Finite Group Databasebeta

← C11×#8973 #14586166

Subgroups — C11×#8973 #14586166

Order 2816.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic
2D4×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#1987C211yesmaximal, characteristic, complemented
4C11×#1956C211yesmaximal, characteristic, complemented
5C2×C11×D4⋊C8C211yesmaximal, characteristic
6C11×#1296C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4—21no—
12C11×#476—22no—
13C11×#476C414yescomplemented
14C2×C11×#106—21no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103—22no—
18C2×C11×#102—21no—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#389—21no—
21C11×#385—22no—
22C11×#384C2211yescharacteristic
23C11×#380—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C11×#340—21no—
26C11×#340—21no—
27C11×D4⋊C8—22no—
28C22×Q8×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11—22no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8C2×C412yescomplemented
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—42no—
42C4×D4×C11—42no—
43C4×D4×C11C2×C412yes—
44C4×D4×C11D412yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—42no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—22no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8C2×C412yescomplemented
65C11×#103—44no—
66C11×#102—24no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C11×#95—22no—
70C11×#95—21no—
71#8973C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—42no—
75C2×Q8×C11—42no—
76C2×Q8×C11—41no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11C22⋊C412yes—
81C2×D4×C11SD1612yes—
82C2×D4×C11Q1612yes—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—44no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—44no—
95C22×C4×C11—41no—
96C22×C4×C11—82no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—44no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4C22⋊C412yes—
124C11×C4⋊C4SD1612yes—
125C11×C22⋊C4—22no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—44no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C22×C411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11#4111yescharacteristic
134C2×#476C2×C1111yescharacteristic
135D4×C4⋊C4C2×C1111yescharacteristic
136#1987C2×C1111yescharacteristic, complemented
137#1956C2×C1111yescharacteristic, complemented
138C2×D4⋊C8C2×C1111yescharacteristic
139#1296C2×C1111yescharacteristic, complemented
140#1279C2×C1111yescharacteristic, complemented
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11#12011yescharacteristic
149Q8×C11—44no—
150Q8×C11—82no—
151D4×C11—22no—
152D4×C11—22no—
153D4×C11—22no—
154D4×C11#10314yescomplemented
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—88no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11C2×C22⋊C411yescharacteristic
178C2×C4×C11C4×D411yescharacteristic
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12311yescharacteristic
183C2×C4×C11C2×SD1611yescharacteristic
184C2×C4×C11C2×SD1611yescharacteristic
185C2×C4×C11C2×Q1611yescharacteristic
186C2×C4×C11#13511yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11#13711yescharacteristic
190C2×C4×C11#13711yescharacteristic
191C8×C11—42no—
192C8×C11—42no—
193C8×C11—81no—
194C2×C4⋊Q8C22×C1111yescharacteristic
195C2×C4×D4—21no—
196C2×C4×D4C22×C1111yescharacteristic
197C22×C4⋊C4—21no—
198#476—22no—
199#476C4×C1114yescomplemented
200C2×#106—21no—
201C2×C4⋊C8C22×C1111yescharacteristic
202C2×C4⋊C8C22×C1111yescharacteristic
203C2×#103—22no—
204C2×#102—21no—
205C2×C4×C8C22×C1111yescharacteristic
206#389—21no—
207#385—22no—
208#384C22×C1111yescharacteristic
209#380—21no—
210C4×C4⋊C4C22×C1111yescharacteristic
211#340—21no—
212#340—21no—
213D4⋊C8—22no—
214C22×C11—24no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11#38611yescharacteristic
222C22×C11#45011yescharacteristic
223C22×C11#45011yescharacteristic
224C22×C11#45111yescharacteristic
225C22×C11#45211yescharacteristic
226C22×C11#45311yescharacteristic
227C22×C11#45411yescharacteristic
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—42no—
231C4×C11—42no—
232C4×C11—82no—
233C4×C11—82no—
234C4×C11—81no—
235C4×C11C2×#10311yescharacteristic
236C4×C11#41711yescharacteristic
237C4×C11C4×SD1611yescharacteristic
238C4×C11#44011yescharacteristic
239C4×C11#46111yescharacteristic
240C4×C11#46311yescharacteristic
241C4×C11#48311yescharacteristic
242C4×C11#48411yescharacteristic
243C22×Q8—21no—
