Finite Group Databasebeta

← C11×#18390 #14595583

Subgroups — C11×#18390 #14595583

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#3209C212yesmaximal, complemented
3C11×#2563C211yesmaximal, characteristic
4C11×#1602C218yesmaximal, complemented
5C11×#1503C212yesmaximal, complemented
6C11×#1460C211yesmaximal, characteristic
7C11×#554—22no—
8C11×#554—24no—
9D4×Q8×C11—22no—
10C11×#544—21no—
11C11×#543C2214yes—
12C11×#533C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—22no—
15C11×#518—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C11×#494—22no—
18C11×#487—22no—
19C11×#462—24no—
20C11×#451C2218yes—
21C11×#431C2212yes—
22C11×#393C2214yes—
23C11×#390—21no—
24C11×#382—21no—
25C11×#380—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#328C2218yes—
28C11×#323C2214yes—
29C22×Q8×C11—22no—
30C22×Q8×C11C2312yes—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11D412yes—
33C2×C11×Q16—28no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D412yes—
39C11×#125—24no—
40C11×#125—22no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8C2314yes—
48C4×Q8×C11—22no—
49C4×Q8×C11D414yes—
50C4×D4×C11—24no—
51C4×D4×C11—24no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4C2312yes—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C11×C4⋊C8—22no—
67C11×#103—28no—
68C11×C22⋊C8C2314yes—
69C4×C8×C11—22no—
70C11×#95—24no—
71C11×#95C2312yes—
72#18390C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11C2×D412yes—
74C2×Q8×C11—24no—
75C2×Q8×C11—22no—
76C2×Q8×C11—24no—
77C2×Q8×C11—82no—
78C2×Q8×C11—84no—
79C2×Q8×C11C2×D414yes—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11Q1614yescomplemented
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—44no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C11×Q16—88no—
95C2×C8×C11—24no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4C2×D414yes—
109C11×C22⋊C4—28no—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—24no—
112C11×C22⋊C4—84no—
113C42×C11—24no—
114C42×C11—42no—
115C42×C11C2×D412yes—
116C42×C11C2×D412yes—
117#3501C2×C1111yescharacteristic
118#3209C2×C1112yescomplemented
119#2563C2×C1111yescharacteristic
120#1602C2×C1118yescomplemented
121#1503C2×C1112yescomplemented
122#1460C2×C1111yescharacteristic
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11C2×Q1614yes—
128C23×C11C22×D411yescharacteristic
129Q8×C11—44no—
130Q8×C11—48no—
131Q8×C11—44no—
132Q8×C11—84no—
133D4×C11—28no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—44no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—44no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11—84no—
148C2×C4×C11—84no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12012yes—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11C2×Q1612yes—
153C2×C4×C11#13712yes—
154C2×C4×C11C22×D412yes—
155C8×C11—44no—
156#554—22no—
157#554—24no—
158D4×Q8—22no—
159#544—21no—
160#543C22×C1114yes—
161#533C22×C1112yes—
162C2×C4⋊Q8C22×C1111yescharacteristic
163C2×C22⋊Q8—22no—
164#518—21no—
165C2×C4×D4C22×C1111yescharacteristic
166#494—22no—
167#487—22no—
168#462—24no—
169#451C22×C1118yes—
170#431C22×C1112yes—
171#393C22×C1114yes—
172#390—21no—
173#382—21no—
174#380—22no—
175C4×C4⋊C4C22×C1111yescharacteristic
176#328C22×C1118yes—
177#323C22×C1114yes—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—24no—
