Finite Group Databasebeta

← C11×#23895 #14601088

Subgroups — C11×#23895 #14601088

Order 2816.

2002 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 2002 conjugacy classes of subgroups — too many to draw. Only its 282 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3484C212yesmaximal, complemented
2C11×#3026C214yesmaximal, complemented
3C11×#2021C214yesmaximal, complemented
4C11×#1913C214yesmaximal, complemented
5C11×#1781C211yesmaximal, characteristic, complemented
6C2×C11×H(5,𝔽2)C2212yescomplemented
7C23×D4×C11C2211yescharacteristic
8C11×#546—28no—
9D42×C11—28no—
10C11×#535—22no—
11C11×#534—22no—
12C11×#534C2214yes—
13C11×#534C2214yescomplemented
14C11×#525—22no—
15C2×C11×#120—22no—
16C2×C11×#120C2214yescomplemented
17C11×#518C2212yescomplemented
18C11×#458—28no—
19C11×B(4,𝔽2)—28no—
20C2×C11×#99C2218yescomplemented
21C2×C11×#99C2214yescomplemented
22C11×#379C2212yescomplemented
23C11×#342C2214yescomplemented
24C25×C11D411yescharacteristic, complemented
25C25×C11C2311yescharacteristic
26C11×H(5,𝔽2)—28no—
27C11×H(5,𝔽2)—44no—
28C2×C11×#41—22no—
29C2×C11×#41—24no—
30C22×D4×C11—22no—
31C22×D4×C11—24no—
32C22×D4×C11—24no—
33C22×D4×C11—24no—
34C22×D4×C11—28no—
35C22×D4×C11—42no—
36C22×D4×C11D412yescomplemented
37C22×D4×C11C2312yes—
38C22×D4×C11C2314yes—
39C23×C4×C11D411yescharacteristic, complemented
40C11×#127—24no—
41C11×#124—24no—
42C11×#123—24no—
43C11×#123—24no—
44C11×#123—28no—
45C11×#123D418yescomplemented
46C11×C22⋊Q8—24no—
47C11×#121—24no—
48C11×#121—28no—
49C11×#121—28no—
50C11×#121—28no—
51C11×#121—44no—
52C11×#120—28no—
53C11×#120—24no—
54C11×#120—24no—
55C11×#120—24no—
56C11×#120—24no—
57C11×#120—28no—
58C11×#120—28no—
59C11×#120D418yescomplemented
60C4×D4×C11—28no—
61C4×D4×C11—28no—
62C11×#117—22no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4C2314yes—
68C2×C11×C22⋊C4C2314yes—
69C11×#99—28no—
70C11×#99—216no—
71#23895C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—22no—
73C24×C11—24no—
74C24×C11—24no—
75C24×C11—22no—
76C24×C11—41no—
77C24×C11—82no—
78C24×C11—82no—
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C24×C11C2×D412yes—
82C24×C11C2×D414yescomplemented
83C24×C11C2411yescharacteristic
84C11×#41—416no—
85C11×#41—44no—
86C11×#41—44no—
87C2×Q8×C11—22no—
88C2×D4×C11—24no—
89C2×D4×C11—24no—
90C2×D4×C11—28no—
91C2×D4×C11—24no—
92C2×D4×C11—22no—
93C2×D4×C11—24no—
94C2×D4×C11—28no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—28no—
98C2×D4×C11—28no—
99C2×D4×C11—28no—
100C2×D4×C11—24no—
101C2×D4×C11—42no—
102C2×D4×C11—416no—
103C2×D4×C11—416no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—44no—
107C2×D4×C11—88no—
108C2×D4×C11—88no—
109C2×D4×C11C2×D418yes—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D414yescomplemented
119C11×C4⋊C4—24no—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—44no—
122C11×C22⋊C4—28no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—28no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—28no—
128C11×C22⋊C4—28no—
129C11×C22⋊C4—48no—
130C11×C22⋊C4—84no—
131C11×C22⋊C4C2×D418yescomplemented
132C42×C11—24no—
133#3484C2×C1112yescomplemented
134#3026C2×C1114yescomplemented
135#2021C2×C1114yescomplemented
136#1913C2×C1114yescomplemented
137#1781C2×C1111yescharacteristic, complemented
138C23×C11—22no—
139C23×C11—22no—
140C23×C11—21no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—24no—
144C23×C11—21no—
145C23×C11—28no—
146C23×C11—42no—
147C23×C11—44no—
148C23×C11—44no—
149C23×C11—48no—
150C23×C11—48no—
151C23×C11—44no—
152C23×C11—44no—
153C23×C11—82no—
154C23×C11—81no—
155C23×C11—81no—
156C23×C11—82no—
