Finite Group Databasebeta

← C11×#2416 #13065254

Subgroups — C11×#2416 #13065254

Order 1408.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C212yesmaximal, complemented
2C2×C11×#121C211yesmaximal, characteristic, complemented
3C2×C11×#121C211yesmaximal, characteristic, complemented
4C2×C4×D4×C11C211yesmaximal, characteristic, complemented
5C22×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#396C212yesmaximal, complemented
7C11×#394C212yesmaximal, complemented
8C11×#390C211yesmaximal, characteristic, complemented
9C11×#389C211yesmaximal, characteristic, complemented
10C11×#386C212yesmaximal, complemented
11C11×#380C211yesmaximal, characteristic, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C22×D4×C11C2212yes—
15C22×D4×C11C2211yescharacteristic
16C23×C4×C11C2211yescharacteristic
17C23×C4×C11C2212yes—
18C23×C4×C11C2211yescharacteristic
19C11×#121—28no—
20C11×#121—24no—
21C11×#121—24no—
22C4×D4×C11—24no—
23C2×C11×C4⋊C4—24no—
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2212yes—
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2212yes—
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2212yes—
33C2×C11×C22⋊C4C2212yes—
34C2×C11×C22⋊C4C2212yes—
35C2×C11×C22⋊C4C2212yes—
36C2×C11×C22⋊C4C2212yes—
37C2×C42×C11C2211yescharacteristic
38C11×#95C2212yes—
39C11×#95C2212yes—
40C24×C11C2312yes—
41C24×C11C2311yescharacteristic
42C24×C11C2311yescharacteristic
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—24no—
46C2×D4×C11—24no—
47C2×D4×C11—24no—
48C2×D4×C11—24no—
49C2×D4×C11—24no—
50C2×D4×C11—22no—
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C2×D4×C11—42no—
54C2×D4×C11D414yescomplemented
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—24no—
58C22×C4×C11—24no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—42no—
63C22×C4×C11D414yescomplemented
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2312yes—
67C22×C4×C11C2312yes—
68C22×C4×C11C2312yes—
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C11×C4⋊C4—24no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4D414yescomplemented
78C11×C22⋊C4—22no—
79C11×C22⋊C4—24no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—24no—
82C11×C22⋊C4—24no—
83C11×C22⋊C4—24no—
84C11×C22⋊C4—42no—
85C42×C11—22no—
86#2416C1111yesmaximal, characteristic, direct product factor, Sylow
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11C2×D412yes—
105C23×C11C2×D412yes—
106C23×C11C2×D412yes—
107C23×C11#4112yes—
108C23×C11C2411yescharacteristic
109D4×C11—28no—
110D4×C11—48no—
111D4×C11—48no—
112D4×C11—44no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—28no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—48no—
133C2×C4×C11—44no—
134C2×C4×C11C2×D412yes—
135C2×C4×C11C2×D412yes—
136C2×C4×C11C2×D414yes—
137C2×C4×C11C2×D412yes—
138C2×C4×C11C2×D412yes—
139C2×C4×C11#4112yes—
140C2×#121C2×C1112yescomplemented
141C2×#121C2×C1111yescharacteristic, complemented
142C2×#121C2×C1111yescharacteristic, complemented
143C2×C4×D4C2×C1111yescharacteristic, complemented
144C22×C4⋊C4C2×C1111yescharacteristic, complemented
145#396C2×C1112yescomplemented
146#394C2×C1112yescomplemented
147#390C2×C1111yescharacteristic, complemented
148#389C2×C1111yescharacteristic, complemented
149#386C2×C1112yescomplemented
150#380C2×C1111yescharacteristic, complemented
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11#12114yescomplemented
172C22×C11C22×D411yescharacteristic
173C22×C11C22×D411yescharacteristic
174C22×C11C22×D411yescharacteristic
175C22×C11C2×#4111yescharacteristic
176C22×C11C2×#4111yescharacteristic
177C22×C11H(5,𝔽2)11yescharacteristic
178C22×C112−1+411yescharacteristic
179C4×C11—22no—
180C4×C11—22no—
181C4×C11—24no—
182C4×C11—41no—
183C4×C11—42no—
184C4×C11—41no—
185C4×C11—42no—
186C4×C11#12114yescomplemented
187C22×D4C22×C1112yes—
188C22×D4C22×C1111yescharacteristic
189C22×D4C22×C1112yes—
190C22×D4C22×C1111yescharacteristic
191C23×C4C22×C1111yescharacteristic
192C23×C4C22×C1112yes—
193C23×C4C22×C1111yescharacteristic
194#121—28no—
195#121—24no—
196#121—24no—
