Finite Group Databasebeta

← C11×#10980 #14588173

Subgroups — C11×#10980 #14588173

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C22×C11×#99C214yesmaximal, complemented
3C11×C22⋊#95C212yesmaximal, complemented
4C23×D4×C11C411yescharacteristic, complemented
5C23×D4×C11C2212yes—
6C24×C4×C11C2211yescharacteristic
7C2×C11×#121—28no—
8C2×C11×#121—24no—
9C22×C11×C4⋊C4C411yescharacteristic, complemented
10C22×C11×C22⋊C4C412yescomplemented
11C22×C11×C22⋊C4C2214yes—
12C2×C11×#99—28no—
13C2×C11×#99—216no—
14C2×C11×#95—24no—
15C25×C11C2×C412yes—
16C25×C11C2311yescharacteristic
17C22×D4×C11—24no—
18C22×D4×C11—24no—
19C22×D4×C11—24no—
20C22×D4×C11—28no—
21C22×D4×C11—28no—
22C22×D4×C11—22no—
23C22×D4×C11—44no—
24C22×D4×C11D418yes—
25C23×C4×C11—24no—
26C23×C4×C11—24no—
27C23×C4×C11—44no—
28C23×C4×C11C2×C412yes—
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11D414yes—
32C11×#121—232no—
33C2×C11×C4⋊C4—24no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C22⋊C4—24no—
36C2×C11×C22⋊C4—24no—
37C2×C11×C22⋊C4—24no—
38C2×C11×C22⋊C4—28no—
39C2×C11×C22⋊C4—28no—
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4D418yescomplemented
42C11×#99—232no—
43C11×#95—48no—
44#10980C1111yesmaximal, characteristic, direct product factor, Sylow
45C24×C11—22no—
46C24×C11—22no—
47C24×C11—28no—
48C24×C11—42no—
49C24×C11—42no—
50C24×C11—44no—
51C24×C11—44no—
52C24×C11C22⋊C414yes—
53C24×C11C22×C411yescharacteristic
54C24×C11C2×D412yes—
55C24×C11C2×D414yes—
56C24×C11C2×D414yes—
57C24×C11#4114yes—
58C2×D4×C11—28no—
59C2×D4×C11—28no—
60C2×D4×C11—216no—
61C2×D4×C11—216no—
62C2×D4×C11—28no—
63C2×D4×C11—416no—
64C2×D4×C11—44no—
65C2×D4×C11—44no—
66C2×D4×C11—48no—
67C2×D4×C11—48no—
68C2×D4×C11—44no—
69C2×D4×C11—44no—
70C2×D4×C11—44no—
71C2×D4×C11—44no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—28no—
78C22×C4×C11—28no—
79C22×C4×C11—28no—
80C22×C4×C11—28no—
81C22×C4×C11—42no—
82C22×C4×C11—44no—
83C22×C4×C11—416no—
84C22×C4×C11—48no—
85C22×C4×C11—48no—
86C22×C4×C11—44no—
87C22×C4×C11—44no—
88C22×C4×C11C22⋊C414yes—
89C22×C4×C11C22⋊C412yes—
90C22×C4×C11C22⋊C412yes—
91C11×C4⋊C4—28no—
92C11×C22⋊C4—216no—
93C11×C22⋊C4—216no—
94C11×C22⋊C4—48no—
95C22×#121C2×C1111yescharacteristic
96C22×#99C2×C1114yescomplemented
97C22⋊#95C2×C1112yescomplemented
98C23×C11—24no—
99C23×C11—22no—
100C23×C11—24no—
101C23×C11—22no—
102C23×C11—24no—
103C23×C11—28no—
104C23×C11—44no—
105C23×C11—48no—
106C23×C11—44no—
107C23×C11—48no—
108C23×C11—44no—
109C23×C11—44no—
110C23×C11—44no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11—44no—
114C23×C11—44no—
115C23×C11—44no—
116C23×C11—816no—
117C23×C11C2×C22⋊C412yes—
118C23×C11C2×C22⋊C411yescharacteristic
119C23×C11C4×D414yes—
120C23×C11#12014yes—
121C23×C11#12014yes—
122C23×C11#12114yes—
123C23×C11#12118yes—
124C23×C11#12314yes—
125C23×C11#12412yes—
126C23×C11#12712yes—
127D4×C11—416no—
128D4×C11—416no—
129D4×C11—416no—
130C2×C4×C11—28no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—28no—
136C2×C4×C11—24no—
137C2×C4×C11—416no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11—44no—
141C2×C4×C11—416no—
142C2×C4×C11—48no—
143C2×C4×C11—88no—
144C2×C4×C11—84no—
145C2×C4×C11—84no—
146C2×C4×C11#9914yescomplemented
147C23×D4C4×C1111yescharacteristic, complemented
148C23×D4C22×C1112yes—
149C24×C4C22×C1111yescharacteristic
150C2×#121—28no—
151C2×#121—24no—
152C22×C4⋊C4C4×C1111yescharacteristic, complemented
153C22×C22⋊C4C4×C1112yescomplemented
154C22×C22⋊C4C22×C1114yes—
155C2×#99—28no—
156C2×#99—216no—
157C2×#95—24no—
158C22×C11—28no—
159C22×C11—24no—
160C22×C11—28no—
161C22×C11—24no—
162C22×C11—22no—
163C22×C11—24no—
164C22×C11—24no—
165C22×C11—22no—
166C22×C11—44no—
167C22×C11—48no—
168C22×C11—44no—
169C22×C11—44no—
170C22×C11—44no—
171C22×C11—44no—
172C22×C11—88no—
173C22×C11—88no—
174C22×C11—88no—
175C22×C11#37911yescharacteristic
