Finite Group Databasebeta

← C11×#22673 #14599866

Subgroups — C11×#22673 #14599866

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#440C212yesmaximal
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2351C211yesmaximal, characteristic, complemented
4C11×#2349C211yesmaximal, characteristic
5C11×#1944C212yesmaximal, complemented
6C11×#1865C212yesmaximal, complemented
7C11×#1864C212yesmaximal
8C11×#1846C211yesmaximal, characteristic, complemented
9C11×#1805C211yesmaximal, characteristic, complemented
10C11×#1804C211yesmaximal, characteristic
11C11×#1770C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C11×#440—28no—
18C4×C11×SD16C418yescomplemented
19C2×C11×#107C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#97C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C11×#389—22no—
30C11×#389C2212yes—
31C11×#389C2212yes—
32C11×#385—22no—
33C11×#382—21no—
34C11×#382C2211yescharacteristic
35C11×#382C2211yescharacteristic
36C11×#380—21no—
37C4×C11×C4⋊C4—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C2×C11×#95—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—22no—
47C2×C11×SD16C2×C414yes—
48C2×C11×SD16D414yes—
49C2×C11×SD16Q814yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×Q8×C11—22no—
54C4×Q8×C11—24no—
55C4×Q8×C11—42no—
56C4×Q8×C11C2×C414yescomplemented
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—42no—
60C4×D4×C11C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C11×#107—24no—
77C11×#106—42no—
78C11×#106C2×C414yescomplemented
79C11×C4⋊C8—22no—
80C11×#103—24no—
81C11×#103C2×C414yescomplemented
82C11×#102—24no—
83C11×#102C2×C414yes—
84C11×#97—24no—
85C4×C8×C11C2×C414yescomplemented
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95D411yescharacteristic
93C11×#95D411yescharacteristic
94#22673C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11C22×C412yes—
100C2×Q8×C11C2×D412yes—
101C2×Q8×C11C2×Q812yes—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11C22×C412yes—
106C2×D4×C11C2×D412yes—
107C2×D4×C11C2×Q812yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—44no—
115C22×C4×C11—44no—
116C22×C4×C11—82no—
117C22×C4×C11—82no—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C11×SD16C4⋊C4116yescomplemented
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C2×D412yes—
132C2×C8×C11C2×Q812yes—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4—82no—
144C11×C4⋊C4C22×C412yes—
145C11×C4⋊C4C22×C412yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—44no—
148C42×C11—24no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—44no—
152C42×C11C22×C412yes—
153C42×C11#4112yes—
154C2×#440C2×C1112yes—
155C2×C4×SD16C2×C1111yescharacteristic
156#2351C2×C1111yescharacteristic, complemented
157#2349C2×C1111yescharacteristic
158#1944C2×C1112yescomplemented
159#1865C2×C1112yescomplemented
160#1864C2×C1112yes—
161#1846C2×C1111yescharacteristic, complemented
162#1805C2×C1111yescharacteristic, complemented
163#1804C2×C1111yescharacteristic
164#1770C2×C1111yescharacteristic, complemented
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11C22×D411yescharacteristic
171Q8×C11—22no—
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×C11C2×C4⋊C414yes—
175D4×C11—22no—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11C2×C4⋊C414yes—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—84no—
201C2×C4×C11—88no—
202C2×C4×C11C4×D412yes—
203C2×C4×C11C4×D412yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×Q811yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C8×C11—22no—
211C8×C11—42no—
212C8×C11C2×C4⋊C414yes—
213C22×SD16C22×C1111yescharacteristic
214C2×C4×Q8C22×C1112yes—
215C2×C4×Q8C22×C1111yescharacteristic
216C2×C4×D4C22×C1112yes—
217C2×C4×D4C22×C1111yescharacteristic
218#440—28no—
219C4×SD16C4×C1118yescomplemented
220C2×#107C22×C1112yes—
221C2×#106C22×C1112yes—
222C2×#106C22×C1111yescharacteristic
223C2×C4⋊C8C22×C1111yescharacteristic
224C2×#103C22×C1112yes—
225C2×#103C22×C1111yescharacteristic
226C2×#102C22×C1112yes—
227C2×#102C22×C1111yescharacteristic
228C2×#97C22×C1112yes—
229C2×C4×C8C22×C1111yescharacteristic
230#389—22no—
231#389C22×C1112yes—
232#389C22×C1112yes—
233#385—22no—
234#382—21no—
235#382C22×C1111yescharacteristic
236#382C22×C1111yescharacteristic
237#380—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C22×C1111yescharacteristic
240C2×#95—21no—
241#340C22×C1112yes—
242#340C22×C1112yes—
243#336C22×C1112yes—
244C22×C11—24no—
245C22×C11—44no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—44no—
249C22×C11C2×C4×D411yescharacteristic
250C22×C11D4211yescharacteristic
251C22×C11D4×Q811yescharacteristic
252C22×C11#57512yes—
