Finite Group Databasebeta

← C11×#22246 #14599439

Subgroups — C11×#22246 #14599439

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#498C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic
3C4×C11×C4⋊Q8C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic
5C11×#1990C211yesmaximal, characteristic
6C11×#1920C214yesmaximal
7C11×#1919C214yesmaximal
8C11×#1834C211yesmaximal, characteristic
9C11×#1744C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11—21no—
13C2×C4×Q8×C11—21no—
14C11×#498C418yescomplemented
15C2×C11×#106C2214yes—
16C2×C4×C8×C11C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C11×#391—21no—
19C11×#391—21no—
20C11×#389—21no—
21C11×#389—21no—
22C11×#389C2212yes—
23C11×#389C2212yes—
24C11×#384C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2212yes—
29C4×C11×C4⋊C4C2212yes—
30C43×C11C2211yescharacteristic
31C11×#340C2214yes—
32C11×#340C2214yes—
33C11×#340C2214yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×C8×C11C2312yes—
39C22×C8×C11C2312yes—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8C2×C414yes—
43C11×C4⋊Q8C2×C414yes—
44C4×Q8×C11—44no—
45C4×Q8×C11—44no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11D411yescharacteristic
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C11×#106C2×C4116yes—
68C4×C8×C11—22no—
69C4×C8×C11C2×C414yes—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—22no—
74#22246C1111yesmaximal, characteristic, direct product factor, Sylow
75C2×Q8×C11—24no—
76C2×Q8×C11—24no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11C22×C414yes—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—44no—
105C11×C4⋊C4—44no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4C22×C414yes—
111C11×C4⋊C4C22×C414yes—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11—22no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—44no—
118C42×C11—44no—
119C42×C11SD1614yes—
120C42×C11C22×C412yes—
121C42×C11#4112yes—
122C2×#498C2×C1111yescharacteristic
123C4×C4⋊Q8C2×C1111yescharacteristic
124C4×C4⋊Q8C2×C1111yescharacteristic
125#1990C2×C1111yescharacteristic
126#1990C2×C1111yescharacteristic
127#1920C2×C1114yes—
128#1919C2×C1114yes—
129#1834C2×C1111yescharacteristic
130#1744C2×C1111yescharacteristic
131C23×C11C22×D411yescharacteristic
132Q8×C11—48no—
133Q8×C11—48no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11C4×D412yes—
157C2×C4×C11C4×D412yes—
158C2×C4×C11C2×SD1612yes—
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11#13512yes—
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×C4×C11#13712yes—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C112−1+412yes—
167C2×C4×C112−1+412yes—
168C8×C11—24no—
169C8×C11—42no—
170C2×C4⋊Q8C22×C1111yescharacteristic
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174#498C4×C1118yescomplemented
175C2×#106C22×C1114yes—
176C2×C4×C8C22×C1111yescharacteristic
177C2×C4×C8C22×C1111yescharacteristic
178#391—21no—
179#391—21no—
180#389—21no—
181#389—21no—
182#389C22×C1112yes—
183#389C22×C1112yes—
184#384C22×C1111yescharacteristic
185#384C22×C1111yescharacteristic
186C4×C4⋊C4—21no—
187C4×C4⋊C4—21no—
188C4×C4⋊C4C22×C1112yes—
189C4×C4⋊C4C22×C1112yes—
190C43C22×C1111yescharacteristic
191#340C22×C1114yes—
192#340C22×C1114yes—
193#340C22×C1114yes—
194#336C22×C1112yes—
195#336C22×C1112yes—
196C22×C11C2×C4×D411yescharacteristic
197C22×C11#53611yescharacteristic
198C22×C11#53611yescharacteristic
199C22×C11C22×SD1611yescharacteristic
200C22×C11C2×#13511yescharacteristic
