Finite Group Databasebeta

← C11×#13374 #14590567

Subgroups — C11×#13374 #14590567

Order 2816.

360 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3163C211yesmaximal, characteristic, complemented
2C11×#2145C211yesmaximal, characteristic
3C2×C11×#360C211yesmaximal, characteristic
4C11×#1976C211yesmaximal, characteristic
5C11×#1386C211yesmaximal, characteristic, complemented
6C11×#1384C211yesmaximal, characteristic, complemented
7C11×#1378C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C11×#544—21no—
10C2×C11×M32C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C11×#501—22no—
13C11×#499—21no—
14C11×#498—21no—
15C11×#428—21no—
16C11×#427C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C11×#421—21no—
20C11×#410—21no—
21C11×#405C2211yescharacteristic
22C11×#360—22no—
23C11×#360—21no—
24C11×#360—21no—
25C2×C11×#41—21no—
26C11×#135—21no—
27C11×#135—21no—
28C11×#135—21no—
29C11×#135—21no—
30C2×C11×Q16Q811yescharacteristic, complemented
31C2×C11×SD16—21no—
32C2×C11×D8Q811yescharacteristic, complemented
33C2×C11×M16D411yescharacteristic
34C22×C8×C11C2311yescharacteristic
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—41no—
37C11×#125—22no—
38C11×#125—41no—
39C11×C22⋊Q8—42no—
40C11×#117—21no—
41C11×#117—21no—
42C11×#117D411yescharacteristic
43C2×C11×C4⋊C4—21no—
44C11×M32—21no—
45C11×M32—21no—
46C11×M32—21no—
47C11×M32—21no—
48C2×C11×C16—21no—
49C2×C11×C16—21no—
50C11×#107—22no—
51C11×#107—21no—
52C11×#107—21no—
53C11×#106—22no—
54C11×#106—21no—
55C11×#106—21no—
56C11×#106D411yescharacteristic
57C11×#106D411yescharacteristic
58C11×#106D412yes—
59C11×#104—42no—
60C11×#99—42no—
61C11×#97—21no—
62C4×C8×C11—21no—
63#13374C1111yesmaximal, characteristic, direct product factor, Sylow
64C11×#41—41no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11—21no—
69C2×Q8×C11—42no—
70C2×D4×C11—21no—
71C2×D4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C11×Q16—21no—
76C11×Q16—21no—
77C11×SD16—41no—
78C11×SD16—41no—
79C11×D8—21no—
80C11×D8—21no—
81C11×M16—21no—
82C11×M16SD1612yes—
83C2×C8×C11—21no—
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×Q811yescharacteristic
87C2×C8×C11#4111yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C11×C4⋊C4—21no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4D812yes—
102C42×C11—21no—
103C42×C11—41no—
104C42×C11—41no—
105C11×C16—41no—
106C11×C16—41no—
107#3163C2×C1111yescharacteristic, complemented
108#2145C2×C1111yescharacteristic
109C2×#360C2×C1111yescharacteristic
110#1976C2×C1111yescharacteristic
111#1386C2×C1111yescharacteristic, complemented
112#1384C2×C1111yescharacteristic, complemented
113#1378C2×C1111yescharacteristic, complemented
114C23×C11—41no—
115C23×C11C2×D811yescharacteristic
116Q8×C11—41no—
117Q8×C11—41no—
118Q8×C11—162no—
119D4×C11—41no—
120D4×C11—41no—
121D4×C11—81no—
122D4×C11—81no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11—161no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C8×C11—22no—
139C8×C11C22⋊Q811yescharacteristic
140C8×C11C22⋊Q811yescharacteristic
141C8×C11#12411yescharacteristic
142C8×C11#12411yescharacteristic
143C2×#135C22×C1111yescharacteristic
144#544—21no—
145C2×M32C22×C1111yescharacteristic
146C2×M32C22×C1111yescharacteristic
147#501—22no—
148#499—21no—
149#498—21no—
150#428—21no—
151#427C22×C1111yescharacteristic
152#427C22×C1111yescharacteristic
153C2×#106C22×C1111yescharacteristic
154#421—21no—
155#410—21no—
156#405C22×C1111yescharacteristic
157#360—22no—
158#360—21no—
159#360—21no—
160C22×C11—41no—
