Finite Group Databasebeta

← C11×#60620 #14637813

Subgroups — C11×#60620 #14637813

Order 2816.

2014 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×#3458C211yesmaximal, characteristic, complemented
2C2×C11×#536C211yesmaximal, characteristic
3C11×#3140C214yesmaximal, complemented
4C11×#3139C214yesmaximal, complemented
5C11×#3137C2116yesmaximal, complemented
6C11×#2896C212yesmaximal
7C2×C11×#419C212yesmaximal, complemented
8C11×#2873C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×M16C2212yes—
12C11×#544—22no—
13C11×#544C2218yescomplemented
14C11×#543—22no—
15C11×#536—24no—
16C11×#536C2218yes—
17C11×#533—24no—
18C11×#533C2214yes—
19C2×C11×C4⋊Q8C2212yes—
20C2×C11×#124C2212yes—
21C2×C11×#123—22no—
22C2×C11×C22⋊Q8—22no—
23C2×C11×#117C2212yes—
24C2×C11×#117C2211yescharacteristic
25C11×#491C22116yescomplemented
26C11×#489C22116yescomplemented
27C11×#488C22116yescomplemented
28C11×#487C22116yescomplemented
29C11×#419C2218yes—
30C11×#419C2214yes—
31C11×#419C2218yescomplemented
32C11×#418C2214yes—
33C11×#417C2218yes—
34C11×#416C2218yes—
35C2×C11×#103C2218yescomplemented
36C11×#405C2218yescomplemented
37C4×C11×M16C2214yes—
38C2×C11×#41—22no—
39C2×C11×#41—28no—
40C2×C11×#41C2314yes—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—28no—
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×Q8×C11C2314yes—
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16—28no—
53C2×C11×M16C2314yes—
54C2×C11×M16C2314yes—
55C22×C8×C11C2314yes—
56C11×C4⋊Q8—28no—
57C11×C4⋊Q8—24no—
58C11×C4⋊Q8C2318yes—
59C11×C4⋊Q8C2318yes—
60C11×#125—28no—
61C11×#125C2318yes—
62C11×#124—24no—
63C11×#124C2318yes—
64C11×#123—216no—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8—216no—
67C11×C22⋊Q8—216no—
68C4×Q8×C11—28no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117D414yes—
72C11×#117C2314yes—
73C11×#117C2314yes—
74C11×#117C2314yes—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4D412yes—
81C2×C42×C11—22no—
82C2×C42×C11C2312yes—
83C11×#103C23132yes—
84C11×#103C23116yes—
85C11×#102C23116yes—
86C11×#97C2318yes—
87C4×C8×C11C2318yes—
88#60620C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—21no—
90C24×C11C2×D411yescharacteristic
91C11×#41—28no—
92C11×#41—28no—
93C11×#41—48no—
94C2×Q8×C11—24no—
95C2×Q8×C11—22no—
96C2×Q8×C11—21no—
97C2×Q8×C11—28no—
98C2×Q8×C11—28no—
99C2×Q8×C11—28no—
100C2×Q8×C11—28no—
101C2×Q8×C11—24no—
102C2×Q8×C11—44no—
103C2×Q8×C11—48no—
104C2×Q8×C11C2414yes—
105C2×Q8×C11C2412yes—
106C2×D4×C11—24no—
107C2×D4×C11—21no—
108C2×D4×C11—24no—
109C2×D4×C11—44no—
110C2×D4×C11C2412yes—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4118yes—
122C22×C4×C11C2411yescharacteristic
123C22×C4×C11C2412yes—
124C11×M16—28no—
125C11×M16—28no—
126C2×C8×C11—28no—
127C2×C8×C11C2418yes—
128C11×C4⋊C4—216no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—216no—
132C11×C4⋊C4C2×D418yes—
133C11×C4⋊C4C2418yes—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—216no—
137C11×C22⋊C4C2×D418yes—
138C42×C11—24no—
139C42×C11—24no—
140C42×C11C2×D414yes—
141C42×C11C2414yes—
142#3458C2×C1111yescharacteristic, complemented
