Finite Group Databasebeta

← C11×#19417 #14596610

Subgroups — C11×#19417 #14596610

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic, complemented
2C11×#3079C211yesmaximal, characteristic
3C11×#3076C211yesmaximal, characteristic
4C11×#2988C211yesmaximal, characteristic
5C11×#1684C212yesmaximal, complemented
6C11×#1683C212yesmaximal, complemented
7C11×#1676C212yesmaximal, complemented
8C11×#1675C212yesmaximal, complemented
9C11×#1571C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C2×C11×#333C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C11×#500C2212yes—
16C11×#487C2212yes—
17C11×#484—22no—
18C11×#479—21no—
19C11×#478—21no—
20C11×#477—21no—
21C11×#477—21no—
22C11×#477C2211yescharacteristic
23C11×#477C2212yes—
24C11×#476C2211yescharacteristic
25C11×#476C2212yes—
26C11×#475—21no—
27C11×#475C2211yescharacteristic
28C11×#474—21no—
29C11×#474C2211yescharacteristic
30C8×Q8×C11C2212yes—
31C8×D4×C11—22no—
32C8×D4×C11C2212yes—
33C11×#431—21no—
34C11×#431C2211yescharacteristic
35C11×#428—21no—
36C11×#427—21no—
37C11×#423C2211yescharacteristic
38C2×C11×C4⋊C8—21no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C11×#417—21no—
42C11×#416—21no—
43C11×#335C2212yes—
44C11×#335C2212yes—
45C11×#333C2212yes—
46C11×#333C2212yes—
47C11×#333C2212yes—
48C11×#332C2212yes—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11—21no—
51C2×C11×M16—21no—
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C22×C8×C11—22no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2312yes—
61C11×#125—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11D411yescharacteristic
67C4×Q8×C11C2311yescharacteristic
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11D411yescharacteristic
71C4×D4×C11C2311yescharacteristic
72C11×#117—21no—
73C11×#117—21no—
74C11×#117D411yescharacteristic
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C11×#107—22no—
80C11×#107—22no—
81C11×#107—21no—
82C11×#107—21no—
83C11×#107—22no—
84C11×#106—21no—
85C11×#106—21no—
86C11×#106—22no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8D411yescharacteristic
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8C2312yes—
94C11×C4⋊C8C2312yes—
95C11×C4⋊C8C2311yescharacteristic
96C11×C4⋊C8C2311yescharacteristic
97C11×#103—21no—
98C11×#103—21no—
99C11×#103—22no—
100C11×#103—22no—
101C11×#103—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×#102—22no—
105C11×C22⋊C8—22no—
106C11×C22⋊C8D412yes—
107C4×C8×C11—22no—
108C4×C8×C11C2312yes—
109#19417C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—22no—
111C11×#41Q1614yes—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—82no—
117C2×Q8×C11C2×D411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C11×M16—42no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—42no—
133C2×C8×C11—81no—
134C2×C8×C11—82no—
135C2×C8×C11C2×D412yes—
136C2×C8×C11C2×D412yes—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4C2×D411yescharacteristic
150C11×C4⋊C4C2×D411yescharacteristic
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—41no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—41no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11#4111yescharacteristic
162C42×C11C2411yescharacteristic
163#3230C2×C1111yescharacteristic, complemented
164#3079C2×C1111yescharacteristic
165#3076C2×C1111yescharacteristic
166#2988C2×C1111yescharacteristic
167#1684C2×C1112yescomplemented
168#1683C2×C1112yescomplemented
169#1676C2×C1112yescomplemented
170#1675C2×C1112yescomplemented
171#1571C2×C1111yescharacteristic, complemented
172#1550C2×C1111yescharacteristic, complemented
173C2×#333C2×C1111yescharacteristic, complemented
174C23×C11—21no—
175C23×C11#12111yescharacteristic
176Q8×C11—21no—
177Q8×C11—41no—
178Q8×C11—41no—
179Q8×C11—81no—
180Q8×C11—82no—
181Q8×C11—82no—
182Q8×C11C2×Q1612yes—
183D4×C11—24no—
184D4×C11—21no—
185D4×C11C2×Q1612yes—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—24no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—81no—
199C2×C4×C11—82no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11C2×Q1612yes—
204C2×C4×C11#13512yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C8×C11—22no—
209C8×C11—22no—
210C8×C11—41no—
211C8×C11—41no—
212C8×C11—42no—
213C8×C11—42no—
214#533C22×C1111yescharacteristic
215C2×C4⋊Q8C22×C1111yescharacteristic
216C4×#41C22×C1111yescharacteristic
217#500C22×C1112yes—
218#487C22×C1112yes—
219#484—22no—
220#479—21no—
221#478—21no—
222#477—21no—
223#477—21no—
224#477C22×C1111yescharacteristic
225#477C22×C1112yes—
226#476C22×C1111yescharacteristic
227#476C22×C1112yes—
228#475—21no—
229#475C22×C1111yescharacteristic
230#474—21no—
231#474C22×C1111yescharacteristic
232C8×Q8C22×C1112yes—
233C8×D4—22no—
234C8×D4C22×C1112yes—
235#431—21no—
236#431C22×C1111yescharacteristic
237#428—21no—
238#427—21no—
