Finite Group Databasebeta

← C11×#34976 #14612169

Subgroups — C11×#34976 #14612169

Order 2816.

2810 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×#41C212yesmaximal, complemented
2C11×#2609C214yesmaximal, complemented
3C11×#2582C211yesmaximal, characteristic, complemented
4C11×#2538C212yesmaximal, complemented
5C11×#2537C211yesmaximal, characteristic, complemented
6C11×#2485C214yesmaximal, complemented
7C11×#2407C214yesmaximal, complemented
8C11×#2392C214yesmaximal, complemented
9C4×C11×C22⋊Q8C214yesmaximal, complemented
10C4×C11×#121C214yesmaximal, complemented
11C11×#2285C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C2×C11×C22⋊Q8C2214yes—
14C2×C11×#121C2214yes—
15C4×C11×#41—216no—
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2212yes—
18C2×C4×D4×C11C2214yes—
19C2×C4×D4×C11C2214yes—
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2214yes—
23C2×C11×#117C2212yes—
24C2×C11×#117C2214yes—
25C2×C11×#117C2212yes—
26C22×C42×C11C2214yes—
27C22×C42×C11C2211yescharacteristic
28C11×#398C2214yes—
29C11×#397C2214yes—
30C11×#396C2218yes—
31C11×#394C2218yes—
32C11×#394C2214yes—
33C11×#392C2214yes—
34C11×#391C2214yes—
35C11×#390C2214yes—
36C11×#389C2214yes—
37C11×#389C2214yes—
38C11×#388C2218yes—
39C11×#387C2218yes—
40C11×#386C2218yes—
41C11×#385C2218yes—
42C11×#384C2211yescharacteristic
43C11×#384C2211yescharacteristic
44C11×#382C2212yes—
45C11×#380C2214yes—
46C11×#380C2214yes—
47C11×#380C2214yes—
48C4×C11×C4⋊C4C2214yes—
49C4×C11×C4⋊C4C2214yes—
50C4×C11×C22⋊C4C2218yes—
51C2×C11×#41—28no—
52C2×C11×#41—28no—
53C2×C11×#41—28no—
54C22×Q8×C11C2312yes—
55C22×D4×C11C2314yes—
56C22×D4×C11C2314yes—
57C22×D4×C11C2312yes—
58C23×C4×C11C2314yes—
59C23×C4×C11C2314yes—
60C23×C4×C11C2314yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C11×C22⋊Q8—216no—
64C11×#121—216no—
65C4×Q8×C11—28no—
66C4×Q8×C11—28no—
67C4×D4×C11—216no—
68C4×D4×C11—216no—
69C4×D4×C11—28no—
70C4×D4×C11—28no—
71C4×D4×C11—48no—
72C11×#117—28no—
73C11×#117—216no—
74C11×#117—44no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2318yes—
89C2×C11×C22⋊C4C2318yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C42×C11—216no—
93C2×C42×C11D418yescomplemented
94C2×C42×C11C2314yes—
95C2×C42×C11C2314yes—
96C2×C42×C11C2314yes—
97C2×C42×C11C2314yes—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101C11×#95C2318yes—
102C11×#95C2318yes—
103C11×#95C2314yes—
104C11×#95C2318yes—
105C11×#95C2314yes—
106#34976C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11C2411yescharacteristic
108C24×C11C2414yes—
109C11×#41—264no—
110C2×Q8×C11—24no—
111C2×Q8×C11—24no—
112C2×Q8×C11#4118yescomplemented
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—216no—
116C2×D4×C11—24no—
117C2×D4×C11—28no—
118C2×D4×C11—24no—
119C2×D4×C11—44no—
120C2×D4×C11#4118yescomplemented
121C22×C4×C11—28no—
122C22×C4×C11—28no—
123C22×C4×C11—28no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—28no—
129C22×C4×C11—28no—
130C22×C4×C11—28no—
131C22×C4×C11—28no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11C2×D418yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2411yescharacteristic
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C11×C4⋊C4—28no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—216no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—44no—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—216no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—48no—
162C42×C11—28no—
163C42×C11—28no—
164C42×C11—28no—
165C42×C11—28no—
166C42×C11C2×D418yes—
167C42×C11C2×D414yes—
168C42×C11C2×D414yes—
169C2×C4×#41C2×C1112yescomplemented
170#2609C2×C1114yescomplemented
171#2582C2×C1111yescharacteristic, complemented
172#2538C2×C1112yescomplemented
