Finite Group Databasebeta

← C11×#9361 #14586554

Subgroups — C11×#9361 #14586554

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3007C211yesmaximal, characteristic
2C11×#2339C211yesmaximal, characteristic
3C11×#1996C211yesmaximal, characteristic, complemented
4C11×#1789C211yesmaximal, characteristic
5C11×#1508C211yesmaximal, characteristic, complemented
6C11×#1305C211yesmaximal, characteristic, complemented
7C11×#1297C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C2×C11×#137C412yescomplemented
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×C4×D4×C11—21no—
12C11×#452—22no—
13C11×#451—21no—
14C11×#450—21no—
15C2×C11×#104—22no—
16C11×#417C412yescomplemented
17C11×#407C2211yescharacteristic
18C11×#407C2211yescharacteristic
19C11×#391—21no—
20C11×#386—22no—
21C11×#381—21no—
22C11×#380C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25C2×C11×#95—21no—
26C11×#342—22no—
27C11×#328—21no—
28C11×#328—21no—
29C2×C11×#41—21no—
30C2×C11×#41—21no—
31C2×C11×#41—44no—
32C2×C11×#41C2×C412yes—
33C2×C11×#41D412yes—
34C22×Q8×C11C2×C411yescharacteristic, complemented
35C22×Q8×C11D411yescharacteristic
36C22×D4×C11—21no—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C23×C4×C11—22no—
40C23×C4×C11C2311yescharacteristic
41C11×#137—44no—
42C2×C11×Q16—22no—
43C2×C11×SD16—22no—
44C2×C11×M16—21no—
45C2×C11×M16C2×C412yescomplemented
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C4×D4×C11—44no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11—21no—
60C2×C42×C11—21no—
61C11×#104—44no—
62C11×#103—22no—
63C11×#102—22no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×#95—22no—
69C11×#95—22no—
70C11×#95—21no—
71C11×#95—21no—
72C11×#95D411yescharacteristic
73C11×#95D411yescharacteristic
74#9361C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—21no—
76C24×C11C2×D411yescharacteristic
77C11×#41—24no—
78C11×#41—24no—
79C11×#41—42no—
80C11×#41—42no—
81C11×#41—44no—
82C11×#41—44no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11C22⋊C412yes—
89C2×D4×C11—24no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11—44no—
94C2×D4×C11C22⋊C412yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×C4×C11—44no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11—41no—
108C22×C4×C11—82no—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C11×Q16—44no—
116C11×SD16—44no—
117C11×M16—42no—
118C11×M16—42no—
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—44no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—42no—
133C42×C11—42no—
134C42×C11—42no—
135#3007C2×C1111yescharacteristic
136#2339C2×C1111yescharacteristic
137#1996C2×C1111yescharacteristic, complemented
138#1789C2×C1111yescharacteristic
139#1508C2×C1111yescharacteristic, complemented
140#1305C2×C1111yescharacteristic, complemented
141#1297C2×C1111yescharacteristic, complemented
142C23×C11—24no—
143C23×C11—22no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11C4×D411yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11#12111yescharacteristic
154Q8×C11—22no—
155Q8×C11—22no—
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—81no—
159D4×C11—24no—
160D4×C11—22no—
161D4×C11—44no—
162D4×C11—44no—
163D4×C11#9914yes—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—88no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C4×D411yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12311yescharacteristic
195C8×C11—42no—
196C8×C11—81no—
197C22×#41C22×C1111yescharacteristic
198C2×#137C4×C1112yescomplemented
199C2×C22⋊Q8C22×C1111yescharacteristic
200C2×C4×D4—21no—
201#452—22no—
202#451—21no—
203#450—21no—
204C2×#104—22no—
205#417C4×C1112yescomplemented
206#407C22×C1111yescharacteristic
207#407C22×C1111yescharacteristic
208#391—21no—
209#386—22no—
210#381—21no—
211#380C22×C1111yescharacteristic
212C4×C22⋊C4C22×C1111yescharacteristic
213C4×C22⋊C4C22×C1111yescharacteristic
214C2×#95—21no—
215#342—22no—
216#328—21no—
217#328—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—24no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—44no—
228C22×C11—44no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11#38611yescharacteristic
234C22×C11#45511yescharacteristic
