Finite Group Databasebeta

← C11×#61665 #14638858

Subgroups — C11×#61665 #14638858

Order 2816.

2008 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic, complemented
2C11×#3499C211yesmaximal, characteristic
3C11×#3328C214yesmaximal, complemented
4C11×#3302C214yesmaximal, complemented
5D4×C11×Q16C214yesmaximal, complemented
6C11×#3276C214yesmaximal, complemented
7C11×#3209C212yesmaximal, complemented
8C11×#3202C214yesmaximal, complemented
9C11×#3107C212yesmaximal, complemented
10C11×#3011C214yesmaximal, complemented
11C11×#2979C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2212yes—
13C2×C11×#137C2214yes—
14C22×C11×Q16C2214yes—
15C11×#563—22no—
16C11×#559—21no—
17Q82×C11—21no—
18C11×#556C2214yes—
19D4×Q8×C11C2214yes—
20D4×Q8×C11C2214yes—
21C11×#547—24no—
22C11×#547C2214yes—
23C11×#542—24no—
24C11×#536—22no—
25C11×#536C2212yes—
26C11×#536C2214yes—
27C11×#533C2212yes—
28C11×#532—21no—
29C11×#532C2211yescharacteristic
30C2×C11×C4⋊Q8—21no—
31C2×C11×C4⋊Q8C2211yescharacteristic
32C4×C11×#41C2211yescharacteristic
33C11×#494C2214yes—
34C11×#487C2214yes—
35C11×#485C2214yes—
36C11×#485C2218yes—
37C11×#475C2212yes—
38C11×#474C2212yes—
39C11×#470C2218yes—
40C11×#467C2218yes—
41C11×#462C2214yes—
42C11×#462C2214yes—
43C11×#462C2212yes—
44C11×#461C2212yes—
45C11×#452C2214yes—
46C11×#452C2218yes—
47C11×#451C2218yes—
48C11×#451C2218yes—
49C11×#451C2218yes—
50C4×C11×Q16C2214yes—
51C4×C11×SD16C2214yes—
52C11×#436C2214yes—
53C8×D4×C11C2214yes—
54C11×#431C2212yes—
55C11×#419C2214yes—
56C11×#416C2214yes—
57C11×#408C2214yes—
58C11×2−1+4—44no—
59C11×2−1+4—44no—
60C2×C11×#41—22no—
61C2×C11×#41—24no—
62C2×C11×#41C2311yescharacteristic
63C2×C11×#41C2314yes—
64C2×C11×#41C2312yes—
65C22×Q8×C11—22no—
66C22×Q8×C11C2314yes—
67C22×Q8×C11C2312yes—
68C22×Q8×C11C2314yes—
69C11×#137—48no—
70C2×C11×Q16—48no—
71C2×C11×Q16C2314yes—
72C2×C11×Q16C2318yes—
73C2×C11×Q16C2318yes—
74C2×C11×SD16C2314yes—
75C2×C11×M16C2314yes—
76C22×C8×C11C2314yes—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—24no—
79C11×C4⋊Q8—24no—
80C11×C4⋊Q8—24no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8D411yescharacteristic
84C11×C4⋊Q8C2312yes—
85C11×C4⋊Q8C2314yes—
86C11×C4⋊Q8C2312yes—
87C11×#127D411yescharacteristic
88C11×#126—28no—
89C11×#125—22no—
90C11×#124—22no—
91C11×#124—24no—
92C11×#124—24no—
93C11×#124D412yes—
94C11×#123—24no—
95C11×#123—24no—
96C11×#123—24no—
97C11×#123—28no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—28no—
100C11×C22⋊Q8—28no—
101C11×C22⋊Q8C2314yes—
102C11×C22⋊Q8C2318yes—
103C11×C22⋊Q8C2318yes—
104C11×#121—24no—
105C11×#121D414yes—
106C4×Q8×C11—24no—
107C4×Q8×C11—22no—
108C4×Q8×C11C2312yes—
109C4×Q8×C11C2314yes—
110C4×D4×C11—24no—
111C4×D4×C11—24no—
112C4×D4×C11—22no—
113C4×D4×C11C2312yes—
114C4×D4×C11C2314yes—
115C11×#117—22no—
116C11×#117—21no—
117C11×#117C2311yescharacteristic
118C11×#117C2314yes—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—24no—
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C11×#107C2314yes—
124C11×#106C2314yes—
125C11×C4⋊C8C2312yes—
