Finite Group Databasebeta

← C11×#23223 #14600416

Subgroups — C11×#23223 #14600416

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic
2C11×#2369C211yesmaximal, characteristic, complemented
3C11×#2366C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic, complemented
5C11×#1982C211yesmaximal, characteristic
6C11×#1936C212yesmaximal, complemented
7C11×#1925C212yesmaximal, complemented
8C11×#1862C212yesmaximal, complemented
9C4×C11×#107C211yesmaximal, characteristic, complemented
10C11×#1770C211yesmaximal, characteristic, complemented
11C11×#1762C212yesmaximal, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2212yes—
16C11×#486C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#97C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#391—22no—
27C11×#390—21no—
28C11×#390C2212yes—
29C11×#389—21no—
30C11×#389C2212yes—
31C11×#386—22no—
32C4×C11×C4⋊C4—21no—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2211yescharacteristic
41C11×#336C2212yes—
42C22×Q8×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×C4×C11—22no—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yescomplemented
52C11×#127—22no—
53C11×#127C2×C414yes—
54C4×D4×C11—24no—
55C4×D4×C11—42no—
56C4×D4×C11—44no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11—22no—
72C2×C42×C11C2312yes—
73C2×C42×C11C2311yescharacteristic
74C11×#107—22no—
75C11×#107—22no—
76C11×C4⋊C8—22no—
77C11×#102—24no—
78C11×#102—42no—
79C11×#102C2×C418yescomplemented
80C11×#102C2×C418yescomplemented
81C11×#97—42no—
82C4×C8×C11C2×C414yescomplemented
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95D412yes—
88#23223C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—22no—
90C2×Q8×C11—24no—
91C2×Q8×C11—81no—
92C2×Q8×C11—81no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—81no—
103C2×D4×C11—81no—
104C2×D4×C11C22×C414yes—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11C22×C412yes—
126C2×C8×C11C22×C412yes—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4C22×C414yes—
139C11×C4⋊C4#4112yes—
140C11×C4⋊C4#4112yes—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—44no—
143C11×C22⋊C4—82no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—42no—
147C42×C11—42no—
148C42×C11—82no—
149C42×C11C22×C412yes—
150C42×C11#4112yes—
151C2×#486C2×C1111yescharacteristic
152#2369C2×C1111yescharacteristic, complemented
153#2366C2×C1111yescharacteristic
154#1987C2×C1111yescharacteristic, complemented
155#1982C2×C1111yescharacteristic
156#1936C2×C1112yescomplemented
157#1925C2×C1112yescomplemented
158#1862C2×C1112yescomplemented
159C4×#107C2×C1111yescharacteristic, complemented
160#1770C2×C1111yescharacteristic, complemented
161#1762C2×C1112yescomplemented
162C23×C11—24no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11C22×D411yescharacteristic
170Q8×C11—84no—
171D4×C11—24no—
172D4×C11—24no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—48no—
176D4×C11—84no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—24no—
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—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—88no—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C4×D412yes—
203C2×C4×C11AGL(1,ℤ/8)12yes—
204C2×C4×C11#13712yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C8×C11—22no—
212C8×C11—22no—
213C8×C11—42no—
214C2×C4⋊Q8C22×C1111yescharacteristic
215C2×#127C22×C1111yescharacteristic
216C2×C4×D4—21no—
217C2×C4×D4C22×C1112yes—
218#486C4×C1118yescomplemented
219C2×#107C22×C1111yescharacteristic
220C2×#107C22×C1111yescharacteristic
221C2×C4⋊C8C22×C1111yescharacteristic
222C2×#102C22×C1112yes—
223C2×#102C22×C1112yes—
224C2×#102C22×C1112yes—
225C2×#102C22×C1112yes—
226C2×#97C22×C1112yes—
227C2×C4×C8C22×C1111yescharacteristic
228#391—22no—
229#390—21no—
230#390C22×C1112yes—
231#389—21no—
232#389C22×C1112yes—
233#386—22no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4C22×C1111yescharacteristic
236C4×C4⋊C4C22×C1112yes—
237C4×C4⋊C4C22×C1111yescharacteristic
238C4×C4⋊C4C22×C1111yescharacteristic
239#340C22×C1112yes—
240#340C22×C1112yes—
241#340C22×C1111yescharacteristic
242#340C22×C1111yescharacteristic
243#336C22×C1112yes—
244C22×C11—44no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11C2×C4×D411yescharacteristic
252C22×C11#54611yescharacteristic
253C22×C11#54811yescharacteristic
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C22×C11#57611yescharacteristic
257C22×C11#57611yescharacteristic
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11#44014yes—
267C4×C11C4×#4111yescharacteristic
268C4×C11#52011yescharacteristic
269C4×C11#55611yescharacteristic
