Finite Group Databasebeta

← C11×#18399 #14595592

Subgroups — C11×#18399 #14595592

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#3230C211yesmaximal, characteristic, complemented
3C11×#3227C211yesmaximal, characteristic
4C11×#2568C211yesmaximal, characteristic, complemented
5C11×#1615C218yesmaximal, complemented
6C11×#1503C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic
8C11×#1461C211yesmaximal, characteristic, complemented
9C11×#559—21no—
10C11×#557—21no—
11C11×#556—21no—
12C11×#556—22no—
13C11×#554—21no—
14C11×#552—22no—
15C11×#539C2214yes—
16C11×#536—21no—
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C11×#529—22no—
21C11×#520—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C11×#500—21no—
24C11×#498—21no—
25C11×#487—21no—
26C11×#486—21no—
27C11×#484C2214yes—
28C11×#481C2214yes—
29C11×#477—22no—
30C11×#476—22no—
31C11×#431C2211yescharacteristic
32C11×#431C2211yescharacteristic
33C11×#400C2214yes—
34C11×#391—21no—
35C11×#391—22no—
36C11×#382—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#328C2214yes—
39C11×#327C2214yes—
40C11×#324C2214yes—
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11D411yescharacteristic
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8D411yescharacteristic
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8D411yescharacteristic
52C11×#127D411yescharacteristic
53C11×#126—24no—
54C11×#126—24no—
55C11×#125—22no—
56C11×#125—24no—
57C11×#125—21no—
58C11×#124—22no—
59C11×#124—22no—
60C11×#124—21no—
61C11×#123—24no—
62C11×#123—24no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8C2312yes—
68C11×#121—21no—
69C11×#121C2312yes—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D412yes—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—24no—
81C4×D4×C11—21no—
82C4×D4×C11D412yes—
83C11×#117—22no—
84C11×#117—24no—
85C11×#117—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C42×C11—21no—
93C2×C42×C11D412yes—
94C2×C42×C11C2311yescharacteristic
95C11×#107—24no—
96C11×#106—24no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×#103—24no—
100C11×#102—24no—
101C11×C22⋊C8C2312yes—
102C11×C22⋊C8C2312yes—
103C4×C8×C11—21no—
104C4×C8×C11—21no—
105C11×#95—24no—
106C11×#95—24no—
107C11×#95C2312yes—
108#18399C1111yesmaximal, characteristic, direct product factor, Sylow
109C11×#41—42no—
110C11×#41—42no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—44no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11C2×D412yes—
121C2×D4×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4C2×D412yes—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C42×C11—24no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—42no—
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171#3507C2×C1111yescharacteristic
172#3230C2×C1111yescharacteristic, complemented
173#3227C2×C1111yescharacteristic
174#2568C2×C1111yescharacteristic, complemented
175#1615C2×C1118yescomplemented
176#1503C2×C1111yescharacteristic, complemented
177#1502C2×C1111yescharacteristic
178#1461C2×C1111yescharacteristic, complemented
179C23×C11—22no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—42no—
185Q8×C11—42no—
186Q8×C11—82no—
187Q8×C11—82no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—84no—
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#13512yes—
215C2×C4×C11#13712yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C8×C11—42no—
219C8×C11—42no—
220#559—21no—
221#557—21no—
222#556—21no—
223#556—22no—
224#554—21no—
225#552—22no—
226#539C22×C1114yes—
227#536—21no—
228#533C22×C1111yescharacteristic
229#532C22×C1111yescharacteristic
230C2×C4⋊Q8C22×C1111yescharacteristic
231#529—22no—
232#520—21no—
233C2×C4×Q8C22×C1111yescharacteristic
234#500—21no—
235#498—21no—
236#487—21no—
237#486—21no—
238#484C22×C1114yes—
239#481C22×C1114yes—
240#477—22no—
241#476—22no—
242#431C22×C1111yescharacteristic
243#431C22×C1111yescharacteristic
244#400C22×C1114yes—
245#391—21no—
246#391—22no—
247#382—21no—
248C4×C4⋊C4C22×C1111yescharacteristic
249#328C22×C1114yes—
250#327C22×C1114yes—
