Finite Group Databasebeta

← C11×#34044 #14611237

Subgroups — C11×#34044 #14611237

Order 2816.

5406 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×#41C211yesmaximal, characteristic
2C22×C11×#117C212yesmaximal, complemented
3C11×#2311C218yesmaximal, complemented
4C11×#2310C212yesmaximal, complemented
5C11×#2309C212yesmaximal, complemented
6C11×#2308C214yesmaximal, complemented
7C11×#2297C218yesmaximal, complemented
8C11×#2280C214yesmaximal, complemented
9C22×C11×#41—216no—
10C22×C11×#41C4116yescomplemented
11C22×C11×#41C2214yes—
12C22×C11×#41C2214yes—
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×D4×C11C2211yescharacteristic
16C24×C4×C11C2212yes—
17C24×C4×C11C2211yescharacteristic
18C2×C11×#117—216no—
19C2×C11×#117C2214yes—
20C2×C11×#117C2214yes—
21C2×C11×#117C2214yescomplemented
22C2×C11×#117C2214yescomplemented
23C22×C11×C4⋊C4C2214yescomplemented
24C22×C11×C22⋊C4C2214yes—
25C22×C42×C11C2214yescomplemented
26C11×#391C22116yescomplemented
27C11×#390C22116yescomplemented
28C11×#386C22132yescomplemented
29C11×#381C2218yes—
30C11×#380C22116yescomplemented
31C11×#379C2218yes—
32C4×C11×C22⋊C4C22116yescomplemented
33C25×C11C2312yes—
34C25×C11C2311yescharacteristic
35C2×C11×#41—2128no—
36C2×C11×#41—216no—
37C2×C11×#41—216no—
38C2×C11×#41—216no—
39C2×C11×#41—216no—
40C2×C11×#41C2×C4132yescomplemented
41C2×C11×#41C2×C4132yescomplemented
42C22×Q8×C11—28no—
43C22×Q8×C11C2×C418yescomplemented
44C22×Q8×C11C2314yes—
45C22×D4×C11—216no—
46C22×D4×C11—28no—
47C22×D4×C11C2×C4116yes—
48C22×D4×C11C2×C418yescomplemented
49C22×D4×C11C2318yes—
50C22×D4×C11C2314yes—
51C23×C4×C11—216no—
52C23×C4×C11C2×C418yes—
53C23×C4×C11C2×C4116yescomplemented
54C23×C4×C11D4116yes—
55C23×C4×C11C2314yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2314yes—
58C23×C4×C11C2318yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C11×#117—216no—
64C11×#117—216no—
65C11×#117—216no—
66C11×#117—216no—
67C2×C11×C4⋊C4—216no—
68C2×C11×C4⋊C4C2318yes—
69C2×C11×C4⋊C4C2318yes—
70C2×C11×C22⋊C4—216no—
71C2×C11×C22⋊C4C2318yes—
72C2×C11×C22⋊C4C2318yes—
73C2×C11×C22⋊C4C23132yes—
74C2×C42×C11—216no—
75C2×C42×C11C2318yes—
76C2×C42×C11C2318yes—
77C11×#95C23132yes—
78#34044C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—28no—
80C24×C11—44no—
81C24×C11—48no—
82C24×C11C22×C418yes—
83C24×C11C22×C414yes—
84C24×C11C2×D418yes—
85C24×C11C2414yes—
86C24×C11C2411yescharacteristic
87C24×C11C2412yes—
88C11×#41—2128no—
89C11×#41—2128no—
90C2×Q8×C11—232no—
91C2×Q8×C11—28no—
92C2×Q8×C11—28no—
93C2×Q8×C11C22×C4116yes—
94C2×D4×C11—264no—
95C2×D4×C11—216no—
96C2×D4×C11—216no—
97C2×D4×C11—232no—
98C2×D4×C11—28no—
99C2×D4×C11—28no—
100C2×D4×C11C22×C4132yes—
101C2×D4×C11C22×C4116yes—
102C22×C4×C11—28no—
103C22×C4×C11—264no—
104C22×C4×C11—216no—