126C11×C4⋊C8C2312yes—
127C11×#103C2318yes—
128C11×#103C2314yes—
129C11×#103C2318yes—
130C11×#103C2314yes—
131C11×#103C2314yes—
132C11×#102C2314yes—
133C11×C22⋊C8C2314yes—
134C11×C22⋊C8C2318yes—
135C4×C8×C11C2314yes—
136#61665C1111yesmaximal, characteristic, direct product factor, Sylow
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—28no—
140C11×#41—42no—
141C11×#41—42no—
142C11×#41—44no—
143C11×#41—48no—
144C11×#41—416no—
145C2×Q8×C11—22no—
146C2×Q8×C11—24no—
147C2×Q8×C11—22no—
148C2×Q8×C11—24no—
149C2×Q8×C11—28no—
150C2×Q8×C11—44no—
151C2×Q8×C11—42no—
152C2×Q8×C11—42no—
153C2×Q8×C11—48no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C2×Q8×C11C2×D412yes—
157C2×Q8×C11C2414yes—
158C2×Q8×C11C2414yes—
159C2×Q8×C11C2411yescharacteristic
160C2×D4×C11—21no—
161C2×D4×C11—24no—
162C2×D4×C11C2×D414yes—
163C2×D4×C11C2×D414yes—
164C2×D4×C11C2×D412yes—
165C2×D4×C11C2411yescharacteristic
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—22no—
171C22×C4×C11—24no—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2414yes—
175C11×Q16—28no—
176C11×Q16—48no—
177C11×Q16—48no—
178C11×SD16—28no—
179C11×M16—44no—
180C2×C8×C11—44no—
181C2×C8×C11C2414yes—
182C2×C8×C11C2414yes—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—28no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—28no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4C2×D414yes—
194C11×C4⋊C4C2414yes—
195C11×C4⋊C4C2412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—28no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4C2×D418yes—
203C42×C11—21no—
204C42×C11—22no—
205C42×C11—24no—
206C42×C11—24no—
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D411yescharacteristic
209C42×C11C2412yes—
210#3550C2×C1111yescharacteristic, complemented
211#3499C2×C1111yescharacteristic
212#3328C2×C1114yescomplemented
213#3302C2×C1114yescomplemented
214D4×Q16C2×C1114yescomplemented
215#3276C2×C1114yescomplemented
216#3209C2×C1112yescomplemented
217#3202C2×C1114yescomplemented
218#3107C2×C1112yescomplemented
219#3011C2×C1114yescomplemented
220#2979C2×C1111yescharacteristic, complemented
221C23×C11—21no—
222C23×C11C22×D414yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11—24no—
226Q8×C11—24no—
227Q8×C11—24no—
228Q8×C11—24no—
229Q8×C11—42no—
230Q8×C11—48no—
231Q8×C11—44no—
232Q8×C11—44no—
233Q8×C11—84no—
234Q8×C11H(5,𝔽2)12yes—
235D4×C11—24no—
236D4×C11—28no—
237D4×C11—21no—
238D4×C11—42no—
239D4×C11—44no—
240D4×C11—48no—
241D4×C11H(5,𝔽2)12yes—
242C2×C4×C11—24no—
243C2×C4×C11—21no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—48no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—84no—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D414yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C2511yescharacteristic
263C8×C11—24no—
264C8×C11—24no—
265C2×2−1+4C22×C1112yes—
266C2×#137C22×C1114yes—
267C22×Q16C22×C1114yes—
268#563—22no—
269#559—21no—
270Q82—21no—
271#556C22×C1114yes—
272D4×Q8C22×C1114yes—
273D4×Q8C22×C1114yes—
274#547—24no—
275#547C22×C1114yes—
276#542—24no—
