—
281C2×C8C22×C4×C1111yescharacteristic
282C2×C8C2×D4×C1111yescharacteristic
283C2×C8C2×D4×C1111yescharacteristic
284C2×C8C2×D4×C1111yescharacteristic
285C2×C8C11×#4111yescharacteristic
286C2×C8C11×#4111yescharacteristic
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—84no—
290C42—21no—
291C42—21no—
292C16—22no—
293C16—41no—
294C11#1304011yescharacteristic, direct product factor, Sylow
295C23—41no—
296C23—42no—
297C23—82no—
298C23—82no—
299C23—81no—
300C23—81no—
301C23C11×AGL(1,ℤ/8)11yescharacteristic
302Q8—22no—
303Q8—41no—
304D4—22no—
305D4—42no—
306D4—42no—
307D4—42no—
308D4—41no—
309D4—42no—
310D4—81no—
311D4—81no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—82no—
318C2×C4—81no—
319C2×C4C4×D4×C1111yescharacteristic
320C2×C4C11×#12011yescharacteristic
321C2×C4C11×#12111yescharacteristic
322C2×C4C2×C11×D811yescharacteristic
323C2×C4C11×#13511yescharacteristic
324C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
325C8—22no—
326C8—42no—
327C8C2×C11×C22⋊C411yescharacteristic
328C8C4×D4×C1111yescharacteristic
329C8C11×#12111yescharacteristic
330C8C11×#12311yescharacteristic
331C22—22no—
332C22—42no—
333C22—82no—
334C22—82no—
335C22—84no—
336C22—162no—
337C22—161no—
338C22—161no—
339C22C11×#44211yescharacteristic
340C22C11×#44911yescharacteristic
341C22C11×#45911yescharacteristic
342C4—42no—
343C4—81no—
344C4—161no—
345C4C11×#38611yescharacteristic
346C4C4×C11×D811yescharacteristic
347C4C11×#44711yescharacteristic
348C4C11×#46311yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2—162no—
353C2C11×#187911yescharacteristic
354C2C11×AGL(1,ℤ/16)12yes—
subgroupG/H
center, socleC22×C11#442
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#444C2semidirect
3. C2×C11×#361C2semidirect
4. C2×C11×#360C2semidirect
5. C11×#1972C2semidirect
6. C11×#1383C2semidirect
7. C11×#1375C2semidirect
13. C2×C11×SD32C4semidirect
14. C2×C11×D16C4semidirect
68. #13040C11direct (N × H)
88. C11×Q16C22⋊C4semidirect
96. C11×D8C22⋊C4semidirect
119. C2×#444C2×C11semidirect
120. C2×#361C2×C11semidirect
121. C2×#360C2×C11semidirect
122. #1972C2×C11semidirect
123. #1383C2×C11semidirect
124. #1375C2×C11semidirect
166. C2×SD32C4×C11semidirect
167. C2×D16C4×C11semidirect
264. Q16C11×C22⋊C4semidirect
272. D8C11×C22⋊C4semidirect
294. C11#13040direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5092
C2×C11×#4442
C2×C11×#3612
C2×C11×#3602
C11×#19722
C11×#13832
C11×#13752
#1304011