Finite Group Databasebeta

← C11×#19263 #14596456

Subgroups — C11×#19263 #14596456

Order 2816.

628 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×#3167C211yesmaximal, characteristic
2C11×#3113C211yesmaximal, characteristic, complemented
3C11×#3112C211yesmaximal, characteristic
4C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
5C11×#1684C212yesmaximal, complemented
6C11×#1682C212yesmaximal, complemented
7C11×#1672C212yesmaximal, complemented
8C11×#1666C212yesmaximal, complemented
9C11×#1568C211yesmaximal, characteristic, complemented
10C11×#1552C211yesmaximal, characteristic, complemented
11C11×#1551C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C11×#498C2211yescharacteristic
16C11×#492C2211yescharacteristic
17C11×#487C2211yescharacteristic
18C11×#486C2211yescharacteristic
19C11×#483—21no—
20C11×#480—21no—
21C11×#477C2212yes—
22C11×#475C2212yes—
23C11×#465—21no—
24C11×#465—21no—
25C11×#462C2212yes—
26C11×#460C2212yes—
27C11×#451—21no—
28C11×#448—21no—
29C8×Q8×C11—21no—
30C8×Q8×C11—21no—
31C8×Q8×C11C2212yes—
32C8×Q8×C11C2212yes—
33C11×#441—22no—
34C11×#440—22no—
35C4×C11×SD16—21no—
36C4×C11×SD16—21no—
37C11×#432C2211yescharacteristic
38C11×#432C2211yescharacteristic
39C2×C11×C4⋊C8—21no—
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C4×C8×C11—21no—
42C2×C4×C8×C11C2211yescharacteristic
43C11×#335C2212yes—
44C11×#334C2212yes—
45C11×#333C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11D411yescharacteristic
51C2×C11×Q16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16—21no—
54C2×C11×SD16—21no—
55C22×C8×C11—21no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×#127C2311yescharacteristic
62C11×#125—21no—
63C11×#124—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×#121—21no—
67C11×#121—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11D412yes—
73C4×Q8×C11C2312yes—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C11×#117—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C11×#107—22no—
82C11×#106—21no—
83C11×#106—21no—
84C11×#106—22no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—22no—
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—22no—
96C11×#102—21no—
97C11×#102—21no—
98C11×#102—22no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8—21no—
101C11×#97—21no—
102C11×#97—21no—
103C4×C8×C11—22no—
104C4×C8×C11—22no—
105C4×C8×C11D411yescharacteristic
106C4×C8×C11D411yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#19263C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—82no—
111C2×Q8×C11—24no—
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—21no—
122C22×C4×C11—21no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C11×Q16—44no—
128C11×SD16—42no—
129C11×SD16—42no—
130C11×SD16—44no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—41no—
136C2×C8×C11—42no—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
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—41no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—41no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11#4111yescharacteristic
162C42×C11C2411yescharacteristic
163#3167C2×C1111yescharacteristic
164#3113C2×C1111yescharacteristic, complemented
165#3112C2×C1111yescharacteristic
166C2×C8×Q8C2×C1111yescharacteristic, complemented
167#1684C2×C1112yescomplemented
168#1682C2×C1112yescomplemented
169#1672C2×C1112yescomplemented
170#1666C2×C1112yescomplemented
171#1568C2×C1111yescharacteristic, complemented
172#1552C2×C1111yescharacteristic, complemented
173#1551C2×C1111yescharacteristic
174C23×C11—41no—
175C23×C11#12111yescharacteristic
176Q8×C11—24no—
177Q8×C11—22no—
178Q8×C11—42no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—81no—
182Q8×C11#13514yes—
183D4×C11—42no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11—81no—
187D4×C11—82no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—82no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C8×C11—21no—
207C8×C11—21no—
208C8×C11—21no—
209C8×C11—42no—
210C8×C11—42no—
211C8×C11—42no—
212C8×C11#13712yes—
213#533C22×C1111yescharacteristic
214#532C22×C1111yescharacteristic
215C2×C4×Q8C22×C1111yescharacteristic
216#498C22×C1111yescharacteristic
217#492C22×C1111yescharacteristic
218#487C22×C1111yescharacteristic
219#486C22×C1111yescharacteristic
220#483—21no—
221#480—21no—
222#477C22×C1112yes—
223#475C22×C1112yes—
224#465—21no—
225#465—21no—
226#462C22×C1112yes—
227#460C22×C1112yes—
228#451—21no—
229#448—21no—
230C8×Q8—21no—
231C8×Q8—21no—
232C8×Q8C22×C1112yes—
233C8×Q8C22×C1112yes—
