Finite Group Databasebeta

← C11×#24063 #14601256

Subgroups — C11×#24063 #14601256

Order 2816.

1144 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#483C212yesmaximal
3C2×C11×#389C211yesmaximal, characteristic
4C11×#2058C212yesmaximal, complemented
5C11×#2043C212yesmaximal, complemented
6C11×#1872C212yesmaximal
7C11×#1865C214yesmaximal, complemented
8C11×#1817C211yesmaximal, characteristic
9C11×#533—28no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#125—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117—21no—
18C22×C11×C4⋊C4—21no—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#483—28no—
23C2×C11×#106C2214yes—
24C2×C11×#103C2214yes—
25C2×C11×#103C2214yes—
26C2×C11×C22⋊C8C2212yes—
27C11×#389—21no—
28C11×#389—21no—
29C11×#389C2212yes—
30C11×#389C2212yes—
31C2×C11×#95—21no—
32C11×#340C2214yes—
33C11×#336C2212yes—
34C11×#336C2212yes—
35C22×Q8×C11—21no—
36C22×Q8×C11C2312yes—
37C23×C4×C11—21no—
38C23×C4×C11—21no—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C8×C11C2314yes—
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8—24no—
45C11×#125—28no—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8D418yes—
49C4×Q8×C11—28no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C11×#117—28no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—44no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—24no—
70C2×C42×C11—22no—
71C2×C42×C11D411yescharacteristic
72C2×C42×C11D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C11×#106—28no—
76C11×#103—28no—
77C11×#103—28no—
78C11×C22⋊C8—24no—
79C11×#95—22no—
80C11×#95—22no—
81#24063C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—24no—
86C2×Q8×C11—24no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×Q8×C11C2×D414yes—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—41no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11SD1614yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D414yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C8×C11—24no—
116C2×C8×C11—24no—
117C2×C8×C11—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—28no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4—44no—
130C11×C4⋊C4C2×D414yes—
131C11×C4⋊C4#4114yes—
132C11×C22⋊C4—28no—
133C42×C11—28no—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—22no—
138C2×#533C2×C1111yescharacteristic
139C2×#483C2×C1112yes—
140C2×#389C2×C1111yescharacteristic
141#2058C2×C1112yescomplemented
142#2043C2×C1112yescomplemented
143#1872C2×C1112yes—
144#1865C2×C1114yescomplemented
145#1817C2×C1111yescharacteristic
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11#12012yes—
151C23×C11C2×SD1612yes—
152C23×C11#13712yes—
153C23×C11C22×D411yescharacteristic
154Q8×C11—28no—
155Q8×C11—48no—
156Q8×C11—44no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—28no—
166C2×C4×C11—28no—
167C2×C4×C11—21no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—44no—
174C2×C4×C11—48no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—84no—
185C2×C4×C11#12012yes—
186C2×C4×C11C2×SD1612yes—
187C2×C4×C11C2×SD1612yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C22×D412yes—
190C2×C4×C11C2×#4112yes—
191C2×C4×C112−1+412yes—
192C8×C11—44no—
193#533—28no—
194C2×C4⋊Q8C22×C1111yescharacteristic
195C2×C4⋊Q8C22×C1111yescharacteristic
196C2×#125—21no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8C22×C1112yes—
199C2×C4×Q8—21no—
200C2×C4×Q8C22×C1112yes—
201C2×#117—21no—
202C22×C4⋊C4—21no—
203C22×C4⋊C4C22×C1111yescharacteristic
204C22×C4⋊C4C22×C1111yescharacteristic
205C22×C42C22×C1111yescharacteristic
206#483—28no—
207C2×#106C22×C1114yes—
208C2×#103C22×C1114yes—
209C2×#103C22×C1114yes—
210C2×C22⋊C8C22×C1112yes—
211#389—21no—
212#389—21no—
213#389C22×C1112yes—
214#389C22×C1112yes—
215C2×#95—21no—
216#340C22×C1114yes—
217#336C22×C1112yes—
218#336C22×C1112yes—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11#44814yes—
226C22×C11C2×#12011yescharacteristic
