Finite Group Databasebeta

← C11×#22962 #14600155

Subgroups — C11×#22962 #14600155

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic
2C11×#2365C211yesmaximal, characteristic, complemented
3D4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1947C211yesmaximal, characteristic, complemented
6C11×#1942C212yesmaximal, complemented
7C11×#1918C212yesmaximal, complemented
8C11×#1862C212yesmaximal
9C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
10C4×C11×#102C211yesmaximal, characteristic
11C4×C11×#102C212yesmaximal
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×C4×D4×C11C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C22×C11×C4⋊C4—21no—
17C11×#474C418yescomplemented
18C2×C11×#107C2212yes—
19C2×C11×#107C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×C4×C8×C11C2212yes—
26C11×#391—21no—
27C11×#389C2212yes—
28C11×#389C2212yes—
29C11×#387—22no—
30C11×#385—22no—
31C11×#384C2211yescharacteristic
32C11×#380—21no—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C11×#340C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×Q8×C11—21no—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yescomplemented
51C4×Q8×C11—44no—
52C4×D4×C11—24no—
53C4×D4×C11—22no—
54C4×D4×C11—42no—
55C4×D4×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—44no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C42×C11—22no—
72C2×C42×C11—21no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C11×#107—42no—
76C11×#107C2×C418yescomplemented
77C11×C4⋊C8C2×C414yescomplemented
78C11×#102—22no—
79C11×#102C2×C418yes—
80C11×#102Q814yescomplemented
81C4×C8×C11—22no—
82C4×C8×C11—42no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95D412yes—
88#22962C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—21no—
90C2×Q8×C11—24no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11C22×C412yes—
97C2×D4×C11C2×Q812yes—
98C2×D4×C11#4112yes—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—24no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—44no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—21no—
122C2×C8×C11C22×C414yes—
123C2×C8×C11C2×Q812yes—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—44no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4—81no—
137C11×C4⋊C4D814yes—
138C11×C4⋊C4C22×C414yes—
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4C2×Q812yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—44no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—44no—
146C42×C11—42no—
147C42×C11C22×C412yes—
148C42×C11#4112yes—
149C2×#474C2×C1111yescharacteristic
150#2365C2×C1111yescharacteristic, complemented
151D4×C4⋊C4C2×C1111yescharacteristic
152#1990C2×C1111yescharacteristic, complemented
153#1947C2×C1111yescharacteristic, complemented
154#1942C2×C1112yescomplemented
155#1918C2×C1112yescomplemented
156#1862C2×C1112yes—
157C8×C4⋊C4C2×C1111yescharacteristic, complemented
158C4×#102C2×C1112yes—
159C4×#102C2×C1111yescharacteristic
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11C22×D411yescharacteristic
168Q8×C11—48no—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11—22no—
172D4×C11C4×Q814yescomplemented
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
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—48no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—88no—
197C2×C4×C11C4×D412yes—
198C2×C4×C11C4×D412yes—
199C2×C4×C11C2×D814yes—
200C2×C4×C11C2×D812yes—
201C2×C4×C11#13512yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C8×C11—24no—
209C8×C11—22no—
210C8×C11—41no—
211C2×C4⋊Q8C22×C1111yescharacteristic
212C2×C4×Q8—21no—
213C2×C4×D4C22×C1112yes—
214C2×C4×D4C22×C1111yescharacteristic
215C22×C4⋊C4—21no—
216#474C4×C1118yescomplemented
217C2×#107C22×C1112yes—
218C2×#107C22×C1112yes—
219C2×C4⋊C8C22×C1111yescharacteristic
220C2×#102C22×C1111yescharacteristic
221C2×#102C22×C1112yes—
222C2×#102C22×C1111yescharacteristic
223C2×C4×C8C22×C1111yescharacteristic
224C2×C4×C8C22×C1112yes—
225#391—21no—
226#389C22×C1112yes—
227#389C22×C1112yes—
228#387—22no—
229#385—22no—
230#384C22×C1111yescharacteristic
231#380—21no—
232C4×C4⋊C4C22×C1112yes—
233C4×C4⋊C4C22×C1111yescharacteristic
234C4×C4⋊C4C22×C1111yescharacteristic
235#340C22×C1112yes—
236#340C22×C1111yescharacteristic
237#340C22×C1112yes—
238#340C22×C1111yescharacteristic
239#340C22×C1112yes—
240#336C22×C1112yes—
241C22×C11—24no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11#54611yescharacteristic
250C22×C11D4×Q811yescharacteristic
251C22×C11C22×D811yescharacteristic
252C22×C11C2×#13511yescharacteristic
253C22×C11#57711yescharacteristic
254C22×C11#57811yescharacteristic
255C4×C11—22no—
256C4×C11—24no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—44no—
260C4×C11—42no—
