Finite Group Databasebeta

← C11×#10248 #14587441

Subgroups — C11×#10248 #14587441

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic
4C11×#1548C211yesmaximal, characteristic, complemented
5C11×#1503C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C22⋊Q8—22no—
11C2×C4×D4×C11C2211yescharacteristic
12C11×#494—21no—
13C11×#487—21no—
14C11×#478—22no—
15C11×#476—21no—
16C11×#474—21no—
17C11×#462—22no—
18C11×#451—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#428—21no—
22C11×#423C2211yescharacteristic
23C11×#418—21no—
24C11×#399—22no—
25C11×#390—21no—
26C11×#384—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#333—22no—
29C11×#328—22no—
30C11×D4⋊C8—22no—
31C22×Q8×C11D412yes—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×Q16—24no—
35C2×C11×M16—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—48no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#107—22no—
63C11×#106—22no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C11×#102—22no—
70C11×#102—22no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75C11×#95D412yes—
76#10248C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—44no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11Q1612yescomplemented
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—44no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C11×Q16—84no—
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—48no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—48no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129#3209C2×C1111yescharacteristic, complemented
130#3077C2×C1111yescharacteristic
131#2542C2×C1111yescharacteristic
132#1548C2×C1111yescharacteristic, complemented
133#1503C2×C1111yescharacteristic, complemented
134#1478C2×C1111yescharacteristic
135#1303C2×C1111yescharacteristic, complemented
136C23×C11—22no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142Q8×C11—42no—
143Q8×C11—44no—
144Q8×C11—81no—
145Q8×C11—82no—
146D4×C11—22no—
147D4×C11—22no—
148D4×C11—41no—
149D4×C11—41no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—44no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—82no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C2×C4×C11C2×Q1611yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11#13711yescharacteristic
172C2×C4×C11#13711yescharacteristic
173C8×C11—42no—
174C8×C11—42no—
175C8×C11—81no—
176#533C22×C1111yescharacteristic
177C2×C4⋊Q8C22×C1111yescharacteristic
178C2×C22⋊Q8—22no—
179C2×C4×D4C22×C1111yescharacteristic
180#494—21no—
181#487—21no—
182#478—22no—
183#476—21no—
184#474—21no—
185#462—22no—
186#451—22no—
187#431C22×C1111yescharacteristic
188#431C22×C1111yescharacteristic
189#428—21no—
190#423C22×C1111yescharacteristic
191#418—21no—
192#399—22no—
193#390—21no—
194#384—21no—
195C4×C4⋊C4C22×C1111yescharacteristic
196#333—22no—
197#328—22no—
198D4⋊C8—22no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—44no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#39211yescharacteristic
207C22×C11#45111yescharacteristic
208C22×C11#45211yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—44no—
213C4×C11—81no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#45111yescharacteristic
218C4×C11#45211yescharacteristic
219C4×C11#45312yes—
220C4×C11#46711yescharacteristic
221C4×C11#47011yescharacteristic
222C22×Q8D4×C1112yes—
223C22×D4D4×C1111yescharacteristic
224C23×C4—21no—
225C2×Q16—24no—
226C2×M16—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8D4×C1111yescharacteristic
232C4⋊Q8D4×C1111yescharacteristic
233#125—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—48no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C1111yescharacteristic
249C2×C22⋊C4—24no—
250C2×C22⋊C4—21no—
251C2×C42—21no—
252C2×C42C23×C1111yescharacteristic
253#107—22no—
254#106—22no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8D4×C1112yes—
258C4⋊C8D4×C1112yes—
259#103—24no—
260#102—22no—
261#102—22no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C4×C8—21no—
265C4×C8—21no—
266#95D4×C1112yes—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—82no—
270C2×C11#200111yescharacteristic
271C2×C11#200211yescharacteristic
272C2×C11#200911yescharacteristic
273C24—21no—
274C2×Q8—22no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—44no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4C11×Q1612yescomplemented
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—44no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1111yescharacteristic
294Q16—84no—
295M16—41no—
296M16—41no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—41no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—48no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—48no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C42—41no—
319C42—41no—
320C42—41no—
321C42C2×D4×C1111yescharacteristic
322C42C2×D4×C1111yescharacteristic
323C42C2×D4×C1111yescharacteristic
324C42C11×#4111yescharacteristic
325C11#1024811yescharacteristic, direct product factor, Sylow
326C23—22no—
327C23—42no—
328C23—42no—
329C23—41no—
330C23—41no—
331C23C11×#12011yescharacteristic
332Q8—42no—
333Q8—44no—
334Q8—81no—
335Q8—82no—
336D4—22no—
337D4—22no—
338D4—41no—
339D4—41no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4C11×#12011yescharacteristic
354C2×C4C11×#12011yescharacteristic
355C2×C4C11×#12111yescharacteristic
356C2×C4C11×#12111yescharacteristic
357C2×C4C11×#12111yescharacteristic
358C2×C4C11×#12711yescharacteristic
359C2×C4C2×C11×Q1611yescharacteristic
360C2×C4C11×#13511yescharacteristic
361C2×C4C11×#13711yescharacteristic
362C2×C4C11×#13711yescharacteristic
363C8—42no—
364C8—42no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—42no—
370C22—82no—
371C22—81no—
372C22—81no—
373C22C11×#39211yescharacteristic
374C22C11×#45111yescharacteristic
375C22C11×#45211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—44no—
380C4—81no—
381C4—82no—
382C4—81no—
383C4—81no—
384C4C11×#45111yescharacteristic
385C4C11×#45211yescharacteristic
386C4C11×#45312yes—
387C4C11×#46711yescharacteristic
388C4C11×#47011yescharacteristic
389C2—21no—
390C2—21no—
391C2—82no—
392C2C11×#200111yescharacteristic
393C2C11×#200211yescharacteristic
394C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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
1. C11×#3209C2semidirect
4. C11×#1548C2semidirect
5. C11×#1503C2semidirect
7. C11×#1303C2semidirect
76. #10248C11direct (N × H)
88. C2×D4×C11Q16semidirect
129. #3209C2×C11semidirect
132. #1548C2×C11semidirect
133. #1503C2×C11semidirect
135. #1303C2×C11semidirect
284. C2×D4C11×Q16semidirect
325. C11#10248direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#30772
C11×#25422
C11×#15482
C11×#15032
C11×#14782
C11×#13032
#1024811