Finite Group Databasebeta

← C11×#21945 #14599138

Subgroups — C11×#21945 #14599138

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#408C211yesmaximal, characteristic
2C11×#2311C212yesmaximal
3C11×#1854C212yesmaximal, complemented
4C11×#1854C212yesmaximal, complemented
5C11×#1853C212yesmaximal, complemented
6C11×#1852C212yesmaximal, complemented
7C11×#1809C212yesmaximal, complemented
8C11×#1808C211yesmaximal, characteristic, complemented
9C11×#1807C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C2×C11×#107C2212yes—
16C2×C11×#107C2212yes—
17C2×C11×#106C2212yes—
18C2×C11×#106C2212yes—
19C11×#408C418yescomplemented
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C11×#391—22no—
23C11×#390—22no—
24C11×#386—22no—
25C11×#386—22no—
26C11×#380C2212yes—
27C11×#380C2212yes—
28C11×#380C2212yes—
29C11×#380C2212yes—
30C11×#340C2211yescharacteristic
31C11×#340C2211yescharacteristic
32C11×#340C2211yescharacteristic
33C11×#340C2211yescharacteristic
34C11×#340C2212yes—
35C11×#340C2212yes—
36C2×C11×#41—42no—
37C2×C11×#41—42no—
38C2×C11×#41C2×C414yes—
39C2×C11×#41Q814yes—
40C22×Q8×C11D411yescharacteristic
41C22×D4×C11D411yescharacteristic
42C22×D4×C11D412yes—
43C23×C4×C11—22no—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—42no—
47C2×C11×M16C2×C414yescomplemented
48C22×C8×C11—42no—
49C22×C8×C11C2×C414yescomplemented
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×#117—42no—
54C11×#117—42no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—42no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—22no—
68C11×#107—42no—
69C11×#107—42no—
70C11×#106—42no—
71C11×#106—42no—
72C11×C22⋊C8C2×C418yescomplemented
73C11×C22⋊C8C2×C418yescomplemented
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78#21945C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D412yes—
81C11×#41—44no—
82C11×#41—44no—
83C11×#41—48no—
84C2×Q8×C11—42no—
85C2×Q8×C11C4⋊C414yes—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11C4⋊C414yes—
90C2×D4×C11C4⋊C418yes—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—44no—
102C22×C4×C11—82no—
103C22×C4×C11—82no—
104C22×C4×C11C22×C414yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×Q814yes—
109C22×C4×C11C2×Q812yes—
110C22×C4×C11C2411yescharacteristic
111C11×M16—44no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—44no—
117C2×C8×C11C22×C412yes—
118C2×C8×C11C22×C412yes—
119C2×C8×C11C22×C414yes—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—44no—
129C11×C22⋊C4—44no—
130C11×C22⋊C4—82no—
131C11×C22⋊C4—82no—
132C11×C22⋊C4—82no—
133C11×C22⋊C4—82no—
134C42×C11—44no—
135C2×#408C2×C1111yescharacteristic
136#2311C2×C1112yes—
137#1854C2×C1112yescomplemented
138#1854C2×C1112yescomplemented
139#1853C2×C1112yescomplemented
140#1852C2×C1112yescomplemented
141#1809C2×C1112yescomplemented
142#1808C2×C1111yescharacteristic, complemented
143#1807C2×C1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—21no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—21no—
153C23×C11—22no—
154C23×C11C2×C4⋊C414yes—
155C23×C11C2×C4⋊C412yes—
156C23×C11C22×D411yescharacteristic
157Q8×C11—44no—
158D4×C11—48no—
159D4×C11—44no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—88no—
183C2×C4×C11C2×C4⋊C414yes—
184C2×C4×C11C2×C4⋊C412yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11H(5,𝔽2)12yes—
188C2×C4×C11H(5,𝔽2)12yes—
189C8×C11—22no—
190C8×C11—22no—
191C8×C11—24no—
192C22×#41C22×C1111yescharacteristic
193C22×M16C22×C1111yescharacteristic
194C23×C8C22×C1111yescharacteristic
195C2×#117C22×C1112yes—
196C22×C4⋊C4C22×C1112yes—
197C2×#107C22×C1112yes—
198C2×#107C22×C1112yes—
199C2×#106C22×C1112yes—
200C2×#106C22×C1112yes—
201#408C4×C1118yescomplemented
202C2×C22⋊C8C22×C1112yes—
203C2×C22⋊C8C22×C1112yes—
204#391—22no—
205#390—22no—
206#386—22no—
207#386—22no—
208#380C22×C1112yes—
209#380C22×C1112yes—
210#380C22×C1112yes—
211#380C22×C1112yes—
212#340C22×C1111yescharacteristic
213#340C22×C1111yescharacteristic
214#340C22×C1111yescharacteristic
215#340C22×C1111yescharacteristic
216#340C22×C1112yes—
217#340C22×C1112yes—
218C22×C11—22no—
219C22×C11—24no—
220C22×C11—22no—
221C22×C11—24no—
222C22×C11—22no—
223C22×C11—24no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11C22×C4⋊C411yescharacteristic
231C22×C11#53412yes—
