Finite Group Databasebeta

← C2×C11×#1660 #14596176

Subgroups — C2×C11×#1660 #14596176

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#563C211yesmaximal, characteristic
2C2×C11×#501C212yesmaximal, complemented
3C2×C11×#497C211yesmaximal, characteristic
4C11×#1660C218yesmaximal, direct product factor
5C2×C11×#330C212yesmaximal, complemented
6C2×C11×#329C211yesmaximal, characteristic
7C22×C11×Q16—21no—
8C22×C11×SD16—21no—
9C11×#563—24no—
10C11×#563—22no—
11C11×#563C2214yes—
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#126—22no—
15C2×C11×#125C2212yes—
16C2×C11×#124C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8—22no—
19C11×#501—24no—
20C11×#501C2218yescomplemented
21C11×#497—22no—
22C11×#497C2214yes—
23C2×C11×#107—22no—
24C2×C11×#106—22no—
25C2×C11×#97C2211yescharacteristic
26C2×C11×#97C2212yes—
27C11×#330C2218yescomplemented
28C11×#329C2214yes—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×Q16—24no—
35C2×C11×Q16—44no—
36C2×C11×SD16—24no—
37C2×C11×SD16—44no—
38C22×C8×C11—22no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—24no—
41C11×C4⋊Q8—24no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C11×#126—28no—
46C11×#126—28no—
47C11×#125—22no—
48C11×#125—22no—
49C11×#125D414yes—
50C11×#125C2314yes—
51C11×#124—22no—
52C11×#124D412yes—
53C11×#124C2312yes—
54C11×#123—24no—
55C11×#123—24no—
56C11×C22⋊Q8—28no—
57C11×C22⋊Q8—28no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C11×#107—28no—
70C11×#106—28no—
71C11×#97—21no—
72C11×#97—22no—
73C11×#97C2314yes—
74C11×#97C2312yes—
75C2×#1660C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C2×Q8×C11—24no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—41no—
84C2×Q8×C11—82no—
85C2×Q8×C11C2×D412yes—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11C2×D412yes—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—41no—
94C22×C4×C11—82no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C11×Q16—48no—
98C11×SD16—48no—
99C2×C8×C11—28no—
100C2×C8×C11—24no—
101C2×C8×C11—24no—
102C2×C8×C11—22no—
103C11×C4⋊C4—28no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4C2×D414yes—
113C11×C4⋊C4C2×D414yes—
114C11×C22⋊C4—28no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C42×C11—24no—
119C42×C11C2×D412yes—
120C42×C11C2×D411yescharacteristic
121C42×C11C2411yescharacteristic
122C2×#563C2×C1111yescharacteristic
123C2×#501C2×C1112yescomplemented
124C2×#497C2×C1111yescharacteristic
125#1660C2×C1118yesdirect product factor
126C2×#330C2×C1112yescomplemented
127C2×#329C2×C1111yescharacteristic
128C23×C11—22no—
129C23×C11—42no—
130C23×C11—44no—
131C23×C11#12011yescharacteristic
132Q8×C11—42no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—81no—
136Q8×C11—82no—
137Q8×C11—84no—
138D4×C11—42no—
139D4×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—42no—
149C2×C4×C11—84no—
150C2×C4×C11—82no—
151C2×C4×C11#12012yes—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11C22×D412yes—
154C2×C4×C11C22×D411yescharacteristic
155C8×C11—28no—
156C8×C11—24no—
157C22×Q16—21no—
158C22×SD16—21no—
159#563—24no—
160#563—22no—
161#563C22×C1114yes—
162C2×C4⋊Q8—21no—
163C2×C4⋊Q8C22×C1111yescharacteristic
164C2×#126—22no—
165C2×#125C22×C1112yes—
166C2×#124C22×C1111yescharacteristic
167C2×#123—21no—
168C2×C22⋊Q8—22no—
169#501—24no—
170#501C22×C1118yescomplemented
171#497—22no—
172#497C22×C1114yes—
