Finite Group Databasebeta

← C11×#19219 #14596412

Subgroups — C11×#19219 #14596412

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3212C212yesmaximal, complemented
2C11×#3169C211yesmaximal, characteristic, complemented
3C11×#2966C211yesmaximal, characteristic, complemented
4C11×#1702C212yesmaximal, complemented
5C11×#1701C212yesmaximal, complemented
6C11×#1674C211yesmaximal, characteristic, complemented
7C11×#1673C211yesmaximal, characteristic, complemented
8C11×#1668C211yesmaximal, characteristic, complemented
9C11×#1667C211yesmaximal, characteristic, complemented
10C11×#1564C211yesmaximal, characteristic, complemented
11C11×#1553C212yesmaximal, complemented
12C11×#532C2212yes—
13C11×#529C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#495—22no—
16C11×#493C2211yescharacteristic
17C11×#488—22no—
18C11×#486C2212yes—
19C11×#466—21no—
20C11×#466—21no—
21C11×#462C2212yes—
22C11×#461C2212yes—
23C11×#460C2212yes—
24C11×#459C2212yes—
25C11×#452—22no—
26C11×#449—22no—
27C11×#446C2211yescharacteristic
28C8×Q8×C11C2211yescharacteristic
29C4×C11×D8—21no—
30C4×C11×D8—21no—
31C11×#436C2211yescharacteristic
32C11×#435—21no—
33C8×D4×C11—21no—
34C8×D4×C11C2211yescharacteristic
35C11×#433—21no—
36C11×#432C2211yescharacteristic
37C11×#431C2212yes—
38C11×#405—21no—
39C2×C4×C8×C11C2211yescharacteristic
40C11×#335C2211yescharacteristic
41C11×#335C2211yescharacteristic
42C11×#334C2212yes—
43C11×#332C2212yes—
44C11×#332C2212yes—
45C11×#331C2212yes—
46C11×#331C2212yes—
47C2×C11×#41—22no—
48C2×C11×Q16—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×D8—22no—
52C2×C11×D8—21no—
53C2×C11×D8—21no—
54C2×C11×M16—21no—
55C22×C8×C11—21no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C11×C4⋊Q8C2312yes—
59C11×#127C2312yes—
60C11×#126—21no—
61C11×#125D411yescharacteristic
62C11×#124—22no—
63C11×#124D411yescharacteristic
64C11×#123—21no—
65C11×C22⋊Q8D411yescharacteristic
66C11×#121—22no—
67C11×#121—22no—
68C11×#121D411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11—21no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11C2311yescharacteristic
74C11×#117—21no—
75C2×C42×C11C2311yescharacteristic
76C11×#107—21no—
77C11×#107—21no—
78C11×C4⋊C8—21no—
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2311yescharacteristic
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2312yes—
83C11×C4⋊C8C2312yes—
84C11×#103—22no—
85C11×#103—22no—
86C11×#102—22no—
87C11×#102—22no—
88C11×#102—22no—
89C11×#102—22no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8—21no—
92C11×C22⋊C8—21no—
93C11×C22⋊C8—21no—
94C11×#97—21no—
95C11×#97—21no—
96C4×C8×C11—21no—
97C4×C8×C11—22no—
98C4×C8×C11D411yescharacteristic
99C4×C8×C11D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101C4×C8×C11C2311yescharacteristic
102#19219C1111yesmaximal, characteristic, direct product factor, Sylow
103C11×#41—82no—
104C11×#41—82no—
105C2×Q8×C11—22no—
106C2×Q8×C11C2×D411yescharacteristic
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C2×D4×C11C2×D411yescharacteristic
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C11×Q16—82no—
119C11×SD16—82no—
120C11×SD16—82no—
121C11×D8—42no—
122C11×D8—42no—
123C11×D8—82no—
124C11×M16—42no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—41no—
131C2×C8×C11—42no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C2×D411yescharacteristic
