Finite Group Databasebeta

← C11×#22187 #14599380

Subgroups — C11×#22187 #14599380

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#469C211yesmaximal, characteristic
2C4×C11×#121C212yesmaximal, complemented
3C11×#1926C212yesmaximal, complemented
4C11×#1919C212yesmaximal, complemented
5C11×#1895C212yesmaximal, complemented
6C11×#1879C212yesmaximal, complemented
7C11×#1862C212yesmaximal, complemented
8C11×#1809C211yesmaximal, characteristic, complemented
9C11×#1728C211yesmaximal, characteristic, complemented
10C22×C11×D8C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#121C2212yes—
14C2×C4×D4×C11—22no—
15C2×C4×D4×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C11×#469C418yescomplemented
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C11×#390C2212yes—
25C11×#389C2212yes—
26C11×#388—22no—
27C11×#386—22no—
28C11×#380C2212yes—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C22⋊C4—22no—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×D4×C11—22no—
37C22×D4×C11C2312yes—
38C23×C4×C11—22no—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C2×C11×D8—41no—
43C2×C11×D8—41no—
44C2×C11×D8C2×C414yescomplemented
45C2×C11×M16—22no—
46C2×C11×M16—41no—
47C2×C11×M16—41no—
48C2×C11×M16—41no—
49C2×C11×M16—41no—
50C2×C11×M16C2×C414yescomplemented
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#121—24no—
55C11×#121C2×C418yescomplemented
56C4×D4×C11—42no—
57C4×D4×C11—42no—
58C4×D4×C11—48no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C42×C11—22no—
69C2×C42×C11—41no—
70C2×C42×C11—41no—
71C2×C42×C11D412yes—
72C2×C42×C11C2312yes—
73C11×#107—41no—
74C11×#106—41no—
75C11×#106C2×C414yescomplemented
76C11×#102—42no—
77C11×#102—42no—
78C11×#102C2×C418yescomplemented
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82#22187C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—22no—
84C24×C11C2×D411yescharacteristic
85C2×D4×C11—28no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—44no—
92C2×D4×C11—44no—
93C2×D4×C11C22×C414yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—42no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11—44no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11#4112yes—
113C22×C4×C11C2411yescharacteristic
114C11×D8—44no—
115C11×M16—44no—
116C11×M16—44no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11C22×C412yes—
125C2×C8×C11C22×C412yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4C22×C414yes—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—44no—
135C11×C22⋊C4—44no—
136C11×C22⋊C4—44no—
137C11×C22⋊C4—44no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—42no—
141C42×C11—44no—
142C2×#469C2×C1111yescharacteristic
143C4×#121C2×C1112yescomplemented
144#1926C2×C1112yescomplemented
145#1919C2×C1112yescomplemented
146#1895C2×C1112yescomplemented
147#1879C2×C1112yescomplemented
148#1862C2×C1112yescomplemented
149#1809C2×C1111yescharacteristic, complemented
150#1728C2×C1111yescharacteristic, complemented
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—24no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11C4×D412yes—
163C23×C11C22×D411yescharacteristic
164D4×C11—24no—
165D4×C11—24no—
166D4×C11—416no—
167D4×C11—42no—
168D4×C11—42no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—44no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—88no—
192C2×C4×C11C4×D412yes—
193C2×C4×C11AGL(1,ℤ/8)14yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C11H(5,𝔽2)11yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C8×C11—22no—
201C8×C11—22no—
202C8×C11—42no—
203C22×D8C22×C1111yescharacteristic
204C22×M16C22×C1111yescharacteristic
205C22×M16C22×C1111yescharacteristic
206C2×#121C22×C1112yes—
207C2×C4×D4—22no—
208C2×C4×D4C22×C1112yes—
209C22×C42C22×C1111yescharacteristic
210#469C4×C1118yescomplemented
211C2×#107C22×C1111yescharacteristic
212C2×#106C22×C1111yescharacteristic
213C2×#106C22×C1111yescharacteristic
214C2×#102C22×C1112yes—
215C2×#102C22×C1112yes—
216C2×#102C22×C1112yes—
217#390C22×C1112yes—
218#389C22×C1112yes—
219#388—22no—
220#386—22no—
221#380C22×C1112yes—
222C4×C4⋊C4C22×C1112yes—
223C4×C22⋊C4—22no—
224#340C22×C1112yes—
225#340C22×C1112yes—
226#340C22×C1112yes—
227#336C22×C1112yes—
228#336C22×C1112yes—
229C22×C11—22no—
230C22×C11—24no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—42no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11C2×C4×D411yescharacteristic
242C22×C11#53411yescharacteristic
243C22×C11#53711yescharacteristic
244C22×C11C2×AGL(1,ℤ/8)12yes—
245C22×C11#57512yes—
246C4×C11—22no—
247C4×C11—24no—
248C4×C11—42no—