261C4×C11—81no—
262C4×C11—82no—
263C4×C11C4×D814yes—
264C4×C11C2×C4×Q811yescharacteristic
265C4×C11#52011yescharacteristic
266C4×C11#55211yescharacteristic
267C4×C11#55411yescharacteristic
268C22×Q8—21no—
269C22×D4C23×C1111yescharacteristic
270C23×C4—21no—
271C23×C4—22no—
272C22×C8C23×C1111yescharacteristic
273C22×C8C23×C1112yes—
274C22×C8C23×C1111yescharacteristic
275C4⋊Q8—22no—
276C4⋊Q8C2×C4×C1114yescomplemented
277C4×Q8—44no—
278C4×D4—24no—
279C4×D4—22no—
280C4×D4—42no—
281C4×D4C2×C4×C1114yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4D4×C1111yescharacteristic
289C2×C4⋊C4D4×C1111yescharacteristic
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C4⋊C4C23×C1112yes—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C42—22no—
298C2×C42—21no—
299C2×C42C23×C1112yes—
300C2×C42C23×C1111yescharacteristic
301#107—42no—
302#107C2×C4×C1118yescomplemented
303C4⋊C8C2×C4×C1114yescomplemented
304#102—22no—
305#102C2×C4×C1118yes—
306#102Q8×C1114yescomplemented
307C4×C8—22no—
308C4×C8—42no—
309#95—21no—
310#95—22no—
311#95—22no—
312#95—22no—
313#95D4×C1112yes—
314C2×C11—44no—
315C2×C11#236011yescharacteristic
316C2×C11C2×C4×D811yescharacteristic
317C2×C11#294711yescharacteristic
318C2×C11#329411yescharacteristic
319C2×C11#330211yescharacteristic
320C2×C11Q8×D811yescharacteristic
321C2×C11#338111yescharacteristic
322C24—21no—
323C2×Q8—24no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4C22×C4×C1112yes—
330C2×D4C2×Q8×C1112yes—
331C2×D4C11×#4112yes—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—44no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—44no—
342C22×C4—82no—
343C22×C4C2×D4×C1112yes—
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C2×D4×C1112yes—
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C24×C1111yescharacteristic
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8C22×C4×C1114yes—
356C2×C8C2×Q8×C1112yes—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—44no—
367C4⋊C4—42no—
368C4⋊C4—44no—
369C4⋊C4—81no—
370C4⋊C4C11×D814yes—
371C4⋊C4C22×C4×C1114yes—
372C4⋊C4C22×C4×C1112yes—
373C4⋊C4C2×Q8×C1112yes—
374C22⋊C4—24no—
375C22⋊C4—44no—
376C42—22no—
377C42—22no—
378C42—44no—
379C42—42no—
380C42C22×C4×C1112yes—
381C42C11×#4112yes—
382C11#2296211yescharacteristic, direct product factor, Sylow
383C23—22no—
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23C22×D4×C1111yescharacteristic
391Q8—48no—
392D4—22no—
393D4—22no—
394D4—22no—
395D4C4×Q8×C1114yescomplemented
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—48no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—88no—
420C2×C4C4×D4×C1112yes—
421C2×C4C4×D4×C1112yes—
422C2×C4C2×C11×D814yes—
423C2×C4C2×C11×D812yes—
424C2×C4C11×#13512yes—
425C2×C4C23×C4×C1111yescharacteristic
426C2×C4C22×Q8×C1111yescharacteristic
427C2×C4C2×C11×#4111yescharacteristic
428C2×C4C2×C11×#4111yescharacteristic
429C2×C4C11×H(5,𝔽2)11yescharacteristic
430C2×C4C11×2−1+411yescharacteristic
431C8—24no—
432C8—22no—
433C8—41no—
434C22—24no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22C2×C4×D4×C1111yescharacteristic
442C22C11×#54611yescharacteristic
443C22D4×Q8×C1111yescharacteristic
444C22C22×C11×D811yescharacteristic
445C22C2×C11×#13511yescharacteristic
446C22C11×#57711yescharacteristic
447C22C11×#57811yescharacteristic
448C4—22no—
449C4—24no—
450C4—42no—
451C4—44no—
452C4—42no—
453C4—42no—
454C4—82no—
455C4—81no—
456C4C4×C11×D814yes—
457C4C2×C4×Q8×C1111yescharacteristic
458C4C11×#52011yescharacteristic
459C4C11×#55211yescharacteristic
460C4C11×#55411yescharacteristic
461C2—44no—
462C2C11×#236011yescharacteristic
463C2C2×C4×C11×D811yescharacteristic
464C2C11×#294711yescharacteristic
465C2C11×#329411yescharacteristic
466C2C11×#330211yescharacteristic
467C2Q8×C11×D811yescharacteristic
468C2C11×#338111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2365C2semidirect
4. C11×#1990C2semidirect
5. C11×#1947C2semidirect
6. C11×#1942C2semidirect
7. C11×#1918C2semidirect
9. C8×C11×C4⋊C4C2semidirect
17. C11×#474C4semidirect
50. C11×C4⋊Q8C2×C4semidirect
76. C11×#107C2×C4semidirect
77. C11×C4⋊C8C2×C4semidirect
80. C11×#102Q8semidirect
88. #22962C11direct (N × H)
150. #2365C2×C11semidirect
152. #1990C2×C11semidirect
153. #1947C2×C11semidirect
154. #1942C2×C11semidirect
155. #1918C2×C11semidirect
157. C8×C4⋊C4C2×C11semidirect
172. D4×C11C4×Q8semidirect
216. #474C4×C11semidirect
276. C4⋊Q8C2×C4×C11semidirect
302. #107C2×C4×C11semidirect
303. C4⋊C8C2×C4×C11semidirect
306. #102Q8×C11semidirect
382. C11#22962direct (N × H)
395. D4C4×Q8×C11semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C11×#23652
D4×C11×C4⋊C42
C11×#19902
C11×#19472
C11×#19422
C11×#19182
C11×#18622
C8×C11×C4⋊C42
C4×C11×#1022
#2296211