Finite Group Databasebeta

← C11×#34925 #14612118

Subgroups — C11×#34925 #14612118

Order 2816.

3436 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C214yesmaximal, complemented
2C11×#2555C214yesmaximal, complemented
3C11×#2551C211yesmaximal, characteristic, complemented
4C11×#2541C212yesmaximal, complemented
5C11×#2537C211yesmaximal, characteristic, complemented
6C11×#2491C214yesmaximal, complemented
7C11×#2428C214yesmaximal, complemented
8C11×#2388C214yesmaximal, complemented
9C4×C11×#127C211yesmaximal, characteristic, complemented
10C4×C11×#121C214yesmaximal, complemented
11C42×D4×C11C212yesmaximal, complemented
12C22×C11×#41C2214yes—
13C11×#532—232no—
14C2×C11×C4⋊Q8C2214yes—
15C2×C11×#127C2214yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124C2218yes—
18C2×C11×#121C2214yes—
19C2×C11×#121C2218yes—
20C2×C11×#121C2214yes—
21C2×C11×#121C2214yes—
22C2×C4×D4×C11C2218yes—
23C2×C4×D4×C11C2214yes—
24C2×C4×D4×C11C2212yes—
25C2×C4×D4×C11C2212yes—
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2212yes—
28C22×C42×C11C2214yes—
29C11×#395C2214yes—
30C11×#394C2218yes—
31C11×#394C2214yes—
32C11×#393C2214yes—
33C11×#392C2214yes—
34C11×#392C2218yes—
35C11×#390C2214yes—
36C11×#390C2214yes—
37C11×#390C2212yes—
38C11×#389C2214yes—
39C11×#388C2218yes—
40C11×#386C2218yes—
41C11×#384C2211yescharacteristic
42C11×#380C2214yes—
43C4×C11×C4⋊C4C2212yes—
44C4×C11×C4⋊C4C2212yes—
45C4×C11×C4⋊C4C2212yes—
46C4×C11×C22⋊C4C2214yes—
47C4×C11×C22⋊C4C2214yes—
48C4×C11×C22⋊C4C2214yes—
49C4×C11×C22⋊C4C2214yes—
50C43×C11C2211yescharacteristic
51C2×C11×#41—232no—
52C2×C11×#41—48no—
53C22×Q8×C11C2314yes—
54C22×D4×C11C2314yes—
55C22×D4×C11C2318yes—
56C22×D4×C11C2314yes—
57C22×D4×C11C2318yes—
58C22×D4×C11C2312yes—
59C22×D4×C11C2312yes—
60C23×C4×C11C2314yes—
61C23×C4×C11C2314yes—
62C23×C4×C11C2314yes—
63C23×C4×C11C2314yes—
64C11×C4⋊Q8—216no—
65C11×#127—216no—
66C11×#127—24no—
67C11×#124—232no—
68C11×#121—216no—
69C11×#121—216no—
70C11×#121—216no—
71C11×#121—232no—
72C4×D4×C11—232no—
73C4×D4×C11—28no—
74C4×D4×C11—216no—
75C4×D4×C11—28no—
76C4×D4×C11—44no—
77C4×D4×C11D4116yescomplemented
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2318yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C11×C22⋊C4C2318yes—
88C2×C11×C22⋊C4C2318yes—
89C2×C11×C22⋊C4C2318yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C42×C11—216no—
93C2×C42×C11C2314yes—
94C2×C42×C11C2314yes—
95C2×C42×C11C2312yes—
96C2×C42×C11C2314yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2312yes—
100C2×C42×C11C2311yescharacteristic
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11×#95C2314yes—
105C11×#95C2314yes—
106#34925C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11C2414yes—
108C24×C11C2414yes—
109C11×#41—464no—
110C2×Q8×C11—216no—
111C2×Q8×C11—44no—
112C2×D4×C11—216no—
113C2×D4×C11—216no—
114C2×D4×C11—216no—
115C2×D4×C11—28no—
