Finite Group Databasebeta

← C11×#13026 #14590219

Subgroups — C11×#13026 #14590219

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#510C211yesmaximal, characteristic
2C11×#2943C211yesmaximal, characteristic
3C2×C11×#360C211yesmaximal, characteristic
4C11×#2141C211yesmaximal, characteristic, complemented
5C11×#1971C211yesmaximal, characteristic, complemented
6C11×#1386C211yesmaximal, characteristic, complemented
7C11×#1377C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C22×C11×Q16C2211yescharacteristic
10C4×C11×#41—21no—
11C11×#510—22no—
12C11×#510C414yescomplemented
13C2×C11×Q32—21no—
14C2×C11×SD32—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×#103—21no—
24C2×C11×#97C2211yescharacteristic
25C11×#391—21no—
26C11×#360—22no—
27C11×#358—22no—
28C2×C11×#41—21no—
29C22×Q8×C11—21no—
30C11×#135—21no—
31C11×#135—21no—
32C11×#135C2×C412yes—
33C11×#135D412yes—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16C2×C412yescomplemented
40C2×C11×Q16D411yescharacteristic
41C2×C11×SD16—21no—
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×C42×C11—41no—
52C2×C42×C11D411yescharacteristic
53C11×Q32—24no—
54C11×SD32—24no—
55C11×M32—21no—
56C11×M32—21no—
57C11×M32—21no—
58C11×M32C2×C412yescomplemented
59C2×C11×C16—21no—
60C2×C11×C16—21no—
61C11×#107D412yes—
62C11×#106—21no—
63C11×#106—21no—
64C11×#106—21no—
65C11×#103—22no—
66C11×#103—42no—
67C11×#102—22no—
68C11×#97—21no—
69C11×#97—21no—
70C11×#95—42no—
71#13026C1111yesmaximal, characteristic, direct product factor, Sylow
72C11×#41—22no—
73C11×#41—22no—
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11D812yes—
90C22×C4×C11C2×D411yescharacteristic
91C11×Q16—21no—
92C11×Q16—22no—
93C11×Q16—22no—
94C11×Q16—41no—
95C11×Q16—41no—
96C11×Q16C22⋊C412yes—
97C11×SD16—22no—
98C11×SD16—22no—
99C11×D8—21no—
100C11×D8C22⋊C412yes—
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—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—42no—
119C42×C11—41no—
120C11×C16—22no—
121C11×C16—41no—
122C2×#510C2×C1111yescharacteristic
123#2943C2×C1111yescharacteristic
124C2×#360C2×C1111yescharacteristic
125#2141C2×C1111yescharacteristic, complemented
126#1971C2×C1111yescharacteristic, complemented
127#1386C2×C1111yescharacteristic, complemented
128#1377C2×C1111yescharacteristic, complemented
129C23×C11—41no—
130C23×C11C2×D811yescharacteristic
131Q8×C11—22no—
132Q8×C11—41no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—81no—
136Q8×C11—81no—
137D4×C11—22no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—41no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—84no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—82no—
152C2×C4×C11—81no—
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C8×C11—41no—
160C8×C11C2×C22⋊C411yescharacteristic
161C8×C11C4×D411yescharacteristic
162C8×C11#12111yescharacteristic
163C8×C11#12311yescharacteristic
164C2×#135C22×C1111yescharacteristic
165C22×Q16C22×C1111yescharacteristic
166C4×#41—21no—
167#510—22no—
168#510C4×C1114yescomplemented
169C2×Q32—21no—
170C2×SD32—21no—
171C2×M32C22×C1111yescharacteristic
172C2×M32C22×C1111yescharacteristic
173#442—21no—
174#441—21no—
175#440—22no—
176#427C22×C1111yescharacteristic
177C2×#106C22×C1111yescharacteristic
178#416—21no—
179C2×#103—21no—
180C2×#97C22×C1111yescharacteristic
181#391—21no—
182#360—22no—
183#358—22no—
184C22×C11—22no—
185C22×C11—42no—
186C22×C11—82no—
187C22×C11C4×D811yescharacteristic
188C22×C11#44711yescharacteristic
189C22×C11#45911yescharacteristic
190C4×C11—42no—
191C4×C11—42no—
192C4×C11—82no—
193C4×C11—82no—
