Finite Group Databasebeta

← C11×#60688 #14637881

Subgroups — C11×#60688 #14637881

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3444C212yesmaximal, complemented
2C11×#3181C218yesmaximal, complemented
3C11×#3180C218yesmaximal, complemented
4C11×#3162C211yesmaximal, characteristic, complemented
5C11×#3150C211yesmaximal, characteristic, complemented
6C11×#3135C212yesmaximal, complemented
7C11×#3050C214yesmaximal, complemented
8C11×#2943C214yesmaximal, complemented
9C22×C11×#97C211yesmaximal, characteristic, complemented
10C2×C11×#135C2214yes—
11C23×C8×C11C2212yes—
12C11×#533C2214yes—
13C11×#533C2212yes—
14C11×#532C2212yes—
15C11×#532C2214yes—
16C11×#529—24no—
17C11×#529—24no—
18C11×#529C2218yes—
19C11×#525—24no—
20C11×#525C2214yes—
21C4×C11×#41—24no—
22C4×C11×#41C2214yes—
23C22×C42×C11C2211yescharacteristic
24C11×#501C2218yescomplemented
25C11×#497C2214yescomplemented
26C11×#496C2214yescomplemented
27C11×#491C2214yescomplemented
28C11×#490C2214yescomplemented
29C11×#489C2218yescomplemented
30C11×#467C2218yes—
31C11×#466C2218yes—
32C11×#465C22116yes—
33C11×#442C2218yescomplemented
34C11×#441C2218yescomplemented
35C11×#440C22116yescomplemented
36C11×#427C2214yes—
37C11×#416C2218yes—
38C2×C11×#97C2211yescharacteristic
39C2×C11×#97C2218yes—
40C2×C11×#97C2212yes—
41C2×C11×#97C2211yescharacteristic
42C2×C11×#41—24no—
43C2×C11×#41C2314yes—
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C11×#135—216no—
47C2×C11×Q16C2314yes—
48C2×C11×SD16C2318yes—
49C2×C11×D8C2314yes—
50C22×C8×C11—28no—
51C22×C8×C11C2312yes—
52C22×C8×C11C2318yes—
53C22×C8×C11C2312yes—
54C11×C4⋊Q8C2312yes—
55C11×C4⋊Q8C2314yes—
56C11×#127C2312yes—
57C11×#126—28no—
58C11×#125—24no—
59C11×#125C2314yes—
60C11×#124—24no—
61C11×#124C2314yes—
62C11×#123—28no—
63C11×#123—24no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8C2318yes—
67C11×#121—24no—
68C11×#121—24no—
69C11×#121C2318yes—
70C11×#120—24no—
71C4×Q8×C11—24no—
72C4×Q8×C11—24no—
73C4×Q8×C11C2318yes—
74C4×D4×C11—28no—
75C4×D4×C11—28no—
76C4×D4×C11—28no—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C4×D4×C11C2318yes—
80C11×#117—24no—
81C11×#117—28no—
82C11×#117—24no—
83C11×#117C2314yes—
84C2×C42×C11—24no—
85C2×C42×C11D414yes—
86C2×C42×C11D412yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2314yes—
89C2×C42×C11C2311yescharacteristic
90C11×#107C2318yes—
91C11×#106C2318yes—
92C11×#103C23116yes—
93C11×#102C23116yes—
94C11×#97C2314yes—
95C11×#97C2314yes—
96C11×#97C2318yes—
97#60688C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11C2×D411yescharacteristic
99C11×#41—216no—
100C11×#41—416no—
101C2×Q8×C11—24no—
102C2×Q8×C11C2414yes—
103C2×D4×C11—24no—
104C2×D4×C11—28no—
105C2×D4×C11—24no—
106C2×D4×C11C2414yes—
107C22×C4×C11—24no—
108C22×C4×C11—28no—
109C22×C4×C11—24no—
110C22×C4×C11—44no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D414yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D414yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2412yes—
118C22×C4×C11C2411yescharacteristic
119C11×Q16—28no—
120C11×SD16—216no—
121C11×D8—28no—
122C2×C8×C11—216no—
123C2×C8×C11—24no—
124C2×C8×C11#4118yescomplemented
125C2×C8×C11C2414yes—
126C2×C8×C11C2414yes—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4C2418yes—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—28no—
137C11×C22⋊C4—28no—