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C11×C22⋊C4—21no—
148C11×C22⋊C4—21no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—42no—
151C42×C11—21no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11#4111yescharacteristic
155C42×C11C2411yescharacteristic
156#3212C2×C1112yescomplemented
157#3169C2×C1111yescharacteristic, complemented
158#2966C2×C1111yescharacteristic, complemented
159#1702C2×C1112yescomplemented
160#1701C2×C1112yescomplemented
161#1674C2×C1111yescharacteristic, complemented
162#1673C2×C1111yescharacteristic, complemented
163#1668C2×C1111yescharacteristic, complemented
164#1667C2×C1111yescharacteristic, complemented
165#1564C2×C1111yescharacteristic, complemented
166#1553C2×C1112yescomplemented
167C23×C11—21no—
168C23×C11—42no—
169C23×C11#12111yescharacteristic
170Q8×C11—21no—
171Q8×C11—21no—
172Q8×C11—42no—
173Q8×C11—42no—
174D4×C11—21no—
175D4×C11—21no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—82no—
182D4×C11—84no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—84no—
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C8×C11—21no—
202C8×C11—21no—
203C8×C11—21no—
204C8×C11—41no—
205C8×C11—41no—
206C8×C11—42no—
207C8×C11—42no—
208C8×C11#13512yes—
209#532C22×C1112yes—
210#529C22×C1111yescharacteristic
211#500C22×C1111yescharacteristic
212#495—22no—
213#493C22×C1111yescharacteristic
214#488—22no—
215#486C22×C1112yes—
216#466—21no—
217#466—21no—
218#462C22×C1112yes—
219#461C22×C1112yes—
220#460C22×C1112yes—
221#459C22×C1112yes—
222#452—22no—
223#449—22no—
224#446C22×C1111yescharacteristic
225C8×Q8C22×C1111yescharacteristic
226C4×D8—21no—
227C4×D8—21no—
228#436C22×C1111yescharacteristic
229#435—21no—
230C8×D4—21no—
231C8×D4C22×C1111yescharacteristic
232#433—21no—
233#432C22×C1111yescharacteristic
234#431C22×C1112yes—
235#405—21no—
236C2×C4×C8C22×C1111yescharacteristic
237#335C22×C1111yescharacteristic
238#335C22×C1111yescharacteristic
239#334C22×C1112yes—
240#332C22×C1112yes—
241#332C22×C1112yes—
242#331C22×C1112yes—
243#331C22×C1112yes—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11C2×#12111yescharacteristic
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11—41no—
261C4×C11—82no—
262C4×C11C2×#13511yescharacteristic
263C4×C11#57511yescharacteristic
264C4×C11#57611yescharacteristic
265C4×C11#57611yescharacteristic
266C2×#41—22no—
267C2×Q16—22no—
268C2×SD16—22no—
269C2×SD16—22no—
270C2×D8—22no—
271C2×D8—21no—
272C2×D8—21no—
273C2×M16—21no—
274C22×C8—21no—
275C22×C8D4×C1111yescharacteristic
276C22×C8D4×C1111yescharacteristic
277C4⋊Q8C23×C1112yes—
278#127C23×C1112yes—
279#126—21no—
280#125D4×C1111yescharacteristic
281#124—22no—
282#124D4×C1111yescharacteristic
283#123—21no—
284C22⋊Q8D4×C1111yescharacteristic
285#121—22no—
286#121—22no—
287#121D4×C1111yescharacteristic
288C4×Q8C23×C1111yescharacteristic
289C4×D4—21no—
290C4×D4—22no—
291C4×D4—22no—
292C4×D4C23×C1111yescharacteristic
293#117—21no—
294C2×C42C23×C1111yescharacteristic
295#107—21no—
296#107—21no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8C23×C1111yescharacteristic
300C4⋊C8C23×C1111yescharacteristic
301C4⋊C8C23×C1112yes—
302C4⋊C8C23×C1112yes—
303#103—22no—
304#103—22no—
305#102—22no—
306#102—22no—
307#102—22no—
308#102—22no—
