Finite Group Databasebeta

← C11×#19432 #14596625

Subgroups — C11×#19432 #14596625

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic
4C11×#2983C211yesmaximal, characteristic, complemented
5C11×#1698C214yesmaximal, complemented
6C11×#1686C214yesmaximal, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C11×#1545C211yesmaximal, characteristic
9C11×#1542C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C11×#533C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C11×#492C2212yes—
15C11×#486C2212yes—
16C11×#479—22no—
17C11×#477C2212yescomplemented
18C11×#475C2212yescomplemented
19C11×#460—22no—
20C11×#460—22no—
21C11×#460C2214yes—
22C11×#450—22no—
23C11×#446—22no—
24C11×#446C2214yescomplemented
25C11×#432—22no—
26C11×#431C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#428—21no—
29C11×#423C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C11×#419—21no—
32C2×C11×#102—21no—
33C11×#335C2214yescomplemented
34C11×#333C2212yescomplemented
35C11×#332C2212yescomplemented
36C11×#331C2214yes—
37C22×Q8×C11D411yescharacteristic
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C2×C11×SD16—24no—
42C2×C11×SD16—24no—
43C2×C11×SD16—44no—
44C2×C11×M16—21no—
45C22×C8×C11—21no—
46C11×C4⋊Q8C2311yescharacteristic
47C11×C4⋊Q8C2311yescharacteristic
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127C2312yes—
52C11×#125—21no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11D412yes—
60C4×Q8×C11C2312yes—
61C11×#117—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C11×#107—22no—
67C11×#106—22no—
68C11×C4⋊C8—24no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—22no—
76C11×#103—22no—
77C11×#102—24no—
78C11×#102—24no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8D412yes—
81C11×#97—24no—
82C4×C8×C11—21no—
83C4×C8×C11C2312yes—
84#19432C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—41no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11C2×D412yes—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—82no—
101C2×D4×C11—82no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C11×SD16—48no—
108C11×SD16—84no—
109C11×M16—42no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—42no—
114C2×C8×C11C2×D414yes—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4C2×D412yes—
125C11×C22⋊C4—41no—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133#3208C2×C1111yescharacteristic
134#3078C2×C1111yescharacteristic, complemented
135C2×#460C2×C1111yescharacteristic
136#2983C2×C1111yescharacteristic, complemented
137#1698C2×C1114yescomplemented
138#1686C2×C1114yescomplemented
139#1571C2×C1111yescharacteristic, complemented
140#1545C2×C1111yescharacteristic
141#1542C2×C1111yescharacteristic, complemented
142C23×C11—42no—
143C23×C11—82no—
144C23×C11—82no—
145C23×C11—82no—
146C23×C11#12111yescharacteristic
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—42no—
150Q8×C11—42no—
151Q8×C11—81no—
152D4×C11—42no—
153D4×C11—42no—
154D4×C11—44no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—82no—
158D4×C11—82no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)12yes—
171C2×C4×C11#13712yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C8×C11—24no—
176C8×C11—42no—
177C8×C11—42no—
178C8×C11—42no—
179C22×SD16—21no—
180#533C22×C1111yescharacteristic
181C2×#127C22×C1111yescharacteristic
182C2×C4×Q8C22×C1111yescharacteristic
183#492C22×C1112yes—
184#486C22×C1112yes—
185#479—22no—
186#477C22×C1112yescomplemented
187#475C22×C1112yescomplemented
188#460—22no—
189#460—22no—
190#460C22×C1114yes—
191#450—22no—
192#446—22no—
193#446C22×C1114yescomplemented
194#432—22no—
195#431C22×C1111yescharacteristic
196#431C22×C1111yescharacteristic
197#428—21no—
198#423C22×C1111yescharacteristic
199C2×C4⋊C8C22×C1111yescharacteristic
200#419—21no—
201C2×#102—21no—
202#335C22×C1114yescomplemented
203#333C22×C1112yescomplemented
204#332C22×C1112yescomplemented
205#331C22×C1114yes—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—164no—