143C2×#536C2×C1111yescharacteristic
144#3140C2×C1114yescomplemented
145#3139C2×C1114yescomplemented
146#3137C2×C11116yescomplemented
147#2896C2×C1112yes—
148C2×#419C2×C1112yescomplemented
149#2873C2×C1111yescharacteristic, complemented
150C23×C11—22no—
151C23×C11—42no—
152C23×C11—44no—
153C23×C11—42no—
154C23×C11#12414yes—
155C23×C11C22×D411yescharacteristic
156C23×C11C22×D412yes—
157Q8×C11—28no—
158Q8×C11—24no—
159Q8×C11—48no—
160Q8×C11—44no—
161Q8×C11—42no—
162Q8×C11—88no—
163D4×C11—24no—
164D4×C11—48no—
165D4×C11—42no—
166C2×C4×C11—28no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—44no—
170C2×C4×C11—42no—
171C2×C4×C11—44no—
172C2×C4×C11—48no—
173C2×C4×C11—48no—
174C2×C4×C11—84no—
175C2×C4×C11#12414yes—
176C2×C4×C11#12418yes—
177C2×C4×C11C22×D418yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D412yes—
180C2×C4×C11C2×#4114yes—
181C2×C4×C11C2×#4114yes—
182C2×C4×C11C2×#4114yes—
183C2×C4×C11C2511yescharacteristic
184C8×C11—28no—
185C22×#41C22×C1111yescharacteristic
186C23×Q8C22×C1111yescharacteristic
187C22×M16C22×C1112yes—
188#544—22no—
189#544C22×C1118yescomplemented
190#543—22no—
191#536—24no—
192#536C22×C1118yes—
193#533—24no—
194#533C22×C1114yes—
195C2×C4⋊Q8C22×C1112yes—
196C2×#124C22×C1112yes—
197C2×#123—22no—
198C2×C22⋊Q8—22no—
199C2×#117C22×C1112yes—
200C2×#117C22×C1111yescharacteristic
201#491C22×C11116yescomplemented
202#489C22×C11116yescomplemented
203#488C22×C11116yescomplemented
204#487C22×C11116yescomplemented
205#419C22×C1114yes—
206#419C22×C1118yes—
207#419C22×C1118yescomplemented
208#418C22×C1114yes—
209#417C22×C1118yes—
210#416C22×C1118yes—
211C2×#103C22×C1118yescomplemented
212#405C22×C1118yescomplemented
213C4×M16C22×C1114yes—
214C22×C11—22no—
215C22×C11—24no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—42no—
219C22×C11—84no—
220C22×C11C2×#12412yes—
221C22×C11C2×#12414yes—
222C22×C11C23×D411yescharacteristic
223C4×C11—28no—
224C4×C11—48no—
225C4×C11—42no—
226C4×C11—44no—
227C4×C11C2×#12414yes—
228C4×C11C2×#12412yes—
229C4×C11C22×#4112yes—
230C2×#41—22no—
231C2×#41—28no—
232C2×#41C23×C1114yes—
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—28no—
236C22×Q8C23×C1112yes—
237C22×Q8C23×C1111yescharacteristic
238C22×Q8C23×C1114yes—
239C22×D4—21no—
240C22×D4C23×C1111yescharacteristic
241C23×C4—21no—
242C23×C4—21no—
243C23×C4C23×C1111yescharacteristic
244C2×M16—28no—
245C2×M16C23×C1114yes—
246C2×M16C23×C1114yes—
247C22×C8C23×C1114yes—
248C4⋊Q8—28no—
249C4⋊Q8—24no—
250C4⋊Q8C23×C1118yes—
251C4⋊Q8C23×C1118yes—
252#125—28no—
253#125C23×C1118yes—
254#124—24no—
255#124C23×C1118yes—
256#123—216no—
257C22⋊Q8—28no—
258C22⋊Q8—216no—
259C22⋊Q8—216no—
260C4×Q8—28no—
261#117—22no—
262#117—22no—
263#117D4×C1114yes—
264#117C23×C1114yes—
265#117C23×C1114yes—
266#117C23×C1114yes—
267C2×C4⋊C4—24no—
268C2×C4⋊C4D4×C1112yes—
269C2×C4⋊C4C23×C1114yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4D4×C1112yes—
273C2×C42—22no—
274C2×C42C23×C1112yes—
275#103C23×C11132yes—
276#103C23×C11116yes—
277#102C23×C11116yes—
278#97C23×C1118yes—
279C4×C8C23×C1118yes—
