Finite Group Databasebeta

← C11×#60716 #14637909

Subgroups — C11×#60716 #14637909

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3511C212yesmaximal, complemented
2C11×#3185C212yesmaximal, complemented
3C11×#3184C212yesmaximal, complemented
4C11×#3173C218yesmaximal, complemented
5C11×#3167C214yesmaximal, complemented
6C2×C11×#498C211yesmaximal, characteristic, complemented
7C11×#3147C211yesmaximal, characteristic, complemented
8C11×#3141C212yesmaximal, complemented
9C11×#3060C214yesmaximal, complemented
10C11×#2952C214yesmaximal, complemented
11C4×C11×#131C211yesmaximal, characteristic, complemented
12C2×C11×#135C2214yes—
13C2×C11×#131C2212yes—
14C11×#556—22no—
15C11×#555—22no—
16C11×#554—22no—
17C11×#553—24no—
18C11×#548—24no—
19C11×#547—22no—
20C11×#542C2218yes—
21C11×#537C2214yes—
22C11×#533C2214yes—
23C11×#532C2212yes—
24C11×#532C2214yes—
25C2×C11×C4⋊Q8C2212yes—
26C11×#520C2214yes—
27C4×C11×#41C2211yescharacteristic
28C11×#498C2212yes—
29C11×#498C2214yes—
30C11×#498C2212yes—
31C11×#495C2214yes—
32C11×#494C2211yescharacteristic
33C11×#493C2211yescharacteristic
34C11×#492C2212yes—
35C11×#489C2218yes—
36C11×#487C2214yes—
37C11×#486C2214yes—
38C11×#470C2218yes—
39C11×#469C2218yes—
40C11×#465C22116yes—
41C11×#442C2218yes—
42C11×#441C2218yes—
43C4×C11×SD16C22116yes—
44C2×C11×#106C2214yes—
45C11×#417C2218yes—
46C11×#405C2214yes—
47C11×#405C2212yes—
48C4×C11×M16C2212yes—
49C4×C11×M16C2211yescharacteristic
50C2×C4×C8×C11C2211yescharacteristic
51C2×C4×C8×C11C2212yes—
52C2×C11×#41—24no—
53C2×C11×#41C2314yes—
54C2×C11×#41C2311yescharacteristic
55C22×Q8×C11—22no—
56C11×#135—216no—
57C2×C11×Q16C2314yes—
58C2×C11×SD16C2318yes—
59C2×C11×D8C2314yes—
60C11×#131—28no—
61C2×C11×M16C2312yes—
62C2×C11×M16C2314yes—
63C22×C8×C11C2314yes—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C11×#127C2312yes—
71C11×#126—28no—
72C11×#125—24no—
73C11×#124—28no—
74C11×#124—24no—
75C11×#124C2314yes—
76C11×#123—28no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—28no—
80C11×C22⋊Q8C2318yes—
81C11×#121—24no—
82C11×#121—28no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—24no—
86C11×#121C2318yes—
87C4×Q8×C11—24no—
88C4×Q8×C11D412yes—
89C4×Q8×C11C2318yes—
90C4×D4×C11—28no—
91C4×D4×C11—22no—
92C4×D4×C11—24no—
93C4×D4×C11—22no—
94C4×D4×C11D412yes—
95C4×D4×C11D414yes—
96C4×D4×C11C2318yes—
97C11×#117—24no—
98C11×#117—24no—
99C11×#117C2311yescharacteristic
100C11×#117C2312yes—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4C2314yes—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2312yes—
106C11×#106C2318yes—
107C11×#106C2318yes—
108C11×#103C23116yes—
109C11×#102C23116yes—
110C11×#97C2312yes—
111C11×#97C2314yes—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2312yes—
115C4×C8×C11C2312yes—
116C4×C8×C11C2314yes—
117#60716C1111yesmaximal, characteristic, direct product factor, Sylow
118C11×#41—24no—
119C11×#41—216no—
120C11×#41—88no—
121C2×Q8×C11—24no—
122C2×Q8×C11—24no—
123C2×Q8×C11—84no—
124C2×Q8×C11C2×D411yescharacteristic
125C2×Q8×C11C2414yes—
126C2×D4×C11—24no—
127C2×D4×C11—28no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11C2×D412yes—
131C2×D4×C11C2×D411yescharacteristic
132C2×D4×C11C2414yes—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—28no—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2411yescharacteristic
140C11×Q16—28no—
141C11×SD16—216no—
142C11×D8—28no—
143C11×M16—28no—
144C11×M16—24no—
145C2×C8×C11—28no—
146C2×C8×C11#4118yescomplemented
147C2×C8×C11C2414yes—
148C2×C8×C11C2412yes—
149C2×C8×C11C2412yes—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D414yes—