116C2×D4×C11—216no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—216no—
120C2×D4×C11—28no—
121C2×D4×C11—24no—
122C2×D4×C11—28no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—48no—
126C2×D4×C11—48no—
127C2×D4×C11—44no—
128C2×D4×C11C2×D418yes—
129C22×C4×C11—28no—
130C22×C4×C11—28no—
131C22×C4×C11—28no—
132C22×C4×C11—28no—
133C22×C4×C11—216no—
134C22×C4×C11—28no—
135C22×C4×C11—28no—
136C22×C4×C11—28no—
137C22×C4×C11—28no—
138C22×C4×C11—44no—
139C22×C4×C11C2×D4116yes—
140C22×C4×C11C2411yescharacteristic
141C22×C4×C11C2414yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2411yescharacteristic
149C11×C4⋊C4—216no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4C2×D418yes—
154C11×C4⋊C4#4118yescomplemented
155C11×C22⋊C4—216no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—216no—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—216no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4C2×D4116yes—
163C42×C11—28no—
164C42×C11—28no—
165C42×C11—28no—
166C42×C11—24no—
167C42×C11—22no—
168C42×C11—41no—
169C42×C11C2×D418yes—
170C42×C11#4114yescomplemented
171C2×#532C2×C1114yescomplemented
172#2555C2×C1114yescomplemented
173#2551C2×C1111yescharacteristic, complemented
174#2541C2×C1112yescomplemented
175#2537C2×C1111yescharacteristic, complemented
176#2491C2×C1114yescomplemented
177#2428C2×C1114yescomplemented
178#2388C2×C1114yescomplemented
179C4×#127C2×C1111yescharacteristic, complemented
180C4×#121C2×C1114yescomplemented
181C42×D4C2×C1112yescomplemented
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11C22×D418yes—
194C23×C11C2511yescharacteristic
195Q8×C11—416no—
196D4×C11—216no—
197D4×C11—432no—
198D4×C11—432no—
199D4×C11—48no—
200D4×C11—416no—
201D4×C11—416no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—232no—
211C2×C4×C11—24no—
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—21no—
217C2×C4×C11—24no—
218C2×C4×C11—416no—
219C2×C4×C11—416no—
220C2×C4×C11—416no—
221C2×C4×C11C22×D414yes—
222C2×C4×C11C22×D418yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C2×#4112yes—
226C2×C4×C11C2×#4118yes—
227C2×C4×C11C2×#4114yes—
228C2×C4×C11C2×#4114yes—
229C2×C4×C11H(5,𝔽2)12yes—
230C22×#41C22×C1114yes—
231#532—232no—
232C2×C4⋊Q8C22×C1114yes—
233C2×#127C22×C1111yescharacteristic
234C2×#127C22×C1114yes—
235C2×#124C22×C1118yes—
236C2×#121C22×C1114yes—
237C2×#121C22×C1118yes—
238C2×#121C22×C1114yes—
239C2×#121C22×C1114yes—
240C2×C4×D4C22×C1114yes—
241C2×C4×D4C22×C1118yes—
242C2×C4×D4C22×C1112yes—
243C2×C4×D4C22×C1112yes—
244C2×C4×D4C22×C1112yes—
245C2×C4×D4C22×C1112yes—
246C22×C42C22×C1114yes—
247#395C22×C1114yes—
248#394C22×C1118yes—
249#394C22×C1114yes—
250#393C22×C1114yes—
251#392C22×C1114yes—
252#392C22×C1118yes—
253#390C22×C1114yes—
254#390C22×C1112yes—
255#390C22×C1114yes—
256#389C22×C1114yes—
257#388C22×C1118yes—
258#386C22×C1118yes—
259#384C22×C1111yescharacteristic
260#380C22×C1114yes—