234#441—22no—
235#440—22no—
236C4×SD16—21no—
237C4×SD16—21no—
238#432C22×C1111yescharacteristic
239#432C22×C1111yescharacteristic
240C2×C4⋊C8—21no—
241C2×C4⋊C8C22×C1111yescharacteristic
242C2×C4×C8—21no—
243C2×C4×C8C22×C1111yescharacteristic
244#335C22×C1112yes—
245#334C22×C1112yes—
246#333C22×C1112yes—
247#332C22×C1112yes—
248#332C22×C1112yes—
249#331C22×C1112yes—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11#47112yes—
256C22×C11C2×#12111yescharacteristic
257C4×C11—21no—
258C4×C11—24no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11C2×#13512yes—
267C4×C11C2×#13711yescharacteristic
268C4×C11#57511yescharacteristic
269C2×#41—21no—
270C22×Q8D4×C1111yescharacteristic
271C2×Q16—22no—
272C2×SD16—22no—
273C2×SD16—21no—
274C2×SD16—21no—
275C22×C8—21no—
276C22×C8D4×C1111yescharacteristic
277C22×C8D4×C1111yescharacteristic
278C4⋊Q8C23×C1111yescharacteristic
279C4⋊Q8C23×C1111yescharacteristic
280C4⋊Q8C23×C1111yescharacteristic
281#127C23×C1111yescharacteristic
282#125—21no—
283#124—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286#121—21no—
287#121—21no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8D4×C1112yes—
293C4×Q8C23×C1112yes—
294C4×D4—21no—
295C4×D4—21no—
296#117—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4D4×C1111yescharacteristic
299C2×C42—21no—
300C2×C42C23×C1111yescharacteristic
301#107—22no—
302#106—21no—
303#106—21no—
304#106—22no—
305C4⋊C8—22no—
306C4⋊C8—22no—
307C4⋊C8—21no—
308C4⋊C8C23×C1112yes—
309C4⋊C8C23×C1112yes—
310C4⋊C8C23×C1112yes—
311#103—22no—
312#103—22no—
313#103—21no—
314#103—21no—
315#103—22no—
316#102—21no—
317#102—21no—
318#102—22no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321#97—21no—
322#97—21no—
323C4×C8—22no—
324C4×C8—22no—
325C4×C8D4×C1111yescharacteristic
326C4×C8D4×C1111yescharacteristic
327C4×C8C23×C1111yescharacteristic
328C4×C8C23×C1111yescharacteristic
329C2×C11—22no—
330C2×C11—161no—
331C2×C11#303711yescharacteristic
332C2×C11#305011yescharacteristic
333C2×C11C2×#47111yescharacteristic
334#41—82no—
335C2×Q8—24no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8C2×D4×C1112yes—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C11×#4111yescharacteristic
351Q16—44no—
352SD16—42no—
353SD16—44no—
354SD16—42no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—42no—
361C2×C8C2×D4×C1111yescharacteristic
362C2×C8C2×D4×C1111yescharacteristic
363C2×C8C2×D4×C1111yescharacteristic
364C2×C8C2×D4×C1111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C2×D4×C1112yes—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C42—22no—
381C42—22no—
382C42—41no—
383C42C2×D4×C1111yescharacteristic
384C42C2×D4×C1111yescharacteristic
385C42C11×#4111yescharacteristic
386C42C24×C1111yescharacteristic
387C11#1926311yescharacteristic, direct product factor, Sylow
388C23—41no—
389C23C11×#12111yescharacteristic
390Q8—24no—
391Q8—22no—
392Q8—42no—
393Q8—41no—
394Q8—41no—
395Q8—81no—
396Q8C11×#13514yes—
397D4—42no—
398D4—41no—
399D4—41no—
400D4—81no—
401D4—82no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4C11×#12111yescharacteristic
415C2×C4C11×#12111yescharacteristic
416C2×C4C11×#12111yescharacteristic
417C2×C4C22×D4×C1111yescharacteristic
418C2×C4C22×D4×C1111yescharacteristic
419C2×C4C2×C11×#4111yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8—42no—
424C8—42no—
425C8—42no—
426C8C11×#13712yes—
427C22—21no—
428C22—21no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C11×#47112yes—
433C22C2×C11×#12111yescharacteristic
434C4—21no—
435C4—24no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4C2×C11×#13512yes—
444C4C2×C11×#13711yescharacteristic
445C4C11×#57511yescharacteristic
446C2—22no—
447C2—161no—
448C2C11×#303711yescharacteristic
449C2C11×#305011yescharacteristic
450C2C2×C11×#47111yescharacteristic
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
2. C11×#3113C2semidirect
4. C2×C8×Q8×C11C2semidirect
5. C11×#1684C2semidirect
6. C11×#1682C2semidirect
7. C11×#1672C2semidirect
8. C11×#1666C2semidirect
9. C11×#1568C2semidirect
10. C11×#1552C2semidirect
109. #19263C11direct (N × H)
164. #3113C2×C11semidirect
166. C2×C8×Q8C2×C11semidirect
167. #1684C2×C11semidirect
168. #1682C2×C11semidirect
169. #1672C2×C11semidirect
170. #1666C2×C11semidirect
171. #1568C2×C11semidirect
172. #1552C2×C11semidirect
387. C11#19263direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31672
C11×#31132
C11×#31122
C2×C8×Q8×C112
C11×#16842
C11×#16822
C11×#16722
C11×#16662
C11×#15682
C11×#15522
C11×#15512
#1926311