Finite Group Databasebeta

← C11×#9909 #14587102

Subgroups — C11×#9909 #14587102

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2857C211yesmaximal, characteristic
2C11×#1797C211yesmaximal, characteristic
3C4×C11×#95C211yesmaximal, characteristic
4C11×#1294C214yesmaximal
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C22×C42×C11—21no—
8C22×C42×C11C2211yescharacteristic
9C2×C11×C4⋊C8—21no—
10C2×C11×C22⋊C8C2212yes—
11C11×#391—21no—
12C11×#389—21no—
13C11×#389C412yescomplemented
14C11×#384C411yescharacteristic, complemented
15C11×#380—21no—
16C11×#380C2212yes—
17C2×C11×#95—21no—
18C2×C11×#95C2212yes—
19C11×#336—21no—
20C22×Q8×C11—21no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×C8×C11—22no—
26C11×C4⋊Q8—42no—
27C11×C22⋊Q8—42no—
28C11×C22⋊Q8—42no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C22⋊C4—22no—
36C2×C42×C11—24no—
37C2×C42×C11—42no—
38C2×C42×C11—42no—
39C2×C42×C11—42no—
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2×C411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C11×C4⋊C8—42no—
45C11×C22⋊C8—24no—
46C11×#95—24no—
47C11×#95—22no—
48C11×#95—22no—
49C11×#95—22no—
50C11×#95Q814yescomplemented
51#9909C1111yesmaximal, characteristic, direct product factor, Sylow
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—24no—
59C22×C4×C11—24no—
60C22×C4×C11—24no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11D812yes—
77C22×C4×C11SD1612yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×Q812yes—
81C22×C4×C11#4112yes—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C2×C8×C11—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—44no—
90C11×C4⋊C4—42no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11—48no—
98#2857C2×C1111yescharacteristic
99#1797C2×C1111yescharacteristic
100C4×#95C2×C1111yescharacteristic
101#1294C2×C1114yes—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11C22⋊Q812yes—
108C23×C11C2×D811yescharacteristic
109C23×C11C2×SD1611yescharacteristic
110C23×C11#13712yes—
111Q8×C11—84no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—28no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—44no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11#9912yes—
142C2×C4×C11#10212yes—
143C2×C4×C11#10212yes—
144C2×C4×C11#10412yes—
145C2×C4×C11#10412yes—
146C2×C4×C11C4×Q812yes—
147C2×C4×C11#12411yescharacteristic
148C2×C4×C11C4⋊Q811yescharacteristic
149C8×C11—82no—
150C2×C4⋊Q8C4×C1111yescharacteristic, complemented
151C2×C22⋊Q8—21no—
152C22×C42—21no—
153C22×C42C22×C1111yescharacteristic
154C2×C4⋊C8—21no—
155C2×C22⋊C8C22×C1112yes—
156#391—21no—
157#389—21no—
158#389C4×C1112yescomplemented
159#384C4×C1111yescharacteristic, complemented
160#380—21no—
161#380C22×C1112yes—
162C2×#95—21no—
163C2×#95C22×C1112yes—
164#336—21no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11#39111yescharacteristic
174C22×C11C2×#9911yescharacteristic
175C22×C11#41011yescharacteristic
176C22×C11C2×#10211yescharacteristic
177C22×C11#41911yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C22×C11C2×#10411yescharacteristic
180C22×C11#47412yes—
181C22×C11#47512yes—
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—22no—
186C4×C11—22no—
187C4×C11—48no—
188C4×C11—41no—
189C4×C11—82no—
190C4×C11—82no—
191C4×C11#32714yes—
192C22×Q8—21no—
193C23×C4—22no—
194C23×C4D4×C1111yescharacteristic
195C23×C4D4×C1111yescharacteristic
196C23×C4C23×C1111yescharacteristic
197C22×C8—22no—
198C4⋊Q8—42no—
199C22⋊Q8—42no—
200C22⋊Q8—42no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C1112yes—
206C2×C4⋊C4C2×C4×C1112yes—
207C2×C22⋊C4—22no—
208C2×C42—24no—
209C2×C42—42no—
210C2×C42—42no—
211C2×C42—42no—
212C2×C42C2×C4×C1111yescharacteristic
213C2×C42C2×C4×C1111yescharacteristic
214C2×C42D4×C1111yescharacteristic
215C2×C42D4×C1111yescharacteristic
216C4⋊C8—42no—
217C22⋊C8—24no—
218#95—24no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95Q8×C1114yescomplemented
223C2×C11—22no—
224C2×C11—22no—
225C2×C11C2×#32711yescharacteristic
226C2×C11#150211yescharacteristic
227C2×C11#150611yescharacteristic
228C2×C11#150811yescharacteristic
229C2×C11#198811yescharacteristic
230C2×C11#199411yescharacteristic
231C2×C11#199611yescharacteristic
232C24C2×D4×C1111yescharacteristic
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—42no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4C11×C22⋊C411yescharacteristic
253C22×C4C11×C22⋊C411yescharacteristic
254C22×C4C11×C22⋊C411yescharacteristic
255C22×C4C11×C22⋊C411yescharacteristic
256C22×C4C11×D812yes—
257C22×C4C11×SD1612yes—
258C22×C4C22×C4×C1111yescharacteristic
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C2×Q8×C1112yes—
261C22×C4C11×#4112yes—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—44no—
270C4⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—22no—
274C42—22no—
275C42—41no—
276C42—41no—
277C42—48no—
278C11#990911yescharacteristic, direct product factor, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23C2×C11×C22⋊C411yescharacteristic
284C23C11×C22⋊Q812yes—
285C23C2×C11×D811yescharacteristic
286C23C2×C11×SD1611yescharacteristic
287C23C11×#13712yes—
288Q8—84no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—28no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4C11×#9912yes—
319C2×C4C11×#10212yes—
320C2×C4C11×#10212yes—
321C2×C4C11×#10412yes—
322C2×C4C11×#10412yes—
323C2×C4C4×Q8×C1112yes—
324C2×C4C11×#12411yescharacteristic
325C2×C4C11×C4⋊Q811yescharacteristic
326C8—82no—
327C22—22no—
328C22—22no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22C11×#39111yescharacteristic
336C22C2×C11×#9911yescharacteristic
337C22C11×#41011yescharacteristic
338C22C2×C11×#10211yescharacteristic
339C22C11×#41911yescharacteristic
340C22C2×C11×#10411yescharacteristic
341C22C2×C11×#10411yescharacteristic
342C22C11×#47412yes—
343C22C11×#47512yes—
344C4—21no—
345C4—22no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—48no—
350C4—41no—
351C4—82no—
352C4—82no—
353C4C11×#32714yes—
354C2—22no—
355C2—22no—
356C2C2×C11×#32711yescharacteristic
357C2C11×#150211yescharacteristic
358C2C11×#150611yescharacteristic
359C2C11×#150811yescharacteristic
360C2C11×#198811yescharacteristic
361C2C11×#199411yescharacteristic
362C2C11×#199611yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
13. C11×#389C4semidirect
14. C11×#384C4semidirect
50. C11×#95Q8semidirect
51. #9909C11direct (N × H)
150. C2×C4⋊Q8C4×C11semidirect
158. #389C4×C11semidirect
159. #384C4×C11semidirect
222. #95Q8×C11semidirect
278. C11#9909direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28572
C11×#17972
C4×C11×#952
C11×#12942
#990911