261C4×C4⋊C4C22×C1112yes—
262C4×C4⋊C4C22×C1112yes—
263C4×C4⋊C4C22×C1112yes—
264C4×C22⋊C4C22×C1114yes—
265C4×C22⋊C4C22×C1114yes—
266C4×C22⋊C4C22×C1114yes—
267C4×C22⋊C4C22×C1114yes—
268C43C22×C1111yescharacteristic
269C22×C11—28no—
270C22×C11—28no—
271C22×C11—28no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—48no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—48no—
280C22×C11—44no—
281C22×C11C23×D412yes—
282C22×C11C22×#4111yescharacteristic
283C22×C11C22×#4112yes—
284C22×C11C2×H(5,𝔽2)11yescharacteristic
285C22×C11#58511yescharacteristic
286C4×C11—22no—
287C4×C11—28no—
288C4×C11—24no—
289C4×C11—28no—
290C4×C11—44no—
291C4×C11—44no—
292C4×C11—41no—
293C4×C11#53218yescomplemented
294C4×C11D4214yes—
295C2×#41—232no—
296C2×#41—48no—
297C22×Q8C23×C1114yes—
298C22×D4C23×C1114yes—
299C22×D4C23×C1118yes—
300C22×D4C23×C1114yes—
301C22×D4C23×C1118yes—
302C22×D4C23×C1112yes—
303C22×D4C23×C1112yes—
304C23×C4C23×C1114yes—
305C23×C4C23×C1114yes—
306C23×C4C23×C1114yes—
307C23×C4C23×C1114yes—
308C4⋊Q8—216no—
309#127—216no—
310#127—24no—
311#124—232no—
312#121—216no—
313#121—216no—
314#121—216no—
315#121—232no—
316C4×D4—232no—
317C4×D4—28no—
318C4×D4—216no—
319C4×D4—28no—
320C4×D4—44no—
321C4×D4D4×C11116yescomplemented
322C2×C4⋊C4C23×C1114yes—
323C2×C4⋊C4C23×C1118yes—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1112yes—
327C2×C4⋊C4C23×C1112yes—
328C2×C22⋊C4C23×C1118yes—
329C2×C22⋊C4C23×C1118yes—
330C2×C22⋊C4C23×C1118yes—
331C2×C22⋊C4C23×C1114yes—
332C2×C22⋊C4C23×C1114yes—
333C2×C22⋊C4C23×C1118yes—
334C2×C22⋊C4C23×C1114yes—
335C2×C22⋊C4C23×C1114yes—
336C2×C42—216no—
337C2×C42C23×C1111yescharacteristic
338C2×C42C23×C1114yes—
339C2×C42C23×C1112yes—
340C2×C42C23×C1114yes—
341C2×C42C23×C1114yes—
342C2×C42C23×C1111yescharacteristic
343C2×C42C23×C1112yes—
344C2×C42C23×C1111yescharacteristic
345#95C23×C1114yes—
346#95C23×C1114yes—
347#95C23×C1114yes—
348#95C23×C1114yes—
349#95C23×C1114yes—
350C2×C11—48no—
351C2×C11—84no—
352C2×C11C2×#53212yes—
353C2×C11#346011yescharacteristic
354C2×C11C2×D4211yescharacteristic
355C2×C11D4×#4112yes—
356C2×C11#348311yescharacteristic
357C24C24×C1114yes—
358C24C24×C1114yes—
359#41—464no—
360C2×Q8—216no—
361C2×Q8—44no—
362C2×D4—216no—
363C2×D4—216no—
364C2×D4—216no—
365C2×D4—28no—
366C2×D4—216no—
367C2×D4—24no—
368C2×D4—24no—
369C2×D4—216no—
370C2×D4—28no—
371C2×D4—24no—
372C2×D4—28no—
373C2×D4—42no—
374C2×D4—48no—
375C2×D4—44no—
376C2×D4—42no—
377C2×D4—48no—
378C2×D4C2×D4×C1118yes—
379C22×C4—28no—
380C22×C4—28no—
381C22×C4—28no—
382C22×C4—28no—
383C22×C4—216no—
384C22×C4—28no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—28no—
388C22×C4—44no—
389C22×C4C2×D4×C11116yes—
390C22×C4C24×C1111yescharacteristic
391C22×C4C24×C1114yes—
392C22×C4C24×C1114yes—
393C22×C4C24×C1112yes—
394C22×C4C24×C1114yes—
395C22×C4C24×C1111yescharacteristic
396C22×C4C24×C1114yes—
397C22×C4C24×C1111yescharacteristic
