Finite Group Databasebeta

← C11×#11392 #14588585

Subgroups — C11×#11392 #14588585

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic
2C2×C11×#343C211yesmaximal, characteristic
3C11×#1736C212yesmaximal
4C2×C11×#339C212yesmaximal
5C11×C4⋊#95C211yesmaximal, characteristic
6C22×C11×M16C2212yes—
7C11×#544—24no—
8C11×#544—22no—
9C11×#544C414yescomplemented
10C2×C11×C4⋊Q8—22no—
11C2×C11×#125—22no—
12C2×C11×C22⋊Q8—22no—
13C2×C11×#117C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C2×C11×#95—22no—
18C11×#343—22no—
19C11×#340—22no—
20C11×#340—22no—
21C11×#339—24no—
22C22×Q8×C11—22no—
23C23×C4×C11—21no—
24C23×C4×C11—21no—
25C23×C4×C11D412yes—
26C23×C4×C11C2311yescharacteristic
27C2×C11×M16—22no—
28C2×C11×M16—22no—
29C2×C11×M16—22no—
30C2×C11×M16—22no—
31C2×C11×M16—22no—
32C2×C11×M16Q814yescomplemented
33C22×C8×C11—22no—
34C11×C4⋊Q8—28no—
35C11×C4⋊Q8—28no—
36C11×#125—28no—
37C11×#125—28no—
38C11×C22⋊Q8—28no—
39C11×C22⋊Q8—28no—
40C11×#117—22no—
41C11×#117—22no—
42C11×#117C2×C414yes—
43C11×#117D414yes—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4Q812yescomplemented
56C2×C11×C22⋊C4—22no—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—21no—
61C2×C42×C11Q812yescomplemented
62C11×#95—44no—
63#11392C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11C2×D411yescharacteristic
65C2×Q8×C11—28no—
66C2×Q8×C11—82no—
67C2×Q8×C11—82no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C22⋊C414yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×Q812yes—
92C22×C4×C11C2×Q811yescharacteristic
93C22×C4×C11C2×Q811yescharacteristic
94C22×C4×C11#4112yes—
95C22×C4×C11#4111yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C11×M16—24no—
98C11×M16—24no—
99C11×M16—42no—
100C11×M16—42no—
101C2×C8×C11—24no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—216no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4C22⋊C414yes—
113C11×C4⋊C4C22⋊C414yes—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C42×C11—24no—
117C42×C11—24no—
118C42×C11—24no—
119C42×C11—42no—
120C2×#544C2×C1111yescharacteristic
121C2×#343C2×C1111yescharacteristic
122#1736C2×C1112yes—
123C2×#339C2×C1112yes—
124C4⋊#95C2×C1111yescharacteristic
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11#12011yescharacteristic
131C23×C11#12011yescharacteristic
132C23×C11C22⋊Q811yescharacteristic
133C23×C11C22⋊Q811yescharacteristic
134C23×C11#12411yescharacteristic
135C23×C11C4⋊Q811yescharacteristic
136Q8×C11—88no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11—82no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C4×Q812yes—
162C2×C4×C11C4×Q811yescharacteristic
163C2×C4×C11C4×Q811yescharacteristic
164C2×C4×C11#12012yes—
165C2×C4×C11C22⋊Q812yes—
166C2×C4×C11C22⋊Q812yes—
167C2×C4×C11C22⋊Q812yes—
168C2×C4×C11C22⋊Q812yes—
169C2×C4×C11C22⋊Q812yes—
170C2×C4×C11#12412yes—
171C2×C4×C11#12412yes—
172C2×C4×C11#12411yescharacteristic
173C2×C4×C11C4⋊Q812yes—
174C2×C4×C11C4⋊Q812yes—
175C2×C4×C11C4⋊Q811yescharacteristic
176C8×C11—44no—
177C22×M16C22×C1112yes—
178#544—24no—
179#544—22no—
180#544C4×C1114yescomplemented
181C2×C4⋊Q8—22no—
182C2×#125—22no—
183C2×C22⋊Q8—22no—
184C2×#117C22×C1112yes—
185C22×C4⋊C4C22×C1111yescharacteristic
186C22×C4⋊C4C22×C1111yescharacteristic
187C22×C42C22×C1111yescharacteristic
188C2×#95—22no—
189#343—22no—
190#340—22no—
191#340—22no—
192#339—24no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11#37911yescharacteristic
206C22×C11#39111yescharacteristic
207C22×C11#39111yescharacteristic
208C22×C11#39311yescharacteristic
209C22×C11#39311yescharacteristic
210C22×C11#39511yescharacteristic
211C22×C11#39511yescharacteristic
212C22×C11#45311yescharacteristic
213C22×C11#45411yescharacteristic
214C22×C11#45511yescharacteristic
215C22×C11#45611yescharacteristic
216C4×C11—44no—
217C4×C11—44no—
218C4×C11—44no—
219C4×C11—44no—
220C4×C11—82no—
221C4×C11#39112yes—
222C4×C11#39112yes—
223C4×C11#39312yes—
224C4×C11#39512yes—
