Finite Group Databasebeta

← C11×#22117 #14599310

Subgroups — C11×#22117 #14599310

Order 2816.

836 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C11×#2293C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic, complemented
5C11×#1947C211yesmaximal, characteristic, complemented
6C11×#1944C212yesmaximal, complemented
7C11×#1936C212yesmaximal
8C11×#1925C212yesmaximal
9C11×#1920C212yesmaximal, complemented
10C11×#1802C211yesmaximal, characteristic
11C11×#1767C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117—21no—
16C11×#476C418yescomplemented
17C2×C11×#107C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#97C2212yes—
24C11×#391—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389—21no—
28C11×#389C2211yescharacteristic
29C11×#389C2212yes—
30C11×#389C2211yescharacteristic
31C11×#388—21no—
32C11×#388—21no—
33C11×#384C2211yescharacteristic
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C43×C11C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C8×C11C2312yes—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yes—
51C4×Q8×C11—44no—
52C4×D4×C11—22no—
53C4×D4×C11C2×C414yes—
54C11×#117—44no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C11×#107—42no—
81C11×#106C2×C418yes—
82C11×C4⋊C8—22no—
83C11×C4⋊C8C2×C414yes—
84C11×#102—42no—
85C11×#102C2×C418yes—
86C11×#97—42no—
87C11×#95—21no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95—22no—
92#22117C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—21no—
94C2×Q8×C11—24no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C22×C412yes—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11C22×C414yes—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4C22×C414yes—
139C11×C4⋊C4C22×C412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4—42no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11—41no—
153C42×C11—42no—
154C42×C11—44no—
155C42×C11C22×C412yes—
156C42×C11#4112yes—
157C2×#476C2×C1111yescharacteristic
158C4×C4⋊Q8C2×C1111yescharacteristic, complemented
159#2293C2×C1111yescharacteristic
160#1987C2×C1111yescharacteristic, complemented
161#1947C2×C1111yescharacteristic, complemented
162#1944C2×C1112yescomplemented
163#1936C2×C1112yes—
164#1925C2×C1112yes—
165#1920C2×C1112yescomplemented
166#1802C2×C1111yescharacteristic
167#1767C2×C1111yescharacteristic, complemented
168C23×C11—22no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11C22×D411yescharacteristic
176Q8×C11—48no—
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—41no—
180D4×C11—41no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—48no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11C4×D412yes—
211C2×C4×C11C4×D412yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C8×C11—24no—
222C8×C11—42no—
223C2×C4⋊Q8C22×C1111yescharacteristic
224C2×C4×Q8—21no—
225C2×C4×D4C22×C1111yescharacteristic
226C2×#117—21no—
227#476C4×C1118yescomplemented
228C2×#107C22×C1112yes—
229C2×#106C22×C1112yes—
230C2×C4⋊C8C22×C1111yescharacteristic
231C2×C4⋊C8C22×C1111yescharacteristic
232C2×#102C22×C1112yes—
233C2×#102C22×C1112yes—
234C2×#97C22×C1112yes—
235#391—21no—
236#390C22×C1111yescharacteristic
237#390C22×C1111yescharacteristic
238#389—21no—
239#389C22×C1112yes—
240#389C22×C1111yescharacteristic
241#389C22×C1111yescharacteristic
242#388—21no—
243#388—21no—
244#384C22×C1111yescharacteristic
245C4×C4⋊C4—21no—
246C4×C4⋊C4C22×C1112yes—
247C4×C4⋊C4C22×C1111yescharacteristic
248C4×C22⋊C4—21no—
249C43C22×C1111yescharacteristic
250#340C22×C1112yes—
251#340C22×C1112yes—
252#340C22×C1112yes—
253#340C22×C1112yes—
254#336C22×C1112yes—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11C2×C4×D411yescharacteristic
263C22×C11#53611yescharacteristic
264C22×C11#53711yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C22×C11#57511yescharacteristic
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11—82no—
279C4×C11#44014yes—
280C4×C11#51911yescharacteristic
281C4×C11#52011yescharacteristic
282C4×C11#54111yescharacteristic
283C4×C11#54211yescharacteristic
284C22×Q8—21no—
285C22×D4C23×C1111yescharacteristic
286C23×C4—21no—
287C22×C8C23×C1112yes—
288C22×C8C23×C1112yes—
289C4⋊Q8—22no—
290C4⋊Q8C2×C4×C1114yes—
291C4×Q8—44no—