232C22×C11#57611yescharacteristic
233C22×C11#57712yes—
234C22×C11#57811yescharacteristic
235C4×C11—24no—
236C4×C11—22no—
237C4×C11—82no—
238C4×C11—82no—
239C4×C11—82no—
240C4×C11—82no—
241C4×C11#51811yescharacteristic
242C4×C11#51811yescharacteristic
243C4×C11#54312yes—
244C2×#41—42no—
245C2×#41—42no—
246C2×#41C2×C4×C1114yes—
247C2×#41Q8×C1114yes—
248C22×Q8D4×C1111yescharacteristic
249C22×D4D4×C1111yescharacteristic
250C22×D4D4×C1112yes—
251C23×C4—22no—
252C23×C4C23×C1112yes—
253C23×C4C23×C1111yescharacteristic
254C2×M16—42no—
255C2×M16C2×C4×C1114yescomplemented
256C22×C8—42no—
257C22×C8C2×C4×C1114yescomplemented
258C22×C8C23×C1111yescharacteristic
259C22×C8C23×C1111yescharacteristic
260C22×C8C23×C1112yes—
261#117—42no—
262#117—42no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4C23×C1112yes—
267C2×C4⋊C4C23×C1112yes—
268C2×C4⋊C4C23×C1112yes—
269C2×C4⋊C4C23×C1112yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C42—22no—
276#107—42no—
277#107—42no—
278#106—42no—
279#106—42no—
280C22⋊C8C2×C4×C1118yescomplemented
281C22⋊C8C2×C4×C1118yescomplemented
282#95—22no—
283#95—22no—
284#95—22no—
285#95—22no—
286C2×C11—44no—
287C2×C11—42no—
288C2×C11#231511yescharacteristic
289C2×C11#291211yescharacteristic
290C2×C11#291311yescharacteristic
291C2×C11#319812yes—
292C2×C11#320112yes—
293C24C2×D4×C1111yescharacteristic
294C24C2×D4×C1112yes—
295#41—44no—
296#41—44no—
297#41—48no—
298C2×Q8—42no—
299C2×Q8C11×C4⋊C414yes—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4C11×C4⋊C414yes—
304C2×D4C11×C4⋊C418yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—44no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4C22×C4×C1114yes—
319C22×C4C22×C4×C1112yes—
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1112yes—
322C22×C4C2×Q8×C1114yes—
323C22×C4C2×Q8×C1112yes—
324C22×C4C24×C1111yescharacteristic
325M16—44no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—44no—
331C2×C8C22×C4×C1112yes—
332C2×C8C22×C4×C1112yes—
333C2×C8C22×C4×C1114yes—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—44no—
343C22⋊C4—44no—
344C22⋊C4—82no—
345C22⋊C4—82no—
346C22⋊C4—82no—
347C22⋊C4—82no—
348C42—44no—
349C11#2194511yescharacteristic, direct product factor, Sylow
350C23—22no—
351C23—22no—
352C23—22no—
353C23—21no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—21no—
359C23—22no—
360C23C2×C11×C4⋊C414yes—
361C23C2×C11×C4⋊C412yes—
362C23C22×D4×C1111yescharacteristic
363Q8—44no—
364D4—48no—
365D4—44no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—88no—
389C2×C4C2×C11×C4⋊C414yes—
390C2×C4C2×C11×C4⋊C412yes—
391C2×C4C23×C4×C1111yescharacteristic
392C2×C4C22×Q8×C1111yescharacteristic
393C2×C4C11×H(5,𝔽2)12yes—
394C2×C4C11×H(5,𝔽2)12yes—
395C8—22no—
396C8—22no—
397C8—24no—
398C22—22no—
399C22—24no—
400C22—22no—
401C22—24no—
402C22—22no—
403C22—24no—
404C22—42no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22C22×C11×C4⋊C411yescharacteristic
411C22C11×#53412yes—
412C22C11×#57611yescharacteristic
413C22C11×#57712yes—
414C22C11×#57811yescharacteristic
415C4—24no—
416C4—22no—
417C4—82no—
418C4—82no—
419C4—82no—
420C4—82no—
421C4C11×#51811yescharacteristic
422C4C11×#51811yescharacteristic
423C4C11×#54312yes—
424C2—44no—
425C2—42no—
426C2C11×#231511yescharacteristic
427C2C11×#291211yescharacteristic
428C2C11×#291311yescharacteristic
429C2C11×#319812yes—
430C2C11×#320112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1854C2semidirect
4. C11×#1854C2semidirect
5. C11×#1853C2semidirect
6. C11×#1852C2semidirect
7. C11×#1809C2semidirect
8. C11×#1808C2semidirect
9. C11×#1807C2semidirect
19. C11×#408C4semidirect
47. C2×C11×M16C2×C4semidirect
49. C22×C8×C11C2×C4semidirect
72. C11×C22⋊C8C2×C4semidirect
73. C11×C22⋊C8C2×C4semidirect
78. #21945C11direct (N × H)
137. #1854C2×C11semidirect
138. #1854C2×C11semidirect
139. #1853C2×C11semidirect
140. #1852C2×C11semidirect
141. #1809C2×C11semidirect
142. #1808C2×C11semidirect
143. #1807C2×C11semidirect
201. #408C4×C11semidirect
255. C2×M16C2×C4×C11semidirect
257. C22×C8C2×C4×C11semidirect
280. C22⋊C8C2×C4×C11semidirect
281. C22⋊C8C2×C4×C11semidirect
349. C11#21945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4082
C11×#23112
C11×#18542
C11×#18532
C11×#18522
C11×#18092
C11×#18082
C11×#18072
#2194511