Finite Group Databasebeta

← C11×#19420 #14596613

Subgroups — C11×#19420 #14596613

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4C11×#2975C211yesmaximal, characteristic, complemented
5C11×#1697C214yesmaximal, complemented
6C11×#1685C214yesmaximal, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C11×#1545C211yesmaximal, characteristic, complemented
9C11×#1542C211yesmaximal, characteristic, complemented
10C22×C11×D8—21no—
11C11×#533C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C11×#492C2212yescomplemented
15C11×#486C2212yescomplemented
16C11×#478—22no—
17C11×#476C2212yescomplemented
18C11×#474C2212yescomplemented
19C11×#460—22no—
20C11×#459—22no—
21C11×#459C2214yes—
22C11×#450—22no—
23C11×#436—22no—
24C11×#436C2214yescomplemented
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C11×#428—21no—
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C11×#418—21no—
31C2×C11×#102—21no—
32C11×#407—22no—
33C11×#335C2214yescomplemented
34C11×#333C2212yescomplemented
35C11×#332C2212yescomplemented
36C11×#331C2214yescomplemented
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C2×C11×SD16—24no—
43C2×C11×D8—24no—
44C2×C11×D8—44no—
45C2×C11×M16—21no—
46C2×C11×M16—24no—
47C22×C8×C11—21no—
48C11×C4⋊Q8C2311yescharacteristic
49C11×C4⋊Q8C2311yescharacteristic
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127C2312yes—
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D412yes—
62C4×D4×C11C2312yes—
63C11×#117—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C11×#107—22no—
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#102—22no—
76C11×#102—22no—
77C11×#102—24no—
78C11×#102—24no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8—24no—
81C11×C22⋊C8D412yes—
82C4×C8×C11—21no—
83C4×C8×C11C2312yes—
84#19420C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—21no—
86C24×C11—41no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
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—
102C2×D4×C11C2×D412yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C11×SD16—84no—
111C11×D8—48no—
112C11×M16—42no—
113C11×M16—84no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D414yes—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4C2×D412yes—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—41no—
130C42×C11—41no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C42×C11C2411yescharacteristic
135#3208C2×C1111yescharacteristic, complemented
136#3077C2×C1111yescharacteristic, complemented
137C2×#459C2×C1111yescharacteristic
138#2975C2×C1111yescharacteristic, complemented
139#1697C2×C1114yescomplemented
140#1685C2×C1114yescomplemented
141#1571C2×C1111yescharacteristic, complemented
142#1545C2×C1111yescharacteristic, complemented
143#1542C2×C1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—81no—
148C23×C11—81no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11#12111yescharacteristic
153Q8×C11—42no—
154Q8×C11—81no—
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—44no—
160D4×C11—42no—
161D4×C11—82no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—44no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—82no—
172C2×C4×C11—81no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11#13712yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C8×C11—24no—
182C8×C11—42no—
183C8×C11—42no—
184C8×C11—42no—
185C22×D8—21no—
186#533C22×C1111yescharacteristic
187C2×#127C22×C1111yescharacteristic
188C2×C4×D4C22×C1111yescharacteristic
189#492C22×C1112yescomplemented
190#486C22×C1112yescomplemented
191#478—22no—
192#476C22×C1112yescomplemented
193#474C22×C1112yescomplemented
194#460—22no—
195#459—22no—
196#459C22×C1114yes—
197#450—22no—
198#436—22no—
199#436C22×C1114yescomplemented
200#431C22×C1111yescharacteristic
201#431C22×C1111yescharacteristic
202#428—21no—
203#423C22×C1111yescharacteristic
204C2×C4⋊C8C22×C1111yescharacteristic
205#418—21no—
206C2×#102—21no—
207#407—22no—
208#335C22×C1114yescomplemented
209#333C22×C1112yescomplemented
210#332C22×C1112yescomplemented
211#331C22×C1114yescomplemented
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—84no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—164no—
222C22×C11#46812yes—