194C4×C11—161no—
195C4×C11#38611yescharacteristic
196C4×C11#44211yescharacteristic
197C4×C11#44911yescharacteristic
198C4×C11#46311yescharacteristic
199C2×#41—21no—
200C22×Q8—21no—
201#135—21no—
202#135—21no—
203#135C2×C4×C1112yes—
204#135D4×C1112yes—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16C2×C4×C1112yescomplemented
211C2×Q16D4×C1111yescharacteristic
212C2×SD16—21no—
213C2×D8D4×C1111yescharacteristic
214C22×C8D4×C1111yescharacteristic
215C22×C8C23×C1111yescharacteristic
216C4×Q8—22no—
217C4×D4—22no—
218C4×D4—42no—
219#117—21no—
220#117—41no—
221C2×C4⋊C4—21no—
222C2×C42—41no—
223C2×C42D4×C1111yescharacteristic
224Q32—24no—
225SD32—24no—
226M32—21no—
227M32—21no—
228M32—21no—
229M32C2×C4×C1112yescomplemented
230C2×C16—21no—
231C2×C16—21no—
232#107D4×C1112yes—
233#106—21no—
234#106—21no—
235#106—21no—
236#103—22no—
237#103—42no—
238#102—22no—
239#97—21no—
240#97—21no—
241#95—42no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—82no—
245C2×C11#187911yescharacteristic
246C2×C11#219112yes—
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—22no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C11×D812yes—
265C22×C4C2×D4×C1111yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—21no—
269Q16—41no—
270Q16—41no—
271Q16C11×C22⋊C412yes—
272SD16—22no—
273SD16—22no—
274D8—21no—
275D8C11×C22⋊C412yes—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8C22×C4×C1111yescharacteristic
280C2×C8C2×D4×C1111yescharacteristic
281C2×C8C2×D4×C1111yescharacteristic
282C2×C8C2×D4×C1111yescharacteristic
283C2×C8C11×#4111yescharacteristic
284C2×C8C11×#4111yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—42no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C42—21no—
292C42—21no—
293C42—42no—
294C42—41no—
295C16—22no—
296C16—41no—
297C11#1302611yescharacteristic, direct product factor, Sylow
298C23—41no—
299C23C2×C11×D811yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—84no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4—81no—
322C2×C4C4×D4×C1111yescharacteristic
323C2×C4C11×#12011yescharacteristic
324C2×C4C11×#12111yescharacteristic
325C2×C4C11×#13511yescharacteristic
326C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
327C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
328C8—41no—
329C8C2×C11×C22⋊C411yescharacteristic
330C8C4×D4×C1111yescharacteristic
331C8C11×#12111yescharacteristic
332C8C11×#12311yescharacteristic
333C22—22no—
334C22—42no—
335C22—82no—
336C22C4×C11×D811yescharacteristic
337C22C11×#44711yescharacteristic
338C22C11×#45911yescharacteristic
339C4—42no—
340C4—42no—
341C4—82no—
342C4—82no—
343C4—161no—
344C4C11×#38611yescharacteristic
345C4C11×#44211yescharacteristic
346C4C11×#44911yescharacteristic
347C4C11×#46311yescharacteristic
348C2—21no—
349C2—21no—
350C2—82no—
351C2C11×#187911yescharacteristic
352C2C11×#219112yes—
subgroupG/H
center, socleC22×C11#447
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#135C22
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
4. C11×#2141C2semidirect
5. C11×#1971C2semidirect
6. C11×#1386C2semidirect
7. C11×#1377C2semidirect
12. C11×#510C4semidirect
39. C2×C11×Q16C2×C4semidirect
58. C11×M32C2×C4semidirect
71. #13026C11direct (N × H)
125. #2141C2×C11semidirect
126. #1971C2×C11semidirect
127. #1386C2×C11semidirect
128. #1377C2×C11semidirect
168. #510C4×C11semidirect
210. C2×Q16C2×C4×C11semidirect
229. M32C2×C4×C11semidirect
297. C11#13026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5102
C11×#29432
C2×C11×#3602
C11×#21412
C11×#19712
C11×#13862
C11×#13772
#1302611