253C22×C11#57712yes—
254C4×C11—24no—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—82no—
262C4×C11—82no—
263C4×C11C22×C4⋊C411yescharacteristic
264C4×C11#52011yescharacteristic
265C4×C11#54711yescharacteristic
266C4×C11#55411yescharacteristic
267C22×Q8C23×C1111yescharacteristic
268C22×D4C23×C1111yescharacteristic
269C23×C4—21no—
270C23×C4—22no—
271C2×SD16C2×C4×C1114yes—
272C2×SD16D4×C1114yes—
273C2×SD16Q8×C1114yes—
274C22×C8C23×C1112yes—
275C22×C8C23×C1111yescharacteristic
276C22×C8C23×C1111yescharacteristic
277C4×Q8—22no—
278C4×Q8—24no—
279C4×Q8—42no—
280C4×Q8C2×C4×C1114yescomplemented
281C4×D4—24no—
282C4×D4—22no—
283C4×D4—42no—
284C4×D4C2×C4×C1114yes—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4D4×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C4⋊C4C23×C1111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—22no—
296C2×C42—21no—
297C2×C42—22no—
298C2×C42C23×C1112yes—
299C2×C42C23×C1111yescharacteristic
300#107—24no—
301#106—42no—
302#106C2×C4×C1114yescomplemented
303C4⋊C8—22no—
304#103—24no—
305#103C2×C4×C1114yescomplemented
306#102—24no—
307#102C2×C4×C1114yes—
308#97—24no—
309C4×C8C2×C4×C1114yescomplemented
310#95—21no—
311#95—22no—
312#95—21no—
313#95—22no—
314#95—21no—
315#95—21no—
316#95D4×C1111yescharacteristic
317#95D4×C1111yescharacteristic
318C2×C11—44no—
319C2×C11D4×C4⋊C411yescharacteristic
320C2×C11#294311yescharacteristic
321C2×C11#294911yescharacteristic
322C2×C11#327512yes—
323C2×C11#338812yes—
324C24—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8C22×C4×C1112yes—
329C2×Q8C2×D4×C1112yes—
330C2×Q8C2×Q8×C1112yes—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4C22×C4×C1112yes—
335C2×D4C2×D4×C1112yes—
336C2×D4C2×Q8×C1112yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—82no—
346C22×C4—82no—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C24×C1111yescharacteristic
352SD16C11×C4⋊C4116yescomplemented
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8C22×C4×C1112yes—
359C2×C8C22×C4×C1112yes—
360C2×C8C2×D4×C1112yes—
361C2×C8C2×Q8×C1112yes—
362C4⋊C4—24no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—42no—
370C4⋊C4—44no—
371C4⋊C4—44no—
372C4⋊C4—82no—
373C4⋊C4C22×C4×C1112yes—
374C4⋊C4C22×C4×C1112yes—
375C22⋊C4—24no—
376C22⋊C4—44no—
377C42—24no—
378C42—22no—
379C42—22no—
380C42—44no—
381C42C22×C4×C1112yes—
382C42C11×#4112yes—
383C11#2267311yescharacteristic, direct product factor, Sylow
384C23—22no—
385C23—22no—
386C23—22no—
387C23—42no—
388C23—42no—
389C23C22×D4×C1111yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—22no—
393Q8C2×C11×C4⋊C414yes—
394D4—22no—
395D4—22no—
396D4—22no—
397D4C2×C11×C4⋊C414yes—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—84no—
420C2×C4—88no—
421C2×C4C4×D4×C1112yes—
422C2×C4C4×D4×C1112yes—
423C2×C4C23×C4×C1111yescharacteristic
424C2×C4C22×D4×C1111yescharacteristic
425C2×C4C22×Q8×C1111yescharacteristic
426C2×C4C2×C11×#4111yescharacteristic
427C2×C4C11×H(5,𝔽2)11yescharacteristic
428C2×C4C11×2−1+411yescharacteristic
429C8—22no—
430C8—42no—
431C8C2×C11×C4⋊C414yes—
432C22—24no—
433C22—42no—
434C22—42no—
435C22—44no—
436C22—44no—
437C22C2×C4×D4×C1111yescharacteristic
438C22D42×C1111yescharacteristic
439C22D4×Q8×C1111yescharacteristic
440C22C11×#57512yes—
441C22C11×#57712yes—
442C4—22no—
443C4—22no—
444C4—24no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—82no—
450C4—82no—
451C4C22×C11×C4⋊C411yescharacteristic
452C4C11×#52011yescharacteristic
453C4C11×#54711yescharacteristic
454C4C11×#55411yescharacteristic
455C2—44no—
456C2D4×C11×C4⋊C411yescharacteristic
457C2C11×#294311yescharacteristic
458C2C11×#294911yescharacteristic
459C2C11×#327512yes—
460C2C11×#338812yes—
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
3. C11×#2351C2semidirect
5. C11×#1944C2semidirect
6. C11×#1865C2semidirect
8. C11×#1846C2semidirect
9. C11×#1805C2semidirect
11. C11×#1770C2semidirect
18. C4×C11×SD16C4semidirect
56. C4×Q8×C11C2×C4semidirect
78. C11×#106C2×C4semidirect
81. C11×#103C2×C4semidirect
85. C4×C8×C11C2×C4semidirect
94. #22673C11direct (N × H)
123. C11×SD16C4⋊C4semidirect
156. #2351C2×C11semidirect
158. #1944C2×C11semidirect
159. #1865C2×C11semidirect
161. #1846C2×C11semidirect
162. #1805C2×C11semidirect
164. #1770C2×C11semidirect
219. C4×SD16C4×C11semidirect
280. C4×Q8C2×C4×C11semidirect
302. #106C2×C4×C11semidirect
305. #103C2×C4×C11semidirect
309. C4×C8C2×C4×C11semidirect
352. SD16C11×C4⋊C4semidirect
383. C11#22673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4402
C2×C4×C11×SD162
C11×#23512
C11×#23492
C11×#19442
C11×#18652
C11×#18642
C11×#18462
C11×#18052
C11×#18042
C11×#17702
#2267311