Finite Group Databasebeta

← C11×#32923 #14610116

Subgroups — C11×#32923 #14610116

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×2−1+4C211yesmaximal, characteristic
2C11×#3039C212yesmaximal, complemented
3C2×C11×#456C212yesmaximal
4C11×#2546C211yesmaximal, characteristic, complemented
5C11×#1886C212yesmaximal, complemented
6C11×#1882C214yesmaximal, complemented
7C11×#1806C212yesmaximal, complemented
8C11×#1801C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4C2211yescharacteristic
10C2×C11×#137C2214yes—
11C2×C11×C4⋊Q8C2212yes—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C11×#520—22no—
14C11×#520—22no—
15C11×#520C2212yes—
16C11×#519—22no—
17C11×#519C2211yescharacteristic
18C4×C11×#41—22no—
19C4×C11×#41—22no—
20C4×C11×#41C2212yes—
21C2×C4×Q8×C11—22no—
22C2×C4×Q8×C11C2211yescharacteristic
23C11×#462—22no—
24C11×#462—22no—
25C11×#461—22no—
26C11×#461—22no—
27C11×#456—28no—
28C11×#423C2212yes—
29C2×C11×#104C2214yes—
30C11×#419C2214yes—
31C2×C11×#101C2212yes—
32C11×#398—22no—
33C11×#391C2212yes—
34C11×#389—22no—
35C4×C11×C4⋊C4C2211yescharacteristic
36C11×#343C2212yes—
37C11×#339C2214yes—
38C11×2−1+4—24no—
39C11×2−1+4—22no—
40C11×2−1+4D414yes—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41C2312yes—
44C22×Q8×C11—22no—
45C22×Q8×C11C2312yes—
46C22×Q8×C11C2311yescharacteristic
47C11×#137—28no—
48C11×#137—28no—
49C2×C11×Q16—24no—
50C2×C11×SD16—24no—
51C2×C11×M16C2314yes—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11D412yes—
65C4×Q8×C11D412yes—
66C4×D4×C11—22no—
67C4×D4×C11—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—22no—
73C4×D4×C11D412yes—
74C4×D4×C11D412yes—
75C11×#117—24no—
76C11×#117—24no—
77C11×#117—22no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117C2312yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D412yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—24no—
90C2×C42×C11—22no—
91C2×C42×C11D412yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2311yescharacteristic
94C11×C4⋊C8—22no—
95C11×C4⋊C8—22no—
96C11×#104—28no—
97C11×#103—24no—
98C11×#103—24no—
99C11×#101—24no—
100C11×#95—21no—
101C11×#95—24no—
102#32923C1111yesmaximal, characteristic, direct product factor, Sylow
103C11×#41—28no—
104C11×#41—28no—
105C11×#41—28no—
106C11×#41—28no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41C2×D414yes—
110C11×#41#4114yes—
111C2×Q8×C11—22no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—24no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—24no—
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11C2×D412yes—
122C2×Q8×C11#4112yes—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C11×Q16—48no—
139C11×SD16—48no—
140C11×M16—24no—
141C11×M16—24no—
142C2×C8×C11—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—48no—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4C2×D412yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C42×C11—24no—
162C42×C11—24no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11C2×D412yes—
171C42×C11C2×D412yes—
172C4×2−1+4C2×C1111yescharacteristic
173#3039C2×C1112yescomplemented
174C2×#456C2×C1112yes—
175#2546C2×C1111yescharacteristic, complemented
176#1886C2×C1112yescomplemented
177#1882C2×C1114yescomplemented
178#1806C2×C1112yescomplemented
179#1801C2×C1111yescharacteristic, complemented
180C23×C11—22no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—28no—
183Q8×C11—24no—
184Q8×C11—22no—
185Q8×C11—24no—
186Q8×C11—44no—
187Q8×C11—44no—
188Q8×C11#12114yes—
189D4×C11—28no—
190D4×C11—24no—
191D4×C11—24no—
192D4×C11—22no—
193D4×C11#12114yes—
194C2×C4×C11—216no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—44no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—82no—
214C2×C4×C11—84no—
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12012yes—
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12114yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D412yes—
221C2×C4×C11C2×#4112yes—
222C2×C4×C11C2×#4111yescharacteristic
223C8×C11—44no—
224C2×2−1+4C22×C1111yescharacteristic
225C2×#137C22×C1114yes—
226C2×C4⋊Q8C22×C1112yes—
227C2×C4⋊Q8C22×C1111yescharacteristic
228#520—22no—
229#520—22no—
230#520C22×C1112yes—
231#519—22no—
232#519C22×C1111yescharacteristic
233C4×#41—22no—
234C4×#41—22no—
235C4×#41C22×C1112yes—
236C2×C4×Q8—22no—
237C2×C4×Q8C22×C1111yescharacteristic
238#462—22no—
239#462—22no—
240#461—22no—
241#461—22no—
242#456—28no—
243#423C22×C1112yes—
244C2×#104C22×C1114yes—
245#419C22×C1114yes—
246C2×#101C22×C1112yes—
247#398—22no—