105C22×C4×C11—216no—
106C22×C4×C11—216no—
107C22×C4×C11—416no—
108C22×C4×C11C22⋊C4164yescomplemented
109C22×C4×C11C22×C418yes—
110C22×C4×C11C22×C4116yes—
111C22×C4×C11C22×C4116yes—
112C22×C4×C11C22×C414yes—
113C22×C4×C11C22×C414yes—
114C22×C4×C11C22×C418yes—
115C22×C4×C11C22×C418yes—
116C22×C4×C11C2×D418yes—
117C22×C4×C11C2×D418yes—
118C22×C4×C11C2×D418yes—
119C22×C4×C11C2×D418yes—
120C22×C4×C11C2×D418yes—
121C22×C4×C11C2×D418yes—
122C22×C4×C11C24116yes—
123C22×C4×C11C2414yes—
124C22×C4×C11C2412yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C11×C4⋊C4—216no—
128C11×C4⋊C4—216no—
129C11×C22⋊C4—216no—
130C11×C22⋊C4—216no—
131C11×C22⋊C4—432no—
132C42×C11—216no—
133C42×C11—216no—
134C23×#41C2×C1111yescharacteristic
135C22×#117C2×C1112yescomplemented
136#2311C2×C1118yescomplemented
137#2310C2×C1112yescomplemented
138#2309C2×C1112yescomplemented
139#2308C2×C1114yescomplemented
140#2297C2×C1118yescomplemented
141#2280C2×C1114yescomplemented
142C23×C11—28no—
143C23×C11—24no—
144C23×C11—216no—
145C23×C11—28no—
146C23×C11—216no—
147C23×C11—48no—
148C23×C11—416no—
149C23×C11—416no—
150C23×C11—432no—
151C23×C11C2×C22⋊C4116yes—
152C23×C11C23×C418yes—
153C23×C11C23×C412yes—
154C23×C11C23×C414yes—
155C23×C11C22×D414yes—
156C23×C11C22×D414yes—
157C23×C11C22×D414yes—
158C23×C11C2511yescharacteristic
159Q8×C11—232no—
160D4×C11—264no—
161D4×C11—232no—
162C2×C4×C11—216no—
163C2×C4×C11—28no—
164C2×C4×C11—232no—
165C2×C4×C11—232no—
166C2×C4×C11—216no—
167C2×C4×C11—232no—
168C2×C4×C11—432no—
169C2×C4×C11C2×C22⋊C4116yes—
170C2×C4×C11C2×C22⋊C4116yes—
171C2×C4×C11C2×C22⋊C4132yes—
172C2×C4×C11C2×C22⋊C4132yes—
173C2×C4×C11C23×C418yes—
174C2×C4×C11C23×C412yes—
175C2×C4×C11C23×C412yes—
176C2×C4×C11C23×C414yes—
177C2×C4×C11C22×D414yes—
178C2×C4×C11C22×D414yes—
179C2×C4×C11C22×D414yes—
180C2×C4×C11C22×D414yes—
181C22×#41—216no—
182C22×#41C4×C11116yescomplemented
183C22×#41C22×C1114yes—
184C22×#41C22×C1114yes—
185C23×Q8C22×C1111yescharacteristic
186C23×D4C22×C1112yes—
187C23×D4C22×C1111yescharacteristic
188C24×C4C22×C1112yes—
189C24×C4C22×C1111yescharacteristic
190C2×#117—216no—
191C2×#117C22×C1114yes—
192C2×#117C22×C1114yes—
193C2×#117C22×C1114yescomplemented
194C2×#117C22×C1114yescomplemented
195C22×C4⋊C4C22×C1114yescomplemented
196C22×C22⋊C4C22×C1114yes—
197C22×C42C22×C1114yescomplemented
198#391C22×C11116yescomplemented
199#390C22×C11116yescomplemented
200#386C22×C11132yescomplemented
201#381C22×C1118yes—
202#380C22×C11116yescomplemented
203#379C22×C1118yes—
204C4×C22⋊C4C22×C11116yescomplemented
205C22×C11—24no—
206C22×C11—28no—
207C22×C11—28no—
208C22×C11—28no—
209C22×C11—28no—
210C22×C11—28no—
211C22×C11—216no—
212C22×C11—416no—
213C22×C11—432no—
214C22×C11—416no—
215C22×C11C22×C22⋊C414yes—
216C22×C11C22×C22⋊C418yes—
