Finite Group Databasebeta

← C11×#10250 #14587443

Subgroups — C11×#10250 #14587443

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C11×#2548C211yesmaximal, characteristic
4C11×#1545C211yesmaximal, characteristic
5C11×#1503C211yesmaximal, characteristic, complemented
6C11×#1479C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×C11×#124—21no—
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#492—21no—
13C11×#486—21no—
14C11×#479—22no—
15C11×#477—21no—
16C11×#475—21no—
17C11×#460—22no—
18C11×#450—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#428—21no—
22C11×#423C2211yescharacteristic
23C11×#419—21no—
24C11×#394—22no—
25C11×#390—22no—
26C11×#390—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#331—22no—
29C11×#328—22no—
30C11×Q8⋊C8—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D412yes—
35C2×C11×SD16—24no—
36C2×C11×M16—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#125—21no—
44C11×#124—42no—
45C11×#124—42no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C11×#117—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—24no—
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×#107—22no—
64C11×#106—22no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—22no—
70C11×#103—22no—
71C11×#102—24no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8—21no—
74C4×C8×C11—21no—
75C4×C8×C11—21no—
76C11×#95D412yes—
77#10250C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11SD1612yescomplemented
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—44no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—82no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C11×SD16—84no—
106C11×M16—41no—
107C11×M16—41no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—48no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—84no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134#3208C2×C1111yescharacteristic
135#3078C2×C1111yescharacteristic, complemented
136#2548C2×C1111yescharacteristic
137#1545C2×C1111yescharacteristic
138#1503C2×C1111yescharacteristic, complemented
139#1479C2×C1111yescharacteristic, complemented
140#1303C2×C1111yescharacteristic, complemented
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11#12011yescharacteristic
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151Q8×C11—42no—
152Q8×C11—81no—
153D4×C11—44no—
154D4×C11—82no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11C2×SD1611yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11#13711yescharacteristic
183C8×C11—42no—
184C8×C11—42no—
185C8×C11—81no—
186#533C22×C1111yescharacteristic
187C2×#127C22×C1111yescharacteristic
188C2×#124—21no—
189C2×C4×Q8C22×C1111yescharacteristic
190#492—21no—
191#486—21no—
192#479—22no—
193#477—21no—
194#475—21no—
195#460—22no—
196#450—22no—
197#431C22×C1111yescharacteristic
198#431C22×C1111yescharacteristic
199#428—21no—
200#423C22×C1111yescharacteristic
201#419—21no—
202#394—22no—
203#390—22no—
204#390—21no—
205C4×C4⋊C4C22×C1111yescharacteristic
206#331—22no—
207#328—22no—
208Q8⋊C8—22no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—84no—
212C22×C11—84no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11#39211yescharacteristic
217C22×C11#45011yescharacteristic
218C22×C11#45211yescharacteristic
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—42no—
223C4×C11—82no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11#44811yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#45512yes—
230C4×C11#46511yescharacteristic
231C4×C11#46811yescharacteristic
232C22×Q8D4×C1111yescharacteristic
233C22×D4—21no—
234C22×D4—21no—
235C22×D4D4×C1112yes—
236C2×SD16—24no—
237C2×M16—21no—
238C4⋊Q8D4×C1111yescharacteristic
239C4⋊Q8D4×C1111yescharacteristic
240#127—21no—
241#127—21no—
242#127—21no—
243#127—21no—
244#125—21no—
245#124—42no—
246#124—42no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255#117—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C1111yescharacteristic
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42C23×C1111yescharacteristic
264#107—22no—
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C1112yes—
269C4⋊C8D4×C1112yes—
270#103—22no—
271#103—22no—
272#102—24no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277#95D4×C1112yes—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—162no—
281C2×C11#200011yescharacteristic
282C2×C11#200411yescharacteristic
283C2×C11#200811yescharacteristic
284C24—22no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8C11×SD1612yescomplemented
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—44no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—82no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1111yescharacteristic
311SD16—84no—
312M16—41no—
313M16—41no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—41no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C22⋊C4—48no—
329C22⋊C4—41no—
330C22⋊C4—84no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—41no—
336C42C2×D4×C1111yescharacteristic
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C11×#4111yescharacteristic
340C11#1025011yescharacteristic, direct product factor, Sylow
341C23—44no—
342C23—44no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23C11×#12011yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—42no—
352Q8—81no—
353D4—44no—
354D4—82no—
355D4—82no—
356D4—82no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4C11×#12011yescharacteristic
374C2×C4C11×#12011yescharacteristic
375C2×C4C11×#12111yescharacteristic
376C2×C4C11×#12111yescharacteristic
377C2×C4C11×#12111yescharacteristic
378C2×C4C11×#12711yescharacteristic
379C2×C4C2×C11×SD1611yescharacteristic
380C2×C4C11×#13511yescharacteristic
381C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
382C2×C4C11×#13711yescharacteristic
383C8—42no—
384C8—42no—
385C8—81no—
386C22—21no—
387C22—21no—
388C22—84no—
389C22—84no—
390C22—82no—
391C22—82no—
392C22—82no—
393C22C11×#39211yescharacteristic
394C22C11×#45011yescharacteristic
395C22C11×#45211yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—82no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4C11×#44811yescharacteristic
405C4C11×#44911yescharacteristic
406C4C11×#45512yes—
407C4C11×#46511yescharacteristic
408C4C11×#46811yescharacteristic
409C2—21no—
410C2—21no—
411C2—162no—
412C2C11×#200011yescharacteristic
413C2C11×#200411yescharacteristic
414C2C11×#200811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×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×#3078C2semidirect
5. C11×#1503C2semidirect
6. C11×#1479C2semidirect
7. C11×#1303C2semidirect
77. #10250C11direct (N × H)
86. C2×Q8×C11SD16semidirect
135. #3078C2×C11semidirect
138. #1503C2×C11semidirect
139. #1479C2×C11semidirect
140. #1303C2×C11semidirect
292. C2×Q8C11×SD16semidirect
340. C11#10250direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32082
C11×#30782
C11×#25482
C11×#15452
C11×#15032
C11×#14792
C11×#13032
#1025011