173#2537C2×C1111yescharacteristic, complemented
174#2485C2×C1114yescomplemented
175#2407C2×C1114yescomplemented
176#2392C2×C1114yescomplemented
177C4×C22⋊Q8C2×C1114yescomplemented
178C4×#121C2×C1114yescomplemented
179#2285C2×C1111yescharacteristic, complemented
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—21no—
187C23×C11—24no—
188C23×C11—21no—
189C23×C11—24no—
190C23×C11C22×D412yes—
191C23×C11C2×#4118yes—
192C23×C11C2511yescharacteristic
193Q8×C11—216no—
194D4×C11—232no—
195D4×C11—216no—
196D4×C11—416no—
197C2×C4×C11—232no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—216no—
205C2×C4×C11—28no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—28no—
210C2×C4×C11—28no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—416no—
217C2×C4×C11—416no—
218C2×C4×C11C22×D414yes—
219C2×C4×C11C22×D412yes—
220C2×C4×C11C22×D414yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C2×#4118yes—
223C2×C4×C11C2×#4114yes—
224C2×C4×C11C2×#4114yes—
225C2×C4×C11H(5,𝔽2)12yes—
226C2×C4×C112−1+412yes—
227C22×#41C22×C1112yes—
228C2×C22⋊Q8C22×C1114yes—
229C2×#121C22×C1114yes—
230C4×#41—216no—
231C2×C4×Q8C22×C1112yes—
232C2×C4×Q8C22×C1112yes—
233C2×C4×D4C22×C1114yes—
234C2×C4×D4C22×C1114yes—
235C2×C4×D4C22×C1112yes—
236C2×C4×D4C22×C1112yes—
237C2×C4×D4C22×C1114yes—
238C2×#117C22×C1114yes—
239C2×#117C22×C1112yes—
240C2×#117C22×C1112yes—
241C22×C42C22×C1114yes—
242C22×C42C22×C1111yescharacteristic
243#398C22×C1114yes—
244#397C22×C1114yes—
245#396C22×C1118yes—
246#394C22×C1114yes—
247#394C22×C1118yes—
248#392C22×C1114yes—
249#391C22×C1114yes—
250#390C22×C1114yes—
251#389C22×C1114yes—
252#389C22×C1114yes—
253#388C22×C1118yes—
254#387C22×C1118yes—
255#386C22×C1118yes—
256#385C22×C1118yes—
257#384C22×C1111yescharacteristic
258#384C22×C1111yescharacteristic
259#382C22×C1112yes—
260#380C22×C1114yes—
261#380C22×C1114yes—
262#380C22×C1114yes—
263C4×C4⋊C4C22×C1114yes—
264C4×C4⋊C4C22×C1114yes—
265C4×C22⋊C4C22×C1118yes—
266C22×C11—24no—
267C22×C11—28no—
268C22×C11—22no—
269C22×C11—28no—
270C22×C11—28no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—41no—
274C22×C11—42no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—41no—
278C22×C11C23×D411yescharacteristic
279C22×C11C22×#4112yes—
280C22×C11C22×#4112yes—
281C22×C11C2×H(5,𝔽2)11yescharacteristic
282C22×C11C2×2−1+411yescharacteristic
283C4×C11—24no—
284C4×C11—28no—
285C4×C11—22no—
286C4×C11—44no—
287C4×C11—44no—
288C4×C11—44no—
289C4×C11—44no—
290C4×C11#52518yes—
291C4×C11#53714yes—
292C2×#41—28no—
293C2×#41—28no—
294C2×#41—28no—
295C22×Q8C23×C1112yes—
296C22×D4C23×C1114yes—
297C22×D4C23×C1114yes—
298C22×D4C23×C1112yes—
299C23×C4C23×C1114yes—
300C23×C4C23×C1114yes—
301C23×C4C23×C1114yes—
302C23×C4C23×C1111yescharacteristic
303C23×C4C23×C1112yes—
304C22⋊Q8—216no—
305#121—216no—
306C4×Q8—28no—
307C4×Q8—28no—
308C4×D4—216no—
309C4×D4—216no—
310C4×D4—28no—
311C4×D4—28no—
312C4×D4—48no—
313#117—28no—
314#117—216no—
315#117—44no—
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1114yes—
319C2×C4⋊C4C23×C1114yes—
320C2×C4⋊C4C23×C1114yes—
321C2×C4⋊C4C23×C1114yes—
322C2×C4⋊C4C23×C1118yes—
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1114yes—
326C2×C22⋊C4C23×C1114yes—
327C2×C22⋊C4C23×C1114yes—
328C2×C22⋊C4C23×C1114yes—
329C2×C22⋊C4C23×C1118yes—
330C2×C22⋊C4C23×C1118yes—
331C2×C22⋊C4C23×C1114yes—
332C2×C22⋊C4C23×C1118yes—
333C2×C42—216no—
334C2×C42D4×C1118yescomplemented
335C2×C42C23×C1114yes—
336C2×C42C23×C1114yes—
337C2×C42C23×C1114yes—
338C2×C42C23×C1114yes—
339C2×C42C23×C1111yescharacteristic
340C2×C42C23×C1111yescharacteristic
341C2×C42C23×C1112yes—
342#95C23×C1118yes—
343#95C23×C1118yes—
344#95C23×C1114yes—
345#95C23×C1118yes—
346#95C23×C1114yes—
347C2×C11—42no—
348C2×C11—48no—
349C2×C11C2×#52512yes—