398C22×C4C24×C1112yes—
399C4⋊C4—216no—
400C4⋊C4—28no—
401C4⋊C4—24no—
402C4⋊C4—42no—
403C4⋊C4C2×D4×C1118yes—
404C4⋊C4C11×#4118yescomplemented
405C22⋊C4—216no—
406C22⋊C4—216no—
407C22⋊C4—216no—
408C22⋊C4—28no—
409C22⋊C4—28no—
410C22⋊C4—216no—
411C22⋊C4—44no—
412C22⋊C4C2×D4×C11116yes—
413C42—28no—
414C42—28no—
415C42—28no—
416C42—24no—
417C42—22no—
418C42—41no—
419C42C2×D4×C1118yes—
420C42C11×#4114yescomplemented
421C11#3492511yescharacteristic, direct product factor, Sylow
422C23—24no—
423C23—24no—
424C23—24no—
425C23—24no—
426C23—24no—
427C23—24no—
428C23—28no—
429C23—28no—
430C23—24no—
431C23—24no—
432C23—24no—
433C23C22×D4×C1118yes—
434C23C25×C1111yescharacteristic
435Q8—416no—
436D4—216no—
437D4—432no—
438D4—432no—
439D4—48no—
440D4—416no—
441D4—416no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—232no—
451C2×C4—24no—
452C2×C4—28no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—416no—
459C2×C4—416no—
460C2×C4—416no—
461C2×C4C22×D4×C1114yes—
462C2×C4C22×D4×C1118yes—
463C2×C4C22×D4×C1114yes—
464C2×C4C22×D4×C1114yes—
465C2×C4C2×C11×#4112yes—
466C2×C4C2×C11×#4118yes—
467C2×C4C2×C11×#4114yes—
468C2×C4C2×C11×#4114yes—
469C2×C4C11×H(5,𝔽2)12yes—
470C22—28no—
471C22—28no—
472C22—28no—
473C22—44no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—48no—
478C22—44no—
479C22—44no—
480C22—48no—
481C22—44no—
482C22C23×D4×C1112yes—
483C22C22×C11×#4111yescharacteristic
484C22C22×C11×#4112yes—
485C22C2×C11×H(5,𝔽2)11yescharacteristic
486C22C11×#58511yescharacteristic
487C4—22no—
488C4—28no—
489C4—24no—
490C4—28no—
491C4—44no—
492C4—44no—
493C4—41no—
494C4C11×#53218yescomplemented
495C4D42×C1114yes—
496C2—48no—
497C2—84no—
498C2C2×C11×#53212yes—
499C2C11×#346011yescharacteristic
500C2C2×D42×C1111yescharacteristic
501C2D4×C11×#4112yes—
502C2C11×#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×C11×#532C2semidirect
2. C11×#2555C2semidirect
3. C11×#2551C2semidirect
4. C11×#2541C2semidirect
5. C11×#2537C2semidirect
6. C11×#2491C2semidirect
7. C11×#2428C2semidirect
8. C11×#2388C2semidirect
9. C4×C11×#127C2semidirect
10. C4×C11×#121C2semidirect
11. C42×D4×C11C2semidirect
77. C4×D4×C11D4semidirect
106. #34925C11direct (N × H)
154. C11×C4⋊C4#41semidirect
170. C42×C11#41semidirect
171. C2×#532C2×C11semidirect
172. #2555C2×C11semidirect
173. #2551C2×C11semidirect
174. #2541C2×C11semidirect
175. #2537C2×C11semidirect
176. #2491C2×C11semidirect
177. #2428C2×C11semidirect
178. #2388C2×C11semidirect
179. C4×#127C2×C11semidirect
180. C4×#121C2×C11semidirect
181. C42×D4C2×C11semidirect
293. C4×C11#532semidirect
321. C4×D4D4×C11semidirect
404. C4⋊C4C11×#41semidirect
420. C42C11×#41semidirect
421. C11#34925direct (N × H)
494. C4C11×#532semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C11×#25552
C11×#25512
C11×#25412
C11×#25372
C11×#24912
C11×#24282
C11×#23882
C4×C11×#1272
C4×C11×#1212
C42×D4×C112
#3492511