239#423C22×C1111yescharacteristic
240C2×C4⋊C8—21no—
241C2×C4⋊C8C22×C1111yescharacteristic
242C2×C4⋊C8C22×C1111yescharacteristic
243#417—21no—
244#416—21no—
245#335C22×C1112yes—
246#335C22×C1112yes—
247#333C22×C1112yes—
248#333C22×C1112yes—
249#333C22×C1112yes—
250#332C22×C1112yes—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—22no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11#46712yes—
257C22×C11C2×#12111yescharacteristic
258C4×C11—21no—
259C4×C11—22no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—41no—
263C4×C11—41no—
264C4×C11—81no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11#46712yes—
268C4×C11C22×Q1611yescharacteristic
269C4×C11C2×#13511yescharacteristic
270C4×C11#57711yescharacteristic
271C4×C11#57811yescharacteristic
272C2×#41D4×C1111yescharacteristic
273C22×Q8—21no—
274C2×M16—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—22no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8C23×C1112yes—
282C4⋊Q8C23×C1111yescharacteristic
283C4⋊Q8C23×C1111yescharacteristic
284#125—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8D4×C1111yescharacteristic
290C4×Q8C23×C1111yescharacteristic
291C4×D4—21no—
292C4×D4—21no—
293C4×D4D4×C1111yescharacteristic
294C4×D4C23×C1111yescharacteristic
295#117—21no—
296#117—21no—
297#117D4×C1111yescharacteristic
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C42—21no—
301C2×C42C23×C1111yescharacteristic
302#107—22no—
303#107—22no—
304#107—21no—
305#107—21no—
306#107—22no—
307#106—21no—
308#106—21no—
309#106—22no—
310C4⋊C8—22no—
311C4⋊C8—21no—
312C4⋊C8—21no—
313C4⋊C8—21no—
314C4⋊C8D4×C1111yescharacteristic
315C4⋊C8D4×C1111yescharacteristic
316C4⋊C8C23×C1112yes—
317C4⋊C8C23×C1112yes—
318C4⋊C8C23×C1111yescharacteristic
319C4⋊C8C23×C1111yescharacteristic
320#103—21no—
321#103—21no—
322#103—22no—
323#103—22no—
324#103—22no—
325#102—21no—
326#102—21no—
327#102—22no—
328C22⋊C8—22no—
329C22⋊C8D4×C1112yes—
330C4×C8—22no—
331C4×C8C23×C1112yes—
332C2×C11—22no—
333C2×C11—42no—
334C2×C11#304611yescharacteristic
335C2×C11C2×#46711yescharacteristic
336C2×C11#306811yescharacteristic
337#41—22no—
338#41C11×Q1614yes—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—41no—
343C2×Q8—82no—
344C2×Q8C2×D4×C1111yescharacteristic
345C2×D4—21no—
346C2×D4C2×D4×C1111yescharacteristic
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C11×#4111yescharacteristic
354M16—42no—
355C2×C8—22no—
356C2×C8—21no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8—42no—
360C2×C8—82no—
361C2×C8—81no—
362C2×C8C2×D4×C1112yes—
363C2×C8C2×D4×C1112yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C2×D4×C1111yescharacteristic
377C4⋊C4C2×D4×C1111yescharacteristic
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—41no—
382C42—21no—
383C42—21no—
384C42—21no—
385C42—41no—
386C42C2×D4×C1111yescharacteristic
387C42C2×D4×C1111yescharacteristic
388C42C11×#4111yescharacteristic
389C42C24×C1111yescharacteristic
390C11#1941711yescharacteristic, direct product factor, Sylow
391C23—21no—
392C23C11×#12111yescharacteristic
393Q8—21no—
394Q8—41no—
395Q8—41no—
396Q8—81no—
397Q8—82no—
398Q8—82no—
399Q8C2×C11×Q1612yes—
400D4—24no—
401D4—21no—
402D4C2×C11×Q1612yes—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—82no—
417C2×C4C11×#12111yescharacteristic
418C2×C4C11×#12111yescharacteristic
419C2×C4C11×#12111yescharacteristic
420C2×C4C2×C11×Q1612yes—
421C2×C4C11×#13512yes—
422C2×C4C22×D4×C1111yescharacteristic
423C2×C4C22×D4×C1111yescharacteristic
424C2×C4C2×C11×#4111yescharacteristic
425C8—22no—
426C8—22no—
427C8—41no—
428C8—41no—
429C8—42no—
430C8—42no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22C11×#46712yes—
437C22C2×C11×#12111yescharacteristic
438C4—21no—
439C4—22no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—81no—
445C4—82no—
446C4—81no—
447C4C11×#46712yes—
448C4C22×C11×Q1611yescharacteristic
449C4C2×C11×#13511yescharacteristic
450C4C11×#57711yescharacteristic
451C4C11×#57811yescharacteristic
452C2—22no—
453C2—42no—
454C2C11×#304611yescharacteristic
455C2C2×C11×#46711yescharacteristic
456C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#41D4
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×#3230C2semidirect
5. C11×#1684C2semidirect
6. C11×#1683C2semidirect
7. C11×#1676C2semidirect
8. C11×#1675C2semidirect
9. C11×#1571C2semidirect
10. C11×#1550C2semidirect
11. C2×C11×#333C2semidirect
109. #19417C11direct (N × H)
163. #3230C2×C11semidirect
167. #1684C2×C11semidirect
168. #1683C2×C11semidirect
169. #1676C2×C11semidirect
170. #1675C2×C11semidirect
171. #1571C2×C11semidirect
172. #1550C2×C11semidirect
173. C2×#333C2×C11semidirect
390. C11#19417direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#30792
C11×#30762
C11×#29882
C11×#16842
C11×#16832
C11×#16762
C11×#16752
C11×#15712
C11×#15502
C2×C11×#3332
#1941711