Finite Group Databasebeta

← C11×#21862 #14599055

Subgroups — C11×#21862 #14599055

Order 2816.

1138 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×#529C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2285C211yesmaximal, characteristic, complemented
4C11×#1991C212yesmaximal, complemented
5C11×#1958C212yesmaximal, complemented
6C11×#1875C212yesmaximal
7C11×#1873C212yesmaximal, complemented
8C11×#1803C212yesmaximal, complemented
9C11×#1802C212yesmaximal, complemented
10C11×#529—24no—
11C11×#529C418yescomplemented
12C2×C11×#126—21no—
13C2×C11×#125C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C2×C11×#117C2212yes—
23C22×C42×C11C2211yescharacteristic
24C11×#431—24no—
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#103C2214yes—
27C2×C11×#102C2214yes—
28C2×C11×C22⋊C8C2212yes—
29C2×C4×C8×C11C2212yes—
30C11×#384C2212yes—
31C11×#382C2212yes—
32C11×#380—21no—
33C11×#380—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4—21no—
36C11×#340C2214yes—
37C11×#340C2214yes—
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11C2314yes—
46C11×#126—28no—
47C11×#125—22no—
48C11×#125C2×C414yes—
49C11×#124—22no—
50C11×#124C2×C414yes—
51C11×#123—28no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8C2×C414yes—
54C11×#121—22no—
55C11×#121C2×C414yes—
56C4×Q8×C11—22no—
57C4×Q8×C11C2×C414yes—
58C4×D4×C11—28no—
59C4×D4×C11—22no—
60C4×D4×C11C2×C414yes—
61C11×#117—28no—
62C11×#117—44no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11C2×C414yes—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D414yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×C4⋊C8—24no—
87C11×#103—44no—
88C11×#102—44no—
89C11×C22⋊C8—24no—
90C4×C8×C11—24no—
91C11×#95—22no—
92C11×#95—22no—
93#21862C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C412yes—
100C2×D4×C11—24no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11C22×C412yes—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—42no—
115C22×C4×C11—44no—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C8×C11—24no—
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4C22×C412yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—44no—
147C42×C11—24no—
148C42×C11—44no—
149C42×C11C22⋊C414yes—
150C42×C11C22⋊C414yes—
151C42×C11C22×C412yes—
152C42×C11C22×C412yes—
153C42×C11C2×D412yes—
154C42×C11C2×D412yes—
155C2×#529C2×C1111yescharacteristic
156C2×#431C2×C1111yescharacteristic, complemented
157#2285C2×C1111yescharacteristic, complemented
158#1991C2×C1112yescomplemented
159#1958C2×C1112yescomplemented
160#1875C2×C1112yes—
161#1873C2×C1112yescomplemented
162#1803C2×C1112yescomplemented
163#1802C2×C1112yescomplemented
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11C2×C22⋊C412yes—
174C23×C11C22×D411yescharacteristic
175Q8×C11—24no—
176Q8×C11—42no—
177D4×C11—24no—
178D4×C11—48no—
179D4×C11—42no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—28no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—44no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—48no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C412yes—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11#13514yes—
206C2×C4×C11C23×C411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11H(5,𝔽2)12yes—
209C2×C4×C112−1+412yes—
210C8×C11—44no—
211#529—24no—
212#529C4×C1118yescomplemented
213C2×#126—21no—
214C2×#125C22×C1111yescharacteristic
215C2×#124C22×C1111yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8C22×C1111yescharacteristic
218C2×#121C22×C1111yescharacteristic
219C2×C4×Q8C22×C1111yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C22×C1111yescharacteristic
222C2×#117—21no—
223C2×#117C22×C1112yes—
224C22×C42C22×C1111yescharacteristic
225#431—24no—
226C2×C4⋊C8C22×C1112yes—
227C2×#103C22×C1114yes—
228C2×#102C22×C1114yes—
229C2×C22⋊C8C22×C1112yes—
230C2×C4×C8C22×C1112yes—
231#384C22×C1112yes—
232#382C22×C1112yes—
233#380—21no—
234#380—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237#340C22×C1114yes—
238#340C22×C1114yes—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11C22×C22⋊C411yescharacteristic
250C22×C11#53511yescharacteristic
251C22×C11#53611yescharacteristic
252C22×C11C2×#13512yes—
253C22×C11#57512yes—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—84no—
262C4×C11#41614yes—
263C4×C11#52012yes—