225C22×Q8—22no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4D4×C1112yes—
229C23×C4C23×C1111yescharacteristic
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16Q8×C1114yescomplemented
236C22×C8—22no—
237C4⋊Q8—28no—
238C4⋊Q8—28no—
239#125—28no—
240#125—28no—
241C22⋊Q8—28no—
242C22⋊Q8—28no—
243#117—22no—
244#117—22no—
245#117C2×C4×C1114yes—
246#117D4×C1114yes—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4C2×C4×C1112yes—
255C2×C4⋊C4D4×C1112yes—
256C2×C4⋊C4D4×C1112yes—
257C2×C4⋊C4D4×C1112yes—
258C2×C4⋊C4Q8×C1112yescomplemented
259C2×C22⋊C4—22no—
260C2×C42—22no—
261C2×C42—22no—
262C2×C42—22no—
263C2×C42—21no—
264C2×C42Q8×C1112yescomplemented
265#95—44no—
266C2×C11—21no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11#144611yescharacteristic
271C2×C11#179211yescharacteristic
272C2×C11#179311yescharacteristic
273C2×C11#202711yescharacteristic
274C2×C11#202811yescharacteristic
275C2×C11#206011yescharacteristic
276C2×C11#206111yescharacteristic
277C24C2×D4×C1111yescharacteristic
278C2×Q8—28no—
279C2×Q8—82no—
280C2×Q8—82no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4C11×C22⋊C414yes—
300C22×C4C22×C4×C1111yescharacteristic
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1112yes—
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C2×Q8×C1112yes—
305C22×C4C2×Q8×C1111yescharacteristic
306C22×C4C2×Q8×C1111yescharacteristic
307C22×C4C11×#4112yes—
308C22×C4C11×#4111yescharacteristic
309C22×C4C11×#4111yescharacteristic
310M16—24no—
311M16—24no—
312M16—42no—
313M16—42no—
314C2×C8—24no—
315C2×C8—42no—
316C2×C8—42no—
317C4⋊C4—28no—
318C4⋊C4—216no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—24no—
324C4⋊C4—42no—
325C4⋊C4C11×C22⋊C414yes—
326C4⋊C4C11×C22⋊C414yes—
327C22⋊C4—24no—
328C22⋊C4—24no—
329C42—24no—
330C42—24no—
331C42—24no—
332C42—42no—
333C11#1139211yescharacteristic, direct product factor, Sylow
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23C2×C11×C22⋊C411yescharacteristic
339C23C11×#12011yescharacteristic
340C23C11×#12011yescharacteristic
341C23C11×C22⋊Q811yescharacteristic
342C23C11×C22⋊Q811yescharacteristic
343C23C11×#12411yescharacteristic
344C23C11×C4⋊Q811yescharacteristic
345Q8—88no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4C2×C11×C22⋊C412yes—
370C2×C4C4×Q8×C1112yes—
371C2×C4C4×Q8×C1111yescharacteristic
372C2×C4C4×Q8×C1111yescharacteristic
373C2×C4C11×#12012yes—
374C2×C4C11×C22⋊Q812yes—
375C2×C4C11×C22⋊Q812yes—
376C2×C4C11×C22⋊Q812yes—
377C2×C4C11×C22⋊Q812yes—
378C2×C4C11×C22⋊Q812yes—
379C2×C4C11×#12412yes—
380C2×C4C11×#12412yes—
381C2×C4C11×#12411yescharacteristic
382C2×C4C11×C4⋊Q812yes—
383C2×C4C11×C4⋊Q812yes—
384C2×C4C11×C4⋊Q811yescharacteristic
385C8—44no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22C11×#37911yescharacteristic
399C22C11×#39111yescharacteristic
400C22C11×#39111yescharacteristic
401C22C11×#39311yescharacteristic
402C22C11×#39311yescharacteristic
403C22C11×#39511yescharacteristic
404C22C11×#39511yescharacteristic
405C22C11×#45311yescharacteristic
406C22C11×#45411yescharacteristic
407C22C11×#45511yescharacteristic
408C22C11×#45611yescharacteristic
409C4—44no—
410C4—44no—
411C4—44no—
412C4—44no—
413C4—82no—
414C4C11×#39112yes—
415C4C11×#39112yes—
416C4C11×#39312yes—
417C4C11×#39512yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2C11×#144611yescharacteristic
423C2C11×#179211yescharacteristic
424C2C11×#179311yescharacteristic
425C2C11×#202711yescharacteristic
426C2C11×#202811yescharacteristic
427C2C11×#206011yescharacteristic
428C2C11×#206111yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
9. C11×#544C4semidirect
32. C2×C11×M16Q8semidirect
55. C2×C11×C4⋊C4Q8semidirect
61. C2×C42×C11Q8semidirect
63. #11392C11direct (N × H)
180. #544C4×C11semidirect
235. C2×M16Q8×C11semidirect
258. C2×C4⋊C4Q8×C11semidirect
264. C2×C42Q8×C11semidirect
333. C11#11392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#3432
C11×#17362
C2×C11×#3392
C11×C4⋊#952
#1139211