Finite Group Databasebeta

← C11×#19217 #14596410

Subgroups — C11×#19217 #14596410

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3249C211yesmaximal, characteristic, complemented
2C11×#3246C211yesmaximal, characteristic
3C11×#3131C211yesmaximal, characteristic
4C11×#2960C211yesmaximal, characteristic, complemented
5C11×#1700C212yesmaximal, complemented
6C11×#1698C212yesmaximal, complemented
7C11×#1684C212yesmaximal, complemented
8C11×#1682C212yesmaximal, complemented
9C2×C11×#335C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C11×#533C2211yescharacteristic
14C11×#532C2211yescharacteristic
15C11×#488—21no—
16C11×#488—21no—
17C11×#487C2211yescharacteristic
18C11×#487C2211yescharacteristic
19C11×#486C2211yescharacteristic
20C11×#486C2211yescharacteristic
21C11×#477—21no—
22C11×#477C2212yes—
23C11×#476—21no—
24C11×#475C2212yes—
25C11×#467—22no—
26C11×#465—22no—
27C11×#462—21no—
28C11×#462C2212yes—
29C11×#461—21no—
30C11×#460C2212yes—
31C11×#446—21no—
32C11×#446C2212yes—
33C8×Q8×C11—21no—
34C8×Q8×C11C2212yes—
35C11×#424—21no—
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C11×#416—21no—
40C11×#416—21no—
41C11×#405—21no—
42C2×C4×C8×C11C2211yescharacteristic
43C11×#335C2212yes—
44C11×#335C2212yes—
45C11×#333C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C2×C11×Q16—22no—
51C2×C11×SD16—22no—
52C2×C11×M16—21no—
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×#127C2311yescharacteristic
63C11×#125—21no—
64C11×#125—21no—
65C11×#124—21no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8D412yes—
70C11×#121—21no—
71C11×#121—21no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11C2312yes—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C11×#117—21no—
79C11×#117—21no—
80C2×C42×C11C2311yescharacteristic
81C11×#107—22no—
82C11×#106—22no—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2312yes—
89C11×C4⋊C8C2312yes—
90C11×C4⋊C8C2312yes—
91C11×#103—22no—
92C11×#103—22no—
93C11×#103—21no—
94C11×#103—21no—
95C11×#103—21no—
96C11×#103—21no—
97C11×#103—22no—
98C11×#102—21no—
99C11×#102—21no—
100C11×#102—21no—
101C11×#102—21no—
102C11×#102—22no—
103C11×#97—22no—
104C4×C8×C11—22no—
105C4×C8×C11D411yescharacteristic
106C4×C8×C11D411yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#19217C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—42no—
111C11×#41—42no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11C2×D412yes—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C11×Q16—82no—
126C11×SD16—82no—
127C11×M16—42no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—81no—
134C2×C8×C11—81no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4—41no—
157C42×C11—22no—
158C42×C11—41no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11#4111yescharacteristic
162C42×C11C2411yescharacteristic
163#3249C2×C1111yescharacteristic, complemented
164#3246C2×C1111yescharacteristic
165#3131C2×C1111yescharacteristic
166#2960C2×C1111yescharacteristic, complemented
167#1700C2×C1112yescomplemented
168#1698C2×C1112yescomplemented
169#1684C2×C1112yescomplemented
170#1682C2×C1112yescomplemented
171C2×#335C2×C1111yescharacteristic, complemented
172#1550C2×C1111yescharacteristic, complemented
173#1547C2×C1111yescharacteristic
174C23×C11—41no—
175C23×C11#12111yescharacteristic
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—42no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—41no—
182Q8×C11—41no—
183Q8×C11—81no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—41no—
188D4×C11—81no—
189D4×C11—82no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—82no—
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#13512yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C8×C11—21no—
208C8×C11—21no—
209C8×C11—21no—
210C8×C11—21no—
211C8×C11—42no—
212C8×C11—42no—
213C8×C11—42no—
214#533C22×C1111yescharacteristic
215#533C22×C1111yescharacteristic
216#532C22×C1111yescharacteristic
217#488—21no—
218#488—21no—
219#487C22×C1111yescharacteristic
220#487C22×C1111yescharacteristic
221#486C22×C1111yescharacteristic
222#486C22×C1111yescharacteristic
223#477—21no—
224#477C22×C1112yes—
225#476—21no—
226#475C22×C1112yes—
227#467—22no—
228#465—22no—
229#462—21no—
230#462C22×C1112yes—
231#461—21no—
232#460C22×C1112yes—
233#446—21no—
234#446C22×C1112yes—
235C8×Q8—21no—
236C8×Q8C22×C1112yes—
237#424—21no—
238#423C22×C1111yescharacteristic
239C2×C4⋊C8C22×C1111yescharacteristic