217C22×C11C24×C411yescharacteristic
218C22×C11C23×D412yes—
219C22×C11#58514yes—
220C4×C11—28no—
221C4×C11—416no—
222C4×C11C22×C22⋊C414yes—
223C4×C11C22×C22⋊C414yes—
224C4×C11C22×C22⋊C418yes—
225C25C23×C1112yes—
226C25C23×C1111yescharacteristic
227C2×#41—2128no—
228C2×#41—216no—
229C2×#41—216no—
230C2×#41—216no—
231C2×#41—216no—
232C2×#41C2×C4×C11132yescomplemented
233C2×#41C2×C4×C11132yescomplemented
234C22×Q8—28no—
235C22×Q8C2×C4×C1118yescomplemented
236C22×Q8C23×C1114yes—
237C22×D4—216no—
238C22×D4—28no—
239C22×D4C2×C4×C11116yes—
240C22×D4C2×C4×C1118yescomplemented
241C22×D4C23×C1118yes—
242C22×D4C23×C1114yes—
243C23×C4—216no—
244C23×C4C2×C4×C1118yes—
245C23×C4C2×C4×C11116yescomplemented
246C23×C4D4×C11116yes—
247C23×C4C23×C1112yes—
248C23×C4C23×C1114yes—
249C23×C4C23×C1114yes—
250C23×C4C23×C1118yes—
251C23×C4C23×C1112yes—
252C23×C4C23×C1111yescharacteristic
253C23×C4C23×C1111yescharacteristic
254C23×C4C23×C1112yes—
255#117—216no—
256#117—216no—
257#117—216no—
258#117—216no—
259C2×C4⋊C4—216no—
260C2×C4⋊C4C23×C1118yes—
261C2×C4⋊C4C23×C1118yes—
262C2×C22⋊C4—216no—
263C2×C22⋊C4C23×C1118yes—
264C2×C22⋊C4C23×C1118yes—
265C2×C22⋊C4C23×C11132yes—
266C2×C42—216no—
267C2×C42C23×C1118yes—
268C2×C42C23×C1118yes—
269#95C23×C11132yes—
270C2×C11—24no—
271C2×C11—28no—
272C2×C11—48no—
273C2×C11C23×C22⋊C411yescharacteristic
274C2×C11#342812yes—
275C2×C11#344914yes—
276C24—28no—
277C24—44no—
278C24—48no—
279C24C22×C4×C1118yes—
280C24C22×C4×C1114yes—
281C24C2×D4×C1118yes—
282C24C24×C1114yes—
283C24C24×C1111yescharacteristic
284C24C24×C1112yes—
285#41—2128no—
286#41—2128no—
287C2×Q8—232no—
288C2×Q8—28no—
289C2×Q8—28no—
290C2×Q8C22×C4×C11116yes—
291C2×D4—264no—
292C2×D4—216no—
293C2×D4—216no—
294C2×D4—232no—
295C2×D4—28no—
296C2×D4—28no—
297C2×D4C22×C4×C11132yes—
298C2×D4C22×C4×C11116yes—
299C22×C4—28no—
300C22×C4—264no—
301C22×C4—216no—
302C22×C4—216no—
303C22×C4—216no—
304C22×C4—416no—
305C22×C4C11×C22⋊C4164yescomplemented
306C22×C4C22×C4×C1118yes—
307C22×C4C22×C4×C11116yes—
308C22×C4C22×C4×C11116yes—
309C22×C4C22×C4×C1114yes—
310C22×C4C22×C4×C1114yes—
311C22×C4C22×C4×C1118yes—
312C22×C4C22×C4×C1118yes—
313C22×C4C2×D4×C1118yes—
314C22×C4C2×D4×C1118yes—
315C22×C4C2×D4×C1118yes—
316C22×C4C2×D4×C1118yes—
317C22×C4C2×D4×C1118yes—
318C22×C4C2×D4×C1118yes—
319C22×C4C24×C11116yes—
320C22×C4C24×C1114yes—
321C22×C4C24×C1111yescharacteristic
322C22×C4C24×C1112yes—
323C22×C4C24×C1111yescharacteristic
324C4⋊C4—216no—
325C4⋊C4—216no—
326C22⋊C4—216no—
327C22⋊C4—216no—
328C22⋊C4—432no—
329C42—216no—
330C42—216no—
331C11#3404411yescharacteristic, direct product factor, Sylow
332C23—28no—
333C23—24no—
334C23—216no—
335C23—28no—
336C23—216no—
337C23—48no—
338C23—416no—
339C23—416no—
340C23—432no—
341C23C2×C11×C22⋊C4116yes—