251#324C22×C1114yes—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11C2×#12011yescharacteristic
258C22×C11C2×#13511yescharacteristic
259C22×C11C2×#13711yescharacteristic
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—82no—
269C4×C11—82no—
270C4×C11#45212yes—
271C4×C11#45212yes—
272C4×C11#45412yes—
273C2×#41—21no—
274C22×Q8—21no—
275C22×Q8D4×C1111yescharacteristic
276C4⋊Q8—22no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8D4×C1111yescharacteristic
282C4⋊Q8D4×C1111yescharacteristic
283C4⋊Q8D4×C1111yescharacteristic
284#127D4×C1111yescharacteristic
285#126—24no—
286#126—24no—
287#125—22no—
288#125—24no—
289#125—21no—
290#124—22no—
291#124—22no—
292#124—21no—
293#123—24no—
294#123—24no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—24no—
298C22⋊Q8—21no—
299C22⋊Q8C23×C1112yes—
300#121—21no—
301#121C23×C1112yes—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8D4×C1112yes—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—24no—
313C4×D4—21no—
314C4×D4D4×C1112yes—
315#117—22no—
316#117—24no—
317#117—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4D4×C1111yescharacteristic
322C2×C4⋊C4C23×C1112yes—
323C2×C4⋊C4C23×C1112yes—
324C2×C42—21no—
325C2×C42D4×C1112yes—
326C2×C42C23×C1111yescharacteristic
327#107—24no—
328#106—24no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331#103—24no—
332#102—24no—
333C22⋊C8C23×C1112yes—
334C22⋊C8C23×C1112yes—
335C4×C8—21no—
336C4×C8—21no—
337#95—24no—
338#95—24no—
339#95C23×C1112yes—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—82no—
343C2×C11C2×#45211yescharacteristic
344C2×C11C2×#45411yescharacteristic
345C2×C11#302811yescharacteristic
346#41—42no—
347#41—42no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—44no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8C2×D4×C1112yes—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4C2×D4×C1112yes—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4C2×D4×C1112yes—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C24×C1111yescharacteristic
371C2×C8—22no—
372C2×C8—22no—
373C4⋊C4—24no—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C1112yes—
392C4⋊C4C2×D4×C1112yes—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C42—24no—
400C42—22no—
401C42—22no—
402C42—22no—
403C42—42no—
404C42C2×D4×C1111yescharacteristic
405C42C2×D4×C1111yescharacteristic
406C42C2×D4×C1111yescharacteristic
407C42C2×D4×C1111yescharacteristic
408C11#1839911yescharacteristic, direct product factor, Sylow
409C23—22no—
410C23C22×D4×C1111yescharacteristic
411Q8—42no—
412Q8—42no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416Q8—82no—
417Q8—82no—
418D4—42no—
419D4—42no—
420D4—42no—
421D4—42no—
422D4—42no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—84no—
440C2×C4C11×#12011yescharacteristic
441C2×C4C11×#12011yescharacteristic
442C2×C4C11×#12011yescharacteristic
443C2×C4C11×#12011yescharacteristic
444C2×C4C11×#13512yes—
445C2×C4C11×#13712yes—
446C2×C4C22×D4×C1111yescharacteristic
447C2×C4C22×D4×C1111yescharacteristic
448C8—42no—
449C8—42no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22C2×C11×#12011yescharacteristic
456C22C2×C11×#13511yescharacteristic
457C22C2×C11×#13711yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—82no—
467C4—82no—
468C4C11×#45212yes—
469C4C11×#45212yes—
470C4C11×#45412yes—
471C2—21no—
472C2—21no—
473C2—82no—
474C2C2×C11×#45211yescharacteristic
475C2C2×C11×#45411yescharacteristic
476C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#532C22
LCSG ▷ C22×C4 ▷ 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×#3230C2semidirect
4. C11×#2568C2semidirect
5. C11×#1615C2semidirect
6. C11×#1503C2semidirect
8. C11×#1461C2semidirect
108. #18399C11direct (N × H)
172. #3230C2×C11semidirect
174. #2568C2×C11semidirect
175. #1615C2×C11semidirect
176. #1503C2×C11semidirect
178. #1461C2×C11semidirect
408. C11#18399direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#32302
C11×#32272
C11×#25682
C11×#16152
C11×#15032
C11×#15022
C11×#14612
#1839911