176C22×C11#38614yes—
177C22×C11#39012yes—
178C22×C11#39214yes—
179C22×C11#39414yes—
180C22×C11C2×#9912yes—
181C22×C11#41012yes—
182C4×C11—24no—
183C4×C11—44no—
184C4×C11—42no—
185C4×C11—88no—
186C25C2×C4×C1112yes—
187C25C23×C1111yescharacteristic
188C22×D4—24no—
189C22×D4—24no—
190C22×D4—24no—
191C22×D4—28no—
192C22×D4—28no—
193C22×D4—22no—
194C22×D4—44no—
195C22×D4D4×C1118yes—
196C23×C4—24no—
197C23×C4—24no—
198C23×C4—44no—
199C23×C4C2×C4×C1112yes—
200C23×C4C2×C4×C1111yescharacteristic
201C23×C4C2×C4×C1111yescharacteristic
202C23×C4D4×C1114yes—
203#121—232no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—22no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—28no—
210C2×C22⋊C4—28no—
211C2×C22⋊C4—24no—
212C2×C22⋊C4D4×C1118yescomplemented
213#99—232no—
214#95—48no—
215C2×C11—24no—
216C2×C11—24no—
217C2×C11—24no—
218C2×C11—84no—
219C2×C11#143811yescharacteristic
220C2×C11#178111yescharacteristic
221C2×C11#178211yescharacteristic
222C2×C11#196414yes—
223C24—22no—
224C24—22no—
225C24—28no—
226C24—42no—
227C24—42no—
228C24—44no—
229C24—44no—
230C24C11×C22⋊C414yes—
231C24C22×C4×C1111yescharacteristic
232C24C2×D4×C1112yes—
233C24C2×D4×C1114yes—
234C24C2×D4×C1114yes—
235C24C11×#4114yes—
236C2×D4—28no—
237C2×D4—28no—
238C2×D4—216no—
239C2×D4—216no—
240C2×D4—28no—
241C2×D4—416no—
242C2×D4—44no—
243C2×D4—44no—
244C2×D4—48no—
245C2×D4—48no—
246C2×D4—44no—
247C2×D4—44no—
248C2×D4—44no—
249C2×D4—44no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—28no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—416no—
262C22×C4—48no—
263C22×C4—48no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4C11×C22⋊C412yes—
267C22×C4C11×C22⋊C414yes—
268C22×C4C11×C22⋊C412yes—
269C4⋊C4—28no—
270C22⋊C4—216no—
271C22⋊C4—216no—
272C22⋊C4—48no—
273C11#1098011yescharacteristic, direct product factor, Sylow
274C23—24no—
275C23—22no—
276C23—24no—
277C23—22no—
278C23—24no—
279C23—28no—
280C23—44no—
281C23—48no—
282C23—44no—
283C23—48no—
284C23—44no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23—44no—
289C23—44no—
290C23—44no—
291C23—44no—
292C23—816no—
293C23C2×C11×C22⋊C412yes—
294C23C2×C11×C22⋊C411yescharacteristic
295C23C4×D4×C1114yes—
296C23C11×#12014yes—
297C23C11×#12014yes—
298C23C11×#12114yes—
299C23C11×#12118yes—
300C23C11×#12314yes—
301C23C11×#12412yes—
302C23C11×#12712yes—
303D4—416no—
304D4—416no—
305D4—416no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—416no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—416no—
318C2×C4—48no—
319C2×C4—88no—
320C2×C4—84no—
321C2×C4—84no—
322C2×C4C11×#9914yescomplemented
323C22—28no—
324C22—24no—
325C22—28no—
326C22—24no—
327C22—22no—
328C22—24no—
329C22—24no—
330C22—22no—
331C22—44no—
332C22—48no—
333C22—44no—
334C22—44no—
335C22—44no—
336C22—44no—
337C22—88no—
338C22—88no—
339C22—88no—
340C22C11×#37911yescharacteristic
341C22C11×#38614yes—
342C22C11×#39012yes—
343C22C11×#39214yes—
344C22C11×#39414yes—
345C22C2×C11×#9912yes—
346C22C11×#41012yes—
347C4—24no—
348C4—44no—
349C4—42no—
350C4—88no—
351C2—24no—
352C2—24no—
353C2—24no—
354C2—84no—
355C2C11×#143811yescharacteristic
356C2C11×#178111yescharacteristic
357C2C11×#178211yescharacteristic
358C2C11×#196414yes—
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC22×C11×#121C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#99C2semidirect
3. C11×C22⋊#95C2semidirect
4. C23×D4×C11C4semidirect
9. C22×C11×C4⋊C4C4semidirect
10. C22×C11×C22⋊C4C4semidirect
41. C2×C11×C22⋊C4D4semidirect
44. #10980C11direct (N × H)
96. C22×#99C2×C11semidirect
97. C22⋊#95C2×C11semidirect
146. C2×C4×C11#99semidirect
147. C23×D4C4×C11semidirect
152. C22×C4⋊C4C4×C11semidirect
153. C22×C22⋊C4C4×C11semidirect
212. C2×C22⋊C4D4×C11semidirect
273. C11#10980direct (N × H)
322. C2×C4C11×#99semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C22×C11×#992
C11×C22⋊#952
#1098011