Finite Group Databasebeta

← C11×#23918 #14601111

Subgroups — C11×#23918 #14601111

Order 2816.

2596 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C212yesmaximal, complemented
2C2×C11×#447C214yesmaximal, complemented
3C11×#1999C214yesmaximal, complemented
4C11×#1874C214yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic, complemented
6C23×D4×C11—22no—
7C23×D4×C11C2212yescomplemented
8C24×C4×C11C2211yescharacteristic
9C22×C11×D8C2214yescomplemented
10C2×C11×#121—22no—
11C2×C11×#121—22no—
12C2×C11×#121—216no—
13C2×C11×#121C2214yes—
14C2×C11×#121C2214yescomplemented
15C22×C11×C4⋊C4C2212yescomplemented
16C22×C11×C22⋊C4—22no—
17C11×#447—216no—
18C2×C11×#102C2218yescomplemented
19C2×C11×C22⋊C8C2214yescomplemented
20C2×C11×C22⋊C8C2212yescomplemented
21C11×#340C2214yescomplemented
22C25×C11—22no—
23C25×C11D411yescharacteristic
24C22×D4×C11—216no—
25C22×D4×C11—24no—
26C22×D4×C11—24no—
27C22×D4×C11—28no—
28C22×D4×C11—22no—
29C22×D4×C11—28no—
30C22×D4×C11—44no—
31C22×D4×C11—48no—
32C22×D4×C11—48no—
33C22×D4×C11C2314yes—
34C23×C4×C11—22no—
35C23×C4×C11—28no—
36C23×C4×C11—42no—
37C23×C4×C11D412yes—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C2×C11×D8—216no—
42C2×C11×D8—44no—
43C22×C8×C11C2314yes—
44C11×#121—216no—
45C11×#121—216no—
46C11×#121—28no—
47C11×#121—28no—
48C11×#121—28no—
49C11×#121D4116yescomplemented
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—28no—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C22⋊C4—216no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C11×#102—216no—
57C11×C22⋊C8—28no—
58C11×C22⋊C8—42no—
59#23918C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—24no—
61C24×C11—24no—
62C24×C11—28no—
63C24×C11—24no—
64C24×C11—41no—
65C24×C11—41no—
66C24×C11—44no—
67C24×C11—44no—
68C24×C11—44no—
69C24×C11—44no—
70C24×C11—44no—
71C24×C11—44no—
72C24×C11D814yescomplemented
73C24×C11C2×D411yescharacteristic
74C24×C11C2×D412yes—
75C2×D4×C11—28no—
76C2×D4×C11—216no—
77C2×D4×C11—216no—
78C2×D4×C11—28no—
79C2×D4×C11—24no—
80C2×D4×C11—28no—
81C2×D4×C11—432no—
82C2×D4×C11—44no—
83C2×D4×C11—464no—
84C2×D4×C11—48no—
85C2×D4×C11—48no—
86C2×D4×C11—48no—
87C2×D4×C11—48no—
88C2×D4×C11—44no—
89C2×D4×C11C2×D418yescomplemented
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—28no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—41no—
100C22×C4×C11—42no—
101C22×C4×C11—416no—
102C22×C4×C11—44no—
103C22×C4×C11—44no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D418yes—
107C22×C4×C11C2411yescharacteristic
108C11×D8—416no—
109C2×C8×C11—28no—
110C2×C8×C11—24no—
111C11×C4⋊C4—28no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4C2×D418yescomplemented
114C11×C22⋊C4—216no—
115C11×C22⋊C4—216no—
116C22×#121C2×C1112yescomplemented
117C2×#447C2×C1114yescomplemented
118#1999C2×C1114yescomplemented
119#1874C2×C1114yescomplemented
120#1779C2×C1111yescharacteristic, complemented
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—21no—
127C23×C11—22no—
128C23×C11—21no—
129C23×C11—216no—
130C23×C11—28no—
131C23×C11—44no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—48no—
135C23×C11—416no—
136C23×C11—416no—
137C23×C11—416no—
