Finite Group Databasebeta

← C11×#23452 #14600645

Subgroups — C11×#23452 #14600645

Order 2816.

1498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C11×#417C212yesmaximal
3C11×#2297C211yesmaximal, characteristic
4C11×#2024C214yesmaximal, complemented
5C11×#2023C214yesmaximal, complemented
6C11×#1736C212yesmaximal, complemented
7C11×#1728C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×Q8×C11—21no—
10C22×C11×M16C2212yes—
11C2×C11×C4⋊Q8—28no—
12C2×C11×C4⋊Q8—22no—
13C2×C11×C4⋊Q8C2214yes—
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C11×#417—28no—
19C2×C11×#103C2214yes—
20C2×C11×#102C2214yes—
21C11×#391C2212yes—
22C11×#390C2212yes—
23C11×#386—21no—
24C11×#386—21no—
25C4×C11×C22⋊C4—22no—
26C11×#340C2218yes—
27C11×#336C2214yes—
28C2×C11×#41—22no—
29C2×C11×#41—24no—
30C2×C11×#41—24no—
31C2×C11×#41Q814yescomplemented
32C22×Q8×C11—28no—
33C22×Q8×C11—24no—
34C22×Q8×C11—48no—
35C22×Q8×C11C2311yescharacteristic
36C22×D4×C11—21no—
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11—22no—
39C23×C4×C11—21no—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C2×C11×M16—24no—
44C2×C11×M16—24no—
45C2×C11×M16—24no—
46C22×C8×C11C2314yes—
47C11×C4⋊Q8—216no—
48C11×C4⋊Q8—216no—
49C11×#117—24no—
50C2×C11×C4⋊C4—28no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4D418yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2314yes—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C42×C11—24no—
61C2×C42×C11—21no—
62C2×C42×C11D412yes—
63C2×C42×C11C2312yes—
64C11×#103—28no—
65C11×#102—28no—
66C11×#95—22no—
67C11×#95—22no—
68#23452C1111yesmaximal, characteristic, direct product factor, Sylow
69C24×C11—21no—
70C24×C11C2×D411yescharacteristic
71C11×#41—216no—
72C11×#41—48no—
73C2×Q8×C11—216no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—432no—
78C2×Q8×C11—48no—
79C2×Q8×C11—48no—
80C2×Q8×C11C2×Q812yescomplemented
81C2×D4×C11—24no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11C2×Q812yescomplemented
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—28no—
93C22×C4×C11—21no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—48no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D414yes—
104C22×C4×C11C2×Q812yes—
105C22×C4×C11#4114yes—
106C22×C4×C11#4112yes—
107C22×C4×C11C2411yescharacteristic
108C11×M16—48no—
109C2×C8×C11—24no—
110C2×C8×C11—24no—
111C2×C8×C11—24no—
112C11×C4⋊C4—216no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4C2×D418yes—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—44no—
119C11×C22⋊C4—44no—
120C42×C11—24no—
121C42×C11—24no—
122C42×C11—42no—
123C22×C4⋊Q8C2×C1111yescharacteristic, complemented
124C2×#417C2×C1112yes—
125#2297C2×C1111yescharacteristic
126#2024C2×C1114yescomplemented
127#2023C2×C1114yescomplemented
128#1736C2×C1112yescomplemented
129#1728C2×C1111yescharacteristic, complemented
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11#12012yes—
138C23×C11C22⋊Q812yes—
139C23×C11#12412yes—
140C23×C11C22×D411yescharacteristic
141Q8×C11—24no—
142Q8×C11—432no—
143Q8×C11—42no—
144D4×C11—24no—
145D4×C11—48no—
146D4×C11—42no—
147C2×C4×C11—28no—
148C2×C4×C11—28no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—28no—
154C2×C4×C11—22no—
155C2×C4×C11—416no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—48no—
159C2×C4×C11—48no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11#12012yes—
164C2×C4×C11C22⋊Q818yes—
165C2×C4×C11C22⋊Q812yes—
166C2×C4×C11#12418yes—
167C2×C4×C11#12412yes—
168C2×C4×C11AGL(1,ℤ/8)14yes—
169C2×C4×C11#13714yes—
170C2×C4×C11C22×D412yes—
171C2×C4×C11C22×Q811yescharacteristic
172C2×C4×C11C2×#4112yes—
173C2×C4×C11C2×#4111yescharacteristic
174C8×C11—44no—
175C22×#41C22×C1111yescharacteristic
176C23×Q8—21no—
177C22×M16C22×C1112yes—
178C2×C4⋊Q8—28no—
179C2×C4⋊Q8—22no—
180C2×C4⋊Q8C22×C1114yes—
181C2×#117C22×C1111yescharacteristic
182C22×C4⋊C4—21no—
183C22×C4⋊C4C22×C1112yes—
184C22×C42C22×C1111yescharacteristic
185#417—28no—
186C2×#103C22×C1114yes—
187C2×#102C22×C1114yes—
188#391C22×C1112yes—
189#390C22×C1112yes—
190#386—21no—
191#386—21no—
192C4×C22⋊C4—22no—
193#340C22×C1118yes—
194#336C22×C1114yes—
195C22×C11—24no—
196C22×C11—24no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—44no—
200C22×C11—42no—
201C22×C11—82no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11#39314yes—
205C22×C11C2×#12011yescharacteristic
206C22×C11C2×C22⋊Q811yescharacteristic
