Finite Group Databasebeta

← C11×#19177 #14596370

Subgroups — C11×#19177 #14596370

Order 2816.

650 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
1C11×#3141C211yesmaximal, characteristic
2C11×#3103C211yesmaximal, characteristic
3C2×C11×#462C211yesmaximal, characteristic, complemented
4Q8×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1702C212yesmaximal, complemented
6C11×#1700C212yesmaximal, complemented
7C11×#1682C212yesmaximal, complemented
8C11×#1680C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1549C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic
12C22×C11×Q16—21no—
13C11×#532C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#489—22no—
17C11×#487C2212yes—
18C11×#486C2212yes—
19C11×#481—21no—
20C11×#475C2211yescharacteristic
21C11×#475C2211yescharacteristic
22C11×#462—21no—
23C11×#462—21no—
24C11×#462C2212yes—
25C11×#462C2212yes—
26C11×#460C2211yescharacteristic
27C11×#460C2211yescharacteristic
28C11×#448—21no—
29C11×#446—22no—
30C11×#446C2212yes—
31C8×Q8×C11C2212yes—
32C4×C11×SD16—21no—
33C4×C11×SD16—21no—
34C11×#431C2211yescharacteristic
35C11×#423—21no—
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C11×#417—21no—
39C11×#417—21no—
40C2×C11×#103—21no—
41C4×C11×M16—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yes—
44C11×#334C2212yes—
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11D411yescharacteristic
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C2×C11×Q16—44no—
55C2×C11×SD16—21no—
56C2×C11×SD16—21no—
57C2×C11×M16—21no—
58C2×C11×M16D411yescharacteristic
59C2×C11×M16D411yescharacteristic
60C22×C8×C11—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8C2312yes—
65C11×C4⋊Q8C2311yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#124—21no—
68C11×#121—21no—
69C11×#121—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11D411yescharacteristic
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#106—21no—
85C11×#106—21no—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C11×C4⋊C8C2312yes—
92C11×C4⋊C8C2311yescharacteristic
93C11×C4⋊C8C2311yescharacteristic
94C11×#103—21no—
95C11×#103—21no—
96C11×#103—22no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#103—22no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×C22⋊C8—21no—
105C11×#97—22no—
106C11×#97D412yes—
107C4×C8×C11—22no—
108C4×C8×C11—21no—
109C4×C8×C11C2312yes—
110#19177C1111yesmaximal, characteristic, direct product factor, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—41no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11—41no—
121C2×Q8×C11C2×D411yescharacteristic
122C2×Q8×C11C2×D411yescharacteristic
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C11×Q16—44no—
135C11×Q16—44no—
136C11×SD16—42no—
137C11×SD16—42no—
138C11×M16—22no—
139C11×M16—22no—
140C11×M16—42no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—42no—
146C2×C8×C11C2×D412yes—
147C2×C8×C11C2×D412yes—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4C2×D411yescharacteristic
160C11×C4⋊C4C2×D411yescharacteristic
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11#4111yescharacteristic
170C42×C11C2411yescharacteristic
171#3141C2×C1111yescharacteristic
172#3103C2×C1111yescharacteristic
173C2×#462C2×C1111yescharacteristic, complemented
174Q8×M16C2×C1111yescharacteristic, complemented
175#1702C2×C1112yescomplemented
176#1700C2×C1112yescomplemented
177#1682C2×C1112yescomplemented
178#1680C2×C1112yescomplemented
179#1565C2×C1111yescharacteristic, complemented
180#1549C2×C1111yescharacteristic, complemented
181#1547C2×C1111yescharacteristic
182C23×C11—41no—
183C23×C11#12111yescharacteristic
184Q8×C11—21no—
185Q8×C11—21no—
186Q8×C11—21no—
187Q8×C11—42no—
188Q8×C11—41no—
189Q8×C11—42no—
190Q8×C11—41no—
191Q8×C11—42no—
192Q8×C11—82no—
193Q8×C11AGL(1,ℤ/8)12yes—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—81no—
199D4×C11—82no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—81no—
211C2×C4×C11—82no—
212C2×C4×C11—82no—
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#13512yes—
217C2×C4×C11#13712yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C8×C11—22no—
222C8×C11—22no—
223C8×C11—42no—
224C8×C11—42no—
225C8×C11—41no—
226C8×C11—41no—
227C22×Q16—21no—
228#532C22×C1111yescharacteristic
229C2×C4⋊Q8C22×C1111yescharacteristic
230C2×C4×Q8C22×C1111yescharacteristic
231#489—22no—
232#487C22×C1112yes—
233#486C22×C1112yes—
234#481—21no—
235#475C22×C1111yescharacteristic
236#475C22×C1111yescharacteristic
237#462—21no—
238#462—21no—
239#462C22×C1112yes—
240#462C22×C1112yes—
241#460C22×C1111yescharacteristic
242#460C22×C1111yescharacteristic
243#448—21no—
244#446—22no—
245#446C22×C1112yes—
246C8×Q8C22×C1112yes—
247C4×SD16—21no—
248C4×SD16—21no—
249#431C22×C1111yescharacteristic
250#423—21no—