212C22×C11#46812yes—
213C22×C11C2×#12111yescharacteristic
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—42no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11#46812yes—
222C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C11C2×#13711yescharacteristic
224C4×C11#57712yes—
225C22×Q8D4×C1111yescharacteristic
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C2×SD16—24no—
230C2×SD16—24no—
231C2×SD16—44no—
232C2×M16—21no—
233C22×C8—21no—
234C4⋊Q8C23×C1111yescharacteristic
235C4⋊Q8C23×C1111yescharacteristic
236#127—21no—
237#127—21no—
238#127—21no—
239#127C23×C1112yes—
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8D4×C1112yes—
248C4×Q8C23×C1112yes—
249#117—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C1111yescharacteristic
252C2×C42—21no—
253C2×C42C23×C1111yescharacteristic
254#107—22no—
255#106—22no—
256C4⋊C8—24no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C1112yes—
260C4⋊C8C23×C1112yes—
261C4⋊C8C23×C1112yes—
262C4⋊C8C23×C1112yes—
263#103—22no—
264#103—22no—
265#102—24no—
266#102—24no—
267C22⋊C8—21no—
268C22⋊C8D4×C1112yes—
269#97—24no—
270C4×C8—21no—
271C4×C8C23×C1112yes—
272C2×C11—22no—
273C2×C11—162no—
274C2×C11#304311yescharacteristic
275C2×C11C2×#46811yescharacteristic
276C2×C11#306811yescharacteristic
277C24—41no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8C2×D4×C1112yes—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—82no—
293C2×D4—82no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C11×#4111yescharacteristic
299SD16—48no—
300SD16—84no—
301M16—42no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—42no—
306C2×C8C2×D4×C1114yes—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4C2×D4×C1112yes—
317C22⋊C4—41no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42C2×D4×C1111yescharacteristic
322C42C2×D4×C1111yescharacteristic
323C42C11×#4111yescharacteristic
324C42C24×C1111yescharacteristic
325C11#1943211yescharacteristic, direct product factor, Sylow
326C23—42no—
327C23—82no—
328C23—82no—
329C23—82no—
330C23C11×#12111yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—42no—
334Q8—42no—
335Q8—81no—
336D4—42no—
337D4—42no—
338D4—44no—
339D4—82no—
340D4—82no—
341D4—82no—
342D4—82no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4C11×#12111yescharacteristic
352C2×C4C11×#12111yescharacteristic
353C2×C4C11×#12111yescharacteristic
354C2×C4C11×AGL(1,ℤ/8)12yes—
355C2×C4C11×#13712yes—
356C2×C4C22×D4×C1111yescharacteristic
357C2×C4C22×D4×C1111yescharacteristic
358C2×C4C2×C11×#4111yescharacteristic
359C8—24no—
360C8—42no—
361C8—42no—
362C8—42no—
363C22—21no—
364C22—21no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—164no—
369C22C11×#46812yes—
370C22C2×C11×#12111yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4C11×#46812yes—
379C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
380C4C2×C11×#13711yescharacteristic
381C4C11×#57712yes—
382C2—22no—
383C2—162no—
384C2C11×#304311yescharacteristic
385C2C2×C11×#46811yescharacteristic
386C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ 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
4. C11×#2983C2semidirect
5. C11×#1698C2semidirect
6. C11×#1686C2semidirect
7. C11×#1571C2semidirect
9. C11×#1542C2semidirect
17. C11×#477C22semidirect
18. C11×#475C22semidirect
24. C11×#446C22semidirect
33. C11×#335C22semidirect
34. C11×#333C22semidirect
35. C11×#332C22semidirect
84. #19432C11direct (N × H)
134. #3078C2×C11semidirect
136. #2983C2×C11semidirect
137. #1698C2×C11semidirect
138. #1686C2×C11semidirect
139. #1571C2×C11semidirect
141. #1542C2×C11semidirect
186. #477C22×C11semidirect
187. #475C22×C11semidirect
193. #446C22×C11semidirect
202. #335C22×C11semidirect
203. #333C22×C11semidirect
204. #332C22×C11semidirect
325. C11#19432direct (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
C2×C11×#4602
C11×#29832
C11×#16982
C11×#16862
C11×#15712
C11×#15452
C11×#15422
#1943211