207C22×C11C2×#12411yescharacteristic
208C22×C11C2×AGL(1,ℤ/8)12yes—
209C22×C11C2×#13712yes—
210C4×C11—24no—
211C4×C11—24no—
212C4×C11—42no—
213C4×C11—48no—
214C4×C11—82no—
215C4×C11#39314yes—
216C4×C11C2×C22⋊Q812yes—
217C4×C11C2×#12412yes—
218C2×#41—22no—
219C2×#41—24no—
220C2×#41—24no—
221C2×#41Q8×C1114yescomplemented
222C22×Q8—28no—
223C22×Q8—24no—
224C22×Q8—48no—
225C22×Q8C23×C1111yescharacteristic
226C22×D4—21no—
227C22×D4C23×C1111yescharacteristic
228C23×C4—22no—
229C23×C4—21no—
230C23×C4D4×C1111yescharacteristic
231C23×C4D4×C1111yescharacteristic
232C23×C4C23×C1111yescharacteristic
233C2×M16—24no—
234C2×M16—24no—
235C2×M16—24no—
236C22×C8C23×C1114yes—
237C4⋊Q8—216no—
238C4⋊Q8—216no—
239#117—24no—
240C2×C4⋊C4—28no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4D4×C1118yes—
245C2×C4⋊C4C23×C1112yes—
246C2×C4⋊C4C23×C1114yes—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42—24no—
251C2×C42—21no—
252C2×C42D4×C1112yes—
253C2×C42C23×C1112yes—
254#103—28no—
255#102—28no—
256#95—22no—
257#95—22no—
258C2×C11—24no—
259C2×C11—82no—
260C2×C11C2×#39311yescharacteristic
261C2×C11#300311yescharacteristic
262C2×C11#300411yescharacteristic
263C2×C11#307912yes—
264C2×C11#314112yes—
265C24—21no—
266C24C2×D4×C1111yescharacteristic
267#41—216no—
268#41—48no—
269C2×Q8—216no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—432no—
274C2×Q8—48no—
275C2×Q8—48no—
276C2×Q8C2×Q8×C1112yescomplemented
277C2×D4—24no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4C2×Q8×C1112yescomplemented
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—28no—
289C22×C4—21no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—48no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C2×D4×C1112yes—
297C22×C4C2×D4×C1112yes—
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C2×D4×C1114yes—
300C22×C4C2×Q8×C1112yes—
301C22×C4C11×#4114yes—
302C22×C4C11×#4112yes—
303C22×C4C24×C1111yescharacteristic
304M16—48no—
305C2×C8—24no—
306C2×C8—24no—
307C2×C8—24no—
308C4⋊C4—216no—
309C4⋊C4—28no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4C2×D4×C1118yes—
313C22⋊C4—42no—
314C22⋊C4—44no—
315C22⋊C4—44no—
316C42—24no—
317C42—24no—
318C42—42no—
319C11#2345211yescharacteristic, direct product factor, Sylow
320C23—22no—
321C23—22no—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—42no—
326C23—42no—
327C23C11×#12012yes—
328C23C11×C22⋊Q812yes—
329C23C11×#12412yes—
330C23C22×D4×C1111yescharacteristic
331Q8—24no—
332Q8—432no—
333Q8—42no—
334D4—24no—
335D4—48no—
336D4—42no—
337C2×C4—28no—
338C2×C4—28no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—28no—
344C2×C4—22no—
345C2×C4—416no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—48no—
349C2×C4—48no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4C11×#12012yes—
354C2×C4C11×C22⋊Q818yes—
355C2×C4C11×C22⋊Q812yes—
356C2×C4C11×#12418yes—
357C2×C4C11×#12412yes—
358C2×C4C11×AGL(1,ℤ/8)14yes—
359C2×C4C11×#13714yes—
360C2×C4C22×D4×C1112yes—
361C2×C4C22×Q8×C1111yescharacteristic
362C2×C4C2×C11×#4112yes—
363C2×C4C2×C11×#4111yescharacteristic
364C8—44no—
365C22—22no—
366C22—22no—
367C22—24no—
368C22—24no—
369C22—42no—
370C22—44no—
371C22—81no—
372C22—81no—
373C22—82no—
374C22C11×#39314yes—
375C22C2×C11×#12011yescharacteristic
376C22C2×C11×C22⋊Q811yescharacteristic
377C22C2×C11×#12411yescharacteristic
378C22C2×C11×AGL(1,ℤ/8)12yes—
379C22C2×C11×#13712yes—
380C4—24no—
381C4—24no—
382C4—42no—
383C4—48no—
384C4—82no—
385C4C11×#39314yes—
386C4C2×C11×C22⋊Q812yes—
387C4C2×C11×#12412yes—
388C2—24no—
389C2—82no—
390C2C2×C11×#39311yescharacteristic
391C2C11×#300311yescharacteristic
392C2C11×#300411yescharacteristic
393C2C11×#307912yes—
394C2C11×#314112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊Q8C2semidirect
4. C11×#2024C2semidirect
5. C11×#2023C2semidirect
6. C11×#1736C2semidirect
7. C11×#1728C2semidirect
31. C2×C11×#41Q8semidirect
68. #23452C11direct (N × H)
80. C2×Q8×C11C2×Q8semidirect
87. C2×D4×C11C2×Q8semidirect
123. C22×C4⋊Q8C2×C11semidirect
126. #2024C2×C11semidirect
127. #2023C2×C11semidirect
128. #1736C2×C11semidirect
129. #1728C2×C11semidirect
221. C2×#41Q8×C11semidirect
276. C2×Q8C2×Q8×C11semidirect
283. C2×D4C2×Q8×C11semidirect
319. C11#23452direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#4172
C11×#22972
C11×#20242
C11×#20232
C11×#17362
C11×#17282
#2345211