138C23×C11—44no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11—88no—
145C23×C11—88no—
146C23×C11—88no—
147C23×C11—88no—
148C23×C11#12014yes—
149C23×C11C2×D812yes—
150C23×C11C2×D814yes—
151C23×C11AGL(1,ℤ/8)14yes—
152C23×C11C22×D411yescharacteristic
153D4×C11—216no—
154D4×C11—416no—
155D4×C11—432no—
156D4×C11—432no—
157D4×C11—48no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—216no—
161C2×C4×C11—22no—
162C2×C4×C11—28no—
163C2×C4×C11—21no—
164C2×C4×C11—44no—
165C2×C4×C11—48no—
166C2×C4×C11—416no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—44no—
170C2×C4×C11#12014yes—
171C2×C4×C11C22×D414yes—
172C2×C4×C11H(5,𝔽2)12yes—
173C8×C11—44no—
174C23×D4—22no—
175C23×D4C22×C1112yescomplemented
176C24×C4C22×C1111yescharacteristic
177C22×D8C22×C1114yescomplemented
178C2×#121—22no—
179C2×#121—22no—
180C2×#121—216no—
181C2×#121C22×C1114yes—
182C2×#121C22×C1114yescomplemented
183C22×C4⋊C4C22×C1112yescomplemented
184C22×C22⋊C4—22no—
185#447—216no—
186C2×#102C22×C1118yescomplemented
187C2×C22⋊C8C22×C1114yescomplemented
188C2×C22⋊C8C22×C1112yescomplemented
189#340C22×C1114yescomplemented
190C22×C11—24no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—24no—
194C22×C11—24no—
195C22×C11—24no—
196C22×C11—22no—
197C22×C11—24no—
198C22×C11—416no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—42no—
202C22×C11—48no—
203C22×C11—48no—
204C22×C11—48no—
205C22×C11—832no—
206C22×C11—84no—
207C22×C11—84no—
208C22×C11—84no—
209C22×C11—84no—
210C22×C11#44718yescomplemented
211C22×C11C2×#12012yes—
212C22×C11#53411yescharacteristic
213C22×C11C22×D811yescharacteristic
214C22×C11C2×AGL(1,ℤ/8)12yes—
215C22×C11#57511yescharacteristic
216C4×C11—24no—
217C4×C11—41no—
218C4×C11—48no—
219C4×C11D4214yes—
220C25—22no—
221C25D4×C1111yescharacteristic
222C22×D4—216no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—28no—
226C22×D4—22no—
227C22×D4—28no—
228C22×D4—44no—
229C22×D4—48no—
230C22×D4—48no—
231C22×D4C23×C1114yes—
232C23×C4—22no—
233C23×C4—28no—
234C23×C4—42no—
235C23×C4D4×C1112yes—
236C23×C4D4×C1111yescharacteristic
237C23×C4C23×C1111yescharacteristic
238C23×C4C23×C1112yes—
239C2×D8—216no—
240C2×D8—44no—
241C22×C8C23×C1114yes—
242#121—216no—
243#121—216no—
244#121—28no—
245#121—28no—
246#121—28no—
247#121D4×C11116yescomplemented
248C2×C4⋊C4—22no—
249C2×C4⋊C4—28no—
250C2×C4⋊C4C23×C1114yes—
251C2×C22⋊C4—216no—
252C2×C22⋊C4—24no—
253C2×C22⋊C4—24no—
254#102—216no—
255C22⋊C8—28no—
256C22⋊C8—42no—
257C2×C11—28no—
258C2×C11—42no—
259C2×C11—88no—
260C2×C11#240311yescharacteristic
261C2×C11C2×#44712yes—
262C2×C11#300612yes—
263C2×C11#318611yescharacteristic
264C2×C11#319211yescharacteristic
265C24—24no—
266C24—24no—
267C24—28no—
268C24—24no—
269C24—41no—
270C24—41no—
271C24—44no—
272C24—44no—
273C24—44no—
274C24—44no—
275C24—44no—
276C24—44no—
277C24C11×D814yescomplemented
278C24C2×D4×C1111yescharacteristic
279C24C2×D4×C1112yes—
280C2×D4—28no—
281C2×D4—216no—
282C2×D4—216no—
283C2×D4—28no—
284C2×D4—24no—
285C2×D4—28no—
286C2×D4—432no—
287C2×D4—44no—
288C2×D4—464no—
289C2×D4—48no—
290C2×D4—48no—
291C2×D4—48no—
292C2×D4—48no—
293C2×D4—44no—
294C2×D4C2×D4×C1118yescomplemented
