Finite Group Databasebeta

← C11×#23612 #14600805

Subgroups — C11×#23612 #14600805

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#427C211yesmaximal, characteristic, complemented
2C2×C11×#424C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic
4C22×C11×#102C211yesmaximal, characteristic
5C11×#2317C211yesmaximal, characteristic, complemented
6C11×#2309C211yesmaximal, characteristic
7C11×#2067C214yesmaximal, complemented
8C11×#2065C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#427—24no—
18C2×C11×#107C2212yescomplemented
19C2×C11×#106C2212yescomplemented
20C11×#424—24no—
21C2×C11×C4⋊C8C2212yescomplemented
22C2×C11×C4⋊C8C2212yescomplemented
23C11×#418—24no—
24C2×C11×#102—24no—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2214yes—
28C11×#390—21no—
29C11×#390—21no—
30C11×#390C2214yes—
31C11×#389C2214yescomplemented
32C11×#385—22no—
33C11×#384—21no—
34C11×#382—21no—
35C11×#379—22no—
36C11×#340C2214yescomplemented
37C25×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11Q814yes—
45C22×D4×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C22×C8×C11—22no—
52C22×C8×C11—22no—
53C22×C8×C11D414yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#117—22no—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117—22no—
61C11×#117—22no—
62C11×#117D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2312yes—
80C11×#107—24no—
81C11×#106—24no—
82C11×C4⋊C8—24no—
83C11×C4⋊C8—24no—
84C11×#102—24no—
85C11×#102—24no—
86C11×#102—28no—
87C11×#95—24no—
88#23612C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—42no—
92C24×C11—42no—
93C24×C11—82no—
94C24×C11—82no—
95C24×C11C2×D411yescharacteristic
96C2×D4×C11—28no—
97C2×D4×C11—28no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—44no—
108C2×D4×C11C2×Q814yes—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—82no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×Q812yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C11×M16—44no—
125C2×C8×C11—28no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11C2×D412yes—
134C2×C8×C11C2×D412yes—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—84no—
144C11×C4⋊C4C2×D414yes—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—84no—
149C11×C22⋊C4—84no—
150C42×C11—24no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—42no—
154C2×#427C2×C1111yescharacteristic, complemented
155C2×#424C2×C1111yescharacteristic, complemented
156C2×#418C2×C1111yescharacteristic
157C22×#102C2×C1111yescharacteristic
158#2317C2×C1111yescharacteristic, complemented
159#2309C2×C1111yescharacteristic
160#2067C2×C1114yescomplemented
161#2065C2×C1114yescomplemented
162#1736C2×C1111yescharacteristic, complemented
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—48no—
171C23×C11—88no—
172C23×C11—88no—
173C23×C11—84no—
174C23×C11—84no—
175C23×C11#12112yes—
176C23×C11#12112yes—
177C23×C11C22⋊Q812yes—
178C23×C11C22×D411yescharacteristic
179D4×C11—24no—
180D4×C11—24no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—48no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—84no—
197C2×C4×C11#12114yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11C22⋊Q814yes—
201C2×C4×C11C22⋊Q814yes—
202C2×C4×C11C22⋊Q812yes—
203C2×C4×C11#12614yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×Q811yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C8×C11—22no—
211C8×C11—22no—
212C8×C11—42no—
213C23×D4C22×C1111yescharacteristic
214C22×M16C22×C1111yescharacteristic
215C23×C8C22×C1111yescharacteristic
216C2×#117C22×C1111yescharacteristic
217C2×#117C22×C1111yescharacteristic
218C2×#117C22×C1111yescharacteristic
219C22×C4⋊C4C22×C1111yescharacteristic
220#427—24no—
221C2×#107C22×C1112yescomplemented
222C2×#106C22×C1112yescomplemented
223#424—24no—
224C2×C4⋊C8C22×C1112yescomplemented
225C2×C4⋊C8C22×C1112yescomplemented
226#418—24no—
227C2×#102—24no—
228C2×#102C22×C1112yes—
229C2×#102C22×C1114yes—
230C2×#102C22×C1112yes—
231#390—21no—
232#390—21no—
233#390C22×C1114yes—
234#389C22×C1114yescomplemented
235#385—22no—
236#384—21no—
237#382—21no—
238#379—22no—
239#340C22×C1114yescomplemented
240C22×C11—24no—
241C22×C11—24no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—48no—
245C22×C11—44no—
246C22×C11—816no—
247C22×C11—84no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11#39614yes—
251C22×C11C2×#12111yescharacteristic
252C22×C11C2×#12111yescharacteristic
253C22×C11C2×C22⋊Q811yescharacteristic
254C22×C11#57612yes—
255C22×C11#57712yes—
256C4×C11—44no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—82no—
260C4×C11—82no—
261C4×C11#39614yes—
262C4×C11C2×#12111yescharacteristic
263C4×C11C2×C22⋊Q811yescharacteristic
