Finite Group Databasebeta

← C11×#23988 #14601181

Subgroups — C11×#23988 #14601181

Order 2816.

1466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3491C211yesmaximal, characteristic, complemented
2C11×#2613C212yesmaximal, complemented
3C11×#2309C211yesmaximal, characteristic, complemented
4C11×#2029C212yesmaximal, complemented
5C11×#2021C212yesmaximal, complemented
6C11×#1899C212yesmaximal, complemented
7C11×#1889C214yesmaximal, complemented
8C11×#1820C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C11×#552—24no—
11C11×#551—24no—
12C11×#543C2211yescharacteristic
13C11×#539—22no—
14C11×#534C2211yescharacteristic
15C11×#529—22no—
16C2×C11×#123C2212yes—
17C2×C11×#120C2214yes—
18C11×#518C2212yes—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#99C2214yes—
22C11×#394—24no—
23C11×#392—24no—
24C11×#390—22no—
25C11×#390—22no—
26C11×#381C2212yes—
27C11×#379C2212yes—
28C11×#379C2214yes—
29C11×#379C2212yes—
30C11×#342C2212yes—
31C11×#342C2214yes—
32C11×#342C2212yes—
33C25×C11C2312yes—
34C22×D4×C11—24no—
35C22×D4×C11—24no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—24no—
39C22×D4×C11—42no—
40C22×D4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C11×#126—24no—
43C11×#126—24no—
44C11×#125—22no—
45C11×#125—24no—
46C11×#124—22no—
47C11×#123—24no—
48C11×#123—22no—
49C11×#123—22no—
50C11×#123—24no—
51C11×#123—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×#121—22no—
56C11×#120—22no—
57C11×#120—28no—
58C11×#120—44no—
59C4×Q8×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—24no—
62C4×D4×C11—24no—
63C11×#117—24no—
64C11×#117—24no—
65C11×#117—22no—
66C11×#117—42no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D412yescomplemented
69C2×C11×C4⋊C4D414yescomplemented
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4D414yescomplemented
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2312yes—
78C2×C11×C22⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4C2312yes—
81C2×C42×C11—21no—
82C2×C42×C11D412yescomplemented
83C11×#99—44no—
84C11×#95—24no—
85#23988C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11—22no—
87C24×C11—24no—
88C24×C11—22no—
89C24×C11—24no—
90C24×C11—84no—
91C24×C11C2×D412yes—
92C24×C11#4114yes—
93C24×C11C2411yescharacteristic
94C2×Q8×C11—22no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—416no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—48no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—88no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D414yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D414yes—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—42no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—48no—
141C11×C22⋊C4—84no—
142C11×C22⋊C4—84no—
143C11×C22⋊C4—88no—
144C42×C11—24no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—42no—
148#3491C2×C1111yescharacteristic, complemented
149#2613C2×C1112yescomplemented
150#2309C2×C1111yescharacteristic, complemented
151#2029C2×C1112yescomplemented
152#2021C2×C1112yescomplemented
153#1899C2×C1112yescomplemented
154#1889C2×C1114yescomplemented
155#1820C2×C1111yescharacteristic, complemented
156C23×C11—22no—
157C23×C11—24no—
158C23×C11—28no—
159C23×C11—24no—
160C23×C11—42no—
161C23×C11—44no—
162C23×C11—44no—
163C23×C11—48no—
164C23×C11—48no—
165C23×C11—44no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—44no—
169C23×C11—84no—
170C23×C11—84no—
171C23×C11—88no—
172C23×C11C22×D411yescharacteristic
173C23×C11C22×D412yes—
174C23×C11C2×#4112yes—
175C23×C11H(5,𝔽2)12yes—
176Q8×C11—82no—
177D4×C11—48no—
178D4×C11—48no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—44no—
182D4×C11—82no—
183D4×C11—816no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—28no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—42no—
195C2×C4×C11—44no—
196C2×C4×C11—42no—
197C2×C4×C11—44no—
198C2×C4×C11—48no—
199C2×C4×C11—42no—
200C2×C4×C11—44no—
201C2×C4×C11—84no—
202C2×C4×C11#12012yes—
203C2×C4×C11#12012yes—
204C23×D4C22×C1111yescharacteristic
205#552—24no—
206#551—24no—
207#543C22×C1111yescharacteristic
208#539—22no—
209#534C22×C1111yescharacteristic
210#529—22no—
211C2×#123C22×C1112yes—
212C2×#120C22×C1114yes—
213#518C22×C1112yes—
214C2×#117C22×C1111yescharacteristic
215C2×#117C22×C1111yescharacteristic
216C2×#99C22×C1114yes—
217#394—24no—
218#392—24no—
219#390—22no—
220#390—22no—
221#381C22×C1112yes—
222#379C22×C1112yes—
223#379C22×C1112yes—
224#379C22×C1114yes—
225#342C22×C1112yes—
226#342C22×C1112yes—