159C11×C4⋊C4C2418yes—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4C2×D412yes—
166C11×C22⋊C4C2×D414yes—
167C42×C11—28no—
168C42×C11C2×D412yes—
169C42×C11C2×D414yes—
170C42×C11C2411yescharacteristic
171C42×C11C2412yes—
172C42×C11C2411yescharacteristic
173#3511C2×C1112yescomplemented
174#3185C2×C1112yescomplemented
175#3184C2×C1112yescomplemented
176#3173C2×C1118yescomplemented
177#3167C2×C1114yescomplemented
178C2×#498C2×C1111yescharacteristic, complemented
179#3147C2×C1111yescharacteristic, complemented
180#3141C2×C1112yescomplemented
181#3060C2×C1114yescomplemented
182#2952C2×C1114yescomplemented
183C4×#131C2×C1111yescharacteristic, complemented
184C23×C11—24no—
185C23×C11C22×D412yes—
186C23×C11C22×D411yescharacteristic
187Q8×C11—22no—
188Q8×C11—28no—
189Q8×C11—48no—
190Q8×C11—84no—
191D4×C11—24no—
192D4×C11—22no—
193D4×C11—28no—
194D4×C11—48no—
195D4×C11—44no—
196D4×C11—44no—
197D4×C11—88no—
198C2×C4×C11—24no—
199C2×C4×C11—28no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—28no—
203C2×C4×C11—48no—
204C2×C4×C11—88no—
205C2×C4×C11—84no—
206C2×C4×C11C22×D414yes—
207C2×C4×C11C22×D412yes—
208C2×C4×C11C22×D412yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D412yes—
211C2×C4×C11C2×#4114yes—
212C2×C4×C11C2511yescharacteristic
213C8×C11—24no—
214C8×C11C2×#4114yes—
215C8×C11C2×#4114yes—
216C2×#135C22×C1114yes—
217C2×#131C22×C1112yes—
218#556—22no—
219#555—22no—
220#554—22no—
221#553—24no—
222#548—24no—
223#547—22no—
224#542C22×C1118yes—
225#537C22×C1114yes—
226#533C22×C1114yes—
227#532C22×C1112yes—
228#532C22×C1114yes—
229C2×C4⋊Q8C22×C1112yes—
230#520C22×C1114yes—
231C4×#41C22×C1111yescharacteristic
232#498C22×C1112yes—
233#498C22×C1114yes—
234#498C22×C1112yes—
235#495C22×C1114yes—
236#494C22×C1111yescharacteristic
237#493C22×C1111yescharacteristic
238#492C22×C1112yes—
239#489C22×C1118yes—
240#487C22×C1114yes—
241#486C22×C1114yes—
242#470C22×C1118yes—
243#469C22×C1118yes—
244#465C22×C11116yes—
245#442C22×C1118yes—
246#441C22×C1118yes—
247C4×SD16C22×C11116yes—
248C2×#106C22×C1114yes—
249#417C22×C1118yes—
250#405C22×C1114yes—
251#405C22×C1112yes—
252C4×M16C22×C1111yescharacteristic
253C4×M16C22×C1112yes—
254C2×C4×C8C22×C1111yescharacteristic
255C2×C4×C8C22×C1112yes—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—24no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11#53212yes—
263C22×C11C23×D411yescharacteristic
264C4×C11—22no—
265C4×C11—24no—
266C4×C11—22no—
267C4×C11—44no—
268C4×C11—48no—
269C4×C11#53212yes—
270C4×C11#57714yes—
271C4×C11C22×#4112yes—
272C2×#41—24no—
273C2×#41C23×C1114yes—
274C2×#41C23×C1111yescharacteristic
275C22×Q8—22no—
276#135—216no—
277C2×Q16C23×C1114yes—
278C2×SD16C23×C1118yes—
279C2×D8C23×C1114yes—
280#131—28no—
281C2×M16C23×C1112yes—
282C2×M16C23×C1114yes—
283C22×C8C23×C1114yes—
284C22×C8C23×C1112yes—
285C4⋊Q8—22no—
286C4⋊Q8—22no—
287C4⋊Q8C23×C1112yes—
288C4⋊Q8C23×C1114yes—
289C4⋊Q8C23×C1114yes—
290#127C23×C1112yes—
291#126—28no—
292#125—24no—
293#124—28no—
294#124—24no—
295#124C23×C1114yes—
296#123—28no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299C22⋊Q8—28no—
300C22⋊Q8C23×C1118yes—
301#121—24no—
302#121—28no—
303#121—22no—
304#121—22no—
305#121—24no—
306#121C23×C1118yes—
307C4×Q8—24no—
308C4×Q8D4×C1112yes—
309C4×Q8C23×C1118yes—
310C4×D4—28no—
311C4×D4—22no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4D4×C1112yes—
315C4×D4D4×C1114yes—
316C4×D4C23×C1118yes—
317#117—24no—
318#117—24no—
319#117C23×C1111yescharacteristic