235C22×C11#45611yescharacteristic
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11—82no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11C2×#9912yes—
247C2×#41—21no—
248C2×#41—21no—
249C2×#41—44no—
250C2×#41C2×C4×C1112yes—
251C2×#41D4×C1112yes—
252C22×Q8C2×C4×C1111yescharacteristic, complemented
253C22×Q8D4×C1111yescharacteristic
254C22×D4—21no—
255C22×D4D4×C1111yescharacteristic
256C23×C4—21no—
257C23×C4—22no—
258C23×C4C23×C1111yescharacteristic
259#137—44no—
260C2×Q16—22no—
261C2×SD16—22no—
262C2×M16—21no—
263C2×M16C2×C4×C1112yescomplemented
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C4×D4—44no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
272C2×C22⋊C4—21no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4D4×C1112yes—
277C2×C42—21no—
278C2×C42—21no—
279#104—44no—
280#103—22no—
281#102—22no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286#95—22no—
287#95—22no—
288#95—21no—
289#95—21no—
290#95D4×C1111yescharacteristic
291#95D4×C1111yescharacteristic
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—41no—
295C2×C11—41no—
296C2×C11—44no—
297C2×C11#188211yescharacteristic
298C2×C11#189811yescharacteristic
299C2×C11#190611yescharacteristic
300C24—21no—
301C24C2×D4×C1111yescharacteristic
302#41—24no—
303#41—24no—
304#41—42no—
305#41—42no—
306#41—44no—
307#41—44no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8C11×C22⋊C412yes—
314C2×D4—24no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—44no—
319C2×D4C11×C22⋊C412yes—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—44no—
330C22×C4—44no—
331C22×C4—44no—
332C22×C4—41no—
333C22×C4—82no—
334C22×C4C22×C4×C1111yescharacteristic
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C2×D4×C1111yescharacteristic
337C22×C4C2×D4×C1111yescharacteristic
338C22×C4C11×#4111yescharacteristic
339C22×C4C11×#4111yescharacteristic
340Q16—44no—
341SD16—44no—
342M16—42no—
343M16—42no—
344C2×C8—22no—
345C2×C8—41no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—42no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C22⋊C4—22no—
352C22⋊C4—42no—
353C22⋊C4—44no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—42no—
358C42—42no—
359C42—42no—
360C11#936111yescharacteristic, direct product factor, Sylow
361C23—24no—
362C23—22no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—42no—
368C23—41no—
369C23—41no—
370C23C4×D4×C1111yescharacteristic
371C23C11×#12011yescharacteristic
372C23C11×#12111yescharacteristic
373Q8—22no—
374Q8—22no—
375Q8—42no—
376Q8—42no—
377Q8—81no—
378D4—24no—
379D4—22no—
380D4—44no—
381D4—44no—
382D4C11×#9914yes—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—88no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4C2×C11×C22⋊C411yescharacteristic
411C2×C4C4×D4×C1111yescharacteristic
412C2×C4C11×#12111yescharacteristic
413C2×C4C11×#12311yescharacteristic
414C8—42no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—24no—
423C22—21no—
424C22—21no—
425C22—44no—
426C22—44no—
427C22—42no—
428C22—42no—
429C22—81no—
430C22—81no—
431C22C11×#38611yescharacteristic
432C22C11×#45511yescharacteristic
433C22C11×#45611yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—42no—
439C4—82no—
440C4—81no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4C2×C11×#9912yes—
445C2—21no—
446C2—21no—
447C2—41no—
448C2—41no—
449C2—44no—
450C2C11×#188211yescharacteristic
451C2C11×#189811yescharacteristic
452C2C11×#190611yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C11×#1996C2semidirect
5. C11×#1508C2semidirect
6. C11×#1305C2semidirect
7. C11×#1297C2semidirect
9. C2×C11×#137C4semidirect
16. C11×#417C4semidirect
34. C22×Q8×C11C2×C4semidirect
45. C2×C11×M16C2×C4semidirect
53. C2×C11×C4⋊C4C2×C4semidirect
74. #9361C11direct (N × H)
137. #1996C2×C11semidirect
139. #1508C2×C11semidirect
140. #1305C2×C11semidirect
141. #1297C2×C11semidirect
198. C2×#137C4×C11semidirect
205. #417C4×C11semidirect
252. C22×Q8C2×C4×C11semidirect
263. C2×M16C2×C4×C11semidirect
271. C2×C4⋊C4C2×C4×C11semidirect
360. C11#9361direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30072
C11×#23392
C11×#19962
C11×#17892
C11×#15082
C11×#13052
C11×#12972
#936111