280C2×C11—22no—
281C2×C11—24no—
282C2×C11—82no—
283C2×C11C22×#12411yescharacteristic
284C2×C11#358612yes—
285C24—21no—
286C24C2×D4×C1111yescharacteristic
287#41—28no—
288#41—28no—
289#41—48no—
290C2×Q8—24no—
291C2×Q8—22no—
292C2×Q8—21no—
293C2×Q8—28no—
294C2×Q8—28no—
295C2×Q8—28no—
296C2×Q8—28no—
297C2×Q8—24no—
298C2×Q8—44no—
299C2×Q8—48no—
300C2×Q8C24×C1114yes—
301C2×Q8C24×C1112yes—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—24no—
305C2×D4—44no—
306C2×D4C24×C1112yes—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—44no—
313C22×C4—44no—
314C22×C4C2×D4×C1114yes—
315C22×C4C2×D4×C1112yes—
316C22×C4C2×D4×C1111yescharacteristic
317C22×C4C11×#4118yes—
318C22×C4C24×C1111yescharacteristic
319C22×C4C24×C1112yes—
320M16—28no—
321M16—28no—
322C2×C8—28no—
323C2×C8C24×C1118yes—
324C4⋊C4—216no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—216no—
328C4⋊C4C2×D4×C1118yes—
329C4⋊C4C24×C1118yes—
330C22⋊C4—24no—
331C22⋊C4—24no—
332C22⋊C4—216no—
333C22⋊C4C2×D4×C1118yes—
334C42—24no—
335C42—24no—
336C42C2×D4×C1114yes—
337C42C24×C1114yes—
338C11#6062011yescharacteristic, direct product factor, Sylow
339C23—22no—
340C23—42no—
341C23—44no—
342C23—42no—
343C23C11×#12414yes—
344C23C22×D4×C1111yescharacteristic
345C23C22×D4×C1112yes—
346Q8—28no—
347Q8—24no—
348Q8—48no—
349Q8—44no—
350Q8—42no—
351Q8—88no—
352D4—24no—
353D4—48no—
354D4—42no—
355C2×C4—28no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—48no—
362C2×C4—48no—
363C2×C4—84no—
364C2×C4C11×#12414yes—
365C2×C4C11×#12418yes—
366C2×C4C22×D4×C1118yes—
367C2×C4C22×D4×C1111yescharacteristic
368C2×C4C22×D4×C1112yes—
369C2×C4C2×C11×#4114yes—
370C2×C4C2×C11×#4114yes—
371C2×C4C2×C11×#4114yes—
372C2×C4C25×C1111yescharacteristic
373C8—28no—
374C22—22no—
375C22—24no—
376C22—44no—
377C22—42no—
378C22—44no—
379C22—84no—
380C22C2×C11×#12412yes—
381C22C2×C11×#12414yes—
382C22C23×D4×C1111yescharacteristic
383C4—28no—
384C4—42no—
385C4—44no—
386C4—48no—
387C4C2×C11×#12414yes—
388C4C2×C11×#12412yes—
389C4C22×C11×#4112yes—
390C2—22no—
391C2—24no—
392C2—82no—
393C2C22×C11×#12411yescharacteristic
394C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3458C2semidirect
3. C11×#3140C2semidirect
4. C11×#3139C2semidirect
5. C11×#3137C2semidirect
7. C2×C11×#419C2semidirect
8. C11×#2873C2semidirect
13. C11×#544C22semidirect
25. C11×#491C22semidirect
26. C11×#489C22semidirect
27. C11×#488C22semidirect
28. C11×#487C22semidirect
31. C11×#419C22semidirect
35. C2×C11×#103C22semidirect
36. C11×#405C22semidirect
88. #60620C11direct (N × H)
142. #3458C2×C11semidirect
144. #3140C2×C11semidirect
145. #3139C2×C11semidirect
146. #3137C2×C11semidirect
148. C2×#419C2×C11semidirect
149. #2873C2×C11semidirect
189. #544C22×C11semidirect
201. #491C22×C11semidirect
202. #489C22×C11semidirect
203. #488C22×C11semidirect
204. #487C22×C11semidirect
207. #419C22×C11semidirect
211. C2×#103C22×C11semidirect
212. #405C22×C11semidirect
338. C11#60620direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34582
C2×C11×#5362
C11×#31402
C11×#31392
C11×#31372
C11×#28962
C2×C11×#4192
C11×#28732
#6062011