292C4×D4—22no—
293C4×D4C2×C4×C1114yes—
294#117—44no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4C23×C1111yescharacteristic
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C4⋊C4C23×C1112yes—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42—22no—
313C2×C42D4×C1111yescharacteristic
314C2×C42D4×C1111yescharacteristic
315C2×C42D4×C1111yescharacteristic
316C2×C42D4×C1111yescharacteristic
317C2×C42C23×C1111yescharacteristic
318C2×C42C23×C1111yescharacteristic
319C2×C42C23×C1111yescharacteristic
320#107—42no—
321#106C2×C4×C1118yes—
322C4⋊C8—22no—
323C4⋊C8C2×C4×C1114yes—
324#102—42no—
325#102C2×C4×C1118yes—
326#97—42no—
327#95—21no—
328#95—21no—
329#95—22no—
330#95—21no—
331#95—22no—
332C2×C11—82no—
333C2×C11#232311yescharacteristic
334C2×C11C2×#44011yescharacteristic
335C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
336C2×C11#323511yescharacteristic
337C2×C11#323811yescharacteristic
338C2×C11#325211yescharacteristic
339C2×C11#325311yescharacteristic
340C24—21no—
341C2×Q8—24no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4C22×C4×C1112yes—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4C2×D4×C1111yescharacteristic
359C22×C4C2×D4×C1111yescharacteristic
360C22×C4C2×D4×C1111yescharacteristic
361C22×C4C2×D4×C1111yescharacteristic
362C22×C4C2×D4×C1111yescharacteristic
363C22×C4C2×D4×C1111yescharacteristic
364C22×C4C24×C1111yescharacteristic
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8C22×C4×C1114yes—
371C4⋊C4—24no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—44no—
384C4⋊C4—42no—
385C4⋊C4C22×C4×C1114yes—
386C4⋊C4C22×C4×C1112yes—
387C22⋊C4—24no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—42no—
391C22⋊C4—42no—
392C42—22no—
393C42—22no—
394C42—22no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42—41no—
400C42—42no—
401C42—44no—
402C42C22×C4×C1112yes—
403C42C11×#4112yes—
404C11#2211711yescharacteristic, direct product factor, Sylow
405C23—22no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23C22×D4×C1111yescharacteristic
413Q8—48no—
414D4—22no—
415D4—22no—
416D4—41no—
417D4—41no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—48no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4C4×D4×C1112yes—
448C2×C4C4×D4×C1112yes—
449C2×C4C11×AGL(1,ℤ/8)12yes—
450C2×C4C11×AGL(1,ℤ/8)12yes—
451C2×C4C11×#13712yes—
452C2×C4C23×C4×C1111yescharacteristic
453C2×C4C2×C11×#4111yescharacteristic
454C2×C4C11×H(5,𝔽2)11yescharacteristic
455C2×C4C11×2−1+411yescharacteristic
456C2×C4C11×2−1+411yescharacteristic
457C2×C4C11×2−1+411yescharacteristic
458C8—24no—
459C8—42no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22C2×C4×D4×C1111yescharacteristic
468C22C11×#53611yescharacteristic
469C22C11×#53711yescharacteristic
470C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
471C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
472C22C2×C11×#13711yescharacteristic
473C22C11×#57511yescharacteristic
474C4—22no—
475C4—22no—
476C4—42no—
477C4—44no—
478C4—41no—
479C4—41no—
480C4—41no—
481C4—81no—
482C4—81no—
483C4—82no—
484C4C11×#44014yes—
485C4C11×#51911yescharacteristic
486C4C11×#52011yescharacteristic
487C4C11×#54111yescharacteristic
488C4C11×#54211yescharacteristic
489C2—82no—
490C2C11×#232311yescharacteristic
491C2C2×C11×#44011yescharacteristic
492C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
493C2C11×#323511yescharacteristic
494C2C11×#323811yescharacteristic
495C2C11×#325211yescharacteristic
496C2C11×#325311yescharacteristic
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 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×C4⋊Q8C2semidirect
4. C11×#1987C2semidirect
5. C11×#1947C2semidirect
6. C11×#1944C2semidirect
9. C11×#1920C2semidirect
11. C11×#1767C2semidirect
16. C11×#476C4semidirect
92. #22117C11direct (N × H)
158. C4×C4⋊Q8C2×C11semidirect
160. #1987C2×C11semidirect
161. #1947C2×C11semidirect
162. #1944C2×C11semidirect
165. #1920C2×C11semidirect
167. #1767C2×C11semidirect
227. #476C4×C11semidirect
404. C11#22117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C4×C11×C4⋊Q82
C11×#22932
C11×#19872
C11×#19472
C11×#19442
C11×#19362
C11×#19252
C11×#19202
C11×#18022
C11×#17672
#2211711