Finite Group Databasebeta

← C11×#2714 #13065552

Subgroups — C11×#2714 #13065552

Order 1408.

598 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×#126C211yesmaximal, characteristic, complemented
2C2×C11×#121C211yesmaximal, characteristic, complemented
3C11×#397C211yesmaximal, characteristic, complemented
4C11×#394C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6C11×#392C211yesmaximal, characteristic, complemented
7C11×#392C211yesmaximal, characteristic, complemented
8C11×#392C211yesmaximal, characteristic, complemented
9C11×#390C211yesmaximal, characteristic, complemented
10C11×#390C211yesmaximal, characteristic, complemented
11C11×#390C211yesmaximal, characteristic, complemented
12C11×#388C211yesmaximal, characteristic, complemented
13C11×#387C211yesmaximal, characteristic, complemented
14C11×#386C211yesmaximal, characteristic, complemented
15C11×#385C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C22×D4×C11C2211yescharacteristic
21C22×D4×C11C2211yescharacteristic
22C23×C4×C11C2211yescharacteristic
23C11×#126—24no—
24C11×#121—24no—
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C11×C22⋊C4C2211yescharacteristic
37C2×C11×C22⋊C4C2211yescharacteristic
38C2×C11×C22⋊C4C2211yescharacteristic
39C2×C11×C22⋊C4C2211yescharacteristic
40C2×C11×C22⋊C4C2211yescharacteristic
41C2×C11×C22⋊C4C2211yescharacteristic
42C2×C11×C22⋊C4C2211yescharacteristic
43C2×C11×C22⋊C4C2211yescharacteristic
44C2×C11×C22⋊C4C2211yescharacteristic
45C2×C42×C11C2211yescharacteristic
46C2×C42×C11C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C22×C4×C11—22no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2311yescharacteristic
82C22×C4×C11C2311yescharacteristic
83C22×C4×C11C2311yescharacteristic
84C22×C4×C11C2311yescharacteristic
85C22×C4×C11C2311yescharacteristic
86C22×C4×C11C2311yescharacteristic
87C22×C4×C11C2311yescharacteristic
88C22×C4×C11C2311yescharacteristic
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4D414yescomplemented
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—22no—
110C42×C11—41no—
111#2714C1111yesmaximal, characteristic, direct product factor, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11#4112yes—
140C23×C11C2411yescharacteristic
141D4×C11—44no—
142D4×C11—44no—
143D4×C11—44no—
144D4×C11—44no—
145D4×C11—44no—
146D4×C11—44no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—44no—
177C2×C4×C11C2×D412yes—
178C2×C4×C11C2×D412yes—
179C2×C4×C11C2×D412yes—
180C2×C4×C11#4112yes—
181C2×#126C2×C1111yescharacteristic, complemented
182C2×#121C2×C1111yescharacteristic, complemented
183#397C2×C1111yescharacteristic, complemented
184#394C2×C1111yescharacteristic, complemented
185#394C2×C1111yescharacteristic, complemented
186#392C2×C1111yescharacteristic, complemented
187#392C2×C1111yescharacteristic, complemented
188#392C2×C1111yescharacteristic, complemented
189#390C2×C1111yescharacteristic, complemented
190#390C2×C1111yescharacteristic, complemented
191#390C2×C1111yescharacteristic, complemented
192#388C2×C1111yescharacteristic, complemented
193#387C2×C1111yescharacteristic, complemented
194#386C2×C1111yescharacteristic, complemented
195#385C2×C1111yescharacteristic, complemented
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11C22×D411yescharacteristic
225C22×C11C2×#4111yescharacteristic
226C22×C11C2×#4111yescharacteristic
227C22×C11H(5,𝔽2)11yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C22×C11H(5,𝔽2)11yescharacteristic
230C22×C11H(5,𝔽2)11yescharacteristic
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242C22×D4C22×C1111yescharacteristic
243C22×D4C22×C1111yescharacteristic
244C22×D4C22×C1111yescharacteristic
245C22×D4C22×C1111yescharacteristic
246C22×D4C22×C1111yescharacteristic
247C22×D4C22×C1111yescharacteristic
248C23×C4C22×C1111yescharacteristic
249#126—24no—
250#121—24no—
251C2×C4⋊C4C22×C1111yescharacteristic
252C2×C4⋊C4C22×C1111yescharacteristic
253C2×C4⋊C4C22×C1111yescharacteristic
254C2×C4⋊C4C22×C1111yescharacteristic
255C2×C4⋊C4C22×C1111yescharacteristic
256C2×C22⋊C4C22×C1111yescharacteristic
