Finite Group Databasebeta

← C11×#22279 #14599472

Subgroups — C11×#22279 #14599472

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#496C211yesmaximal, characteristic
2C11×#2328C211yesmaximal, characteristic, complemented
3C11×#2326C211yesmaximal, characteristic, complemented
4C11×#1958C211yesmaximal, characteristic, complemented
5C11×#1957C211yesmaximal, characteristic, complemented
6C11×#1880C212yesmaximal, complemented
7C11×#1879C212yesmaximal, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1836C211yesmaximal, characteristic, complemented
11C11×#1746C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C11×#496C418yescomplemented
20C2×C11×#103C2212yes—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#390C2212yes—
29C11×#388—22no—
30C11×#386—22no—
31C11×#386—22no—
32C11×#385—22no—
33C11×#384C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C11×#376C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#336C2212yes—
39C11×#336C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11C2311yescharacteristic
43C22×D4×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C2×C11×SD16—42no—
47C2×C11×SD16—42no—
48C2×C11×SD16C2×C418yescomplemented
49C2×C11×D8—42no—
50C2×C11×D8—42no—
51C2×C11×D8C2×C418yescomplemented
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C11×#127—22no—
55C11×#127C2×C414yescomplemented
56C11×#124—22no—
57C11×#124C2×C414yescomplemented
58C4×Q8×C11—42no—
59C4×D4×C11—42no—
60C4×D4×C11—42no—
61C4×D4×C11—42no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#103—42no—
78C11×#102—42no—
79C11×#102—42no—
80C11×#102—42no—
81C11×#97C2×C414yescomplemented
82C4×C8×C11—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95D412yes—
86C11×#95D412yes—
87#22279C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—21no—
89C24×C11—22no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C22×C412yes—
94C2×D4×C11—28no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C2×D4×C11C22×C412yes—
106C2×D4×C11C22×C414yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—44no—
112C22×C4×C11—42no—
113C22×C4×C11—82no—
114C22×C4×C11—82no—
115C22×C4×C11—82no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2411yescharacteristic
121C11×SD16—48no—
122C11×D8—48no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11C22×C414yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—82no—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4—44no—
138C11×C22⋊C4—82no—
139C11×C22⋊C4—82no—
140C11×C22⋊C4—82no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—42no—
144C42×C11C22×C412yes—
145C42×C11#4112yes—
146C2×#496C2×C1111yescharacteristic
147#2328C2×C1111yescharacteristic, complemented
148#2326C2×C1111yescharacteristic, complemented
149#1958C2×C1111yescharacteristic, complemented
150#1957C2×C1111yescharacteristic, complemented
151#1880C2×C1112yescomplemented
152#1879C2×C1112yescomplemented
153#1879C2×C1112yescomplemented
154#1877C2×C1112yescomplemented
155#1836C2×C1111yescharacteristic, complemented
156#1746C2×C1111yescharacteristic, complemented
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11C22×D411yescharacteristic
170Q8×C11—24no—
171Q8×C11—42no—
172D4×C11—24no—
173D4×C11—24no—
174D4×C11—24no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—88no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—84no—
199C2×C4×C11—88no—
200C2×C4×C11C4×D414yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)12yes—
204C2×C4×C11H(5,𝔽2)12yes—
205C8×C11—24no—
206C8×C11—42no—
207C22×SD16C22×C1112yes—
208C22×D8C22×C1112yes—
209C2×#127C22×C1111yescharacteristic
210C2×#124C22×C1111yescharacteristic
211C2×C4×Q8C22×C1111yescharacteristic
212C2×C4×D4C22×C1111yescharacteristic
213C2×C4×D4C22×C1112yes—
214#496C4×C1118yescomplemented
215C2×#103C22×C1112yes—
216C2×#102C22×C1112yes—
217C2×#102C22×C1112yes—
218C2×#102C22×C1112yes—
219C2×#97C22×C1111yescharacteristic
220C2×C4×C8C22×C1111yescharacteristic
221#391C22×C1111yescharacteristic
222#390C22×C1111yescharacteristic
223#390C22×C1112yes—
224#388—22no—
225#386—22no—
226#386—22no—
227#385—22no—
228#384C22×C1111yescharacteristic
229#382C22×C1111yescharacteristic
230#376C22×C1111yescharacteristic
231#340C22×C1112yes—
232#340C22×C1112yes—
233#336C22×C1112yes—
234#336C22×C1112yes—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—44no—
238C22×C11—44no—
239C22×C11—44no—
240C22×C11—81no—
241C22×C11—82no—
242C22×C11—81no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#53511yescharacteristic
249C22×C11#53511yescharacteristic
250C22×C11#57612yes—
