Finite Group Databasebeta

← C11×#24316 #14601509

Subgroups — C11×#24316 #14601509

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C11×#3077C212yesmaximal, complemented
3C11×#2328C211yesmaximal, characteristic
4C11×#2061C212yesmaximal, complemented
5C11×#2027C212yesmaximal, complemented
6C11×#1995C212yesmaximal, complemented
7C11×#1887C212yesmaximal
8C11×#1856C212yesmaximal, complemented
9C11×#1800C211yesmaximal, characteristic, complemented
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—22no—
15C11×#533C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×C22⋊Q8—22no—
18C11×#518C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C11×#478—24no—
22C11×#476—22no—
23C11×#474—22no—
24C11×#428C2214yes—
25C11×#423C2212yes—
26C11×#418C2214yes—
27C2×C11×#100C2212yes—
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#386—22no—
31C11×#386—22no—
32C11×#382C2211yescharacteristic
33C11×#376C2211yescharacteristic
34C11×#343C2212yes—
35C11×#339C2214yes—
36C11×#339C2214yes—
37C22×Q8×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2311yescharacteristic
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D412yes—
43C2×C11×M16C2314yes—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8D412yescomplemented
46C11×C4⋊Q8D412yescomplemented
47C11×#127—22no—
48C11×#127Q814yescomplemented
49C11×#125—24no—
50C11×#125D414yescomplemented
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—28no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117C2314yes—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#107—24no—
80C11×#106—24no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—22no—
83C11×#102—24no—
84C11×#102—24no—
85C11×#100—24no—
86C11×#95—21no—
87C11×#95—21no—
88C11×#95—22no—
89#24316C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C24×C11C2×D412yes—
92C2×Q8×C11—24no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—84no—
96C2×D4×C11—28no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—82no—
103C2×D4×C11—82no—
104C2×D4×C11C2×Q812yes—
105C2×D4×C11C2×Q812yescomplemented
106C2×D4×C11#4112yes—
107C22×C4×C11—21no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11—82no—
116C22×C4×C11—82no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C11×M16—24no—
122C11×M16—24no—
123C2×C8×C11—24no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—28no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4C2×D414yes—
133C11×C4⋊C4C2×D414yes—
134C11×C22⋊C4—28no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—82no—
140C11×C22⋊C4—82no—
141C42×C11—24no—
142C42×C11—21no—
143C42×C11—22no—
144C42×C11C2×D412yes—
145C42×C11C2×D412yes—
146C42×C11C2×Q812yescomplemented
147#3501C2×C1111yescharacteristic, complemented
148#3077C2×C1112yescomplemented
149#2328C2×C1111yescharacteristic
150#2061C2×C1112yescomplemented
151#2027C2×C1112yescomplemented
152#1995C2×C1112yescomplemented
153#1887C2×C1112yes—
154#1856C2×C1112yescomplemented
155#1800C2×C1111yescharacteristic, complemented
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11C22⋊Q814yes—
166C23×C11C22×D411yescharacteristic
167Q8×C11—44no—
168Q8×C11—82no—
169Q8×C11—84no—
170D4×C11—24no—
171D4×C11—24no—
172D4×C11—24no—
173D4×C11—42no—
174D4×C11—88no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—44no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—82no—
191C2×C4×C11—84no—
192C2×C4×C11—84no—
193C2×C4×C11—84no—
194C2×C4×C11#12012yes—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11C22×D412yes—
198C2×C4×C11C22×Q811yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C112−1+412yes—
201C8×C11—44no—
202#554—22no—
203#554—24no—
204D4×Q8—22no—
205#544C22×C1112yes—
206#543—22no—
207#533C22×C1112yes—
208C2×#127C22×C1111yescharacteristic
209C2×C22⋊Q8—22no—
210#518C22×C1112yes—
211C2×C4×D4C22×C1111yescharacteristic
212C2×C4×D4C22×C1111yescharacteristic
213#478—24no—
214#476—22no—
215#474—22no—
216#428C22×C1114yes—
217#423C22×C1112yes—
218#418C22×C1114yes—
219C2×#100C22×C1112yes—
220#390C22×C1111yescharacteristic
221#390C22×C1111yescharacteristic
222#386—22no—
223#386—22no—
224#382C22×C1111yescharacteristic
225#376C22×C1111yescharacteristic
226#343C22×C1112yes—
227#339C22×C1114yes—
228#339C22×C1114yes—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—24no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11C2×#12011yescharacteristic
242C22×C11C2×C22⋊Q811yescharacteristic
243C22×C11#53611yescharacteristic
