Finite Group Databasebeta

← C11×#22181 #14599374

Subgroups — C11×#22181 #14599374

Order 2816.

1062 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×#466C211yesmaximal, characteristic
2C4×C11×#121C212yesmaximal, complemented
3C11×#1925C212yesmaximal, complemented
4C11×#1918C212yesmaximal, complemented
5C11×#1893C212yesmaximal, complemented
6C11×#1879C212yesmaximal, complemented
7C11×#1862C212yesmaximal, complemented
8C11×#1808C211yesmaximal, characteristic, complemented
9C2×C11×#336C211yesmaximal, characteristic, complemented
10C22×C11×D8C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#121C2212yes—
14C2×C4×D4×C11—22no—
15C2×C4×D4×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C11×#466C418yescomplemented
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C11×#390C2212yes—
25C11×#389C2212yes—
26C11×#388—22no—
27C11×#386—22no—
28C11×#380C2212yes—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C22⋊C4—22no—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×D4×C11—22no—
37C22×D4×C11C2312yes—
38C23×C4×C11—22no—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C2×C11×D8—41no—
43C2×C11×D8—41no—
44C2×C11×D8C2×C414yescomplemented
45C22×C8×C11—22no—
46C22×C8×C11—41no—
47C22×C8×C11—41no—
48C22×C8×C11—41no—
49C22×C8×C11—41no—
50C22×C8×C11C2×C414yescomplemented
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#121—24no—
55C11×#121C2×C418yescomplemented
56C4×D4×C11—42no—
57C4×D4×C11—42no—
58C4×D4×C11—48no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C42×C11—22no—
69C2×C42×C11—41no—
70C2×C42×C11—41no—
71C2×C42×C11D412yes—
72C2×C42×C11C2312yes—
73C11×#107—41no—
74C11×#107—41no—
75C11×#107C2×C414yescomplemented
76C11×#102—42no—
77C11×#102—42no—
78C11×#102C2×C418yescomplemented
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82#22181C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—22no—
84C24×C11C2×D411yescharacteristic
85C2×D4×C11—28no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—44no—
92C2×D4×C11—44no—
93C2×D4×C11C22×C414yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—44no—
107C22×C4×C11—44no—
108C22×C4×C11—44no—
109C22×C4×C11D814yescomplemented
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C11×D8—44no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—44no—
125C2×C8×C11—44no—
126C2×C8×C11C22×C412yes—
127C2×C8×C11C22×C412yes—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—44no—
134C11×C4⋊C4C22×C414yes—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—44no—
137C11×C22⋊C4—44no—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—44no—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11—42no—
143C42×C11—44no—
144C2×#466C2×C1111yescharacteristic
145C4×#121C2×C1112yescomplemented
146#1925C2×C1112yescomplemented
147#1918C2×C1112yescomplemented
148#1893C2×C1112yescomplemented
149#1879C2×C1112yescomplemented
150#1862C2×C1112yescomplemented
151#1808C2×C1111yescharacteristic, complemented
152C2×#336C2×C1111yescharacteristic, complemented
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—24no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11C4×D412yes—
165C23×C11C2×D812yes—
166C23×C11#13512yes—
167C23×C11C22×D411yescharacteristic
168D4×C11—24no—
169D4×C11—24no—
170D4×C11—416no—
171D4×C11—42no—
172D4×C11—42no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—44no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—88no—
196C2×C4×C11C4×D412yes—
197C2×C4×C11C2×D814yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11H(5,𝔽2)11yescharacteristic
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×C4×C11H(5,𝔽2)11yescharacteristic
203C2×C4×C112−1+411yescharacteristic
204C8×C11—22no—
205C8×C11—22no—
206C8×C11—42no—
207C22×D8C22×C1111yescharacteristic
208C23×C8C22×C1111yescharacteristic
209C23×C8C22×C1111yescharacteristic
210C2×#121C22×C1112yes—
211C2×C4×D4—22no—
212C2×C4×D4C22×C1112yes—
213C22×C42C22×C1111yescharacteristic
214#466C4×C1118yescomplemented
215C2×#107C22×C1111yescharacteristic
216C2×#107C22×C1111yescharacteristic
217C2×#107C22×C1111yescharacteristic
218C2×#102C22×C1112yes—
219C2×#102C22×C1112yes—
220C2×#102C22×C1112yes—
221#390C22×C1112yes—
222#389C22×C1112yes—
223#388—22no—
224#386—22no—
225#380C22×C1112yes—
226C4×C4⋊C4C22×C1112yes—
227C4×C22⋊C4—22no—
228#340C22×C1112yes—
229#340C22×C1112yes—
230#340C22×C1112yes—
231#336C22×C1112yes—
232#336C22×C1112yes—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—44no—
240C22×C11—44no—
241C22×C11—44no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11C4×D814yes—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#53411yescharacteristic
249C22×C11#53711yescharacteristic
250C22×C11C22×D811yescharacteristic
251C22×C11C2×#13511yescharacteristic
252C22×C11#57511yescharacteristic
253C22×C11#57511yescharacteristic
254C4×C11—22no—