244C22×D4D4×C1111yescharacteristic
245C23×C4—21no—
246C23×C4—22no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8C2×C4×C1112yescomplemented
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—42no—
257C4×D4—42no—
258C4×D4C2×C4×C1112yes—
259C4×D4D4×C1112yes—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4D4×C1111yescharacteristic
268C2×C4⋊C4D4×C1111yescharacteristic
269C2×C4⋊C4D4×C1111yescharacteristic
270C2×C4⋊C4D4×C1112yes—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—22no—
273C2×C42—21no—
274C2×C42C23×C1111yescharacteristic
275#106—24no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8C2×C4×C1112yescomplemented
280#103—44no—
281#102—24no—
282C4×C8—21no—
283C4×C8—21no—
284#95—22no—
285#95—21no—
286C2×C11—44no—
287C2×C11#162911yescharacteristic
288C2×C11#163211yescharacteristic
289C2×C11#163511yescharacteristic
290C2×C11#163711yescharacteristic
291C2×C11#187211yescharacteristic
292C2×C11#187711yescharacteristic
293C2×C11#188311yescharacteristic
294C24—21no—
295C2×Q8—22no—
296C2×Q8—42no—
297C2×Q8—42no—
298C2×Q8—41no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4C11×C22⋊C412yes—
303C2×D4C11×SD1612yes—
304C2×D4C11×Q1612yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—44no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—44no—
317C22×C4—41no—
318C22×C4—82no—
319C22×C4C2×D4×C1111yescharacteristic
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1111yescharacteristic
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—42no—
338C4⋊C4—44no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4C11×C22⋊C412yes—
346C4⋊C4C11×SD1612yes—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—44no—
350C42—41no—
351C42—41no—
352C42C22×C4×C1111yescharacteristic
353C42C2×D4×C1111yescharacteristic
354C42C11×#4111yescharacteristic
355C42C11×#4111yescharacteristic
356C11#897311yescharacteristic, direct product factor, Sylow
357C23—22no—
358C23—22no—
359C23—22no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23C11×#12011yescharacteristic
365Q8—44no—
366Q8—82no—
367D4—22no—
368D4—22no—
369D4—22no—
370D4C11×#10314yescomplemented
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—88no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4C2×C11×C22⋊C411yescharacteristic
394C2×C4C4×D4×C1111yescharacteristic
395C2×C4C4×D4×C1111yescharacteristic
396C2×C4C11×#12111yescharacteristic
397C2×C4C11×#12111yescharacteristic
398C2×C4C11×#12311yescharacteristic
399C2×C4C2×C11×SD1611yescharacteristic
400C2×C4C2×C11×SD1611yescharacteristic
401C2×C4C2×C11×Q1611yescharacteristic
402C2×C4C11×#13511yescharacteristic
403C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
404C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
405C2×C4C11×#13711yescharacteristic
406C2×C4C11×#13711yescharacteristic
407C8—42no—
408C8—42no—
409C8—81no—
410C22—24no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—42no—
417C22C11×#38611yescharacteristic
418C22C11×#45011yescharacteristic
419C22C11×#45011yescharacteristic
420C22C11×#45111yescharacteristic
421C22C11×#45211yescharacteristic
422C22C11×#45311yescharacteristic
423C22C11×#45411yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—82no—
429C4—82no—
430C4—81no—
431C4C2×C11×#10311yescharacteristic
432C4C11×#41711yescharacteristic
433C4C4×C11×SD1611yescharacteristic
434C4C11×#44011yescharacteristic
435C4C11×#46111yescharacteristic
436C4C11×#46311yescharacteristic
437C4C11×#48311yescharacteristic
438C4C11×#48411yescharacteristic
439C2—44no—
440C2C11×#162911yescharacteristic
441C2C11×#163211yescharacteristic
442C2C11×#163511yescharacteristic
443C2C11×#163711yescharacteristic
444C2C11×#187211yescharacteristic
445C2C11×#187711yescharacteristic
446C2C11×#188311yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1987C2semidirect
4. C11×#1956C2semidirect
6. C11×#1296C2semidirect
7. C11×#1279C2semidirect
13. C11×#476C4semidirect
38. C11×C4⋊Q8C2×C4semidirect
64. C11×C4⋊C8C2×C4semidirect
71. #8973C11direct (N × H)
136. #1987C2×C11semidirect
137. #1956C2×C11semidirect
139. #1296C2×C11semidirect
140. #1279C2×C11semidirect
154. D4×C11#103semidirect
199. #476C4×C11semidirect
253. C4⋊Q8C2×C4×C11semidirect
279. C4⋊C8C2×C4×C11semidirect
356. C11#8973direct (N × H)
370. D4C11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4762
D4×C11×C4⋊C42
C11×#19872
C11×#19562
C2×C11×D4⋊C82
C11×#12962
C11×#12792
#897311