264C4×C11#53712yes—
265C22×Q8C23×C1111yescharacteristic
266C22×D4—21no—
267C22×D4C23×C1111yescharacteristic
268C23×C4—21no—
269C23×C4D4×C1111yescharacteristic
270C23×C4D4×C1111yescharacteristic
271C23×C4C23×C1111yescharacteristic
272C22×C8C23×C1114yes—
273#126—28no—
274#125—22no—
275#125C2×C4×C1114yes—
276#124—22no—
277#124C2×C4×C1114yes—
278#123—28no—
279C22⋊Q8—22no—
280C22⋊Q8C2×C4×C1114yes—
281#121—22no—
282#121C2×C4×C1114yes—
283C4×Q8—22no—
284C4×Q8C2×C4×C1114yes—
285C4×D4—28no—
286C4×D4—22no—
287C4×D4C2×C4×C1114yes—
288#117—28no—
289#117—44no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4C23×C1114yes—
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C4⋊C4C23×C1111yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—22no—
305C2×C42—21no—
306C2×C42—22no—
307C2×C42C2×C4×C1114yes—
308C2×C42D4×C1111yescharacteristic
309C2×C42D4×C1111yescharacteristic
310C2×C42D4×C1114yes—
311C2×C42C23×C1111yescharacteristic
312C2×C42C23×C1111yescharacteristic
313C4⋊C8—24no—
314#103—44no—
315#102—44no—
316C22⋊C8—24no—
317C4×C8—24no—
318#95—22no—
319#95—22no—
320C2×C11—42no—
321C2×C11—82no—
322C2×C11#231111yescharacteristic
323C2×C11C2×#41611yescharacteristic
324C2×C11#289611yescharacteristic
325C2×C11#321212yes—
326C2×C11#323312yes—
327C24—21no—
328C24C2×D4×C1111yescharacteristic
329C2×Q8—21no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8C22×C4×C1112yes—
333C2×D4—24no—
334C2×D4—21no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—44no—
338C2×D4C22×C4×C1112yes—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4C11×C22⋊C414yes—
350C22×C4C11×C22⋊C414yes—
351C22×C4C22×C4×C1112yes—
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C2×D4×C1111yescharacteristic
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1112yes—
357C22×C4C2×D4×C1111yescharacteristic
358C22×C4C24×C1111yescharacteristic
359C2×C8—24no—
360C2×C8—24no—
361C2×C8—24no—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—44no—
371C4⋊C4—44no—
372C4⋊C4C22×C4×C1112yes—
373C4⋊C4C22×C4×C1112yes—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—24no—
379C22⋊C4—44no—
380C42—24no—
381C42—44no—
382C42C11×C22⋊C414yes—
383C42C11×C22⋊C414yes—
384C42C22×C4×C1112yes—
385C42C22×C4×C1112yes—
386C42C2×D4×C1112yes—
387C42C2×D4×C1112yes—
388C11#2186211yescharacteristic, direct product factor, Sylow
389C23—21no—
390C23—21no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—41no—
395C23—41no—
396C23—42no—
397C23—42no—
398C23C2×C11×C22⋊C412yes—
399C23C22×D4×C1111yescharacteristic
400Q8—24no—
401Q8—42no—
402D4—24no—
403D4—48no—
404D4—42no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—28no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—44no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—48no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4C2×C11×C22⋊C412yes—
426C2×C4C2×C11×C22⋊C412yes—
427C2×C4C2×C11×C22⋊C412yes—
428C2×C4C2×C11×C22⋊C412yes—
429C2×C4C2×C11×C22⋊C412yes—
430C2×C4C11×#13514yes—
431C2×C4C23×C4×C1111yescharacteristic
432C2×C4C22×D4×C1111yescharacteristic
433C2×C4C11×H(5,𝔽2)12yes—
434C2×C4C11×2−1+412yes—
435C8—44no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—82no—
445C22—82no—
446C22C22×C11×C22⋊C411yescharacteristic
447C22C11×#53511yescharacteristic
448C22C11×#53611yescharacteristic
449C22C2×C11×#13512yes—
450C22C11×#57512yes—
451C4—22no—
452C4—22no—
453C4—22no—
454C4—22no—
455C4—42no—
456C4—42no—
457C4—42no—
458C4—84no—
459C4C11×#41614yes—
460C4C11×#52012yes—
461C4C11×#53712yes—
462C2—42no—
463C2—82no—
464C2C11×#231111yescharacteristic
465C2C2×C11×#41611yescharacteristic
466C2C11×#289611yescharacteristic
467C2C11×#321212yes—
468C2C11×#323312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#431C2semidirect
3. C11×#2285C2semidirect
4. C11×#1991C2semidirect
5. C11×#1958C2semidirect
7. C11×#1873C2semidirect
8. C11×#1803C2semidirect
9. C11×#1802C2semidirect
11. C11×#529C4semidirect
93. #21862C11direct (N × H)
156. C2×#431C2×C11semidirect
157. #2285C2×C11semidirect
158. #1991C2×C11semidirect
159. #1958C2×C11semidirect
161. #1873C2×C11semidirect
162. #1803C2×C11semidirect
163. #1802C2×C11semidirect
212. #529C4×C11semidirect
388. C11#21862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4312
C11×#22852
C11×#19912
C11×#19582
C11×#18752
C11×#18732
C11×#18032
C11×#18022
#2186211