277#536—22no—
278#536C22×C1112yes—
279#536C22×C1114yes—
280#533C22×C1112yes—
281#532—21no—
282#532C22×C1111yescharacteristic
283C2×C4⋊Q8—21no—
284C2×C4⋊Q8C22×C1111yescharacteristic
285C4×#41C22×C1111yescharacteristic
286#494C22×C1114yes—
287#487C22×C1114yes—
288#485C22×C1118yes—
289#485C22×C1114yes—
290#475C22×C1112yes—
291#474C22×C1112yes—
292#470C22×C1118yes—
293#467C22×C1118yes—
294#462C22×C1114yes—
295#462C22×C1112yes—
296#462C22×C1114yes—
297#461C22×C1112yes—
298#452C22×C1114yes—
299#452C22×C1118yes—
300#451C22×C1118yes—
301#451C22×C1118yes—
302#451C22×C1118yes—
303C4×Q16C22×C1114yes—
304C4×SD16C22×C1114yes—
305#436C22×C1114yes—
306C8×D4C22×C1114yes—
307#431C22×C1112yes—
308#419C22×C1114yes—
309#416C22×C1114yes—
310#408C22×C1114yes—
311C22×C11—21no—
312C22×C11—22no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—28no—
316C22×C11—42no—
317C22×C11C23×D411yescharacteristic
318C4×C11—21no—
319C4×C11—22no—
320C4×C11—24no—
321C4×C11—22no—
322C4×C11—44no—
323C4×C11—44no—
324C4×C11—42no—
325C4×C11—44no—
326C4×C11#57814yes—
327C4×C11C2×H(5,𝔽2)11yescharacteristic
328C4×C11C2×H(5,𝔽2)11yescharacteristic
3292−1+4—44no—
3302−1+4—44no—
331C2×#41—22no—
332C2×#41—24no—
333C2×#41C23×C1111yescharacteristic
334C2×#41C23×C1114yes—
335C2×#41C23×C1112yes—
336C22×Q8—22no—
337C22×Q8C23×C1114yes—
338C22×Q8C23×C1112yes—
339C22×Q8C23×C1114yes—
340#137—48no—
341C2×Q16—48no—
342C2×Q16C23×C1114yes—
343C2×Q16C23×C1118yes—
344C2×Q16C23×C1118yes—
345C2×SD16C23×C1114yes—
346C2×M16C23×C1114yes—
347C22×C8C23×C1114yes—
348C4⋊Q8—22no—
349C4⋊Q8—24no—
350C4⋊Q8—24no—
351C4⋊Q8—24no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8D4×C1111yescharacteristic
355C4⋊Q8C23×C1114yes—
356C4⋊Q8C23×C1112yes—
357C4⋊Q8C23×C1112yes—
358#127D4×C1111yescharacteristic
359#126—28no—
360#125—22no—
361#124—22no—
362#124—24no—
363#124—24no—
364#124D4×C1112yes—
365#123—24no—
366#123—24no—
367#123—24no—
368#123—28no—
369C22⋊Q8—22no—
370C22⋊Q8—28no—
371C22⋊Q8—28no—
372C22⋊Q8C23×C1114yes—
373C22⋊Q8C23×C1118yes—
374C22⋊Q8C23×C1118yes—
375#121—24no—
376#121D4×C1114yes—
377C4×Q8—24no—
378C4×Q8—22no—
379C4×Q8C23×C1112yes—
380C4×Q8C23×C1114yes—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4C23×C1112yes—
385C4×D4C23×C1114yes—
386#117—22no—
387#117—21no—
388#117C23×C1111yescharacteristic
389#117C23×C1114yes—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C42—21no—
393C2×C42C23×C1111yescharacteristic
394#107C23×C1114yes—
395#106C23×C1114yes—
396C4⋊C8C23×C1112yes—
397C4⋊C8C23×C1112yes—
398#103C23×C1118yes—
399#103C23×C1114yes—
400#103C23×C1118yes—
401#103C23×C1114yes—
402#103C23×C1114yes—
403#102C23×C1114yes—
404C22⋊C8C23×C1114yes—
405C22⋊C8C23×C1118yes—
406C4×C8C23×C1114yes—
407C2×C11—41no—
408C2×C11—44no—
409C2×C11—42no—
410C2×C11#348411yescharacteristic
411C2×C11C2×#57812yes—
412#41—22no—
413#41—22no—
414#41—28no—
415#41—42no—
416#41—42no—
417#41—44no—
418#41—48no—
419#41—416no—
420C2×Q8—22no—
421C2×Q8—24no—
422C2×Q8—22no—
423C2×Q8—24no—
424C2×Q8—28no—
425C2×Q8—44no—
426C2×Q8—42no—
427C2×Q8—42no—
