Finite Group Databasebeta

← C11×#32974 #14610167

Subgroups — C11×#32974 #14610167

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×2−1+4C211yesmaximal, characteristic
2C11×#3080C212yesmaximal, complemented
3C11×#2565C211yesmaximal, characteristic, complemented
4C11×#1860C212yesmaximal, complemented
5C11×#1859C212yesmaximal, complemented
6C11×#1857C211yesmaximal, characteristic, complemented
7C11×#1857C211yesmaximal, characteristic, complemented
8C11×#1806C212yesmaximal, complemented
9C11×#1801C211yesmaximal, characteristic, complemented
10C11×#1793C211yesmaximal, characteristic
11C11×#1793C211yesmaximal, characteristic
12C2×C11×2−1+4C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C11×#520—22no—
15C11×#520—22no—
16C11×#520C2212yes—
17C11×#519—22no—
18C11×#519C2211yescharacteristic
19C4×C11×#41—22no—
20C4×C11×#41—22no—
21C4×C11×#41C2212yes—
22C2×C4×Q8×C11—22no—
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#479—22no—
25C11×#479—22no—
26C11×#478—22no—
27C11×#478—22no—
28C11×#428C2212yes—
29C11×#428C2212yes—
30C11×#423C2212yes—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#417C2212yes—
34C11×#417C2212yes—
35C2×C11×#101C2211yescharacteristic
36C2×C11×#101C2211yescharacteristic
37C11×#398—22no—
38C11×#391C2211yescharacteristic
39C11×#391C2211yescharacteristic
40C11×#387—22no—
41C11×#384C2211yescharacteristic
42C11×#382C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C11×#343C2212yes—
45C11×#339C2212yes—
46C11×#339C2212yes—
47C11×2−1+4—24no—
48C11×2−1+4—22no—
49C11×2−1+4Q814yes—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41C2312yes—
53C22×Q8×C11—22no—
54C22×Q8×C11C2311yescharacteristic
55C2×C11×M16C2312yes—
56C2×C11×M16C2312yes—
57C11×#125—22no—
58C11×#125—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—24no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11D412yes—
68C4×Q8×C11D412yes—
69C4×D4×C11—22no—
70C4×D4×C11—24no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—24no—
75C4×D4×C11—22no—
76C4×D4×C11D412yes—
77C4×D4×C11D412yes—
78C11×#117—24no—
79C11×#117—24no—
80C11×#117—22no—
81C11×#117—22no—
82C11×#117—22no—
83C11×#117C2312yes—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C42×C11—24no—
95C2×C42×C11—22no—
96C2×C42×C11D412yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×#107—22no—
101C11×#107—22no—
102C11×#106—22no—
103C11×#106—22no—
104C11×C4⋊C8—22no—
105C11×C4⋊C8—22no—
106C11×#104—24no—
107C11×#104—24no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#101—22no—
113C11×#101—22no—
114C11×#95—21no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118#32974C1111yesmaximal, characteristic, direct product factor, Sylow
119C11×#41—28no—
120C11×#41—28no—
121C11×#41—28no—
122C11×#41—28no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41C2×Q814yes—
126C11×#41#4114yes—
127C2×Q8×C11—22no—
128C2×Q8×C11—28no—
129C2×Q8×C11—28no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×Q812yes—
134C2×Q8×C11#4112yes—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11—24no—
179C42×C11—24no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11C2×D412yes—
188C42×C11C2×D412yes—
189C4×2−1+4C2×C1111yescharacteristic
190#3080C2×C1112yescomplemented
191#2565C2×C1111yescharacteristic, complemented
192#1860C2×C1112yescomplemented
193#1859C2×C1112yescomplemented
194#1857C2×C1111yescharacteristic, complemented
195#1857C2×C1111yescharacteristic, complemented
196#1806C2×C1112yescomplemented
197#1801C2×C1111yescharacteristic, complemented
198#1793C2×C1111yescharacteristic
199#1793C2×C1111yescharacteristic
200C23×C11—22no—
201C23×C11C22×D411yescharacteristic
202Q8×C11—28no—
203Q8×C11—24no—
204Q8×C11—22no—
205Q8×C11—24no—
206Q8×C11C22⋊Q814yes—
207D4×C11—28no—
208D4×C11—24no—
209D4×C11—24no—
210D4×C11—22no—
211D4×C11C22⋊Q814yes—
212C2×C4×C11—216no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—44no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—82no—
236C2×C4×C11—84no—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12012yes—
240C2×C4×C11C22⋊Q814yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×Q811yescharacteristic
243C2×C4×C11C2×#4112yes—
244C2×C4×C11C2×#4111yescharacteristic
245C8×C11—42no—
246C8×C11—42no—
247C2×2−1+4C22×C1111yescharacteristic
248C2×#125C22×C1111yescharacteristic
249#520—22no—
250#520—22no—
251#520C22×C1112yes—
252#519—22no—
253#519C22×C1111yescharacteristic
254C4×#41—22no—
255C4×#41—22no—
256C4×#41C22×C1112yes—
257C2×C4×Q8—22no—
258C2×C4×Q8C22×C1111yescharacteristic
259#479—22no—
260#479—22no—
261#478—22no—
262#478—22no—
263#428C22×C1112yes—
264#428C22×C1112yes—
265#423C22×C1112yes—
266C2×#104C22×C1112yes—
267C2×#104C22×C1112yes—
268#417C22×C1112yes—
269#417C22×C1112yes—
270C2×#101C22×C1111yescharacteristic