201C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
202C22×C11C2×#13711yescharacteristic
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—44no—
206C4×C11—44no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—82no—
210C4×C11—82no—
211C4×C11C4×SD1614yes—
212C4×C11#44014yes—
213C4×C11#51912yes—
214C4×C11#54112yes—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×C8C23×C1112yes—
218C22×C8C23×C1112yes—
219C4⋊Q8—22no—
220C4⋊Q8—22no—
221C4⋊Q8C2×C4×C1114yes—
222C4⋊Q8C2×C4×C1114yes—
223C4×Q8—44no—
224C4×Q8—44no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C23×C1112yes—
234C2×C4⋊C4C23×C1112yes—
235C2×C4⋊C4C23×C1112yes—
236C2×C4⋊C4C23×C1112yes—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42D4×C1111yescharacteristic
240C2×C42D4×C1111yescharacteristic
241C2×C42D4×C1111yescharacteristic
242C2×C42D4×C1111yescharacteristic
243C2×C42C23×C1111yescharacteristic
244C2×C42C23×C1111yescharacteristic
245C2×C42C23×C1111yescharacteristic
246#106C2×C4×C11116yes—
247C4×C8—22no—
248C4×C8C2×C4×C1114yes—
249#95—22no—
250#95—22no—
251#95—22no—
252#95—22no—
253C2×C11#232711yescharacteristic
254C2×C11C2×C4×SD1611yescharacteristic
255C2×C11C2×#44011yescharacteristic
256C2×C11#322711yescharacteristic
257C2×C11#322811yescharacteristic
258C2×C11#322911yescharacteristic
259C2×C11#323111yescharacteristic
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—42no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4C2×D4×C1111yescharacteristic
271C22×C4C2×D4×C1111yescharacteristic
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C2×D4×C1111yescharacteristic
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C24×C1111yescharacteristic
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8C22×C4×C1114yes—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4C22×C4×C1114yes—
296C4⋊C4C22×C4×C1114yes—
297C42—22no—
298C42—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—44no—
303C42—44no—
304C42C11×SD1614yes—
305C42C22×C4×C1112yes—
306C42C11×#4112yes—
307C11#2224611yescharacteristic, direct product factor, Sylow
308C23C22×D4×C1111yescharacteristic
309Q8—48no—
310Q8—48no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4C4×D4×C1112yes—
334C2×C4C4×D4×C1112yes—
335C2×C4C2×C11×SD1612yes—
336C2×C4C2×C11×SD1612yes—
337C2×C4C2×C11×SD1612yes—
338C2×C4C11×#13512yes—
339C2×C4C11×AGL(1,ℤ/8)12yes—
340C2×C4C11×#13712yes—
341C2×C4C23×C4×C1111yescharacteristic
342C2×C4C2×C11×#4111yescharacteristic
343C2×C4C11×2−1+412yes—
344C2×C4C11×2−1+412yes—
345C8—24no—
346C8—42no—
347C22C2×C4×D4×C1111yescharacteristic
348C22C11×#53611yescharacteristic
349C22C11×#53611yescharacteristic
350C22C22×C11×SD1611yescharacteristic
351C22C2×C11×#13511yescharacteristic
352C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
353C22C2×C11×#13711yescharacteristic
354C4—22no—
355C4—22no—
356C4—44no—
357C4—44no—
358C4—41no—
359C4—41no—
360C4—82no—
361C4—82no—
362C4C4×C11×SD1614yes—
363C4C11×#44014yes—
364C4C11×#51912yes—
365C4C11×#54112yes—
366C2C11×#232711yescharacteristic
367C2C2×C4×C11×SD1611yescharacteristic
368C2C2×C11×#44011yescharacteristic
369C2C11×#322711yescharacteristic
370C2C11×#322811yescharacteristic
371C2C11×#322911yescharacteristic
372C2C11×#323111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
14. C11×#498C4semidirect
74. #22246C11direct (N × H)
174. #498C4×C11semidirect
307. C11#22246direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C4×C11×C4⋊Q82
C11×#19902
C11×#19202
C11×#19192
C11×#18342
C11×#17442
#2224611