227#342C22×C1114yes—
228C22×C11—22no—
229C22×C11—24no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—48no—
233C22×C11—48no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—84no—
240C22×C11—84no—
241C22×C11—88no—
242C22×C11—84no—
243C22×C11C2×#12011yescharacteristic
244C22×C11#52511yescharacteristic
245C22×C11#53511yescharacteristic
246C22×C11#54614yes—
247C4×C11—22no—
248C4×C11—22no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—44no—
252C4×C11—42no—
253C4×C11—82no—
254C4×C11—84no—
255C25C23×C1112yes—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—24no—
261C22×D4—42no—
262C22×D4C23×C1112yes—
263C23×C4C23×C1111yescharacteristic
264#126—24no—
265#126—24no—
266#125—22no—
267#125—24no—
268#124—22no—
269#123—24no—
270#123—22no—
271#123—22no—
272#123—24no—
273#123—22no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277#121—22no—
278#120—22no—
279#120—28no—
280#120—44no—
281C4×Q8—22no—
282C4×D4—22no—
283C4×D4—24no—
284C4×D4—24no—
285#117—24no—
286#117—24no—
287#117—22no—
288#117—42no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4D4×C1112yescomplemented
291C2×C4⋊C4D4×C1114yescomplemented
292C2×C22⋊C4—22no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4D4×C1114yescomplemented
298C2×C22⋊C4C23×C1112yes—
299C2×C22⋊C4C23×C1114yes—
300C2×C22⋊C4C23×C1111yescharacteristic
301C2×C22⋊C4C23×C1111yescharacteristic
302C2×C22⋊C4C23×C1112yes—
303C2×C42—21no—
304C2×C42D4×C1112yescomplemented
305#99—44no—
306#95—24no—
307C2×C11—21no—
308C2×C11—24no—
309C2×C11—21no—
310C2×C11—84no—
311C2×C11—82no—
312C2×C11#240411yescharacteristic
313C2×C11#302712yes—
314C24—22no—
315C24—24no—
316C24—22no—
317C24—24no—
318C24—84no—
319C24C2×D4×C1112yes—
320C24C11×#4114yes—
321C24C24×C1111yescharacteristic
322C2×Q8—22no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—416no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—48no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—88no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4C2×D4×C1112yes—
343C22×C4C2×D4×C1114yes—
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1112yes—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1114yes—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—42no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—48no—
369C22⋊C4—84no—
370C22⋊C4—84no—
371C22⋊C4—88no—
372C42—24no—
373C42—22no—
374C42—22no—
375C42—42no—
376C11#2398811yescharacteristic, direct product factor, Sylow
377C23—22no—
378C23—24no—
379C23—28no—
380C23—24no—
381C23—42no—
382C23—44no—
383C23—44no—
384C23—48no—
385C23—48no—
386C23—44no—
387C23—42no—
388C23—42no—
389C23—44no—
390C23—84no—
391C23—84no—
392C23—88no—
393C23C22×D4×C1111yescharacteristic
394C23C22×D4×C1112yes—
395C23C2×C11×#4112yes—
396C23C11×H(5,𝔽2)12yes—
397Q8—82no—
398D4—48no—
399D4—48no—
400D4—42no—
401D4—42no—
402D4—44no—
403D4—82no—
404D4—816no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—28no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—84no—
423C2×C4C11×#12012yes—
424C2×C4C11×#12012yes—
425C22—22no—
426C22—24no—
427C22—42no—
428C22—42no—
429C22—48no—
430C22—48no—
431C22—44no—
432C22—44no—
433C22—44no—
434C22—42no—
435C22—44no—
436C22—84no—
437C22—84no—
438C22—88no—
439C22—84no—
440C22C2×C11×#12011yescharacteristic
441C22C11×#52511yescharacteristic
442C22C11×#53511yescharacteristic
443C22C11×#54614yes—
444C4—22no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—44no—
449C4—42no—
450C4—84no—
451C4—82no—
452C2—21no—
453C2—24no—
454C2—21no—
455C2—84no—
456C2—82no—
457C2C11×#240411yescharacteristic
458C2C11×#302712yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3491C2semidirect
2. C11×#2613C2semidirect
3. C11×#2309C2semidirect
4. C11×#2029C2semidirect
5. C11×#2021C2semidirect
6. C11×#1899C2semidirect
7. C11×#1889C2semidirect
8. C11×#1820C2semidirect
68. C2×C11×C4⋊C4D4semidirect
69. C2×C11×C4⋊C4D4semidirect
75. C2×C11×C22⋊C4D4semidirect
82. C2×C42×C11D4semidirect
85. #23988C11direct (N × H)
148. #3491C2×C11semidirect
149. #2613C2×C11semidirect
150. #2309C2×C11semidirect
151. #2029C2×C11semidirect
152. #2021C2×C11semidirect
153. #1899C2×C11semidirect
154. #1889C2×C11semidirect
155. #1820C2×C11semidirect
290. C2×C4⋊C4D4×C11semidirect
291. C2×C4⋊C4D4×C11semidirect
297. C2×C22⋊C4D4×C11semidirect
304. C2×C42D4×C11semidirect
376. C11#23988direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34912
C11×#26132
C11×#23092
C11×#20292
C11×#20212
C11×#18992
C11×#18892
C11×#18202
#2398811