Finite Group Databasebeta

← C11×#19063 #14596256

Subgroups — C11×#19063 #14596256

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3556C211yesmaximal, characteristic, complemented
2C11×#3235C212yesmaximal
3C11×#3135C211yesmaximal, characteristic
4C11×#1663C214yesmaximal, complemented
5C11×#1658C214yesmaximal, complemented
6C11×#1537C211yesmaximal, characteristic, complemented
7C11×#1531C212yesmaximal, complemented
8C11×#564C2214yes—
9C11×#557—22no—
10C11×#557—22no—
11C11×#557—22no—
12C11×#541—22no—
13C11×#541—24no—
14C11×#533C2212yes—
15C11×#533C2211yescharacteristic
16C11×#532C2211yescharacteristic
17C11×#501C2214yes—
18C11×#491C2212yes—
19C11×#490C2214yes—
20C11×#490C2212yes—
21C11×#489—22no—
22C11×#482—24no—
23C11×#476—22no—
24C11×#474—22no—
25C11×#432C2212yes—
26C11×#416—22no—
27C2×C11×#97C2211yescharacteristic
28C11×#330C2218yes—
29C11×#330C2214yes—
30C2×C11×#41—21no—
31C22×C8×C11—21no—
32C11×C4⋊Q8—24no—
33C11×C4⋊Q8—22no—
34C11×C4⋊Q8D412yes—
35C11×C4⋊Q8D412yes—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8C2311yescharacteristic
38C11×#127C2311yescharacteristic
39C11×#126—28no—
40C11×#125—24no—
41C11×#125—22no—
42C11×#125—28no—
43C11×#125—28no—
44C11×#125—28no—
45C11×#125C2312yes—
46C11×#125C2314yes—
47C11×#124—21no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—22no—
51C11×#121—22no—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—22no—
59C11×#117D412yes—
60C11×#117D414yes—
61C2×C42×C11C2311yescharacteristic
62C11×#107—24no—
63C11×#106—24no—
64C11×C4⋊C8—22no—
65C11×#103—24no—
66C11×#102—24no—
67C11×#102—24no—
68C11×#102—24no—
69C11×C22⋊C8—22no—
70C11×#97—21no—
71C11×#97C2312yes—
72C11×#97C2314yes—
73#19063C1111yesmaximal, characteristic, direct product factor, Sylow
74C11×#41—44no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C2×C8×C11—22no—
86C2×C8×C11—24no—
87C2×C8×C11—42no—
88C11×C4⋊C4—28no—
89C11×C4⋊C4—28no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4C2×D414yes—
99C11×C4⋊C4C2×D414yes—
100C11×C4⋊C4C2×D414yes—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—42no—
104C42×C11—28no—
105C42×C11—24no—
106C42×C11—22no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D412yes—
109C42×C11C2411yescharacteristic
110#3556C2×C1111yescharacteristic, complemented
111#3235C2×C1112yes—
112#3135C2×C1111yescharacteristic
113#1663C2×C1114yescomplemented
114#1658C2×C1114yescomplemented
115#1537C2×C1111yescharacteristic, complemented
116#1531C2×C1112yescomplemented
117C23×C11—41no—
118C23×C11#12011yescharacteristic
119Q8×C11—44no—
120Q8×C11—44no—
121Q8×C11—42no—
122Q8×C11—44no—
123D4×C11—44no—
124D4×C11—42no—
125D4×C11—82no—
126C2×C4×C11—22no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—82no—
133C2×C4×C11#12012yes—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11C22×D412yes—
136C2×C4×C11C22×D411yescharacteristic
137C8×C11—44no—
138C8×C11—42no—
139#564C22×C1114yes—
140#557—22no—
141#557—22no—
142#557—22no—
143#541—22no—
144#541—24no—
145#533C22×C1111yescharacteristic
146#533C22×C1112yes—
147#532C22×C1111yescharacteristic
148#501C22×C1114yes—
149#491C22×C1112yes—