227C22×C11#52511yescharacteristic
228C22×C11#53611yescharacteristic
229C22×C11C22×SD1611yescharacteristic
230C22×C11C2×#13711yescharacteristic
231C22×C11C2×#13711yescharacteristic
232C22×C11#57511yescharacteristic
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—44no—
238C4×C11—44no—
239C4×C11—41no—
240C4×C11—44no—
241C4×C11—82no—
242C4×C11#54714yes—
243C22×Q8—21no—
244C22×Q8C23×C1112yes—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4D4×C1111yescharacteristic
248C23×C4D4×C1111yescharacteristic
249C23×C4C23×C1111yescharacteristic
250C22×C8C23×C1114yes—
251C4⋊Q8—24no—
252C4⋊Q8—24no—
253#125—28no—
254C22⋊Q8—28no—
255C22⋊Q8—24no—
256C22⋊Q8D4×C1118yes—
257C4×Q8—28no—
258C4×Q8—24no—
259C4×Q8—24no—
260#117—28no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4C23×C1112yes—
274C2×C4⋊C4C23×C1112yes—
275C2×C4⋊C4C23×C1112yes—
276C2×C22⋊C4—22no—
277C2×C42—22no—
278C2×C42—24no—
279C2×C42D4×C1111yescharacteristic
280C2×C42D4×C1111yescharacteristic
281C2×C42C23×C1111yescharacteristic
282C2×C42C23×C1111yescharacteristic
283#106—28no—
284#103—28no—
285#103—28no—
286C22⋊C8—24no—
287#95—22no—
288#95—22no—
289C2×C11—24no—
290C2×C11#240611yescharacteristic
291C2×C11C2×#44811yescharacteristic
292C2×C11#300711yescharacteristic
293C2×C11#310111yescharacteristic
294C2×C11#311311yescharacteristic
295C2×C11#322911yescharacteristic
296C2×C11#323611yescharacteristic
297C24C2×D4×C1111yescharacteristic
298C2×Q8—24no—
299C2×Q8—22no—
300C2×Q8—24no—
301C2×Q8—24no—
302C2×Q8—42no—
303C2×Q8—42no—
304C2×Q8C2×D4×C1114yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4C11×SD1614yes—
323C22×C4C2×D4×C1111yescharacteristic
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1114yes—
326C22×C4C2×D4×C1111yescharacteristic
327C22×C4C2×D4×C1111yescharacteristic
328C22×C4C2×D4×C1111yescharacteristic
329C22×C4C24×C1111yescharacteristic
330C2×C8—24no—
331C2×C8—24no—
332C2×C8—24no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—28no—
337C4⋊C4—24no—
338C4⋊C4—28no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—24no—
342C4⋊C4—42no—
343C4⋊C4—44no—
344C4⋊C4—44no—
345C4⋊C4C2×D4×C1114yes—
346C4⋊C4C11×#4114yes—
347C22⋊C4—28no—
348C42—28no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—22no—
353C11#2406311yescharacteristic, direct product factor, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23C11×#12012yes—
359C23C2×C11×SD1612yes—
360C23C11×#13712yes—
361C23C22×D4×C1111yescharacteristic
362Q8—28no—
363Q8—48no—
364Q8—44no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—28no—
374C2×C4—28no—
375C2×C4—21no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—44no—
382C2×C4—48no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—84no—
393C2×C4C11×#12012yes—
394C2×C4C2×C11×SD1612yes—
395C2×C4C2×C11×SD1612yes—
396C2×C4C11×#13712yes—
397C2×C4C22×D4×C1112yes—
398C2×C4C2×C11×#4112yes—
399C2×C4C11×2−1+412yes—
400C8—44no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22C11×#44814yes—
408C22C2×C11×#12011yescharacteristic
409C22C11×#52511yescharacteristic
410C22C11×#53611yescharacteristic
411C22C22×C11×SD1611yescharacteristic
412C22C2×C11×#13711yescharacteristic
413C22C2×C11×#13711yescharacteristic
414C22C11×#57511yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—44no—
420C4—41no—
421C4—44no—
422C4—44no—
423C4—82no—
424C4C11×#54714yes—
425C2—24no—
426C2C11×#240611yescharacteristic
427C2C2×C11×#44811yescharacteristic
428C2C11×#300711yescharacteristic
429C2C11×#310111yescharacteristic
430C2C11×#311311yescharacteristic
431C2C11×#322911yescharacteristic
432C2C11×#323611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
4. C11×#2058C2semidirect
5. C11×#2043C2semidirect
7. C11×#1865C2semidirect
81. #24063C11direct (N × H)
141. #2058C2×C11semidirect
142. #2043C2×C11semidirect
144. #1865C2×C11semidirect
353. C11#24063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4832
C2×C11×#3892
C11×#20582
C11×#20432
C11×#18722
C11×#18652
C11×#18172
#2406311