309C22⋊C8—22no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313#97—21no—
314#97—21no—
315C4×C8—21no—
316C4×C8—22no—
317C4×C8D4×C1111yescharacteristic
318C4×C8D4×C1111yescharacteristic
319C4×C8C23×C1111yescharacteristic
320C4×C8C23×C1111yescharacteristic
321C2×C11—41no—
322C2×C11—81no—
323C2×C11—162no—
324C2×C11#303511yescharacteristic
325C2×C11#305811yescharacteristic
326C2×C11#306711yescharacteristic
327#41—82no—
328#41—82no—
329C2×Q8—22no—
330C2×Q8C2×D4×C1111yescharacteristic
331C2×D4—21no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—42no—
336C2×D4C2×D4×C1111yescharacteristic
337C22×C4—21no—
338C22×C4—42no—
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C2×D4×C1111yescharacteristic
341C22×C4C11×#4111yescharacteristic
342Q16—82no—
343SD16—82no—
344SD16—82no—
345D8—42no—
346D8—42no—
347D8—82no—
348M16—42no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—21no—
354C2×C8—41no—
355C2×C8—42no—
356C2×C8C2×D4×C1111yescharacteristic
357C2×C8C2×D4×C1111yescharacteristic
358C2×C8C2×D4×C1111yescharacteristic
359C2×C8C2×D4×C1111yescharacteristic
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4C2×D4×C1111yescharacteristic
367C4⋊C4C2×D4×C1111yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C42—21no—
376C42C2×D4×C1111yescharacteristic
377C42C2×D4×C1111yescharacteristic
378C42C11×#4111yescharacteristic
379C42C24×C1111yescharacteristic
380C11#1921911yescharacteristic, direct product factor, Sylow
381C23—21no—
382C23—42no—
383C23C11×#12111yescharacteristic
384Q8—21no—
385Q8—21no—
386Q8—42no—
387Q8—42no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—42no—
392D4—42no—
393D4—42no—
394D4—42no—
395D4—82no—
396D4—84no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—84no—
409C2×C4C11×#12111yescharacteristic
410C2×C4C11×#12111yescharacteristic
411C2×C4C11×#12111yescharacteristic
412C2×C4C22×D4×C1111yescharacteristic
413C2×C4C22×D4×C1111yescharacteristic
414C2×C4C2×C11×#4111yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—41no—
419C8—41no—
420C8—42no—
421C8—42no—
422C8C11×#13512yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22C2×C11×#12111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—82no—
441C4C2×C11×#13511yescharacteristic
442C4C11×#57511yescharacteristic
443C4C11×#57611yescharacteristic
444C4C11×#57611yescharacteristic
445C2—41no—
446C2—81no—
447C2—162no—
448C2C11×#303511yescharacteristic
449C2C11×#305811yescharacteristic
450C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
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×#3212C2semidirect
2. C11×#3169C2semidirect
3. C11×#2966C2semidirect
4. C11×#1702C2semidirect
5. C11×#1701C2semidirect
6. C11×#1674C2semidirect
7. C11×#1673C2semidirect
8. C11×#1668C2semidirect
9. C11×#1667C2semidirect
10. C11×#1564C2semidirect
11. C11×#1553C2semidirect
102. #19219C11direct (N × H)
156. #3212C2×C11semidirect
157. #3169C2×C11semidirect
158. #2966C2×C11semidirect
159. #1702C2×C11semidirect
160. #1701C2×C11semidirect
161. #1674C2×C11semidirect
162. #1673C2×C11semidirect
163. #1668C2×C11semidirect
164. #1667C2×C11semidirect
165. #1564C2×C11semidirect
166. #1553C2×C11semidirect
380. C11#19219direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32122
C11×#31692
C11×#29662
C11×#17022
C11×#17012
C11×#16742
C11×#16732
C11×#16682
C11×#16672
C11×#15642
C11×#15532
#1921911