271C2×#101C22×C1111yescharacteristic
272#398—22no—
273#391C22×C1111yescharacteristic
274#391C22×C1111yescharacteristic
275#387—22no—
276#384C22×C1111yescharacteristic
277#382C22×C1111yescharacteristic
278C4×C4⋊C4C22×C1111yescharacteristic
279#343C22×C1112yes—
280#339C22×C1112yes—
281#339C22×C1112yes—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—24no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11C2×#12011yescharacteristic
288C22×C11C2×C22⋊Q811yescharacteristic
289C22×C11#52511yescharacteristic
290C4×C11—24no—
291C4×C11—24no—
292C4×C11—22no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11C2×C22⋊Q812yes—
303C4×C11#52512yes—
3042−1+4—24no—
3052−1+4—22no—
3062−1+4Q8×C1114yes—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41C23×C1112yes—
310C22×Q8—22no—
311C22×Q8C23×C1111yescharacteristic
312C2×M16C23×C1112yes—
313C2×M16C23×C1112yes—
314#125—22no—
315#125—22no—
316C4×Q8—22no—
317C4×Q8—24no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8D4×C1112yes—
325C4×Q8D4×C1112yes—
326C4×D4—22no—
327C4×D4—24no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—24no—
332C4×D4—22no—
333C4×D4D4×C1112yes—
334C4×D4D4×C1112yes—
335#117—24no—
336#117—24no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117C23×C1112yes—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4D4×C1112yes—
348C2×C4⋊C4C23×C1111yescharacteristic
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C42—24no—
352C2×C42—22no—
353C2×C42D4×C1112yes—
354C2×C42C23×C1111yescharacteristic
355C2×C42C23×C1111yescharacteristic
356C2×C42C23×C1111yescharacteristic
357#107—22no—
358#107—22no—
359#106—22no—
360#106—22no—
361C4⋊C8—22no—
362C4⋊C8—22no—
363#104—24no—
364#104—24no—
365#103—22no—
366#103—22no—
367#102—22no—
368#102—22no—
369#101—22no—
370#101—22no—
371#95—21no—
372#95—22no—
373#95—22no—
374#95—22no—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—44no—
378C2×C11#284811yescharacteristic
379C2×C11#301811yescharacteristic
380C2×C11#302011yescharacteristic
381#41—28no—
382#41—28no—
383#41—28no—
384#41—28no—
385#41—22no—
386#41—22no—
387#41C2×Q8×C1114yes—
388#41C11×#4114yes—
389C2×Q8—22no—
390C2×Q8—28no—
391C2×Q8—28no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8C2×D4×C1112yes—
395C2×Q8C2×Q8×C1112yes—
396C2×Q8C11×#4112yes—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4C2×D4×C1112yes—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4C2×D4×C1112yes—
410C22×C4C2×D4×C1112yes—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C24×C1111yescharacteristic
414M16—22no—
415M16—22no—
416M16—22no—
417M16—22no—
418C2×C8—22no—
419C2×C8—22no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—42no—
430C4⋊C4—44no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—42no—
434C4⋊C4C2×D4×C1112yes—
435C4⋊C4C2×D4×C1112yes—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C42—24no—
441C42—24no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42C2×D4×C1112yes—
450C42C2×D4×C1112yes—
451C11#3297411yescharacteristic, direct product factor, Sylow
452C23—22no—
453C23C22×D4×C1111yescharacteristic
454Q8—28no—
455Q8—24no—
456Q8—22no—
457Q8—24no—
458Q8C11×C22⋊Q814yes—
459D4—28no—
460D4—24no—
461D4—24no—
462D4—22no—
463D4C11×C22⋊Q814yes—
464C2×C4—216no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—82no—
488C2×C4—84no—
489C2×C4C11×#12011yescharacteristic
490C2×C4C11×#12011yescharacteristic
491C2×C4C11×#12012yes—
492C2×C4C11×C22⋊Q814yes—
493C2×C4C22×D4×C1112yes—
494C2×C4C22×Q8×C1111yescharacteristic
495C2×C4C2×C11×#4112yes—
496C2×C4C2×C11×#4111yescharacteristic
497C8—42no—
498C8—42no—
499C22—21no—
500C22—21no—
501C22—24no—
502C22—42no—
503C22—42no—
504C22C2×C11×#12011yescharacteristic
505C22C2×C11×C22⋊Q811yescharacteristic
506C22C11×#52511yescharacteristic
507C4—22no—
508C4—21no—
509C4—21no—
510C4—24no—
511C4—24no—
512C4—42no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4C2×C11×C22⋊Q812yes—
520C4C11×#52512yes—
521C2—21no—
522C2—21no—
523C2—44no—
524C2C11×#284811yescharacteristic
525C2C11×#301811yescharacteristic
526C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×2−1+4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3080C2semidirect
3. C11×#2565C2semidirect
4. C11×#1860C2semidirect
5. C11×#1859C2semidirect
6. C11×#1857C2semidirect
7. C11×#1857C2semidirect
8. C11×#1806C2semidirect
9. C11×#1801C2semidirect
118. #32974C11direct (N × H)
190. #3080C2×C11semidirect
191. #2565C2×C11semidirect
192. #1860C2×C11semidirect
193. #1859C2×C11semidirect
194. #1857C2×C11semidirect
195. #1857C2×C11semidirect
196. #1806C2×C11semidirect
197. #1801C2×C11semidirect
451. C11#32974direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×2−1+42
C11×#30802
C11×#25652
C11×#18602
C11×#18592
C11×#18572
C11×#18062
C11×#18012
C11×#17932
#3297411