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—22no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—44no—
250C4×C11—44no—
251C4×C11—81no—
252C4×C11—81no—
253C4×C11#54812yes—
254C4×C11D4×Q812yes—
255C22×Q8—22no—
256C22×D4—22no—
257C22×D4C23×C1111yescharacteristic
258C22×D4C23×C1111yescharacteristic
259C23×C4—21no—
260C23×C4D4×C1112yes—
261C2×M16C23×C1114yes—
262C4⋊Q8—24no—
263C4⋊Q8D4×C1112yescomplemented
264C4⋊Q8D4×C1112yescomplemented
265#127—22no—
266#127Q8×C1114yescomplemented
267#125—24no—
268#125D4×C1114yescomplemented
269C22⋊Q8—24no—
270C22⋊Q8—24no—
271C22⋊Q8—28no—
272C22⋊Q8—28no—
273C22⋊Q8—22no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×D4—24no—
279C4×D4—24no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—22no—
284#117C23×C1114yes—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C22⋊C4—24no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4D4×C1112yes—
294C2×C42C23×C1111yescharacteristic
295C2×C42C23×C1111yescharacteristic
296C2×C42C23×C1111yescharacteristic
297#107—24no—
298#106—24no—
299C4⋊C8—22no—
300C4⋊C8—22no—
301#102—24no—
302#102—24no—
303#100—24no—
304#95—21no—
305#95—21no—
306#95—22no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—44no—
310C2×C11—82no—
311C2×C11#240911yescharacteristic
312C2×C11#301911yescharacteristic
313C2×C11#302111yescharacteristic
314C24—21no—
315C24C2×D4×C1112yes—
316C2×Q8—24no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—84no—
320C2×D4—28no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—82no—
327C2×D4—82no—
328C2×D4C2×Q8×C1112yes—
329C2×D4C2×Q8×C1112yescomplemented
330C2×D4C11×#4112yes—
331C22×C4—21no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—42no—
339C22×C4—82no—
340C22×C4—82no—
341C22×C4C2×D4×C1112yes—
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C24×C1111yescharacteristic
345M16—24no—
346M16—24no—
347C2×C8—24no—
348C4⋊C4—24no—
349C4⋊C4—28no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4C2×D4×C1114yes—
357C4⋊C4C2×D4×C1114yes—
358C22⋊C4—28no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—82no—
364C22⋊C4—82no—
365C42—24no—
366C42—21no—
367C42—22no—
368C42C2×D4×C1112yes—
369C42C2×D4×C1112yes—
370C42C2×Q8×C1112yescomplemented
371C11#2431611yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—22no—
374C23—22no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23C11×C22⋊Q814yes—
382C23C22×D4×C1111yescharacteristic
383Q8—44no—
384Q8—82no—
385Q8—84no—
386D4—24no—
387D4—24no—
388D4—24no—
389D4—42no—
390D4—88no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—44no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—82no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4C11×#12012yes—
411C2×C4C11×#12011yescharacteristic
412C2×C4C11×#12011yescharacteristic
413C2×C4C22×D4×C1112yes—
414C2×C4C22×Q8×C1111yescharacteristic
415C2×C4C2×C11×#4111yescharacteristic
416C2×C4C11×2−1+412yes—
417C8—44no—
418C22—21no—
419C22—21no—
420C22—24no—
421C22—44no—
422C22—44no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—82no—
427C22—82no—
428C22—81no—
429C22—81no—
430C22C2×C11×#12011yescharacteristic
431C22C2×C11×C22⋊Q811yescharacteristic
432C22C11×#53611yescharacteristic
433C4—21no—
434C4—21no—
435C4—22no—
436C4—42no—
437C4—42no—
438C4—44no—
439C4—44no—
440C4—81no—
441C4—81no—
442C4C11×#54812yes—
443C4D4×Q8×C1112yes—
444C2—21no—
445C2—21no—
446C2—44no—
447C2—82no—
448C2C11×#240911yescharacteristic
449C2C11×#301911yescharacteristic
450C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3501C2semidirect
2. C11×#3077C2semidirect
4. C11×#2061C2semidirect
5. C11×#2027C2semidirect
6. C11×#1995C2semidirect
8. C11×#1856C2semidirect
9. C11×#1800C2semidirect
45. C11×C4⋊Q8D4semidirect
46. C11×C4⋊Q8D4semidirect
48. C11×#127Q8semidirect
50. C11×#125D4semidirect
89. #24316C11direct (N × H)
105. C2×D4×C11C2×Q8semidirect
146. C42×C11C2×Q8semidirect
147. #3501C2×C11semidirect
148. #3077C2×C11semidirect
150. #2061C2×C11semidirect
151. #2027C2×C11semidirect
152. #1995C2×C11semidirect
154. #1856C2×C11semidirect
155. #1800C2×C11semidirect
263. C4⋊Q8D4×C11semidirect
264. C4⋊Q8D4×C11semidirect
266. #127Q8×C11semidirect
268. #125D4×C11semidirect
329. C2×D4C2×Q8×C11semidirect
370. C42C2×Q8×C11semidirect
371. C11#24316direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#30772
C11×#23282
C11×#20612
C11×#20272
C11×#19952
C11×#18872
C11×#18562
C11×#18002
#2431611