181C22×C11—44no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—82no—
185C22×C11C2×#12011yescharacteristic
186C22×C11C22×Q1611yescharacteristic
187C22×C11C2×#13711yescharacteristic
188C4×C11—21no—
189C4×C11—22no—
190C4×C11—42no—
191C4×C11—44no—
192C4×C11—44no—
193C4×C11—82no—
194C4×C11—82no—
195C4×C11#45114yes—
196C4×C11#45512yes—
197C22×Q8—22no—
198C22×Q8C23×C1112yes—
199C22×D4D4×C1111yescharacteristic
200C23×C4D4×C1112yes—
201C2×Q16—28no—
202C4⋊Q8—24no—
203C4⋊Q8—22no—
204C4⋊Q8—22no—
205C4⋊Q8D4×C1112yes—
206C4⋊Q8D4×C1112yes—
207#125—24no—
208#125—22no—
209C22⋊Q8—24no—
210C22⋊Q8—24no—
211C22⋊Q8—28no—
212C22⋊Q8—22no—
213C22⋊Q8—24no—
214C22⋊Q8—28no—
215C22⋊Q8C23×C1114yes—
216C4×Q8—22no—
217C4×Q8D4×C1114yes—
218C4×D4—24no—
219C4×D4—24no—
220C4×D4—22no—
221C4×D4—22no—
222#117—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4D4×C1111yescharacteristic
229C2×C22⋊C4—24no—
230C2×C22⋊C4—24no—
231C2×C22⋊C4C23×C1112yes—
232C2×C42—21no—
233C2×C42C23×C1111yescharacteristic
234C4⋊C8—22no—
235#103—28no—
236C22⋊C8C23×C1114yes—
237C4×C8—22no—
238#95—24no—
239#95C23×C1112yes—
240C2×C11—21no—
241C2×C11—21no—
242C2×C11—44no—
243C2×C11C2×#45111yescharacteristic
244C2×C11C2×#45511yescharacteristic
245C2×C11#302711yescharacteristic
246C24C2×D4×C1112yes—
247C2×Q8—24no—
248C2×Q8—22no—
249C2×Q8—24no—
250C2×Q8—82no—
251C2×Q8—84no—
252C2×Q8C2×D4×C1114yes—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4C11×Q1614yescomplemented
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—44no—
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1112yes—
265C22×C4C2×D4×C1111yescharacteristic
266C22×C4C24×C1111yescharacteristic
267Q16—88no—
268C2×C8—24no—
269C4⋊C4—24no—
270C4⋊C4—28no—
271C4⋊C4—22no—
272C4⋊C4—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4C2×D4×C1114yes—
282C22⋊C4—28no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C22⋊C4—84no—
286C42—24no—
287C42—42no—
288C42C2×D4×C1112yes—
289C42C2×D4×C1112yes—
290C11#1839011yescharacteristic, direct product factor, Sylow
291C23—22no—
292C23—22no—
293C23—42no—
294C23—42no—
295C23C2×C11×Q1614yes—
296C23C22×D4×C1111yescharacteristic
297Q8—44no—
298Q8—48no—
299Q8—44no—
300Q8—84no—
301D4—28no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4—84no—
316C2×C4—84no—
317C2×C4C11×#12011yescharacteristic
318C2×C4C11×#12012yes—
319C2×C4C11×#12011yescharacteristic
320C2×C4C2×C11×Q1612yes—
321C2×C4C11×#13712yes—
322C2×C4C22×D4×C1112yes—
323C8—44no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—44no—
328C22—42no—
329C22—42no—
330C22—82no—
331C22C2×C11×#12011yescharacteristic
332C22C22×C11×Q1611yescharacteristic
333C22C2×C11×#13711yescharacteristic
334C4—21no—
335C4—22no—
336C4—42no—
337C4—44no—
338C4—44no—
339C4—82no—
340C4—82no—
341C4C11×#45114yes—
342C4C11×#45512yes—
343C2—21no—
344C2—21no—
345C2—44no—
346C2C2×C11×#45111yescharacteristic
347C2C2×C11×#45511yescharacteristic
348C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3209C2semidirect
4. C11×#1602C2semidirect
5. C11×#1503C2semidirect
72. #18390C11direct (N × H)
82. C2×D4×C11Q16semidirect
118. #3209C2×C11semidirect
120. #1602C2×C11semidirect
121. #1503C2×C11semidirect
255. C2×D4C11×Q16semidirect
290. C11#18390direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#32092
C11×#25632
C11×#16022
C11×#15032
C11×#14602
#1839011