Finite Group Databasebeta

← C11×#13025 #14590218

Subgroups — C11×#13025 #14590218

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#509C211yesmaximal, characteristic
2C11×#2943C211yesmaximal, characteristic, complemented
3C2×C11×#360C211yesmaximal, characteristic, complemented
4C11×#2140C211yesmaximal, characteristic, complemented
5C11×#1972C211yesmaximal, characteristic, complemented
6C11×#1386C211yesmaximal, characteristic, complemented
7C11×#1377C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C22×C11×D8C2211yescharacteristic
10C4×C11×#41—21no—
11C11×#509—22no—
12C11×#509C414yescomplemented
13C2×C11×SD32—21no—
14C2×C11×D16—21no—
15C2×C11×M32C2211yescharacteristic
16C2×C11×M32C2211yescharacteristic
17C11×#442—21no—
18C11×#441—21no—
19C11×#440—22no—
20C11×#427C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C11×#416—21no—
23C2×C11×#102—21no—
24C2×C11×#97C2211yescharacteristic
25C11×#390—21no—
26C11×#360—22no—
27C11×#357—22no—
28C2×C11×#41—21no—
29C22×D4×C11—21no—
30C11×#135—21no—
31C11×#135—21no—
32C11×#135C2×C412yes—
33C11×#135D412yes—
34C2×C11×Q16D411yescharacteristic
35C2×C11×SD16—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8C2×C412yescomplemented
42C2×C11×D8D411yescharacteristic
43C22×C8×C11D411yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C4×Q8×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—42no—
48C11×#117—21no—
49C11×#117—41no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C22⋊C4—42no—
52C2×C42×C11—41no—
53C2×C42×C11D411yescharacteristic
54C11×SD32—24no—
55C11×D16—24no—
56C11×M32—21no—
57C11×M32—21no—
58C11×M32—21no—
59C11×M32C2×C412yescomplemented
60C2×C11×C16—21no—
61C2×C11×C16—21no—
62C11×#107D412yes—
63C11×#106—21no—
64C11×#106—21no—
65C11×#106—21no—
66C11×#103—22no—
67C11×#102—22no—
68C11×#102—42no—
69C11×#97—21no—
70C11×#97—21no—
71#13025C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—41no—
73C11×#41—22no—
74C11×#41—22no—
75C11×#41—41no—
76C11×#41—41no—
77C2×Q8×C11—21no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11D812yes—
90C22×C4×C11C2×D411yescharacteristic
91C11×Q16—21no—
92C11×Q16C22⋊C412yescomplemented
93C11×SD16—22no—
94C11×SD16—22no—
95C11×D8—21no—
96C11×D8—22no—
97C11×D8—22no—
98C11×D8—41no—
99C11×D8—41no—
100C11×D8C22⋊C412yescomplemented
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11C22×C411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11#4111yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C11×C4⋊C4—22no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—84no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11—42no—
120C42×C11—41no—
121C11×C16—22no—
122C11×C16—41no—
123C2×#509C2×C1111yescharacteristic
124#2943C2×C1111yescharacteristic, complemented
125C2×#360C2×C1111yescharacteristic, complemented
126#2140C2×C1111yescharacteristic, complemented
127#1972C2×C1111yescharacteristic, complemented
128#1386C2×C1111yescharacteristic, complemented
129#1377C2×C1111yescharacteristic, complemented
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11C2×D811yescharacteristic
137Q8×C11—22no—
138Q8×C11—41no—
139D4×C11—22no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—41no—
145D4×C11—81no—
146D4×C11—81no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—84no—
154C2×C4×C11—82no—
155C2×C4×C11—81no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C8×C11—41no—
163C8×C11C2×C22⋊C411yescharacteristic
164C8×C11C4×D411yescharacteristic
165C8×C11#12111yescharacteristic
166C8×C11#12311yescharacteristic
167C2×#135C22×C1111yescharacteristic
168C22×D8C22×C1111yescharacteristic
169C4×#41—21no—
170#509—22no—
171#509C4×C1114yescomplemented
172C2×SD32—21no—
173C2×D16—21no—
174C2×M32C22×C1111yescharacteristic
175C2×M32C22×C1111yescharacteristic
176#442—21no—
177#441—21no—
178#440—22no—
179#427C22×C1111yescharacteristic
180C2×#106C22×C1111yescharacteristic
181#416—21no—
182C2×#102—21no—
183C2×#97C22×C1111yescharacteristic
184#390—21no—
185#360—22no—
186#357—22no—
187C22×C11—22no—
188C22×C11—42no—
189C22×C11—84no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—161no—
193C22×C11—161no—
194C22×C11—162no—