223C22×C11C2×#12111yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11#46812yes—
231C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C11C2×#13711yescharacteristic
233C4×C11#57612yes—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4D4×C1111yescharacteristic
238C23×C4—21no—
239C2×SD16—24no—
240C2×D8—24no—
241C2×D8—44no—
242C2×M16—21no—
243C2×M16—24no—
244C22×C8—21no—
245C4⋊Q8C23×C1111yescharacteristic
246C4⋊Q8C23×C1111yescharacteristic
247#127—21no—
248#127—21no—
249#127—21no—
250#127C23×C1112yes—
251#125—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4D4×C1112yes—
259C4×D4C23×C1112yes—
260#117—21no—
261C2×C4⋊C4D4×C1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C23×C1111yescharacteristic
264#107—22no—
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C1112yes—
269C4⋊C8C23×C1112yes—
270C4⋊C8C23×C1112yes—
271C4⋊C8C23×C1112yes—
272#102—22no—
273#102—22no—
274#102—24no—
275#102—24no—
276C22⋊C8—21no—
277C22⋊C8—24no—
278C22⋊C8D4×C1112yes—
279C4×C8—21no—
280C4×C8C23×C1112yes—
281C2×C11—22no—
282C2×C11—82no—
283C2×C11—162no—
284C2×C11#304111yescharacteristic
285C2×C11C2×#46811yescharacteristic
286C2×C11#306811yescharacteristic
287C24—21no—
288C24—41no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—82no—
303C2×D4—82no—
304C2×D4C2×D4×C1112yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—82no—
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C11×#4111yescharacteristic
312SD16—84no—
313D8—48no—
314M16—42no—
315M16—84no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—42no—
320C2×C8C2×D4×C1114yes—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C2×D4×C1112yes—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C42—41no—
333C42C2×D4×C1111yescharacteristic
334C42C2×D4×C1111yescharacteristic
335C42C11×#4111yescharacteristic
336C42C24×C1111yescharacteristic
337C11#1942011yescharacteristic, direct product factor, Sylow
338C23—22no—
339C23—42no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—82no—
344C23—82no—
345C23—82no—
346C23C11×#12111yescharacteristic
347Q8—42no—
348Q8—81no—
349D4—22no—
350D4—22no—
351D4—42no—
352D4—42no—
353D4—44no—
354D4—42no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—82no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4C11×#12111yescharacteristic
368C2×C4C11×#12111yescharacteristic
369C2×C4C11×#12111yescharacteristic
370C2×C4C11×AGL(1,ℤ/8)12yes—
371C2×C4C11×#13712yes—
372C2×C4C22×D4×C1111yescharacteristic
373C2×C4C22×D4×C1111yescharacteristic
374C2×C4C2×C11×#4111yescharacteristic
375C8—24no—
376C8—42no—
377C8—42no—
378C8—42no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—84no—
385C22—82no—
386C22—82no—
387C22—82no—
388C22—164no—
389C22C11×#46812yes—
390C22C2×C11×#12111yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4C11×#46812yes—
398C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
399C4C2×C11×#13711yescharacteristic
400C4C11×#57612yes—
401C2—22no—
402C2—82no—
403C2—162no—
404C2C11×#304111yescharacteristic
405C2C2×C11×#46811yescharacteristic
406C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#459C2
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
1. C11×#3208C2semidirect
2. C11×#3077C2semidirect
4. C11×#2975C2semidirect
5. C11×#1697C2semidirect
6. C11×#1685C2semidirect
7. C11×#1571C2semidirect
8. C11×#1545C2semidirect
9. C11×#1542C2semidirect
14. C11×#492C22semidirect
15. C11×#486C22semidirect
17. C11×#476C22semidirect
18. C11×#474C22semidirect
24. C11×#436C22semidirect
33. C11×#335C22semidirect
34. C11×#333C22semidirect
35. C11×#332C22semidirect
36. C11×#331C22semidirect
84. #19420C11direct (N × H)
135. #3208C2×C11semidirect
136. #3077C2×C11semidirect
138. #2975C2×C11semidirect
139. #1697C2×C11semidirect
140. #1685C2×C11semidirect
141. #1571C2×C11semidirect
142. #1545C2×C11semidirect
143. #1542C2×C11semidirect
189. #492C22×C11semidirect
190. #486C22×C11semidirect
192. #476C22×C11semidirect
193. #474C22×C11semidirect
199. #436C22×C11semidirect
208. #335C22×C11semidirect
209. #333C22×C11semidirect
210. #332C22×C11semidirect
211. #331C22×C11semidirect
337. C11#19420direct (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×#30772
C2×C11×#4592
C11×#29752
C11×#16972
C11×#16852
C11×#15712
C11×#15452
C11×#15422
#1942011