270C4×C11#55911yescharacteristic
271C22×Q8—21no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4C23×C1112yes—
275C23×C4—22no—
276C22×C8C23×C1112yes—
277C22×C8C23×C1111yescharacteristic
278C22×C8C23×C1111yescharacteristic
279C4⋊Q8—22no—
280C4⋊Q8C2×C4×C1114yescomplemented
281#127—22no—
282#127C2×C4×C1114yes—
283C4×D4—24no—
284C4×D4—42no—
285C4×D4—44no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4D4×C1111yescharacteristic
289C2×C4⋊C4D4×C1111yescharacteristic
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C4⋊C4C23×C1112yes—
293C2×C4⋊C4C23×C1111yescharacteristic
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—22no—
301C2×C42C23×C1112yes—
302C2×C42C23×C1111yescharacteristic
303#107—22no—
304#107—22no—
305C4⋊C8—22no—
306#102—24no—
307#102—42no—
308#102C2×C4×C1118yescomplemented
309#102C2×C4×C1118yescomplemented
310#97—42no—
311C4×C8C2×C4×C1114yescomplemented
312#95—22no—
313#95—21no—
314#95—22no—
315#95—21no—
316#95D4×C1112yes—
317C2×C11—84no—
318C2×C11#236711yescharacteristic
319C2×C11C2×#44011yescharacteristic
320C2×C11#294811yescharacteristic
321C2×C11#332511yescharacteristic
322C2×C11#333311yescharacteristic
323C2×C11#336611yescharacteristic
324C2×C11#337511yescharacteristic
325C24—22no—
326C2×Q8—24no—
327C2×Q8—81no—
328C2×Q8—81no—
329C2×D4—24no—
330C2×D4—24no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—81no—
339C2×D4—81no—
340C2×D4C22×C4×C1114yes—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—44no—
347C22×C4—44no—
348C22×C4—82no—
349C22×C4C2×D4×C1112yes—
350C22×C4C2×D4×C1112yes—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C24×C1111yescharacteristic
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8C22×C4×C1112yes—
362C2×C8C22×C4×C1112yes—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—82no—
374C4⋊C4C22×C4×C1114yes—
375C4⋊C4C11×#4112yes—
376C4⋊C4C11×#4112yes—
377C22⋊C4—44no—
378C22⋊C4—44no—
379C22⋊C4—82no—
380C42—22no—
381C42—22no—
382C42—42no—
383C42—42no—
384C42—82no—
385C42C22×C4×C1112yes—
386C42C11×#4112yes—
387C11#2322311yescharacteristic, direct product factor, Sylow
388C23—24no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23C22×D4×C1111yescharacteristic
396Q8—84no—
397D4—24no—
398D4—24no—
399D4—42no—
400D4—42no—
401D4—48no—
402D4—84no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—88no—
427C2×C4C4×D4×C1112yes—
428C2×C4C4×D4×C1112yes—
429C2×C4C11×AGL(1,ℤ/8)12yes—
430C2×C4C11×#13712yes—
431C2×C4C23×C4×C1111yescharacteristic
432C2×C4C2×C11×#4111yescharacteristic
433C2×C4C2×C11×#4111yescharacteristic
434C2×C4C2×C11×#4111yescharacteristic
435C2×C4C11×H(5,𝔽2)11yescharacteristic
436C2×C4C11×2−1+411yescharacteristic
437C8—22no—
438C8—22no—
439C8—42no—
440C22—44no—
441C22—44no—
442C22—44no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22C2×C4×D4×C1111yescharacteristic
448C22C11×#54611yescharacteristic
449C22C11×#54811yescharacteristic
450C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
451C22C2×C11×#13711yescharacteristic
452C22C11×#57611yescharacteristic
453C22C11×#57611yescharacteristic
454C4—22no—
455C4—44no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—81no—
461C4—81no—
462C4C11×#44014yes—
463C4C4×C11×#4111yescharacteristic
464C4C11×#52011yescharacteristic
465C4C11×#55611yescharacteristic
466C4C11×#55911yescharacteristic
467C2—84no—
468C2C11×#236711yescharacteristic
469C2C2×C11×#44011yescharacteristic
470C2C11×#294811yescharacteristic
471C2C11×#332511yescharacteristic
472C2C11×#333311yescharacteristic
473C2C11×#336611yescharacteristic
474C2C11×#337511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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
2. C11×#2369C2semidirect
4. C11×#1987C2semidirect
6. C11×#1936C2semidirect
7. C11×#1925C2semidirect
8. C11×#1862C2semidirect
9. C4×C11×#107C2semidirect
10. C11×#1770C2semidirect
11. C11×#1762C2semidirect
16. C11×#486C4semidirect
51. C11×C4⋊Q8C2×C4semidirect
79. C11×#102C2×C4semidirect
80. C11×#102C2×C4semidirect
82. C4×C8×C11C2×C4semidirect
88. #23223C11direct (N × H)
152. #2369C2×C11semidirect
154. #1987C2×C11semidirect
156. #1936C2×C11semidirect
157. #1925C2×C11semidirect
158. #1862C2×C11semidirect
159. C4×#107C2×C11semidirect
160. #1770C2×C11semidirect
161. #1762C2×C11semidirect
218. #486C4×C11semidirect
280. C4⋊Q8C2×C4×C11semidirect
308. #102C2×C4×C11semidirect
309. #102C2×C4×C11semidirect
311. C4×C8C2×C4×C11semidirect
387. C11#23223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C11×#23692
C11×#23662
C11×#19872
C11×#19822
C11×#19362
C11×#19252
C11×#18622
C4×C11×#1072
C11×#17702
C11×#17622
#2322311