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—28no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—42no—
306C22×C4—416no—
307C22×C4—44no—
308C22×C4—44no—
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1118yes—
312C22×C4C24×C1111yescharacteristic
313D8—416no—
314C2×C8—28no—
315C2×C8—24no—
316C4⋊C4—28no—
317C4⋊C4—24no—
318C4⋊C4C2×D4×C1118yescomplemented
319C22⋊C4—216no—
320C22⋊C4—216no—
321C11#2391811yescharacteristic, direct product factor, Sylow
322C23—22no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—21no—
328C23—22no—
329C23—21no—
330C23—216no—
331C23—28no—
332C23—44no—
333C23—44no—
334C23—44no—
335C23—48no—
336C23—416no—
337C23—416no—
338C23—416no—
339C23—44no—
340C23—44no—
341C23—44no—
342C23—44no—
343C23—44no—
344C23—44no—
345C23—88no—
346C23—88no—
347C23—88no—
348C23—88no—
349C23C11×#12014yes—
350C23C2×C11×D812yes—
351C23C2×C11×D814yes—
352C23C11×AGL(1,ℤ/8)14yes—
353C23C22×D4×C1111yescharacteristic
354D4—216no—
355D4—416no—
356D4—432no—
357D4—432no—
358D4—48no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—216no—
362C2×C4—22no—
363C2×C4—28no—
364C2×C4—21no—
365C2×C4—44no—
366C2×C4—48no—
367C2×C4—416no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4C11×#12014yes—
372C2×C4C22×D4×C1114yes—
373C2×C4C11×H(5,𝔽2)12yes—
374C8—44no—
375C22—24no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—24no—
380C22—24no—
381C22—22no—
382C22—24no—
383C22—416no—
384C22—41no—
385C22—41no—
386C22—42no—
387C22—48no—
388C22—48no—
389C22—48no—
390C22—832no—
391C22—84no—
392C22—84no—
393C22—84no—
394C22—84no—
395C22C11×#44718yescomplemented
396C22C2×C11×#12012yes—
397C22C11×#53411yescharacteristic
398C22C22×C11×D811yescharacteristic
399C22C2×C11×AGL(1,ℤ/8)12yes—
400C22C11×#57511yescharacteristic
401C4—24no—
402C4—41no—
403C4—48no—
404C4D42×C1114yes—
405C2—28no—
406C2—42no—
407C2—88no—
408C2C11×#240311yescharacteristic
409C2C2×C11×#44712yes—
410C2C11×#300612yes—
411C2C11×#318611yescharacteristic
412C2C11×#319211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#121C2semidirect
2. C2×C11×#447C2semidirect
3. C11×#1999C2semidirect
4. C11×#1874C2semidirect
5. C11×#1779C2semidirect
7. C23×D4×C11C22semidirect
9. C22×C11×D8C22semidirect
14. C2×C11×#121C22semidirect
15. C22×C11×C4⋊C4C22semidirect
18. C2×C11×#102C22semidirect
19. C2×C11×C22⋊C8C22semidirect
20. C2×C11×C22⋊C8C22semidirect
21. C11×#340C22semidirect
49. C11×#121D4semidirect
59. #23918C11direct (N × H)
72. C24×C11D8semidirect
89. C2×D4×C11C2×D4semidirect
113. C11×C4⋊C4C2×D4semidirect
116. C22×#121C2×C11semidirect
117. C2×#447C2×C11semidirect
118. #1999C2×C11semidirect
119. #1874C2×C11semidirect
120. #1779C2×C11semidirect
175. C23×D4C22×C11semidirect
177. C22×D8C22×C11semidirect
182. C2×#121C22×C11semidirect
183. C22×C4⋊C4C22×C11semidirect
186. C2×#102C22×C11semidirect
187. C2×C22⋊C8C22×C11semidirect
188. C2×C22⋊C8C22×C11semidirect
189. #340C22×C11semidirect
210. C22×C11#447semidirect
247. #121D4×C11semidirect
277. C24C11×D8semidirect
294. C2×D4C2×D4×C11semidirect
318. C4⋊C4C2×D4×C11semidirect
321. C11#23918direct (N × H)
395. C22C11×#447semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C2×C11×#4472
C11×#19992
C11×#18742
C11×#17792
#2391811