251#423C22×C1111yescharacteristic
252C2×C4⋊C8C22×C1111yescharacteristic
253#417—21no—
254#417—21no—
255C2×#103—21no—
256C4×M16—21no—
257C4×M16C22×C1111yescharacteristic
258#335C22×C1112yes—
259#334C22×C1112yes—
260#332C22×C1112yes—
261#332C22×C1112yes—
262#332C22×C1112yes—
263#331C22×C1112yes—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#46412yes—
270C22×C11C2×#12111yescharacteristic
271C4×C11—21no—
272C4×C11—22no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11—81no—
279C4×C11—82no—
280C4×C11#46412yes—
281C4×C11C2×#13511yescharacteristic
282C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C11C2×#13711yescharacteristic
284C4×C11#57511yescharacteristic
285C2×#41—21no—
286C22×Q8—21no—
287C22×Q8D4×C1111yescharacteristic
288C2×Q16—22no—
289C2×Q16—22no—
290C2×Q16—44no—
291C2×SD16—21no—
292C2×SD16—21no—
293C2×M16—21no—
294C2×M16D4×C1111yescharacteristic
295C2×M16D4×C1111yescharacteristic
296C22×C8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8C23×C1112yes—
301C4⋊Q8C23×C1111yescharacteristic
302#127C23×C1111yescharacteristic
303#124—21no—
304#121—21no—
305#121—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8D4×C1111yescharacteristic
309C4×Q8D4×C1111yescharacteristic
310C4×Q8C23×C1111yescharacteristic
311C4×Q8C23×C1111yescharacteristic
312C4×D4—21no—
313C4×D4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4D4×C1111yescharacteristic
318C2×C42—21no—
319C2×C42C23×C1111yescharacteristic
320#106—21no—
321#106—21no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8C23×C1112yes—
327C4⋊C8C23×C1112yes—
328C4⋊C8C23×C1111yescharacteristic
329C4⋊C8C23×C1111yescharacteristic
330#103—21no—
331#103—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#103—22no—
336#102—22no—
337#102—22no—
338#102—21no—
339#102—21no—
340C22⋊C8—21no—
341#97—22no—
342#97D4×C1112yes—
343C4×C8—22no—
344C4×C8—21no—
345C4×C8C23×C1112yes—
346C2×C11—22no—
347C2×C11—161no—
348C2×C11C2×#46411yescharacteristic
349C2×C11#305511yescharacteristic
350C2×C11#306911yescharacteristic
351#41—42no—
352#41—42no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×Q8—41no—
361C2×Q8C2×D4×C1111yescharacteristic
362C2×Q8C2×D4×C1111yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—41no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C11×#4111yescharacteristic
374Q16—44no—
375Q16—44no—
376SD16—42no—
377SD16—42no—
378M16—22no—
379M16—22no—
380M16—42no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8—42no—
386C2×C8C2×D4×C1112yes—
387C2×C8C2×D4×C1112yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C1111yescharacteristic
400C4⋊C4C2×D4×C1111yescharacteristic
401C22⋊C4—41no—
402C22⋊C4—41no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42C2×D4×C1111yescharacteristic
408C42C2×D4×C1111yescharacteristic
409C42C11×#4111yescharacteristic
410C42C24×C1111yescharacteristic
411C11#1917711yescharacteristic, direct product factor, Sylow
412C23—41no—
413C23C11×#12111yescharacteristic
414Q8—21no—
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—41no—
419Q8—42no—
420Q8—41no—
421Q8—42no—
422Q8—82no—
423Q8C11×AGL(1,ℤ/8)12yes—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—81no—
429D4—82no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4C11×#12111yescharacteristic
444C2×C4C11×#12111yescharacteristic
445C2×C4C11×#12111yescharacteristic
446C2×C4C11×#13512yes—
447C2×C4C11×#13712yes—
448C2×C4C22×D4×C1111yescharacteristic
449C2×C4C22×D4×C1111yescharacteristic
450C2×C4C2×C11×#4111yescharacteristic
451C8—22no—
452C8—22no—
453C8—42no—
454C8—42no—
455C8—41no—
456C8—41no—
457C22—21no—
458C22—21no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22C11×#46412yes—
463C22C2×C11×#12111yescharacteristic
464C4—21no—
465C4—22no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—82no—
473C4C11×#46412yes—
474C4C2×C11×#13511yescharacteristic
475C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
476C4C2×C11×#13711yescharacteristic
477C4C11×#57511yescharacteristic
478C2—22no—
479C2—161no—
480C2C2×C11×#46411yescharacteristic
481C2C11×#305511yescharacteristic
482C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#462C2semidirect
4. Q8×C11×M16C2semidirect
5. C11×#1702C2semidirect
6. C11×#1700C2semidirect
7. C11×#1682C2semidirect
8. C11×#1680C2semidirect
9. C11×#1565C2semidirect
10. C11×#1549C2semidirect
110. #19177C11direct (N × H)
173. C2×#462C2×C11semidirect
174. Q8×M16C2×C11semidirect
175. #1702C2×C11semidirect
176. #1700C2×C11semidirect
177. #1682C2×C11semidirect
178. #1680C2×C11semidirect
179. #1565C2×C11semidirect
180. #1549C2×C11semidirect
411. C11#19177direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31412
C11×#31032
C2×C11×#4622
Q8×C11×M162
C11×#17022
C11×#17002
C11×#16822
C11×#16802
C11×#15652
C11×#15492
C11×#15472
#1917711