Finite Group Databasebeta

← C11×#10374 #14587567

Subgroups — C11×#10374 #14587567

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2549C211yesmaximal, characteristic, complemented
2C11×#1964C211yesmaximal, characteristic
3C11×#1519C211yesmaximal, characteristic
4C2×C11×#327C211yesmaximal, characteristic
5C11×#1294C211yesmaximal, characteristic, complemented
6C11×#1289C211yesmaximal, characteristic, complemented
7C11×#1282C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8—21no—
9C2×C11×#121C2211yescharacteristic
10C2×C11×#99—21no—
11C2×C11×#99—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#398—21no—
15C11×#395—21no—
16C11×#391—21no—
17C11×#389—21no—
18C11×#385—21no—
19C11×#380C2211yescharacteristic
20C11×#380C2211yescharacteristic
21C4×C11×C22⋊C4C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#327—21no—
26C11×#327—21no—
27C22×Q8×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11Q811yescharacteristic, complemented
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C11×C22⋊Q8—42no—
35C11×C22⋊Q8—42no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4Q811yescharacteristic, complemented
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4D411yescharacteristic
52C2×C11×C22⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C11×#99—42no—
55C11×#99—42no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95D411yescharacteristic
66C11×#95D411yescharacteristic
67C11×#95D411yescharacteristic
68C11×#95D411yescharacteristic
69#10374C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11—21no—
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—42no—
73C2×Q8×C11—42no—
74C2×Q8×C11—81no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—81no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—81no—
96C22×C4×C11—81no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×Q811yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—81no—
106C2×C8×C11—81no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—81no—
114C11×C4⋊C4—81no—
115C11×C4⋊C4—81no—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—21no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4D812yes—
125C11×C22⋊C4SD1612yes—
126C42×C11—81no—
127#2549C2×C1111yescharacteristic, complemented
128#1964C2×C1111yescharacteristic
129#1519C2×C1111yescharacteristic
130C2×#327C2×C1111yescharacteristic
131#1294C2×C1111yescharacteristic, complemented
132#1289C2×C1111yescharacteristic, complemented
133#1282C2×C1111yescharacteristic, complemented
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—81no—
140C23×C11—81no—
141C23×C11#12011yescharacteristic
142C23×C11C22⋊Q811yescharacteristic
143C23×C11#12411yescharacteristic
144C23×C11C2×D811yescharacteristic
145C23×C11C2×SD1611yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11#13711yescharacteristic
148Q8×C11—84no—
149D4×C11—81no—
150D4×C11—81no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11C22⋊Q811yescharacteristic
188C2×C4×C11C22⋊Q811yescharacteristic
189C2×C4×C11#12411yescharacteristic
190C2×C4×C11#12411yescharacteristic
191C8×C11—81no—
192C8×C11—81no—
193C2×C22⋊Q8—21no—
194C2×#121C22×C1111yescharacteristic
195C2×#99—21no—
196C2×#99—21no—
197C2×C22⋊C8C22×C1111yescharacteristic
198C2×C22⋊C8C22×C1111yescharacteristic
199#398—21no—
200#395—21no—
201#391—21no—
202#389—21no—
203#385—21no—
204#380C22×C1111yescharacteristic
205#380C22×C1111yescharacteristic
206C4×C22⋊C4C22×C1111yescharacteristic
207C2×#95C22×C1111yescharacteristic
208#327—21no—
209#327—21no—
210#327—21no—
211#327—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—161no—
226C22×C11—161no—
227C22×C11#39311yescharacteristic
228C22×C11#44711yescharacteristic
229C22×C11#44811yescharacteristic
230C22×C11#47411yescharacteristic
231C22×C11#47611yescharacteristic
232C22×C11#48611yescharacteristic
233C22×C11#48911yescharacteristic
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—161no—
246C22×Q8—21no—
247C22×D4—21no—
248C22×D4Q8×C1111yescharacteristic, complemented
249C23×C4—21no—
250C23×C4C23×C1111yescharacteristic
251C22×C8—21no—
252C22×C8—21no—
253C22⋊Q8—42no—
254C22⋊Q8—42no—
255#121—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4Q8×C1111yescharacteristic, complemented
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4D4×C1111yescharacteristic
271C2×C22⋊C4D4×C1111yescharacteristic
272C2×C42—21no—
273#99—42no—
274#99—42no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95D4×C1111yescharacteristic
285#95D4×C1111yescharacteristic
286#95D4×C1111yescharacteristic
287#95D4×C1111yescharacteristic
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—161no—
295C2×C11#202311yescharacteristic
296C2×C11#203111yescharacteristic
297C2×C11#203211yescharacteristic
298C24—21no—
299C24C2×D4×C1111yescharacteristic
300C2×Q8—42no—
301C2×Q8—42no—
302C2×Q8—81no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—81no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—81no—
324C22×C4—81no—
325C22×C4C2×D4×C1111yescharacteristic
326C22×C4C2×D4×C1111yescharacteristic
327C22×C4C2×Q8×C1111yescharacteristic
328C22×C4C11×#4111yescharacteristic
329C22×C4C11×#4111yescharacteristic
330C22×C4C11×#4111yescharacteristic
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—81no—
334C2×C8—81no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—81no—
342C4⋊C4—81no—
343C4⋊C4—81no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4C11×D812yes—
353C22⋊C4C11×SD1612yes—
354C42—81no—
355C11#1037411yescharacteristic, direct product factor, Sylow
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—81no—
362C23—81no—
363C23C11×#12011yescharacteristic
364C23C11×C22⋊Q811yescharacteristic
365C23C11×#12411yescharacteristic
366C23C2×C11×D811yescharacteristic
367C23C2×C11×SD1611yescharacteristic
368C23C11×AGL(1,ℤ/8)11yescharacteristic
369C23C11×#13711yescharacteristic
370Q8—84no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4C11×C22⋊Q811yescharacteristic
410C2×C4C11×C22⋊Q811yescharacteristic
411C2×C4C11×#12411yescharacteristic
412C2×C4C11×#12411yescharacteristic
413C8—81no—
414C8—81no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—161no—
429C22—161no—
430C22C11×#39311yescharacteristic
431C22C11×#44711yescharacteristic
432C22C11×#44811yescharacteristic
433C22C11×#47411yescharacteristic
434C22C11×#47611yescharacteristic
435C22C11×#48611yescharacteristic
436C22C11×#48911yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—161no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—161no—
456C2C11×#202311yescharacteristic
457C2C11×#203111yescharacteristic
458C2C11×#203211yescharacteristic
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC2×C11×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2549C2semidirect
5. C11×#1294C2semidirect
6. C11×#1289C2semidirect
7. C11×#1282C2semidirect
29. C22×D4×C11Q8semidirect
47. C2×C11×C4⋊C4Q8semidirect
69. #10374C11direct (N × H)
127. #2549C2×C11semidirect
131. #1294C2×C11semidirect
132. #1289C2×C11semidirect
133. #1282C2×C11semidirect
248. C22×D4Q8×C11semidirect
266. C2×C4⋊C4Q8×C11semidirect
355. C11#10374direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25492
C11×#19642
C11×#15192
C2×C11×#3272
C11×#12942
C11×#12892
C11×#12822
#1037411