Finite Group Databasebeta

← C11×#23028 #14600221

Subgroups — C11×#23028 #14600221

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic, complemented
3C22×C11×#106C211yesmaximal, characteristic
4C11×#2360C212yesmaximal
5C11×#1971C211yesmaximal, characteristic, complemented
6C11×#1943C211yesmaximal, characteristic, complemented
7C11×#1927C212yesmaximal, complemented
8C11×#1872C212yesmaximal
9C11×#1865C212yesmaximal, complemented
10C11×#1776C211yesmaximal, characteristic, complemented
11C11×#1752C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C11×#467C418yescomplemented
18C11×#441—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106—24no—
21C2×C11×#106C2212yes—
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C11×#391C2212yes—
31C11×#389—22no—
32C11×#389C2212yes—
33C11×#387—22no—
34C11×#385—22no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C22⋊C4—22no—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C22×Q8×C11C2312yes—
43C23×C4×C11—22no—
44C23×C4×C11C2311yescharacteristic
45C2×C11×Q16—22no—
46C2×C11×Q16—22no—
47C2×C11×Q16C2×C414yescomplemented
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11C2×C414yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8C2×C418yes—
57C4×Q8×C11—24no—
58C4×Q8×C11—42no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C11×#107C2×C414yescomplemented
75C11×#106—22no—
76C11×#106—24no—
77C11×#106D414yes—
78C11×#103—24no—
79C11×#103—42no—
80C11×#103C2×C418yescomplemented
81C11×C22⋊C8—22no—
82C11×#97—22no—
83C11×#97—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95D412yes—
89#23028C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11C2×D411yescharacteristic
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11C22×C414yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11—82no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4112yes—
113C22×C4×C11C2411yescharacteristic
114C11×Q16—28no—
115C2×C8×C11—28no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11C22×C412yes—
125C2×C8×C11C22×C412yes—
126C2×C8×C11C2×D412yes—
127C2×C8×C11#4112yes—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—44no—
134C11×C4⋊C4—44no—
135C11×C4⋊C4—82no—
136C11×C4⋊C4C22×C414yes—
137C11×C4⋊C4C2×D414yes—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—24no—
140C42×C11—21no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11—21no—
144C42×C11—44no—
145C42×C11—82no—
146C2×#467C2×C1111yescharacteristic
147C2×#441C2×C1111yescharacteristic, complemented
148C22×#106C2×C1111yescharacteristic
149#2360C2×C1112yes—
150#1971C2×C1111yescharacteristic, complemented
151#1943C2×C1111yescharacteristic, complemented
152#1927C2×C1112yescomplemented
153#1872C2×C1112yes—
154#1865C2×C1112yescomplemented
155#1776C2×C1111yescharacteristic, complemented
156#1752C2×C1111yescharacteristic
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—22no—
160C23×C11C4×D412yes—
161C23×C11#13714yes—
162C23×C11C22×D411yescharacteristic
163Q8×C11—24no—
164Q8×C11—24no—
165Q8×C11—42no—
166Q8×C11—42no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—42no—
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×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C8×C11—22no—
200C8×C11—41no—
201C8×C11—41no—
202C8×C11C4×D414yes—
203C22×Q16C22×C1111yescharacteristic
204C23×C8C22×C1111yescharacteristic
205C2×C22⋊Q8C22×C1112yes—
206C2×C4×Q8C22×C1112yes—
207C22×C4⋊C4C22×C1112yes—
208#467C4×C1118yescomplemented
209#441—24no—
210C2×#107C22×C1111yescharacteristic
211C2×#106—24no—
212C2×#106C22×C1112yes—
213C2×#106C22×C1111yescharacteristic
214C2×#106C22×C1111yescharacteristic
215C2×#103C22×C1112yes—
216C2×#103C22×C1112yes—
217C2×#103C22×C1112yes—
218C2×C22⋊C8C22×C1111yescharacteristic
219C2×#97C22×C1111yescharacteristic
220C2×#97C22×C1111yescharacteristic
221#391C22×C1112yes—
222#389—22no—
223#389C22×C1112yes—
224#387—22no—
225#385—22no—
226C4×C4⋊C4C22×C1112yes—
227C4×C22⋊C4—22no—
228C4×C22⋊C4C22×C1111yescharacteristic
229#340C22×C1112yes—
230#340C22×C1112yes—
231#336C22×C1111yescharacteristic
232#336C22×C1111yescharacteristic
233C22×C11—24no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—24no—
237C22×C11#44114yescomplemented
238C22×C11C2×C4×D411yescharacteristic
239C22×C11D4211yescharacteristic
240C22×C11#54711yescharacteristic
241C22×C11C2×#13712yes—
242C22×C11#57712yes—
243C4×C11—22no—