255C4×C11—24no—
256C4×C11—42no—
257C4×C11—44no—
258C4×C11—82no—
259C4×C11—82no—
260C4×C11#51811yescharacteristic
261C4×C11#52011yescharacteristic
262C4×C11#53811yescharacteristic
263C4×C11#53911yescharacteristic
264C22×D4—22no—
265C22×D4C23×C1112yes—
266C23×C4—22no—
267C23×C4D4×C1111yescharacteristic
268C23×C4D4×C1111yescharacteristic
269C23×C4C23×C1111yescharacteristic
270C2×D8—41no—
271C2×D8—41no—
272C2×D8C2×C4×C1114yescomplemented
273C22×C8—22no—
274C22×C8—41no—
275C22×C8—41no—
276C22×C8—41no—
277C22×C8—41no—
278C22×C8C2×C4×C1114yescomplemented
279C22×C8C23×C1112yes—
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1111yescharacteristic
282#121—24no—
283#121C2×C4×C1118yescomplemented
284C4×D4—42no—
285C4×D4—42no—
286C4×D4—48no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C42—22no—
297C2×C42—41no—
298C2×C42—41no—
299C2×C42D4×C1112yes—
300C2×C42C23×C1112yes—
301#107—41no—
302#107—41no—
303#107C2×C4×C1114yescomplemented
304#102—42no—
305#102—42no—
306#102C2×C4×C1118yescomplemented
307#95—22no—
308#95—22no—
309#95—22no—
310C2×C11—24no—
311C2×C11—84no—
312C2×C11#232511yescharacteristic
313C2×C11C2×C4×D811yescharacteristic
314C2×C11#294311yescharacteristic
315C2×C11#318611yescharacteristic
316C2×C11#319111yescharacteristic
317C2×C11#324511yescharacteristic
318C2×C11#325011yescharacteristic
319C24—22no—
320C24C2×D4×C1111yescharacteristic
321C2×D4—28no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—44no—
328C2×D4—44no—
329C2×D4C22×C4×C1114yes—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4C11×D814yescomplemented
346C22×C4C22×C4×C1112yes—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1112yes—
350C22×C4C11×#4112yes—
351C22×C4C24×C1111yescharacteristic
352D8—44no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—44no—
361C2×C8—44no—
362C2×C8C22×C4×C1112yes—
363C2×C8C22×C4×C1112yes—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—44no—
370C4⋊C4C22×C4×C1114yes—
371C22⋊C4—28no—
372C22⋊C4—44no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C42—22no—
377C42—22no—
378C42—42no—
379C42—44no—
380C11#2218111yescharacteristic, direct product factor, Sylow
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—24no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23C4×D4×C1112yes—
393C23C2×C11×D812yes—
394C23C11×#13512yes—
395C23C22×D4×C1111yescharacteristic
396D4—24no—
397D4—24no—
398D4—416no—
399D4—42no—
400D4—42no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—88no—
424C2×C4C4×D4×C1112yes—
425C2×C4C2×C11×D814yes—
426C2×C4C23×C4×C1111yescharacteristic
427C2×C4C2×C11×#4111yescharacteristic
428C2×C4C11×H(5,𝔽2)11yescharacteristic
429C2×C4C11×H(5,𝔽2)11yescharacteristic
430C2×C4C11×H(5,𝔽2)11yescharacteristic
431C2×C4C11×2−1+411yescharacteristic
432C8—22no—
433C8—22no—
434C8—42no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—44no—
442C22—44no—
443C22—44no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22—82no—
448C22C4×C11×D814yes—
449C22C2×C4×D4×C1111yescharacteristic
450C22C11×#53411yescharacteristic
451C22C11×#53711yescharacteristic
452C22C22×C11×D811yescharacteristic
453C22C2×C11×#13511yescharacteristic
454C22C11×#57511yescharacteristic
455C22C11×#57511yescharacteristic
456C4—24no—
457C4—22no—
458C4—42no—
459C4—44no—
460C4—82no—
461C4—82no—
462C4C11×#51811yescharacteristic
463C4C11×#52011yescharacteristic
464C4C11×#53811yescharacteristic
465C4C11×#53911yescharacteristic
466C2—24no—
467C2—84no—
468C2C11×#232511yescharacteristic
469C2C2×C4×C11×D811yescharacteristic
470C2C11×#294311yescharacteristic
471C2C11×#318611yescharacteristic
472C2C11×#319111yescharacteristic
473C2C11×#324511yescharacteristic
474C2C11×#325011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#466C2
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. C4×C11×#121C2semidirect
3. C11×#1925C2semidirect
4. C11×#1918C2semidirect
5. C11×#1893C2semidirect
6. C11×#1879C2semidirect
7. C11×#1862C2semidirect
8. C11×#1808C2semidirect
9. C2×C11×#336C2semidirect
17. C11×#466C4semidirect
44. C2×C11×D8C2×C4semidirect
50. C22×C8×C11C2×C4semidirect
55. C11×#121C2×C4semidirect
75. C11×#107C2×C4semidirect
78. C11×#102C2×C4semidirect
82. #22181C11direct (N × H)
109. C22×C4×C11D8semidirect
145. C4×#121C2×C11semidirect
146. #1925C2×C11semidirect
147. #1918C2×C11semidirect
148. #1893C2×C11semidirect
149. #1879C2×C11semidirect
150. #1862C2×C11semidirect
151. #1808C2×C11semidirect
152. C2×#336C2×C11semidirect
214. #466C4×C11semidirect
272. C2×D8C2×C4×C11semidirect
278. C22×C8C2×C4×C11semidirect
283. #121C2×C4×C11semidirect
303. #107C2×C4×C11semidirect
306. #102C2×C4×C11semidirect
345. C22×C4C11×D8semidirect
380. C11#22181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C4×C11×#1212
C11×#19252
C11×#19182
C11×#18932
C11×#18792
C11×#18622
C11×#18082
C2×C11×#3362
#2218111