428C2×Q8—48no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8C2×D4×C1112yes—
432C2×Q8C24×C1114yes—
433C2×Q8C24×C1114yes—
434C2×Q8C24×C1111yescharacteristic
435C2×D4—21no—
436C2×D4—24no—
437C2×D4C2×D4×C1114yes—
438C2×D4C2×D4×C1114yes—
439C2×D4C2×D4×C1112yes—
440C2×D4C24×C1111yescharacteristic
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4C2×D4×C1112yes—
448C22×C4C24×C1111yescharacteristic
449C22×C4C24×C1114yes—
450Q16—28no—
451Q16—48no—
452Q16—48no—
453SD16—28no—
454M16—44no—
455C2×C8—44no—
456C2×C8C24×C1114yes—
457C2×C8C24×C1114yes—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—28no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—28no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4C2×D4×C1114yes—
469C4⋊C4C24×C1114yes—
470C4⋊C4C24×C1112yes—
471C22⋊C4—24no—
472C22⋊C4—21no—
473C22⋊C4—24no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—22no—
477C22⋊C4C2×D4×C1118yes—
478C42—21no—
479C42—22no—
480C42—24no—
481C42—24no—
482C42C2×D4×C1111yescharacteristic
483C42C2×D4×C1111yescharacteristic
484C42C24×C1112yes—
485C11#6166511yescharacteristic, direct product factor, Sylow
486C23—21no—
487C23C22×D4×C1114yes—
488C23C22×D4×C1111yescharacteristic
489Q8—21no—
490Q8—24no—
491Q8—24no—
492Q8—24no—
493Q8—24no—
494Q8—42no—
495Q8—48no—
496Q8—44no—
497Q8—44no—
498Q8—84no—
499Q8C11×H(5,𝔽2)12yes—
500D4—24no—
501D4—28no—
502D4—21no—
503D4—42no—
504D4—44no—
505D4—48no—
506D4C11×H(5,𝔽2)12yes—
507C2×C4—24no—
508C2×C4—21no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—48no—
519C2×C4—48no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—84no—
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×D4×C1114yes—
525C2×C4C22×D4×C1112yes—
526C2×C4C22×D4×C1112yes—
527C2×C4C25×C1111yescharacteristic
528C8—24no—
529C8—24no—
530C22—21no—
531C22—22no—
532C22—24no—
533C22—22no—
534C22—28no—
535C22—42no—
536C22C23×D4×C1111yescharacteristic
537C4—21no—
538C4—22no—
539C4—24no—
540C4—22no—
541C4—44no—
542C4—44no—
543C4—42no—
544C4—44no—
545C4C11×#57814yes—
546C4C2×C11×H(5,𝔽2)11yescharacteristic
547C4C2×C11×H(5,𝔽2)11yescharacteristic
548C2—41no—
549C2—44no—
550C2—42no—
551C2C11×#348411yescharacteristic
552C2C2×C11×#57812yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3499C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3550C2semidirect
3. C11×#3328C2semidirect
4. C11×#3302C2semidirect
5. D4×C11×Q16C2semidirect
6. C11×#3276C2semidirect
7. C11×#3209C2semidirect
8. C11×#3202C2semidirect
9. C11×#3107C2semidirect
10. C11×#3011C2semidirect
11. C11×#2979C2semidirect
136. #61665C11direct (N × H)
210. #3550C2×C11semidirect
212. #3328C2×C11semidirect
213. #3302C2×C11semidirect
214. D4×Q16C2×C11semidirect
215. #3276C2×C11semidirect
216. #3209C2×C11semidirect
217. #3202C2×C11semidirect
218. #3107C2×C11semidirect
219. #3011C2×C11semidirect
220. #2979C2×C11semidirect
485. C11#61665direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#34992
C11×#33282
C11×#33022
D4×C11×Q162
C11×#32762
C11×#32092
C11×#32022
C11×#31072
C11×#30112
C11×#29792
#6166511