264C4×C11C2×C22⋊Q811yescharacteristic
265C4×C11C2×#12611yescharacteristic
266C25—21no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4Q8×C1114yes—
274C22×D4C23×C1112yes—
275C23×C4—21no—
276C23×C4C23×C1111yescharacteristic
277C2×M16—22no—
278C2×M16—22no—
279C2×M16—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8D4×C1114yes—
283C22×C8C23×C1112yes—
284C22×C8C23×C1111yescharacteristic
285C22×C8C23×C1111yescharacteristic
286#117—22no—
287#117—22no—
288#117—22no—
289#117—22no—
290#117—22no—
291#117D4×C1114yes—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4D4×C1111yescharacteristic
297C2×C4⋊C4D4×C1111yescharacteristic
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1112yes—
300C2×C4⋊C4C23×C1112yes—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4D4×C1112yes—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42C23×C1112yes—
309#107—24no—
310#106—24no—
311C4⋊C8—24no—
312C4⋊C8—24no—
313#102—24no—
314#102—24no—
315#102—28no—
316#95—24no—
317C2×C11—24no—
318C2×C11—84no—
319C2×C11C2×#39611yescharacteristic
320C2×C11#304512yes—
321C2×C11#305711yescharacteristic
322C2×C11#305811yescharacteristic
323C2×C11#308112yes—
324C24—22no—
325C24—24no—
326C24—42no—
327C24—42no—
328C24—82no—
329C24—82no—
330C24C2×D4×C1111yescharacteristic
331C2×D4—28no—
332C2×D4—28no—
333C2×D4—24no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—44no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—44no—
343C2×D4C2×Q8×C1114yes—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—82no—
349C22×C4C2×D4×C1112yes—
350C22×C4C2×D4×C1112yes—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1112yes—
354C22×C4C2×Q8×C1112yes—
355C22×C4C11×#4112yes—
356C22×C4C11×#4112yes—
357C22×C4C11×#4112yes—
358C22×C4C24×C1111yescharacteristic
359M16—44no—
360C2×C8—28no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8C2×D4×C1112yes—
369C2×C8C2×D4×C1112yes—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—42no—
378C4⋊C4—84no—
379C4⋊C4C2×D4×C1114yes—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—42no—
383C22⋊C4—84no—
384C22⋊C4—84no—
385C42—24no—
386C42—22no—
387C42—22no—
388C42—42no—
389C11#2361211yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23—22no—
392C23—24no—
393C23—42no—
394C23—42no—
395C23—48no—
396C23—44no—
397C23—44no—
398C23—88no—
399C23—88no—
400C23—84no—
401C23—84no—
402C23C11×#12112yes—
403C23C11×#12112yes—
404C23C11×C22⋊Q812yes—
405C23C22×D4×C1111yescharacteristic
406D4—24no—
407D4—24no—
408D4—42no—
409D4—42no—
410D4—48no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—84no—
424C2×C4C11×#12114yes—
425C2×C4C11×#12112yes—
426C2×C4C11×#12112yes—
427C2×C4C11×C22⋊Q814yes—
428C2×C4C11×C22⋊Q814yes—
429C2×C4C11×C22⋊Q812yes—
430C2×C4C11×#12614yes—
431C2×C4C22×D4×C1111yescharacteristic
432C2×C4C22×D4×C1111yescharacteristic
433C2×C4C22×Q8×C1111yescharacteristic
434C2×C4C2×C11×#4111yescharacteristic
435C2×C4C2×C11×#4111yescharacteristic
436C2×C4C2×C11×#4111yescharacteristic
437C8—22no—
438C8—22no—
439C8—42no—
440C22—24no—
441C22—22no—
442C22—22no—
443C22—24no—
444C22—44no—
445C22—48no—
446C22—816no—
447C22—84no—
448C22—82no—
449C22—82no—
450C22C11×#39614yes—
451C22C2×C11×#12111yescharacteristic
452C22C2×C11×#12111yescharacteristic
453C22C2×C11×C22⋊Q811yescharacteristic
454C22C11×#57612yes—
455C22C11×#57712yes—
456C4—44no—
457C4—42no—
458C4—42no—
459C4—82no—
460C4—82no—
461C4C11×#39614yes—
462C4C2×C11×#12111yescharacteristic
463C4C2×C11×C22⋊Q811yescharacteristic
464C4C2×C11×C22⋊Q811yescharacteristic
465C4C2×C11×#12611yescharacteristic
466C2—24no—
467C2—84no—
468C2C2×C11×#39611yescharacteristic
469C2C11×#304512yes—
470C2C11×#305711yescharacteristic
471C2C11×#305811yescharacteristic
472C2C11×#308112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#427C2semidirect
2. C2×C11×#424C2semidirect
5. C11×#2317C2semidirect
7. C11×#2067C2semidirect
8. C11×#2065C2semidirect
9. C11×#1736C2semidirect
18. C2×C11×#107C22semidirect
19. C2×C11×#106C22semidirect
21. C2×C11×C4⋊C8C22semidirect
22. C2×C11×C4⋊C8C22semidirect
31. C11×#389C22semidirect
36. C11×#340C22semidirect
88. #23612C11direct (N × H)
154. C2×#427C2×C11semidirect
155. C2×#424C2×C11semidirect
158. #2317C2×C11semidirect
160. #2067C2×C11semidirect
161. #2065C2×C11semidirect
162. #1736C2×C11semidirect
221. C2×#107C22×C11semidirect
222. C2×#106C22×C11semidirect
224. C2×C4⋊C8C22×C11semidirect
225. C2×C4⋊C8C22×C11semidirect
234. #389C22×C11semidirect
239. #340C22×C11semidirect
389. C11#23612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4272
C2×C11×#4242
C2×C11×#4182
C22×C11×#1022
C11×#23172
C11×#23092
C11×#20672
C11×#20652
C11×#17362
#2361211