350C2×C11C2×#53711yescharacteristic
351C2×C11#348111yescharacteristic
352C2×C11#348212yes—
353C2×C11#348311yescharacteristic
354C24C24×C1111yescharacteristic
355C24C24×C1114yes—
356#41—264no—
357C2×Q8—24no—
358C2×Q8—24no—
359C2×Q8C11×#4118yescomplemented
360C2×D4—28no—
361C2×D4—28no—
362C2×D4—216no—
363C2×D4—24no—
364C2×D4—28no—
365C2×D4—24no—
366C2×D4—44no—
367C2×D4C11×#4118yescomplemented
368C22×C4—28no—
369C22×C4—28no—
370C22×C4—28no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—28no—
376C22×C4—28no—
377C22×C4—28no—
378C22×C4—28no—
379C22×C4—28no—
380C22×C4—28no—
381C22×C4C2×D4×C1118yes—
382C22×C4C2×D4×C1114yes—
383C22×C4C24×C1114yes—
384C22×C4C24×C1114yes—
385C22×C4C24×C1114yes—
386C22×C4C24×C1114yes—
387C22×C4C24×C1112yes—
388C22×C4C24×C1111yescharacteristic
389C22×C4C24×C1114yes—
390C22×C4C24×C1112yes—
391C22×C4C24×C1111yescharacteristic
392C4⋊C4—28no—
393C4⋊C4—28no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—28no—
397C4⋊C4—28no—
398C4⋊C4—216no—
399C4⋊C4—42no—
400C4⋊C4—42no—
401C4⋊C4—44no—
402C22⋊C4—28no—
403C22⋊C4—216no—
404C22⋊C4—28no—
405C22⋊C4—28no—
406C22⋊C4—216no—
407C22⋊C4—44no—
408C22⋊C4—48no—
409C42—28no—
410C42—28no—
411C42—28no—
412C42—28no—
413C42C2×D4×C1118yes—
414C42C2×D4×C1114yes—
415C42C2×D4×C1114yes—
416C11#3497611yescharacteristic, direct product factor, Sylow
417C23—24no—
418C23—24no—
419C23—22no—
420C23—22no—
421C23—24no—
422C23—24no—
423C23—21no—
424C23—24no—
425C23—21no—
426C23—24no—
427C23C22×D4×C1112yes—
428C23C2×C11×#4118yes—
429C23C25×C1111yescharacteristic
430Q8—216no—
431D4—232no—
432D4—216no—
433D4—416no—
434C2×C4—232no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—216no—
442C2×C4—28no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—28no—
447C2×C4—28no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—416no—
454C2×C4—416no—
455C2×C4C22×D4×C1114yes—
456C2×C4C22×D4×C1112yes—
457C2×C4C22×D4×C1114yes—
458C2×C4C22×D4×C1112yes—
459C2×C4C2×C11×#4118yes—
460C2×C4C2×C11×#4114yes—
461C2×C4C2×C11×#4114yes—
462C2×C4C11×H(5,𝔽2)12yes—
463C2×C4C11×2−1+412yes—
464C22—24no—
465C22—28no—
466C22—22no—
467C22—28no—
468C22—28no—
469C22—44no—
470C22—44no—
471C22—41no—
472C22—42no—
473C22—44no—
474C22—44no—
475C22—41no—
476C22C23×D4×C1111yescharacteristic
477C22C22×C11×#4112yes—
478C22C22×C11×#4112yes—
479C22C2×C11×H(5,𝔽2)11yescharacteristic
480C22C2×C11×2−1+411yescharacteristic
481C4—24no—
482C4—28no—
483C4—22no—
484C4—44no—
485C4—44no—
486C4—44no—
487C4—44no—
488C4C11×#52518yes—
489C4C11×#53714yes—
490C2—42no—
491C2—48no—
492C2C2×C11×#52512yes—
493C2C2×C11×#53711yescharacteristic
494C2C11×#348111yescharacteristic
495C2C11×#348212yes—
496C2C11×#348311yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×C11×#41C2semidirect
2. C11×#2609C2semidirect
3. C11×#2582C2semidirect
4. C11×#2538C2semidirect
5. C11×#2537C2semidirect
6. C11×#2485C2semidirect
7. C11×#2407C2semidirect
8. C11×#2392C2semidirect
9. C4×C11×C22⋊Q8C2semidirect
10. C4×C11×#121C2semidirect
11. C11×#2285C2semidirect
93. C2×C42×C11D4semidirect
106. #34976C11direct (N × H)
112. C2×Q8×C11#41semidirect
120. C2×D4×C11#41semidirect
169. C2×C4×#41C2×C11semidirect
170. #2609C2×C11semidirect
171. #2582C2×C11semidirect
172. #2538C2×C11semidirect
173. #2537C2×C11semidirect
174. #2485C2×C11semidirect
175. #2407C2×C11semidirect
176. #2392C2×C11semidirect
177. C4×C22⋊Q8C2×C11semidirect
178. C4×#121C2×C11semidirect
179. #2285C2×C11semidirect
334. C2×C42D4×C11semidirect
359. C2×Q8C11×#41semidirect
367. C2×D4C11×#41semidirect
416. C11#34976direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×#412
C11×#26092
C11×#25822
C11×#25382
C11×#25372
C11×#24852
C11×#24072
C11×#23922
C4×C11×C22⋊Q82
C4×C11×#1212
C11×#22852
#3497611