257C2×C22⋊C4C22×C1111yescharacteristic
258C2×C22⋊C4C22×C1111yescharacteristic
259C2×C22⋊C4C22×C1111yescharacteristic
260C2×C22⋊C4C22×C1111yescharacteristic
261C2×C22⋊C4C22×C1111yescharacteristic
262C2×C22⋊C4C22×C1111yescharacteristic
263C2×C22⋊C4C22×C1111yescharacteristic
264C2×C22⋊C4C22×C1111yescharacteristic
265C2×C22⋊C4C22×C1111yescharacteristic
266C2×C22⋊C4C22×C1111yescharacteristic
267C2×C22⋊C4C22×C1111yescharacteristic
268C2×C22⋊C4C22×C1111yescharacteristic
269C2×C22⋊C4C22×C1111yescharacteristic
270C2×C22⋊C4C22×C1111yescharacteristic
271C2×C42C22×C1111yescharacteristic
272C2×C42C22×C1111yescharacteristic
273#95C22×C1111yescharacteristic
274#95C22×C1111yescharacteristic
275#95C22×C1111yescharacteristic
276#95C22×C1111yescharacteristic
277#95C22×C1111yescharacteristic
278#95C22×C1111yescharacteristic
279C2×C11—42no—
280C2×C11—81no—
281C2×C11—81no—
282C2×C11—81no—
283C2×C11#53511yescharacteristic
284C2×C11#53811yescharacteristic
285C2×C11#53811yescharacteristic
286C2×C11#54611yescharacteristic
287C2×C11#55011yescharacteristic
288C2×C11#55311yescharacteristic
289C2×C11#56011yescharacteristic
290C24C23×C1111yescharacteristic
291C24C23×C1111yescharacteristic
292C24C23×C1111yescharacteristic
293C24C23×C1111yescharacteristic
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4C23×C1111yescharacteristic
316C22×C4C23×C1111yescharacteristic
317C22×C4C23×C1111yescharacteristic
318C22×C4C23×C1111yescharacteristic
319C22×C4C23×C1111yescharacteristic
320C22×C4C23×C1111yescharacteristic
321C22×C4C23×C1111yescharacteristic
322C22×C4C23×C1111yescharacteristic
323C22×C4C23×C1111yescharacteristic
324C22×C4C23×C1111yescharacteristic
325C22×C4C23×C1111yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4D4×C1114yescomplemented
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—22no—
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—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—22no—
347C42—41no—
348C11#271411yescharacteristic, direct product factor, Sylow
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23C11×#4112yes—
377C23C24×C1111yescharacteristic
378D4—44no—
379D4—44no—
380D4—44no—
381D4—44no—
382D4—44no—
383D4—44no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—44no—
414C2×C4C2×D4×C1112yes—
415C2×C4C2×D4×C1112yes—
416C2×C4C2×D4×C1112yes—
417C2×C4C11×#4112yes—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22C22×D4×C1111yescharacteristic
447C22C2×C11×#4111yescharacteristic
448C22C2×C11×#4111yescharacteristic
449C22C11×H(5,𝔽2)11yescharacteristic
450C22C11×H(5,𝔽2)11yescharacteristic
451C22C11×H(5,𝔽2)11yescharacteristic
452C22C11×H(5,𝔽2)11yescharacteristic
453C4—22no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—41no—
464C2—42no—
465C2—81no—
466C2—81no—
467C2—81no—
468C2C11×#53511yescharacteristic
469C2C11×#53811yescharacteristic
470C2C11×#53811yescharacteristic
471C2C11×#54611yescharacteristic
472C2C11×#55011yescharacteristic
473C2C11×#55311yescharacteristic
474C2C11×#56011yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#126C2semidirect
2. C2×C11×#121C2semidirect
3. C11×#397C2semidirect
4. C11×#394C2semidirect
5. C11×#394C2semidirect
6. C11×#392C2semidirect
7. C11×#392C2semidirect
8. C11×#392C2semidirect
9. C11×#390C2semidirect
10. C11×#390C2semidirect
11. C11×#390C2semidirect
12. C11×#388C2semidirect
13. C11×#387C2semidirect
14. C11×#386C2semidirect
15. C11×#385C2semidirect
93. C11×C4⋊C4D4semidirect
111. #2714C11direct (N × H)
181. C2×#126C2×C11semidirect
182. C2×#121C2×C11semidirect
183. #397C2×C11semidirect
184. #394C2×C11semidirect
185. #394C2×C11semidirect
186. #392C2×C11semidirect
187. #392C2×C11semidirect
188. #392C2×C11semidirect
189. #390C2×C11semidirect
190. #390C2×C11semidirect
191. #390C2×C11semidirect
192. #388C2×C11semidirect
193. #387C2×C11semidirect
194. #386C2×C11semidirect
195. #385C2×C11semidirect
330. C4⋊C4D4×C11semidirect
348. C11#2714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×C11×#1212
C11×#3972
C11×#3942
C11×#3922
C11×#3902
C11×#3882
C11×#3872
C11×#3862
C11×#3852
#271411