150#490C22×C1112yes—
151#490C22×C1114yes—
152#489—22no—
153#482—24no—
154#476—22no—
155#474—22no—
156#432C22×C1112yes—
157#416—22no—
158C2×#97C22×C1111yescharacteristic
159#330C22×C1114yes—
160#330C22×C1118yes—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—81no—
164C22×C11—82no—
165C22×C11C2×#12011yescharacteristic
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—44no—
170C4×C11—44no—
171C4×C11—44no—
172C4×C11—81no—
173C4×C11#45412yes—
174C2×#41—21no—
175C22×C8—21no—
176C4⋊Q8—24no—
177C4⋊Q8—22no—
178C4⋊Q8D4×C1112yes—
179C4⋊Q8D4×C1112yes—
180C4⋊Q8D4×C1112yes—
181C4⋊Q8C23×C1111yescharacteristic
182#127C23×C1111yescharacteristic
183#126—28no—
184#125—24no—
185#125—22no—
186#125—28no—
187#125—28no—
188#125—28no—
189#125C23×C1112yes—
190#125C23×C1114yes—
191#124—21no—
192C22⋊Q8—22no—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195#121—22no—
196C4×Q8—24no—
197C4×Q8—24no—
198C4×Q8—24no—
199C4×Q8—22no—
200C4×Q8—22no—
201C4×Q8—22no—
202C4×D4—22no—
203#117D4×C1112yes—
204#117D4×C1114yes—
205C2×C42C23×C1111yescharacteristic
206#107—24no—
207#106—24no—
208C4⋊C8—22no—
209#103—24no—
210#102—24no—
211#102—24no—
212#102—24no—
213C22⋊C8—22no—
214#97—21no—
215#97C23×C1112yes—
216#97C23×C1114yes—
217C2×C11—41no—
218C2×C11—161no—
219C2×C11C2×#45411yescharacteristic
220C2×C11#302012yes—
221#41—44no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—21no—
226C2×D4—22no—
227C2×D4—21no—
228C2×D4—41no—
229C22×C4—41no—
230C22×C4C2×D4×C1111yescharacteristic
231C22×C4C2×D4×C1112yes—
232C2×C8—22no—
233C2×C8—24no—
234C2×C8—42no—
235C4⋊C4—28no—
236C4⋊C4—28no—
237C4⋊C4—28no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—22no—
245C4⋊C4C2×D4×C1114yes—
246C4⋊C4C2×D4×C1114yes—
247C4⋊C4C2×D4×C1114yes—
248C22⋊C4—22no—
249C22⋊C4—24no—
250C22⋊C4—42no—
251C42—28no—
252C42—24no—
253C42—22no—
254C42C2×D4×C1111yescharacteristic
255C42C2×D4×C1112yes—
256C42C24×C1111yescharacteristic
257C11#1906311yescharacteristic, direct product factor, Sylow
258C23—41no—
259C23C11×#12011yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—42no—
263Q8—44no—
264D4—44no—
265D4—42no—
266D4—82no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—82no—
274C2×C4C11×#12012yes—
275C2×C4C11×#12011yescharacteristic
276C2×C4C22×D4×C1112yes—
277C2×C4C22×D4×C1111yescharacteristic
278C8—42no—
279C8—44no—
280C22—21no—
281C22—22no—
282C22—81no—
283C22—82no—
284C22C2×C11×#12011yescharacteristic
285C4—21no—
286C4—22no—
287C4—22no—
288C4—44no—
289C4—44no—
290C4—44no—
291C4—81no—
292C4C11×#45412yes—
293C2—41no—
294C2—161no—
295C2C2×C11×#45411yescharacteristic
296C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3556C2semidirect
4. C11×#1663C2semidirect
5. C11×#1658C2semidirect
6. C11×#1537C2semidirect
7. C11×#1531C2semidirect
73. #19063C11direct (N × H)
110. #3556C2×C11semidirect
113. #1663C2×C11semidirect
114. #1658C2×C11semidirect
115. #1537C2×C11semidirect
116. #1531C2×C11semidirect
257. C11#19063direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35562
C11×#32352
C11×#31352
C11×#16632
C11×#16582
C11×#15372
C11×#15312
#1906311