251C22×C11#57712yes—
252C4×C11—24no—
253C4×C11—42no—
254C4×C11—41no—
255C4×C11—41no—
256C4×C11—42no—
257C4×C11—81no—
258C4×C11—81no—
259C4×C11—82no—
260C4×C11#51812yes—
261C4×C11#54012yes—
262C22×Q8C23×C1111yescharacteristic
263C22×D4—22no—
264C22×D4C23×C1111yescharacteristic
265C22×D4C23×C1112yes—
266C23×C4—21no—
267C23×C4—22no—
268C2×SD16—42no—
269C2×SD16—42no—
270C2×SD16C2×C4×C1118yescomplemented
271C2×D8—42no—
272C2×D8—42no—
273C2×D8C2×C4×C1118yescomplemented
274C22×C8C23×C1112yes—
275C22×C8C23×C1112yes—
276#127—22no—
277#127C2×C4×C1114yescomplemented
278#124—22no—
279#124C2×C4×C1114yescomplemented
280C4×Q8—42no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—42no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4C23×C1112yes—
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C42—21no—
296C2×C42C23×C1111yescharacteristic
297C2×C42C23×C1111yescharacteristic
298C2×C42C23×C1111yescharacteristic
299#103—42no—
300#102—42no—
301#102—42no—
302#102—42no—
303#97C2×C4×C1114yescomplemented
304C4×C8—22no—
305#95—22no—
306#95—22no—
307#95D4×C1112yes—
308#95D4×C1112yes—
309C2×C11—84no—
310C2×C11—82no—
311C2×C11#232811yescharacteristic
312C2×C11#294612yes—
313C2×C11#322011yescharacteristic
314C2×C11#322111yescharacteristic
315C2×C11#322412yes—
316C24—21no—
317C24—22no—
318C2×Q8—21no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8C22×C4×C1112yes—
322C2×D4—28no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—82no—
332C2×D4—82no—
333C2×D4C22×C4×C1112yes—
334C2×D4C22×C4×C1114yes—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—44no—
340C22×C4—42no—
341C22×C4—82no—
342C22×C4—82no—
343C22×C4—82no—
344C22×C4C2×D4×C1112yes—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1112yes—
348C22×C4C24×C1111yescharacteristic
349SD16—48no—
350D8—48no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8C22×C4×C1114yes—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—42no—
362C4⋊C4—82no—
363C22⋊C4—28no—
364C22⋊C4—42no—
365C22⋊C4—44no—
366C22⋊C4—82no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—22no—
370C42—22no—
371C42—42no—
372C42C22×C4×C1112yes—
373C42C11×#4112yes—
374C11#2227911yescharacteristic, direct product factor, Sylow
375C23—22no—
376C23—24no—
377C23—41no—
378C23—42no—
379C23—42no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23C22×D4×C1111yescharacteristic
388Q8—24no—
389Q8—42no—
390D4—24no—
391D4—24no—
392D4—24no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—88no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—84no—
417C2×C4—88no—
418C2×C4C4×D4×C1114yes—
419C2×C4C23×C4×C1111yescharacteristic
420C2×C4C2×C11×#4111yescharacteristic
421C2×C4C11×H(5,𝔽2)12yes—
422C2×C4C11×H(5,𝔽2)12yes—
423C8—24no—
424C8—42no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22—42no—
429C22—44no—
430C22—81no—
431C22—82no—
432C22—81no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22C2×C4×D4×C1111yescharacteristic
438C22C11×#53511yescharacteristic
439C22C11×#53511yescharacteristic
440C22C11×#57612yes—
441C22C11×#57712yes—
442C4—24no—
443C4—41no—
444C4—41no—
445C4—42no—
446C4—42no—
447C4—81no—
448C4—81no—
449C4—82no—
450C4C11×#51812yes—
451C4C11×#54012yes—
452C2—84no—
453C2—82no—
454C2C11×#232811yescharacteristic
455C2C11×#294612yes—
456C2C11×#322011yescharacteristic
457C2C11×#322111yescharacteristic
458C2C11×#322412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#496C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2328C2semidirect
3. C11×#2326C2semidirect
4. C11×#1958C2semidirect
5. C11×#1957C2semidirect
6. C11×#1880C2semidirect
7. C11×#1879C2semidirect
8. C11×#1879C2semidirect
9. C11×#1877C2semidirect
10. C11×#1836C2semidirect
11. C11×#1746C2semidirect
19. C11×#496C4semidirect
48. C2×C11×SD16C2×C4semidirect
51. C2×C11×D8C2×C4semidirect
55. C11×#127C2×C4semidirect
57. C11×#124C2×C4semidirect
81. C11×#97C2×C4semidirect
87. #22279C11direct (N × H)
147. #2328C2×C11semidirect
148. #2326C2×C11semidirect
149. #1958C2×C11semidirect
150. #1957C2×C11semidirect
151. #1880C2×C11semidirect
152. #1879C2×C11semidirect
153. #1879C2×C11semidirect
154. #1877C2×C11semidirect
155. #1836C2×C11semidirect
156. #1746C2×C11semidirect
214. #496C4×C11semidirect
270. C2×SD16C2×C4×C11semidirect
273. C2×D8C2×C4×C11semidirect
277. #127C2×C4×C11semidirect
279. #124C2×C4×C11semidirect
303. #97C2×C4×C11semidirect
374. C11#22279direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4962
C11×#23282
C11×#23262
C11×#19582
C11×#19572
C11×#18802
C11×#18792
C11×#18772
C11×#18362
C11×#17462
#2227911