244C4×C11—42no—
245C4×C11—44no—
246C4×C11—44no—
247C4×C11—42no—
248C4×C11—44no—
249C4×C11—82no—
250C4×C11C2×C4×D411yescharacteristic
251C4×C11#52011yescharacteristic
252C4×C11#54811yescharacteristic
253C4×C11#55311yescharacteristic
254C22×Q8C23×C1112yes—
255C23×C4—22no—
256C23×C4C23×C1111yescharacteristic
257C2×Q16—22no—
258C2×Q16—22no—
259C2×Q16C2×C4×C1114yescomplemented
260C22×C8—22no—
261C22×C8—22no—
262C22×C8C2×C4×C1114yes—
263C22×C8C23×C1111yescharacteristic
264C22×C8C23×C1111yescharacteristic
265C22×C8C23×C1111yescharacteristic
266C22×C8C23×C1111yescharacteristic
267C22⋊Q8—24no—
268C22⋊Q8C2×C4×C1118yes—
269C4×Q8—24no—
270C4×Q8—42no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4C23×C1112yes—
278C2×C4⋊C4C23×C1112yes—
279C2×C4⋊C4C23×C1112yes—
280C2×C22⋊C4—22no—
281C2×C22⋊C4D4×C1112yes—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42C23×C1111yescharacteristic
285C2×C42C23×C1111yescharacteristic
286#107C2×C4×C1114yescomplemented
287#106—22no—
288#106—24no—
289#106D4×C1114yes—
290#103—24no—
291#103—42no—
292#103C2×C4×C1118yescomplemented
293C22⋊C8—22no—
294#97—22no—
295#97—22no—
296#95—22no—
297#95—22no—
298#95—22no—
299#95—22no—
300#95D4×C1112yes—
301C2×C11—24no—
302C2×C11#236111yescharacteristic
303C2×C11C2×#44111yescharacteristic
304C2×C11#295211yescharacteristic
305C2×C11#326612yes—
306C2×C11#334412yes—
307C24C2×D4×C1111yescharacteristic
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—22no—
312C2×Q8—22no—
313C2×Q8C22×C4×C1114yes—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—44no—
323C22×C4—44no—
324C22×C4—82no—
325C22×C4C22×C4×C1112yes—
326C22×C4C2×D4×C1112yes—
327C22×C4C2×D4×C1112yes—
328C22×C4C2×D4×C1111yescharacteristic
329C22×C4C11×#4112yes—
330C22×C4C24×C1111yescharacteristic
331Q16—28no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—28no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8C22×C4×C1112yes—
342C2×C8C22×C4×C1112yes—
343C2×C8C2×D4×C1112yes—
344C2×C8C11×#4112yes—
345C4⋊C4—28no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—44no—
351C4⋊C4—44no—
352C4⋊C4—82no—
353C4⋊C4C22×C4×C1114yes—
354C4⋊C4C2×D4×C1114yes—
355C22⋊C4—28no—
356C22⋊C4—24no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—44no—
362C42—82no—
363C11#2302811yescharacteristic, direct product factor, Sylow
364C23—21no—
365C23—21no—
366C23—22no—
367C23C4×D4×C1112yes—
368C23C11×#13714yes—
369C23C22×D4×C1111yescharacteristic
370Q8—24no—
371Q8—24no—
372Q8—42no—
373Q8—42no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—88no—
399C2×C4C4×D4×C1112yes—
400C2×C4C23×C4×C1111yescharacteristic
401C2×C4C22×D4×C1111yescharacteristic
402C2×C4C2×C11×#4111yescharacteristic
403C2×C4C2×C11×#4111yescharacteristic
404C2×C4C11×H(5,𝔽2)11yescharacteristic
405C2×C4C11×2−1+411yescharacteristic
406C8—22no—
407C8—41no—
408C8—41no—
409C8C4×D4×C1114yes—
410C22—22no—
411C22—24no—
412C22—24no—
413C22—22no—
414C22C11×#44114yescomplemented
415C22C2×C4×D4×C1111yescharacteristic
416C22D42×C1111yescharacteristic
417C22C11×#54711yescharacteristic
418C22C2×C11×#13712yes—
419C22C11×#57712yes—
420C4—22no—
421C4—44no—
422C4—42no—
423C4—44no—
424C4—42no—
425C4—44no—
426C4—82no—
427C4C2×C4×D4×C1111yescharacteristic
428C4C11×#52011yescharacteristic
429C4C11×#54811yescharacteristic
430C4C11×#55311yescharacteristic
431C2—24no—
432C2C11×#236111yescharacteristic
433C2C2×C11×#44111yescharacteristic
434C2C11×#295211yescharacteristic
435C2C11×#326612yes—
436C2C11×#334412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#441C2semidirect
5. C11×#1971C2semidirect
6. C11×#1943C2semidirect
7. C11×#1927C2semidirect
9. C11×#1865C2semidirect
10. C11×#1776C2semidirect
17. C11×#467C4semidirect
47. C2×C11×Q16C2×C4semidirect
74. C11×#107C2×C4semidirect
80. C11×#103C2×C4semidirect
89. #23028C11direct (N × H)
147. C2×#441C2×C11semidirect
150. #1971C2×C11semidirect
151. #1943C2×C11semidirect
152. #1927C2×C11semidirect
154. #1865C2×C11semidirect
155. #1776C2×C11semidirect
208. #467C4×C11semidirect
237. C22×C11#441semidirect
259. C2×Q16C2×C4×C11semidirect
286. #107C2×C4×C11semidirect
292. #103C2×C4×C11semidirect
363. C11#23028direct (N × H)
414. C22C11×#441semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C11×#4412
C22×C11×#1062
C11×#23602
C11×#19712
C11×#19432
C11×#19272
C11×#18722
C11×#18652
C11×#17762
C11×#17522
#2302811