161C22×C11—81no—
162C22×C11—161no—
163C22×C11#44711yescharacteristic
164C22×C11#47411yescharacteristic
165C22×C11#48611yescharacteristic
166C4×C11—42no—
167C4×C11—81no—
168C4×C11—82no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11—161no—
172C4×C11#39311yescharacteristic
173C4×C11#44811yescharacteristic
174C4×C11#47611yescharacteristic
175C4×C11#48911yescharacteristic
176C2×#41—21no—
177#135—21no—
178#135—21no—
179#135—21no—
180#135—21no—
181C2×Q16Q8×C1111yescharacteristic, complemented
182C2×SD16—21no—
183C2×D8Q8×C1111yescharacteristic, complemented
184C2×M16D4×C1111yescharacteristic
185C22×C8C23×C1111yescharacteristic
186C4⋊Q8—22no—
187C4⋊Q8—41no—
188#125—22no—
189#125—41no—
190C22⋊Q8—42no—
191#117—21no—
192#117—21no—
193#117D4×C1111yescharacteristic
194C2×C4⋊C4—21no—
195M32—21no—
196M32—21no—
197M32—21no—
198M32—21no—
199C2×C16—21no—
200C2×C16—21no—
201#107—22no—
202#107—21no—
203#107—21no—
204#106—22no—
205#106—21no—
206#106—21no—
207#106D4×C1112yes—
208#106D4×C1111yescharacteristic
209#106D4×C1111yescharacteristic
210#104—42no—
211#99—42no—
212#97—21no—
213C4×C8—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11—161no—
218C2×C11#202311yescharacteristic
219#41—41no—
220#41—41no—
221#41—41no—
222#41—41no—
223C2×Q8—21no—
224C2×Q8—42no—
225C2×D4—21no—
226C2×D4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4C2×D4×C1111yescharacteristic
230Q16—21no—
231Q16—21no—
232SD16—41no—
233SD16—41no—
234D8—21no—
235D8—21no—
236M16—21no—
237M16C11×SD1612yes—
238C2×C8—21no—
239C2×C8C2×D4×C1111yescharacteristic
240C2×C8C2×D4×C1111yescharacteristic
241C2×C8C2×Q8×C1111yescharacteristic
242C2×C8C11×#4111yescharacteristic
243C2×C8C11×#4111yescharacteristic
244C2×C8C11×#4111yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4C11×D812yes—
257C42—21no—
258C42—41no—
259C42—41no—
260C16—41no—
261C16—41no—
262C11#1337411yescharacteristic, direct product factor, Sylow
263C23—41no—
264C23C2×C11×D811yescharacteristic
265Q8—41no—
266Q8—41no—
267Q8—162no—
268D4—41no—
269D4—41no—
270D4—81no—
271D4—81no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—161no—
281C2×C4C11×#12011yescharacteristic
282C2×C4C11×C22⋊Q811yescharacteristic
283C2×C4C11×#12411yescharacteristic
284C2×C4C2×C11×SD1611yescharacteristic
285C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
286C2×C4C11×#13711yescharacteristic
287C8—22no—
288C8C11×C22⋊Q811yescharacteristic
289C8C11×C22⋊Q811yescharacteristic
290C8C11×#12411yescharacteristic
291C8C11×#12411yescharacteristic
292C22—41no—
293C22—81no—
294C22—161no—
295C22C11×#44711yescharacteristic
296C22C11×#47411yescharacteristic
297C22C11×#48611yescharacteristic
298C4—42no—
299C4—82no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—161no—
304C4C11×#39311yescharacteristic
305C4C11×#44811yescharacteristic
306C4C11×#47611yescharacteristic
307C4C11×#48911yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—161no—
312C2C11×#202311yescharacteristic
subgroupG/H
center, socleC2×C11#2023
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3163C2semidirect
5. C11×#1386C2semidirect
6. C11×#1384C2semidirect
7. C11×#1378C2semidirect
30. C2×C11×Q16Q8semidirect
32. C2×C11×D8Q8semidirect
63. #13374C11direct (N × H)
107. #3163C2×C11semidirect
111. #1386C2×C11semidirect
112. #1384C2×C11semidirect
113. #1378C2×C11semidirect
181. C2×Q16Q8×C11semidirect
183. C2×D8Q8×C11semidirect
262. C11#13374direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31632
C11×#21452
C2×C11×#3602
C11×#19762
C11×#13862
C11×#13842
C11×#13782
#1337411