320#117C23×C1112yes—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4C23×C1114yes—
324C2×C42C23×C1111yescharacteristic
325C2×C42C23×C1112yes—
326#106C23×C1118yes—
327#106C23×C1118yes—
328#103C23×C11116yes—
329#102C23×C11116yes—
330#97C23×C1114yes—
331#97C23×C1112yes—
332C4×C8C23×C1111yescharacteristic
333C4×C8C23×C1112yes—
334C4×C8C23×C1111yescharacteristic
335C4×C8C23×C1114yes—
336C4×C8C23×C1112yes—
337C2×C11—22no—
338C2×C11—42no—
339C2×C11—84no—
340C2×C11C2×#53211yescharacteristic
341C2×C11C2×#57712yes—
342#41—24no—
343#41—216no—
344#41—88no—
345C2×Q8—24no—
346C2×Q8—24no—
347C2×Q8—84no—
348C2×Q8C2×D4×C1111yescharacteristic
349C2×Q8C24×C1114yes—
350C2×D4—24no—
351C2×D4—28no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4C2×D4×C1112yes—
355C2×D4C2×D4×C1111yescharacteristic
356C2×D4C24×C1114yes—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—28no—
360C22×C4C2×D4×C1112yes—
361C22×C4C2×D4×C1114yes—
362C22×C4C24×C1112yes—
363C22×C4C24×C1111yescharacteristic
364Q16—28no—
365SD16—216no—
366D8—28no—
367M16—24no—
368M16—28no—
369C2×C8—28no—
370C2×C8C11×#4118yescomplemented
371C2×C8C24×C1114yes—
372C2×C8C24×C1112yes—
373C2×C8C24×C1112yes—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—28no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—28no—
381C4⋊C4C2×D4×C1112yes—
382C4⋊C4C2×D4×C1114yes—
383C4⋊C4C24×C1118yes—
384C22⋊C4—28no—
385C22⋊C4—28no—
386C22⋊C4—28no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4C2×D4×C1112yes—
390C22⋊C4C2×D4×C1114yes—
391C42—28no—
392C42C2×D4×C1112yes—
393C42C2×D4×C1114yes—
394C42C24×C1111yescharacteristic
395C42C24×C1112yes—
396C42C24×C1111yescharacteristic
397C11#6071611yescharacteristic, direct product factor, Sylow
398C23—24no—
399C23C22×D4×C1112yes—
400C23C22×D4×C1111yescharacteristic
401Q8—22no—
402Q8—28no—
403Q8—48no—
404Q8—84no—
405D4—24no—
406D4—22no—
407D4—28no—
408D4—48no—
409D4—44no—
410D4—44no—
411D4—88no—
412C2×C4—24no—
413C2×C4—28no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—28no—
417C2×C4—48no—
418C2×C4—88no—
419C2×C4—84no—
420C2×C4C22×D4×C1114yes—
421C2×C4C22×D4×C1112yes—
422C2×C4C22×D4×C1112yes—
423C2×C4C22×D4×C1111yescharacteristic
424C2×C4C22×D4×C1112yes—
425C2×C4C2×C11×#4114yes—
426C2×C4C25×C1111yescharacteristic
427C8—24no—
428C8C2×C11×#4114yes—
429C8C2×C11×#4114yes—
430C22—22no—
431C22—22no—
432C22—24no—
433C22—44no—
434C22—44no—
435C22—44no—
436C22C11×#53212yes—
437C22C23×D4×C1111yescharacteristic
438C4—22no—
439C4—24no—
440C4—22no—
441C4—44no—
442C4—48no—
443C4C11×#53212yes—
444C4C11×#57714yes—
445C4C22×C11×#4112yes—
446C2—22no—
447C2—42no—
448C2—84no—
449C2C2×C11×#53211yescharacteristic
450C2C2×C11×#57712yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3511C2semidirect
2. C11×#3185C2semidirect
3. C11×#3184C2semidirect
4. C11×#3173C2semidirect
5. C11×#3167C2semidirect
6. C2×C11×#498C2semidirect
7. C11×#3147C2semidirect
8. C11×#3141C2semidirect
9. C11×#3060C2semidirect
10. C11×#2952C2semidirect
11. C4×C11×#131C2semidirect
117. #60716C11direct (N × H)
146. C2×C8×C11#41semidirect
173. #3511C2×C11semidirect
174. #3185C2×C11semidirect
175. #3184C2×C11semidirect
176. #3173C2×C11semidirect
177. #3167C2×C11semidirect
178. C2×#498C2×C11semidirect
179. #3147C2×C11semidirect
180. #3141C2×C11semidirect
181. #3060C2×C11semidirect
182. #2952C2×C11semidirect
183. C4×#131C2×C11semidirect
370. C2×C8C11×#41semidirect
397. C11#60716direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35112
C11×#31852
C11×#31842
C11×#31732
C11×#31672
C2×C11×#4982
C11×#31472
C11×#31412
C11×#30602
C11×#29522
C4×C11×#1312
#6071611