197C4×D4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4C22×C1111yescharacteristic
200C2×C4⋊C4C22×C1112yes—
201C2×C4⋊C4C22×C1111yescharacteristic
202C2×C4⋊C4C22×C1111yescharacteristic
203C2×C4⋊C4C22×C1112yes—
204C2×C4⋊C4C22×C1111yescharacteristic
205C2×C22⋊C4C22×C1111yescharacteristic
206C2×C22⋊C4C22×C1111yescharacteristic
207C2×C22⋊C4C22×C1112yes—
208C2×C22⋊C4C22×C1112yes—
209C2×C22⋊C4C22×C1112yes—
210C2×C22⋊C4C22×C1112yes—
211C2×C22⋊C4C22×C1112yes—
212C2×C42C22×C1111yescharacteristic
213#95C22×C1112yes—
214#95C22×C1112yes—
215C2×C11—24no—
216C2×C11—42no—
217C2×C11—82no—
218C2×C11C2×#12111yescharacteristic
219C2×C11C2×#12111yescharacteristic
220C2×C11#53711yescharacteristic
221C2×C11D4211yescharacteristic
222C2×C11#54711yescharacteristic
223C2×C11#54811yescharacteristic
224C2×C11#55311yescharacteristic
225C24C23×C1112yes—
226C24C23×C1111yescharacteristic
227C24C23×C1111yescharacteristic
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—24no—
231C2×D4—24no—
232C2×D4—24no—
233C2×D4—24no—
234C2×D4—24no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—42no—
239C2×D4D4×C1114yescomplemented
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4D4×C1114yescomplemented
249C22×C4C23×C1111yescharacteristic
250C22×C4C23×C1111yescharacteristic
251C22×C4C23×C1112yes—
252C22×C4C23×C1112yes—
253C22×C4C23×C1112yes—
254C22×C4C23×C1111yescharacteristic
255C22×C4C23×C1111yescharacteristic
256C22×C4C23×C1111yescharacteristic
257C4⋊C4—24no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—24no—
261C4⋊C4—22no—
262C4⋊C4D4×C1114yescomplemented
263C22⋊C4—22no—
264C22⋊C4—24no—
265C22⋊C4—22no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C22⋊C4—24no—
269C22⋊C4—42no—
270C42—22no—
271C11#241611yescharacteristic, direct product factor, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23C2×D4×C1112yes—
290C23C2×D4×C1112yes—
291C23C2×D4×C1112yes—
292C23C11×#4112yes—
293C23C24×C1111yescharacteristic
294D4—28no—
295D4—48no—
296D4—48no—
297D4—44no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—28no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—48no—
318C2×C4—44no—
319C2×C4C2×D4×C1112yes—
320C2×C4C2×D4×C1112yes—
321C2×C4C2×D4×C1114yes—
322C2×C4C2×D4×C1112yes—
323C2×C4C2×D4×C1112yes—
324C2×C4C11×#4112yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—22no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22C11×#12114yescomplemented
346C22C22×D4×C1111yescharacteristic
347C22C22×D4×C1111yescharacteristic
348C22C22×D4×C1111yescharacteristic
349C22C2×C11×#4111yescharacteristic
350C22C2×C11×#4111yescharacteristic
351C22C11×H(5,𝔽2)11yescharacteristic
352C22C11×2−1+411yescharacteristic
353C4—22no—
354C4—22no—
355C4—24no—
356C4—41no—
357C4—42no—
358C4—41no—
359C4—42no—
360C4C11×#12114yescomplemented
361C2—24no—
362C2—42no—
363C2—82no—
364C2C2×C11×#12111yescharacteristic
365C2C2×C11×#12111yescharacteristic
366C2C11×#53711yescharacteristic
367C2D42×C1111yescharacteristic
368C2C11×#54711yescharacteristic
369C2C11×#54811yescharacteristic
370C2C11×#55311yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×C11×#121C2semidirect
3. C2×C11×#121C2semidirect
4. C2×C4×D4×C11C2semidirect
5. C22×C11×C4⋊C4C2semidirect
6. C11×#396C2semidirect
7. C11×#394C2semidirect
8. C11×#390C2semidirect
9. C11×#389C2semidirect
10. C11×#386C2semidirect
11. C11×#380C2semidirect
54. C2×D4×C11D4semidirect
63. C22×C4×C11D4semidirect
77. C11×C4⋊C4D4semidirect
86. #2416C11direct (N × H)
140. C2×#121C2×C11semidirect
141. C2×#121C2×C11semidirect
142. C2×#121C2×C11semidirect
143. C2×C4×D4C2×C11semidirect
144. C22×C4⋊C4C2×C11semidirect
145. #396C2×C11semidirect
146. #394C2×C11semidirect
147. #390C2×C11semidirect
148. #389C2×C11semidirect
149. #386C2×C11semidirect
150. #380C2×C11semidirect
171. C22×C11#121semidirect
186. C4×C11#121semidirect
239. C2×D4D4×C11semidirect
248. C22×C4D4×C11semidirect
262. C4⋊C4D4×C11semidirect
271. C11#2416direct (N × H)
345. C22C11×#121semidirect
360. C4C11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×C4×D4×C112
C22×C11×C4⋊C42
C11×#3962
C11×#3942
C11×#3902
C11×#3892
C11×#3862
C11×#3802
#241611