173C2×#107—22no—
174C2×#106—22no—
175C2×#97C22×C1111yescharacteristic
176C2×#97C22×C1112yes—
177#330C22×C1118yescomplemented
178#329C22×C1114yes—
179C22×C11—42no—
180C22×C11—44no—
181C22×C11—84no—
182C22×C11#45312yes—
183C22×C11#45614yes—
184C22×C11C2×#12011yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—44no—
190C4×C11—42no—
191C4×C11—44no—
192C4×C11—82no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8D4×C1111yescharacteristic
196C22×D4D4×C1111yescharacteristic
197C23×C4—21no—
198C2×Q16—24no—
199C2×Q16—44no—
200C2×SD16—24no—
201C2×SD16—44no—
202C22×C8—21no—
203C22×C8—22no—
204C4⋊Q8—24no—
205C4⋊Q8—24no—
206C4⋊Q8—22no—
207C4⋊Q8—21no—
208C4⋊Q8C23×C1112yes—
209#126—28no—
210#126—28no—
211#125—22no—
212#125—22no—
213#125D4×C1114yes—
214#125C23×C1114yes—
215#124—22no—
216#124D4×C1112yes—
217#124C23×C1112yes—
218#123—24no—
219#123—24no—
220C22⋊Q8—28no—
221C22⋊Q8—28no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4D4×C1112yes—
227C2×C4⋊C4D4×C1112yes—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—22no—
231C2×C42—21no—
232C2×C42C23×C1111yescharacteristic
233#107—28no—
234#106—28no—
235#97—21no—
236#97—22no—
237#97C23×C1114yes—
238#97C23×C1112yes—
239C2×C11—82no—
240C2×C11#166014yesdirect product factor
241C2×C11C2×#45311yescharacteristic
242C2×C11C2×#45612yes—
243C24—21no—
244C2×Q8—24no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—41no—
251C2×Q8—82no—
252C2×Q8C2×D4×C1112yes—
253C2×D4—21no—
254C2×D4—42no—
255C2×D4C2×D4×C1112yes—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—41no—
261C22×C4—82no—
262C22×C4C2×D4×C1112yes—
263C22×C4C2×D4×C1111yescharacteristic
264Q16—48no—
265SD16—48no—
266C2×C8—24no—
267C2×C8—28no—
268C2×C8—24no—
269C2×C8—22no—
270C4⋊C4—28no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—42no—
279C4⋊C4C2×D4×C1114yes—
280C4⋊C4C2×D4×C1114yes—
281C22⋊C4—28no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C42—24no—
286C42C2×D4×C1112yes—
287C42C2×D4×C1111yescharacteristic
288C42C24×C1111yescharacteristic
289C11C2×#166011yescharacteristic, direct product factor, Sylow
290C23—22no—
291C23—42no—
292C23—44no—
293C23C11×#12011yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—42no—
297Q8—81no—
298Q8—82no—
299Q8—84no—
300D4—42no—
301D4—81no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—84no—
312C2×C4—82no—
313C2×C4C11×#12012yes—
314C2×C4C11×#12011yescharacteristic
315C2×C4C22×D4×C1112yes—
316C2×C4C22×D4×C1111yescharacteristic
317C8—24no—
318C8—28no—
319C22—42no—
320C22—44no—
321C22—84no—
322C22C11×#45312yes—
323C22C11×#45614yes—
324C22C2×C11×#12011yescharacteristic
325C4—21no—
326C4—21no—
327C4—22no—
328C4—22no—
329C4—44no—
330C4—42no—
331C4—44no—
332C4—82no—
333C2—82no—
334C2C11×#166014yesdirect product factor
335C2C2×C11×#45311yescharacteristic
336C2C2×C11×#45612yes—
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#501C2semidirect
4. C11×#1660C2direct (N × H)
5. C2×C11×#330C2semidirect
20. C11×#501C22semidirect
27. C11×#330C22semidirect
75. C2×#1660C11direct (N × H)
123. C2×#501C2×C11semidirect
125. #1660C2×C11direct (N × H)
126. C2×#330C2×C11semidirect
170. #501C22×C11semidirect
177. #330C22×C11semidirect
240. C2×C11#1660direct (N × H)
289. C11C2×#1660direct (N × H)
334. C2C11×#1660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5632
C2×C11×#5012
C2×C11×#4972
C11×#16602
C2×C11×#3302
C2×C11×#3292
C2×#166011