248#391C22×C1112yes—
249#389—22no—
250C4×C4⋊C4C22×C1111yescharacteristic
251#343C22×C1112yes—
252#339C22×C1114yes—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—24no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11C2×#12011yescharacteristic
259C22×C11C2×#12111yescharacteristic
260C22×C11#52511yescharacteristic
261C4×C11—24no—
262C4×C11—24no—
263C4×C11—21no—
264C4×C11—22no—
265C4×C11—44no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11#45612yescomplemented
271C4×C11C2×#12112yes—
272C4×C11#52512yes—
2732−1+4—24no—
2742−1+4—22no—
2752−1+4D4×C1114yes—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41C23×C1112yes—
279C22×Q8—22no—
280C22×Q8C23×C1112yes—
281C22×Q8C23×C1111yescharacteristic
282#137—28no—
283#137—28no—
284C2×Q16—24no—
285C2×SD16—24no—
286C2×M16C23×C1114yes—
287C4⋊Q8—24no—
288C4⋊Q8—24no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C4×Q8—22no—
292C4×Q8—24no—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8D4×C1112yes—
300C4×Q8D4×C1112yes—
301C4×D4—22no—
302C4×D4—24no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—24no—
307C4×D4—22no—
308C4×D4D4×C1112yes—
309C4×D4D4×C1112yes—
310#117—24no—
311#117—24no—
312#117—22no—
313#117—22no—
314#117—22no—
315#117C23×C1112yes—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C1112yes—
323C2×C4⋊C4C23×C1111yescharacteristic
324C2×C42—24no—
325C2×C42—22no—
326C2×C42D4×C1112yes—
327C2×C42C23×C1112yes—
328C2×C42C23×C1111yescharacteristic
329C4⋊C8—22no—
330C4⋊C8—22no—
331#104—28no—
332#103—24no—
333#103—24no—
334#101—24no—
335#95—21no—
336#95—24no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—44no—
340C2×C11#284711yescharacteristic
341C2×C11C2×#45611yescharacteristic
342C2×C11#302211yescharacteristic
343#41—28no—
344#41—28no—
345#41—28no—
346#41—28no—
347#41—22no—
348#41—22no—
349#41C2×D4×C1114yes—
350#41C11×#4114yes—
351C2×Q8—22no—
352C2×Q8—28no—
353C2×Q8—28no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—24no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—24no—
360C2×Q8C2×D4×C1112yes—
361C2×Q8C2×D4×C1112yes—
362C2×Q8C11×#4112yes—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4C2×D4×C1112yes—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1112yes—
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C24×C1111yescharacteristic
378Q16—48no—
379SD16—48no—
380M16—24no—
381M16—24no—
382C2×C8—24no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—24no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—41no—
392C4⋊C4—42no—
393C4⋊C4—41no—
394C4⋊C4—48no—
395C4⋊C4C2×D4×C1112yes—
396C4⋊C4C2×D4×C1112yes—
397C22⋊C4—24no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C42—24no—
402C42—24no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42—22no—
410C42C2×D4×C1112yes—
411C42C2×D4×C1112yes—
412C11#3292311yescharacteristic, direct product factor, Sylow
413C23—22no—
414C23C22×D4×C1111yescharacteristic
415Q8—28no—
416Q8—24no—
417Q8—22no—
418Q8—24no—
419Q8—44no—
420Q8—44no—
421Q8C11×#12114yes—
422D4—28no—
423D4—24no—
424D4—24no—
425D4—22no—
426D4C11×#12114yes—
427C2×C4—216no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—84no—
448C2×C4C11×#12011yescharacteristic
449C2×C4C11×#12012yes—
450C2×C4C11×#12011yescharacteristic
451C2×C4C11×#12114yes—
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1112yes—
454C2×C4C2×C11×#4112yes—
455C2×C4C2×C11×#4111yescharacteristic
456C8—44no—
457C22—21no—
458C22—21no—
459C22—24no—
460C22—42no—
461C22—42no—
462C22C2×C11×#12011yescharacteristic
463C22C2×C11×#12111yescharacteristic
464C22C11×#52511yescharacteristic
465C4—21no—
466C4—22no—
467C4—24no—
468C4—24no—
469C4—44no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—82no—
474C4C11×#45612yescomplemented
475C4C2×C11×#12112yes—
476C4C11×#52512yes—
477C2—21no—
478C2—21no—
479C2—44no—
480C2C11×#284711yescharacteristic
481C2C2×C11×#45611yescharacteristic
482C2C11×#302211yescharacteristic
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×#3039C2semidirect
4. C11×#2546C2semidirect
5. C11×#1886C2semidirect
6. C11×#1882C2semidirect
7. C11×#1806C2semidirect
8. C11×#1801C2semidirect
102. #32923C11direct (N × H)
173. #3039C2×C11semidirect
175. #2546C2×C11semidirect
176. #1886C2×C11semidirect
177. #1882C2×C11semidirect
178. #1806C2×C11semidirect
179. #1801C2×C11semidirect
270. C4×C11#456semidirect
412. C11#32923direct (N × H)
474. C4C11×#456semidirect

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×#30392
C2×C11×#4562
C11×#25462
C11×#18862
C11×#18822
C11×#18062
C11×#18012
#3292311