342C23C23×C4×C1118yes—
343C23C23×C4×C1112yes—
344C23C23×C4×C1114yes—
345C23C22×D4×C1114yes—
346C23C22×D4×C1114yes—
347C23C22×D4×C1114yes—
348C23C25×C1111yescharacteristic
349Q8—232no—
350D4—264no—
351D4—232no—
352C2×C4—216no—
353C2×C4—28no—
354C2×C4—232no—
355C2×C4—232no—
356C2×C4—216no—
357C2×C4—232no—
358C2×C4—432no—
359C2×C4C2×C11×C22⋊C4116yes—
360C2×C4C2×C11×C22⋊C4116yes—
361C2×C4C2×C11×C22⋊C4132yes—
362C2×C4C2×C11×C22⋊C4132yes—
363C2×C4C23×C4×C1118yes—
364C2×C4C23×C4×C1112yes—
365C2×C4C23×C4×C1112yes—
366C2×C4C23×C4×C1114yes—
367C2×C4C22×D4×C1114yes—
368C2×C4C22×D4×C1114yes—
369C2×C4C22×D4×C1114yes—
370C2×C4C22×D4×C1114yes—
371C22—24no—
372C22—28no—
373C22—28no—
374C22—28no—
375C22—28no—
376C22—28no—
377C22—216no—
378C22—416no—
379C22—432no—
380C22—416no—
381C22C22×C11×C22⋊C414yes—
382C22C22×C11×C22⋊C418yes—
383C22C24×C4×C1111yescharacteristic
384C22C23×D4×C1112yes—
385C22C11×#58514yes—
386C4—28no—
387C4—416no—
388C4C22×C11×C22⋊C414yes—
389C4C22×C11×C22⋊C414yes—
390C4C22×C11×C22⋊C418yes—
391C2—24no—
392C2—28no—
393C2—48no—
394C2C23×C11×C22⋊C411yescharacteristic
395C2C11×#342812yes—
396C2C11×#344914yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC23×C11×#41C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#117C2semidirect
3. C11×#2311C2semidirect
4. C11×#2310C2semidirect
5. C11×#2309C2semidirect
6. C11×#2308C2semidirect
7. C11×#2297C2semidirect
8. C11×#2280C2semidirect
10. C22×C11×#41C4semidirect
21. C2×C11×#117C22semidirect
22. C2×C11×#117C22semidirect
23. C22×C11×C4⋊C4C22semidirect
25. C22×C42×C11C22semidirect
26. C11×#391C22semidirect
27. C11×#390C22semidirect
28. C11×#386C22semidirect
30. C11×#380C22semidirect
32. C4×C11×C22⋊C4C22semidirect
40. C2×C11×#41C2×C4semidirect
41. C2×C11×#41C2×C4semidirect
43. C22×Q8×C11C2×C4semidirect
48. C22×D4×C11C2×C4semidirect
53. C23×C4×C11C2×C4semidirect
78. #34044C11direct (N × H)
108. C22×C4×C11C22⋊C4semidirect
135. C22×#117C2×C11semidirect
136. #2311C2×C11semidirect
137. #2310C2×C11semidirect
138. #2309C2×C11semidirect
139. #2308C2×C11semidirect
140. #2297C2×C11semidirect
141. #2280C2×C11semidirect
182. C22×#41C4×C11semidirect
193. C2×#117C22×C11semidirect
194. C2×#117C22×C11semidirect
195. C22×C4⋊C4C22×C11semidirect
197. C22×C42C22×C11semidirect
198. #391C22×C11semidirect
199. #390C22×C11semidirect
200. #386C22×C11semidirect
202. #380C22×C11semidirect
204. C4×C22⋊C4C22×C11semidirect
232. C2×#41C2×C4×C11semidirect
233. C2×#41C2×C4×C11semidirect
235. C22×Q8C2×C4×C11semidirect
240. C22×D4C2×C4×C11semidirect
245. C23×C4C2×C4×C11semidirect
305. C22×C4C11×C22⋊C4semidirect
331. C11#34044direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×#412
C22×C11×#1172
C11×#23112
C11×#23102
C11×#23092
C11×#23082
C11×#22972
C11×#22802
#3404411