Finite Group Databasebeta

← C11×#19174 #14596367

Subgroups — C11×#19174 #14596367

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3138C211yesmaximal, characteristic
2C11×#3104C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic
4Q8×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1702C212yesmaximal, complemented
6C11×#1698C212yesmaximal, complemented
7C11×#1682C212yesmaximal, complemented
8C11×#1678C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C11×#1545C211yesmaximal, characteristic
12C22×C11×SD16—21no—
13C11×#533C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#490—22no—
17C11×#486C2212yes—
18C11×#486C2212yes—
19C11×#484—21no—
20C11×#477C2211yescharacteristic, complemented
21C11×#477C2211yescharacteristic, complemented
22C11×#462C2211yescharacteristic, complemented
23C11×#462C2211yescharacteristic, complemented
24C11×#460—21no—
25C11×#460—21no—
26C11×#460C2212yes—
27C11×#460C2212yes—
28C11×#451—21no—
29C11×#446—22no—
30C11×#446C2212yescomplemented
31C8×Q8×C11C2212yescomplemented
32C4×C11×Q16—21no—
33C4×C11×Q16—21no—
34C11×#431C2211yescharacteristic
35C11×#423—21no—
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C11×#418—21no—
39C11×#418—21no—
40C2×C11×#102—21no—
41C4×C11×M16—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yescomplemented
44C11×#334C2212yescomplemented
45C11×#333C2212yescomplemented
46C11×#332C2212yescomplemented
47C11×#331C2212yes—
48C11×#331C2212yes—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C2×C11×Q16—21no—
54C2×C11×Q16—21no—
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—44no—
58C2×C11×M16—21no—
59C2×C11×M16D411yescharacteristic
60C2×C11×M16D411yescharacteristic
61C22×C8×C11—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127—21no—
65C11×#127—21no—
66C11×#127—21no—
67C11×#127C2312yes—
68C11×#125—21no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C11×#117—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#107—21no—
85C11×#107—21no—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C11×C4⋊C8C2311yescharacteristic
92C11×C4⋊C8C2311yescharacteristic
93C11×C4⋊C8C2312yes—
94C11×#103—21no—
95C11×#103—21no—
96C11×#103—21no—
97C11×#103—21no—
98C11×#102—22no—
99C11×#102—22no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×C22⋊C8—21no—
105C11×#97—22no—
106C11×#97D412yes—
107C4×C8×C11—22no—
108C4×C8×C11—21no—
109C4×C8×C11C2312yes—
110#19174C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—41no—
117C2×Q8×C11C2×D411yescharacteristic
118C2×Q8×C11C2×D411yescharacteristic
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—82no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C11×Q16—42no—
136C11×Q16—42no—
137C11×SD16—44no—
138C11×SD16—44no—
139C11×M16—22no—
140C11×M16—22no—
141C11×M16—42no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—42no—
147C2×C8×C11C2×D412yes—
148C2×C8×C11C2×D412yes—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4C2×D411yescharacteristic
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C22⋊C4—41no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—41no—
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11#4111yescharacteristic
171C42×C11C2411yescharacteristic
172#3138C2×C1111yescharacteristic
173#3104C2×C1111yescharacteristic, complemented
174C2×#460C2×C1111yescharacteristic
175Q8×M16C2×C1111yescharacteristic, complemented
176#1702C2×C1112yescomplemented
177#1698C2×C1112yescomplemented
178#1682C2×C1112yescomplemented
179#1678C2×C1112yescomplemented
180#1565C2×C1111yescharacteristic, complemented
181#1550C2×C1111yescharacteristic, complemented
182#1545C2×C1111yescharacteristic
183C23×C11—42no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11#12111yescharacteristic
188Q8×C11—21no—
189Q8×C11—21no—
190Q8×C11—21no—
191Q8×C11—42no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—81no—
195Q8×C11AGL(1,ℤ/8)12yes—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—82no—
201D4×C11—82no—
202D4×C11—82no—
203D4×C11—82no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—81no—
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#12111yescharacteristic
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#13512yes—
219C2×C4×C11#13712yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C8×C11—22no—
224C8×C11—22no—
225C8×C11—42no—
226C8×C11—42no—
227C8×C11—41no—
228C8×C11—41no—
229C22×SD16—21no—
230#533C22×C1111yescharacteristic
231C2×#127C22×C1111yescharacteristic
232C2×C4×Q8C22×C1111yescharacteristic
233#490—22no—
234#486C22×C1112yes—
235#486C22×C1112yes—
236#484—21no—
237#477C22×C1111yescharacteristic, complemented
238#477C22×C1111yescharacteristic, complemented
239#462C22×C1111yescharacteristic, complemented
240#462C22×C1111yescharacteristic, complemented
241#460—21no—
242#460—21no—
243#460C22×C1112yes—
244#460C22×C1112yes—
245#451—21no—
246#446—22no—
247#446C22×C1112yescomplemented
248C8×Q8C22×C1112yescomplemented
249C4×Q16—21no—
250C4×Q16—21no—
251#431C22×C1111yescharacteristic
252#423—21no—
253#423C22×C1111yescharacteristic
254C2×C4⋊C8C22×C1111yescharacteristic
255#418—21no—
256#418—21no—
257C2×#102—21no—
258C4×M16—21no—
259C4×M16C22×C1111yescharacteristic