240C2×C4⋊C8C22×C1111yescharacteristic
241#416—21no—
242#416—21no—
243#405—21no—
244C2×C4×C8C22×C1111yescharacteristic
245#335C22×C1112yes—
246#335C22×C1112yes—
247#333C22×C1112yes—
248#332C22×C1112yes—
249#332C22×C1112yes—
250#331C22×C1112yes—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11#46412yes—
257C22×C11C2×#12111yescharacteristic
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11#46412yes—
267C4×C11C2×#13511yescharacteristic
268C4×C11C2×#13711yescharacteristic
269C4×C11#57611yescharacteristic
270C4×C11#57811yescharacteristic
271C2×#41—21no—
272C2×Q16—22no—
273C2×SD16—22no—
274C2×M16—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8D4×C1111yescharacteristic
278C22×C8D4×C1111yescharacteristic
279C4⋊Q8D4×C1111yescharacteristic
280C4⋊Q8D4×C1111yescharacteristic
281C4⋊Q8C23×C1111yescharacteristic
282C4⋊Q8C23×C1111yescharacteristic
283C4⋊Q8C23×C1111yescharacteristic
284#127C23×C1111yescharacteristic
285#125—21no—
286#125—21no—
287#124—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8D4×C1112yes—
292#121—21no—
293#121—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8C23×C1112yes—
298C4×D4—21no—
299C4×D4—21no—
300#117—21no—
301#117—21no—
302C2×C42C23×C1111yescharacteristic
303#107—22no—
304#106—22no—
305C4⋊C8—22no—
306C4⋊C8—22no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8C23×C1112yes—
311C4⋊C8C23×C1112yes—
312C4⋊C8C23×C1112yes—
313#103—22no—
314#103—22no—
315#103—21no—
316#103—21no—
317#103—21no—
318#103—21no—
319#103—22no—
320#102—21no—
321#102—21no—
322#102—21no—
323#102—21no—
324#102—22no—
325#97—22no—
326C4×C8—22no—
327C4×C8D4×C1111yescharacteristic
328C4×C8D4×C1111yescharacteristic
329C4×C8C23×C1111yescharacteristic
330C4×C8C23×C1111yescharacteristic
331C2×C11—22no—
332C2×C11—161no—
333C2×C11C2×#46411yescharacteristic
334C2×C11#306111yescharacteristic
335C2×C11#306711yescharacteristic
336#41—42no—
337#41—42no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8C2×D4×C1112yes—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—41no—
347C22×C4—41no—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C11×#4111yescharacteristic
351Q16—82no—
352SD16—82no—
353M16—42no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—81no—
360C2×C8—81no—
361C2×C8C2×D4×C1111yescharacteristic
362C2×C8C2×D4×C1111yescharacteristic
363C2×C8C2×D4×C1111yescharacteristic
364C2×C8C2×D4×C1111yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4C2×D4×C1112yes—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C42—22no—
384C42—41no—
385C42C2×D4×C1111yescharacteristic
386C42C2×D4×C1111yescharacteristic
387C42C11×#4111yescharacteristic
388C42C24×C1111yescharacteristic
389C11#1921711yescharacteristic, direct product factor, Sylow
390C23—41no—
391C23C11×#12111yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—81no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—81no—
405D4—82no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4C11×#12111yescharacteristic
416C2×C4C11×#12111yescharacteristic
417C2×C4C11×#12111yescharacteristic
418C2×C4C11×#13512yes—
419C2×C4C11×#13712yes—
420C2×C4C22×D4×C1111yescharacteristic
421C2×C4C22×D4×C1111yescharacteristic
422C2×C4C2×C11×#4111yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8—21no—
427C8—42no—
428C8—42no—
429C8—42no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22C11×#46412yes—
436C22C2×C11×#12111yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4C11×#46412yes—
446C4C2×C11×#13511yescharacteristic
447C4C2×C11×#13711yescharacteristic
448C4C11×#57611yescharacteristic
449C4C11×#57811yescharacteristic
450C2—22no—
451C2—161no—
452C2C2×C11×#46411yescharacteristic
453C2C11×#306111yescharacteristic
454C2C11×#306711yescharacteristic
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
1. C11×#3249C2semidirect
4. C11×#2960C2semidirect
5. C11×#1700C2semidirect
6. C11×#1698C2semidirect
7. C11×#1684C2semidirect
8. C11×#1682C2semidirect
9. C2×C11×#335C2semidirect
10. C11×#1550C2semidirect
109. #19217C11direct (N × H)
163. #3249C2×C11semidirect
166. #2960C2×C11semidirect
167. #1700C2×C11semidirect
168. #1698C2×C11semidirect
169. #1684C2×C11semidirect
170. #1682C2×C11semidirect
171. C2×#335C2×C11semidirect
172. #1550C2×C11semidirect
389. C11#19217direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32492
C11×#32462
C11×#31312
C11×#29602
C11×#17002
C11×#16982
C11×#16842
C11×#16822
C2×C11×#3352
C11×#15502
C11×#15472
#1921711