138C42×C11—28no—
139C42×C11—24no—
140C42×C11C2×D414yes—
141C42×C11C2×D414yes—
142C42×C11C2×D412yes—
143C42×C11C2×D412yes—
144C42×C11C2412yes—
145C42×C11C2412yes—
146#3444C2×C1112yescomplemented
147#3181C2×C1118yescomplemented
148#3180C2×C1118yescomplemented
149#3162C2×C1111yescharacteristic, complemented
150#3150C2×C1111yescharacteristic, complemented
151#3135C2×C1112yescomplemented
152#3050C2×C1114yescomplemented
153#2943C2×C1114yescomplemented
154C22×#97C2×C1111yescharacteristic, complemented
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—24no—
158C23×C11C22×D411yescharacteristic
159C23×C11C22×D412yes—
160Q8×C11—28no—
161Q8×C11—48no—
162D4×C11—28no—
163D4×C11—48no—
164D4×C11—48no—
165D4×C11—416no—
166C2×C4×C11—22no—
167C2×C4×C11—28no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—28no—
172C2×C4×C11—42no—
173C2×C4×C11—44no—
174C2×C4×C11—42no—
175C2×C4×C11—416no—
176C2×C4×C11—48no—
177C2×C4×C11C22×D414yes—
178C2×C4×C11C22×D412yes—
179C2×C4×C11C22×D414yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C2×#4114yes—
182C2×C4×C11C2511yescharacteristic
183C8×C11—24no—
184C8×C11C2×#4118yes—
185C2×#135C22×C1114yes—
186C23×C8C22×C1112yes—
187#533C22×C1114yes—
188#533C22×C1112yes—
189#532C22×C1112yes—
190#532C22×C1114yes—
191#529—24no—
192#529—24no—
193#529C22×C1118yes—
194#525—24no—
195#525C22×C1114yes—
196C4×#41—24no—
197C4×#41C22×C1114yes—
198C22×C42C22×C1111yescharacteristic
199#501C22×C1118yescomplemented
200#497C22×C1114yescomplemented
201#496C22×C1114yescomplemented
202#491C22×C1114yescomplemented
203#490C22×C1114yescomplemented
204#489C22×C1118yescomplemented
205#467C22×C1118yes—
206#466C22×C1118yes—
207#465C22×C11116yes—
208#442C22×C1118yescomplemented
209#441C22×C1118yescomplemented
210#440C22×C11116yescomplemented
211#427C22×C1114yes—
212#416C22×C1118yes—
213C2×#97C22×C1111yescharacteristic
214C2×#97C22×C1111yescharacteristic
215C2×#97C22×C1118yes—
216C2×#97C22×C1112yes—
217C22×C11—28no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—44no—
222C22×C11—48no—
223C22×C11#53212yes—
224C22×C11#57514yes—
225C22×C11C23×D411yescharacteristic
226C4×C11—22no—
227C4×C11—24no—
228C4×C11—24no—
229C4×C11—44no—
230C4×C11—48no—
231C4×C11#53212yes—
232C4×C11C22×#4112yes—
233C2×#41—24no—
234C2×#41C23×C1114yes—
235C23×C4D4×C1112yes—
236C23×C4C23×C1111yescharacteristic
237#135—216no—
238C2×Q16C23×C1114yes—
239C2×SD16C23×C1118yes—
240C2×D8C23×C1114yes—
241C22×C8—28no—
242C22×C8C23×C1112yes—
243C22×C8C23×C1118yes—
244C22×C8C23×C1112yes—
245C4⋊Q8C23×C1112yes—
246C4⋊Q8C23×C1114yes—
247#127C23×C1112yes—
248#126—28no—
249#125—24no—
250#125C23×C1114yes—
251#124—24no—
252#124C23×C1114yes—
253#123—28no—
254#123—24no—
255C22⋊Q8—24no—
256C22⋊Q8—24no—
257C22⋊Q8C23×C1118yes—
258#121—24no—
259#121—24no—
260#121C23×C1118yes—
261#120—24no—
262C4×Q8—24no—
263C4×Q8—24no—
264C4×Q8C23×C1118yes—
265C4×D4—28no—
266C4×D4—28no—
267C4×D4—28no—
268C4×D4—24no—
269C4×D4—24no—
270C4×D4C23×C1118yes—
271#117—24no—
272#117—28no—
273#117—24no—
274#117C23×C1114yes—
275C2×C42—24no—
276C2×C42D4×C1114yes—
277C2×C42D4×C1112yes—
278C2×C42C23×C1111yescharacteristic
279C2×C42C23×C1114yes—
280C2×C42C23×C1111yescharacteristic
281#107C23×C1118yes—
282#106C23×C1118yes—
283#103C23×C11116yes—
284#102C23×C11116yes—
285#97C23×C1118yes—
286#97C23×C1114yes—
287#97C23×C1114yes—