195C22×C11C4×D811yescharacteristic
196C22×C11#44711yescharacteristic
197C22×C11#45911yescharacteristic
198C4×C11—42no—
199C4×C11—42no—
200C4×C11—82no—
201C4×C11—161no—
202C4×C11#38611yescharacteristic
203C4×C11#44211yescharacteristic
204C4×C11#44911yescharacteristic
205C4×C11#46311yescharacteristic
206C2×#41—21no—
207C22×D4—21no—
208#135—21no—
209#135—21no—
210#135C2×C4×C1112yes—
211#135D4×C1112yes—
212C2×Q16D4×C1111yescharacteristic
213C2×SD16—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8C2×C4×C1112yescomplemented
220C2×D8D4×C1111yescharacteristic
221C22×C8D4×C1111yescharacteristic
222C22×C8C23×C1111yescharacteristic
223C4×Q8—22no—
224C4×D4—22no—
225C4×D4—42no—
226#117—21no—
227#117—41no—
228C2×C4⋊C4—21no—
229C2×C22⋊C4—42no—
230C2×C42—41no—
231C2×C42D4×C1111yescharacteristic
232SD32—24no—
233D16—24no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32C2×C4×C1112yescomplemented
238C2×C16—21no—
239C2×C16—21no—
240#107D4×C1112yes—
241#106—21no—
242#106—21no—
243#106—21no—
244#103—22no—
245#102—22no—
246#102—42no—
247#97—21no—
248#97—21no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—82no—
252C2×C11—162no—
253C2×C11#187911yescharacteristic
254C2×C11#219012yes—
255C24—41no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C11×D812yes—
273C22×C4C2×D4×C1111yescharacteristic
274Q16—21no—
275Q16C11×C22⋊C412yescomplemented
276SD16—22no—
277SD16—22no—
278D8—22no—
279D8—22no—
280D8—21no—
281D8—41no—
282D8—41no—
283D8C11×C22⋊C412yescomplemented
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8C22×C4×C1111yescharacteristic
288C2×C8C2×D4×C1111yescharacteristic
289C2×C8C2×D4×C1111yescharacteristic
290C2×C8C2×D4×C1111yescharacteristic
291C2×C8C11×#4111yescharacteristic
292C2×C8C11×#4111yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—42no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—84no—
300C42—21no—
301C42—21no—
302C42—42no—
303C42—41no—
304C16—22no—
305C16—41no—
306C11#1302511yescharacteristic, direct product factor, Sylow
307C23—41no—
308C23—42no—
309C23—82no—
310C23—82no—
311C23—81no—
312C23—81no—
313C23C2×C11×D811yescharacteristic
314Q8—22no—
315Q8—41no—
316D4—22no—
317D4—42no—
318D4—42no—
319D4—42no—
320D4—42no—
321D4—41no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—84no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4C4×D4×C1111yescharacteristic
334C2×C4C11×#12011yescharacteristic
335C2×C4C11×#12111yescharacteristic
336C2×C4C11×#13511yescharacteristic
337C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
338C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
339C8—41no—
340C8C2×C11×C22⋊C411yescharacteristic
341C8C4×D4×C1111yescharacteristic
342C8C11×#12111yescharacteristic
343C8C11×#12311yescharacteristic
344C22—22no—
345C22—42no—
346C22—84no—
347C22—82no—
348C22—82no—
349C22—161no—
350C22—161no—
351C22—162no—
352C22C4×C11×D811yescharacteristic
353C22C11×#44711yescharacteristic
354C22C11×#45911yescharacteristic
355C4—42no—
356C4—42no—
357C4—82no—
358C4—161no—
359C4C11×#38611yescharacteristic
360C4C11×#44211yescharacteristic
361C4C11×#44911yescharacteristic
362C4C11×#46311yescharacteristic
363C2—21no—
364C2—21no—
365C2—82no—
366C2—162no—
367C2C11×#187911yescharacteristic
368C2C11×#219012yes—
subgroupG/H
center, socleC22×C11#447
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. C11×#2943C2semidirect
3. C2×C11×#360C2semidirect
4. C11×#2140C2semidirect
5. C11×#1972C2semidirect
6. C11×#1386C2semidirect
7. C11×#1377C2semidirect
12. C11×#509C4semidirect
41. C2×C11×D8C2×C4semidirect
59. C11×M32C2×C4semidirect
71. #13025C11direct (N × H)
92. C11×Q16C22⋊C4semidirect
100. C11×D8C22⋊C4semidirect
124. #2943C2×C11semidirect
125. C2×#360C2×C11semidirect
126. #2140C2×C11semidirect
127. #1972C2×C11semidirect
128. #1386C2×C11semidirect
129. #1377C2×C11semidirect
171. #509C4×C11semidirect
219. C2×D8C2×C4×C11semidirect
237. M32C2×C4×C11semidirect
275. Q16C11×C22⋊C4semidirect
283. D8C11×C22⋊C4semidirect
306. C11#13025direct (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
C11×#29432
C2×C11×#3602
C11×#21402
C11×#19722
C11×#13862
C11×#13772
#1302511