260#335C22×C1112yescomplemented
261#334C22×C1112yescomplemented
262#333C22×C1112yescomplemented
263#332C22×C1112yescomplemented
264#331C22×C1112yes—
265#331C22×C1112yes—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—164no—
272C22×C11#46412yes—
273C22×C11C2×#12111yescharacteristic
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11#46412yes—
284C4×C11C2×#13511yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×#13711yescharacteristic
287C4×C11#57511yescharacteristic
288C22×Q8D4×C1111yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C2×Q16—21no—
293C2×Q16—21no—
294C2×SD16—22no—
295C2×SD16—22no—
296C2×SD16—44no—
297C2×M16—21no—
298C2×M16D4×C1111yescharacteristic
299C2×M16D4×C1111yescharacteristic
300C22×C8—21no—
301C4⋊Q8C23×C1111yescharacteristic
302C4⋊Q8C23×C1111yescharacteristic
303#127—21no—
304#127—21no—
305#127—21no—
306#127C23×C1112yes—
307#125—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C1111yescharacteristic
315C4×Q8D4×C1111yescharacteristic
316C4×Q8C23×C1111yescharacteristic
317C4×Q8C23×C1111yescharacteristic
318#117—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4D4×C1111yescharacteristic
321C2×C42—21no—
322C2×C42C23×C1111yescharacteristic
323#107—21no—
324#107—21no—
325C4⋊C8—22no—
326C4⋊C8—22no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8C23×C1112yes—
330C4⋊C8C23×C1111yescharacteristic
331C4⋊C8C23×C1111yescharacteristic
332C4⋊C8C23×C1112yes—
333#103—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#102—22no—
338#102—22no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343C22⋊C8—21no—
344#97—22no—
345#97D4×C1112yes—
346C4×C8—22no—
347C4×C8—21no—
348C4×C8C23×C1112yes—
349C2×C11—22no—
350C2×C11—162no—
351C2×C11C2×#46411yescharacteristic
352C2×C11#305511yescharacteristic
353C2×C11#306811yescharacteristic
354C24—41no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—41no—
360C2×Q8C2×D4×C1111yescharacteristic
361C2×Q8C2×D4×C1111yescharacteristic
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—82no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C11×#4111yescharacteristic
378Q16—42no—
379Q16—42no—
380SD16—44no—
381SD16—44no—
382M16—22no—
383M16—22no—
384M16—42no—
385C2×C8—22no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8C2×D4×C1112yes—
391C2×C8C2×D4×C1112yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×D4×C1111yescharacteristic
404C4⋊C4C2×D4×C1111yescharacteristic
405C22⋊C4—41no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—41no—
411C42C2×D4×C1111yescharacteristic
412C42C2×D4×C1111yescharacteristic
413C42C11×#4111yescharacteristic
414C42C24×C1111yescharacteristic
415C11#1917411yescharacteristic, direct product factor, Sylow
416C23—42no—
417C23—82no—
418C23—82no—
419C23—82no—
420C23C11×#12111yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—21no—
424Q8—42no—
425Q8—41no—
426Q8—41no—
427Q8—81no—
428Q8C11×AGL(1,ℤ/8)12yes—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—82no—
434D4—82no—
435D4—82no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—81no—
448C2×C4C11×#12111yescharacteristic
449C2×C4C11×#12111yescharacteristic
450C2×C4C11×#12111yescharacteristic
451C2×C4C11×#13512yes—
452C2×C4C11×#13712yes—
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C22×D4×C1111yescharacteristic
455C2×C4C2×C11×#4111yescharacteristic
456C8—22no—
457C8—22no—
458C8—42no—
459C8—42no—
460C8—41no—
461C8—41no—
462C22—21no—
463C22—21no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22C11×#46412yes—
469C22C2×C11×#12111yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—81no—
479C4C11×#46412yes—
480C4C2×C11×#13511yescharacteristic
481C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
482C4C2×C11×#13711yescharacteristic
483C4C11×#57511yescharacteristic
484C2—22no—
485C2—162no—
486C2C2×C11×#46411yescharacteristic
487C2C11×#305511yescharacteristic
488C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#127C22
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
2. C11×#3104C2semidirect
4. Q8×C11×M16C2semidirect
5. C11×#1702C2semidirect
6. C11×#1698C2semidirect
7. C11×#1682C2semidirect
8. C11×#1678C2semidirect
9. C11×#1565C2semidirect
10. C11×#1550C2semidirect
20. C11×#477C22semidirect
21. C11×#477C22semidirect
22. C11×#462C22semidirect
23. C11×#462C22semidirect
30. C11×#446C22semidirect
31. C8×Q8×C11C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#333C22semidirect
46. C11×#332C22semidirect
110. #19174C11direct (N × H)
173. #3104C2×C11semidirect
175. Q8×M16C2×C11semidirect
176. #1702C2×C11semidirect
177. #1698C2×C11semidirect
178. #1682C2×C11semidirect
179. #1678C2×C11semidirect
180. #1565C2×C11semidirect
181. #1550C2×C11semidirect
237. #477C22×C11semidirect
238. #477C22×C11semidirect
239. #462C22×C11semidirect
240. #462C22×C11semidirect
247. #446C22×C11semidirect
248. C8×Q8C22×C11semidirect
260. #335C22×C11semidirect
261. #334C22×C11semidirect
262. #333C22×C11semidirect
263. #332C22×C11semidirect
415. C11#19174direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31382
C11×#31042
C2×C11×#4602
Q8×C11×M162
C11×#17022
C11×#16982
C11×#16822
C11×#16782
C11×#15652
C11×#15502
C11×#15452
#1917411