288C2×C11—22no—
289C2×C11—24no—
290C2×C11—84no—
291C2×C11C2×#53211yescharacteristic
292C2×C11C2×#57512yes—
293C24C2×D4×C1111yescharacteristic
294#41—216no—
295#41—416no—
296C2×Q8—24no—
297C2×Q8C24×C1114yes—
298C2×D4—24no—
299C2×D4—28no—
300C2×D4—24no—
301C2×D4C24×C1114yes—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—28no—
305C22×C4—44no—
306C22×C4C2×D4×C1112yes—
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C2×D4×C1114yes—
309C22×C4C2×D4×C1112yes—
310C22×C4C2×D4×C1114yes—
311C22×C4C2×D4×C1112yes—
312C22×C4C24×C1112yes—
313C22×C4C24×C1111yescharacteristic
314Q16—28no—
315SD16—216no—
316D8—28no—
317C2×C8—24no—
318C2×C8—216no—
319C2×C8C11×#4118yescomplemented
320C2×C8C24×C1114yes—
321C2×C8C24×C1114yes—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—28no—
325C4⋊C4—28no—
326C4⋊C4—28no—
327C4⋊C4C24×C1118yes—
328C22⋊C4—28no—
329C22⋊C4—24no—
330C22⋊C4—28no—
331C22⋊C4—28no—
332C22⋊C4—28no—
333C42—28no—
334C42—24no—
335C42C2×D4×C1112yes—
336C42C2×D4×C1114yes—
337C42C2×D4×C1112yes—
338C42C2×D4×C1114yes—
339C42C24×C1112yes—
340C42C24×C1112yes—
341C11#6068811yescharacteristic, direct product factor, Sylow
342C23—22no—
343C23—24no—
344C23—24no—
345C23C22×D4×C1111yescharacteristic
346C23C22×D4×C1112yes—
347Q8—28no—
348Q8—48no—
349D4—28no—
350D4—48no—
351D4—48no—
352D4—416no—
353C2×C4—22no—
354C2×C4—28no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—28no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—416no—
363C2×C4—48no—
364C2×C4C22×D4×C1114yes—
365C2×C4C22×D4×C1112yes—
366C2×C4C22×D4×C1114yes—
367C2×C4C22×D4×C1111yescharacteristic
368C2×C4C2×C11×#4114yes—
369C2×C4C25×C1111yescharacteristic
370C8—24no—
371C8C2×C11×#4118yes—
372C22—28no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—44no—
377C22—48no—
378C22C11×#53212yes—
379C22C11×#57514yes—
380C22C23×D4×C1111yescharacteristic
381C4—22no—
382C4—24no—
383C4—24no—
384C4—44no—
385C4—48no—
386C4C11×#53212yes—
387C4C22×C11×#4112yes—
388C2—22no—
389C2—24no—
390C2—84no—
391C2C2×C11×#53211yescharacteristic
392C2C2×C11×#57512yes—
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3444C2semidirect
2. C11×#3181C2semidirect
3. C11×#3180C2semidirect
4. C11×#3162C2semidirect
5. C11×#3150C2semidirect
6. C11×#3135C2semidirect
7. C11×#3050C2semidirect
8. C11×#2943C2semidirect
9. C22×C11×#97C2semidirect
24. C11×#501C22semidirect
25. C11×#497C22semidirect
26. C11×#496C22semidirect
27. C11×#491C22semidirect
28. C11×#490C22semidirect
29. C11×#489C22semidirect
33. C11×#442C22semidirect
34. C11×#441C22semidirect
35. C11×#440C22semidirect
97. #60688C11direct (N × H)
124. C2×C8×C11#41semidirect
146. #3444C2×C11semidirect
147. #3181C2×C11semidirect
148. #3180C2×C11semidirect
149. #3162C2×C11semidirect
150. #3150C2×C11semidirect
151. #3135C2×C11semidirect
152. #3050C2×C11semidirect
153. #2943C2×C11semidirect
154. C22×#97C2×C11semidirect
199. #501C22×C11semidirect
200. #497C22×C11semidirect
201. #496C22×C11semidirect
202. #491C22×C11semidirect
203. #490C22×C11semidirect
204. #489C22×C11semidirect
208. #442C22×C11semidirect
209. #441C22×C11semidirect
210. #440C22×C11semidirect
319. C2×C8C11×#41semidirect
341. C11#60688direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34442
C11×#31812
C11×#31802
C11×#31622
C11×#31502
C11×#31352
C11×#30502
C11×#29432
C22×C11×#972
#6068811