249C4×C11—44no—
250C4×C11—82no—
251C4×C11—82no—
252C4×C11#51811yescharacteristic
253C4×C11#52011yescharacteristic
254C4×C11#53811yescharacteristic
255C4×C11#53911yescharacteristic
256C22×D4—22no—
257C22×D4C23×C1112yes—
258C23×C4—22no—
259C23×C4D4×C1111yescharacteristic
260C23×C4D4×C1111yescharacteristic
261C23×C4C23×C1111yescharacteristic
262C2×D8—41no—
263C2×D8—41no—
264C2×D8C2×C4×C1114yescomplemented
265C2×M16—22no—
266C2×M16—41no—
267C2×M16—41no—
268C2×M16—41no—
269C2×M16—41no—
270C2×M16C2×C4×C1114yescomplemented
271C22×C8C23×C1112yes—
272C22×C8C23×C1111yescharacteristic
273C22×C8C23×C1111yescharacteristic
274#121—24no—
275#121C2×C4×C1118yescomplemented
276C4×D4—42no—
277C4×D4—42no—
278C4×D4—48no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4C23×C1112yes—
281C2×C4⋊C4C23×C1112yes—
282C2×C4⋊C4C23×C1112yes—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C42—22no—
289C2×C42—41no—
290C2×C42—41no—
291C2×C42D4×C1112yes—
292C2×C42C23×C1112yes—
293#107—41no—
294#106—41no—
295#106C2×C4×C1114yescomplemented
296#102—42no—
297#102—42no—
298#102C2×C4×C1118yescomplemented
299#95—22no—
300#95—22no—
301#95—22no—
302C2×C11—42no—
303C2×C11—84no—
304C2×C11#232511yescharacteristic
305C2×C11C4×AGL(1,ℤ/8)12yes—
306C2×C11#319211yescharacteristic
307C2×C11#319711yescharacteristic
308C2×C11#325112yes—
309C24—22no—
310C24C2×D4×C1111yescharacteristic
311C2×D4—28no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—44no—
318C2×D4—44no—
319C2×D4C22×C4×C1114yes—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4—44no—
332C22×C4—44no—
333C22×C4—44no—
334C22×C4C22×C4×C1112yes—
335C22×C4C2×D4×C1112yes—
336C22×C4C2×D4×C1111yescharacteristic
337C22×C4C2×D4×C1112yes—
338C22×C4C11×#4112yes—
339C22×C4C24×C1111yescharacteristic
340D8—44no—
341M16—44no—
342M16—44no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8C22×C4×C1112yes—
351C2×C8C22×C4×C1112yes—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—44no—
358C4⋊C4C22×C4×C1114yes—
359C22⋊C4—28no—
360C22⋊C4—44no—
361C22⋊C4—44no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C42—22no—
365C42—22no—
366C42—42no—
367C42—44no—
368C11#2218711yescharacteristic, direct product factor, Sylow
369C23—21no—
370C23—21no—
371C23—22no—
372C23—22no—
373C23—24no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—42no—
380C23C4×D4×C1112yes—
381C23C22×D4×C1111yescharacteristic
382D4—24no—
383D4—24no—
384D4—416no—
385D4—42no—
386D4—42no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—88no—
410C2×C4C4×D4×C1112yes—
411C2×C4C11×AGL(1,ℤ/8)14yes—
412C2×C4C23×C4×C1111yescharacteristic
413C2×C4C2×C11×#4111yescharacteristic
414C2×C4C11×H(5,𝔽2)11yescharacteristic
415C2×C4C11×H(5,𝔽2)11yescharacteristic
416C2×C4C11×H(5,𝔽2)11yescharacteristic
417C2×C4C11×2−1+411yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C22—24no—
422C22—22no—
423C22—41no—
424C22—41no—
425C22—42no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22—82no—
433C22C2×C4×D4×C1111yescharacteristic
434C22C11×#53411yescharacteristic
435C22C11×#53711yescharacteristic
436C22C2×C11×AGL(1,ℤ/8)12yes—
437C22C11×#57512yes—
438C4—24no—
439C4—22no—
440C4—42no—
441C4—44no—
442C4—82no—
443C4—82no—
444C4C11×#51811yescharacteristic
445C4C11×#52011yescharacteristic
446C4C11×#53811yescharacteristic
447C4C11×#53911yescharacteristic
448C2—42no—
449C2—84no—
450C2C11×#232511yescharacteristic
451C2C4×C11×AGL(1,ℤ/8)12yes—
452C2C11×#319211yescharacteristic
453C2C11×#319711yescharacteristic
454C2C11×#325112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#469C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#121C2semidirect
3. C11×#1926C2semidirect
4. C11×#1919C2semidirect
5. C11×#1895C2semidirect
6. C11×#1879C2semidirect
7. C11×#1862C2semidirect
8. C11×#1809C2semidirect
9. C11×#1728C2semidirect
17. C11×#469C4semidirect
44. C2×C11×D8C2×C4semidirect
50. C2×C11×M16C2×C4semidirect
55. C11×#121C2×C4semidirect
75. C11×#106C2×C4semidirect
78. C11×#102C2×C4semidirect
82. #22187C11direct (N × H)
143. C4×#121C2×C11semidirect
144. #1926C2×C11semidirect
145. #1919C2×C11semidirect
146. #1895C2×C11semidirect
147. #1879C2×C11semidirect
148. #1862C2×C11semidirect
149. #1809C2×C11semidirect
150. #1728C2×C11semidirect
210. #469C4×C11semidirect
264. C2×D8C2×C4×C11semidirect
270. C2×M16C2×C4×C11semidirect
275. #121C2×C4×C11semidirect
295. #106C2×C4×C11semidirect
298. #102C2×C4×C11semidirect
368. C11#22187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4692
C4×C11×#1212
C11×#19262
C11×#19192
C11×#18952
C11×#18792
C11×#18622
C11×#18092
C11×#17282
#2218711