157C23×C11—84no—
158C23×C11—82no—
159C23×C11—84no—
160C23×C11—84no—
161C23×C11—84no—
162C23×C11—82no—
163C23×C11#12014yes—
164C23×C11C22×D411yescharacteristic
165C23×C11C22×D414yes—
166C23×C11H(5,𝔽2)12yes—
167Q8×C11—44no—
168D4×C11—216no—
169D4×C11—48no—
170D4×C11—44no—
171D4×C11—48no—
172D4×C11—416no—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—48no—
176D4×C11—88no—
177D4×C11—88no—
178D4×C11—164no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—28no—
182C2×C4×C11—24no—
183C2×C4×C11—28no—
184C2×C4×C11—44no—
185C2×C4×C11—48no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—84no—
189C2×C4×C11—84no—
190C2×C4×C11—84no—
191C2×C4×C11#12014yes—
192C2×H(5,𝔽2)C22×C1112yescomplemented
193C23×D4C22×C1111yescharacteristic
194#546—28no—
195D42—28no—
196#535—22no—
197#534—22no—
198#534C22×C1114yes—
199#534C22×C1114yescomplemented
200#525—22no—
201C2×#120—22no—
202C2×#120C22×C1114yescomplemented
203#518C22×C1112yescomplemented
204#458—28no—
205B(4,𝔽2)—28no—
206C2×#99C22×C1118yescomplemented
207C2×#99C22×C1114yescomplemented
208#379C22×C1112yescomplemented
209#342C22×C1114yescomplemented
210C22×C11—24no—
211C22×C11—22no—
212C22×C11—24no—
213C22×C11—42no—
214C22×C11—44no—
215C22×C11—41no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—42no—
219C22×C11—41no—
220C22×C11—48no—
221C22×C11—44no—
222C22×C11—42no—
223C22×C11—41no—
224C22×C11—44no—
225C22×C11—41no—
226C22×C11—82no—
227C22×C11—88no—
228C22×C11—88no—
229C22×C11—88no—
230C22×C11—164no—
231C22×C11C2×#12012yes—
232C22×C11#53411yescharacteristic
233C22×C11D4214yes—
234C4×C11—24no—
235C4×C11—48no—
236C4×C11—44no—
237C4×C11—84no—
238C25D4×C1111yescharacteristic, complemented
239C25C23×C1111yescharacteristic
240H(5,𝔽2)—28no—
241H(5,𝔽2)—44no—
242C2×#41—22no—
243C2×#41—24no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—28no—
249C22×D4—42no—
250C22×D4D4×C1112yescomplemented
251C22×D4C23×C1112yes—
252C22×D4C23×C1114yes—
253C23×C4D4×C1111yescharacteristic, complemented
254#127—24no—
255#124—24no—
256#123—24no—
257#123—24no—
258#123—28no—
259#123D4×C1118yescomplemented
260C22⋊Q8—24no—
261#121—24no—
262#121—28no—
263#121—28no—
264#121—28no—
265#121—44no—
266#120—28no—
267#120—24no—
268#120—24no—
269#120—24no—
270#120—24no—
271#120—28no—
272#120—28no—
273#120D4×C1118yescomplemented
274C4×D4—28no—
275C4×D4—28no—
276#117—22no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4C23×C1114yes—
282C2×C22⋊C4C23×C1114yes—
283#99—28no—
284#99—216no—
285C2×C11—22no—
286C2×C11—24no—
287C2×C11—21no—
288C2×C11—42no—
289C2×C11—44no—
290C2×C11—81no—
291C2×C11—84no—
292C2×C11#240311yescharacteristic
293C24—22no—
294C24—24no—
295C24—24no—
296C24—22no—
297C24—41no—
298C24—82no—
299C24—82no—
300C24C2×D4×C1111yescharacteristic
301C24C2×D4×C1111yescharacteristic
302C24C2×D4×C1112yes—
303C24C2×D4×C1114yescomplemented
304C24C24×C1111yescharacteristic
305#41—416no—
306#41—44no—
307#41—44no—
308C2×Q8—22no—
309C2×D4—24no—
310C2×D4—24no—
311C2×D4—28no—
312C2×D4—24no—
313C2×D4—22no—
314C2×D4—24no—
315C2×D4—28no—
316C2×D4—24no—
317C2×D4—24no—
318C2×D4—28no—
319C2×D4—28no—
320C2×D4—28no—
321C2×D4—24no—
322C2×D4—42no—
323C2×D4—416no—
324C2×D4—416no—
325C2×D4—44no—
326C2×D4—44no—
327C2×D4—44no—
328C2×D4—88no—
329C2×D4—88no—
330C2×D4C2×D4×C1118yes—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—41no—
338C22×C4C2×D4×C1112yes—
339C22×C4C2×D4×C1114yescomplemented
340C4⋊C4—24no—
341C4⋊C4—28no—
342C4⋊C4—44no—
343C22⋊C4—28no—
344C22⋊C4—24no—
345C22⋊C4—28no—
346C22⋊C4—28no—
347C22⋊C4—24no—
348C22⋊C4—28no—
349C22⋊C4—28no—
350C22⋊C4—48no—
351C22⋊C4—84no—
352C22⋊C4C2×D4×C1118yescomplemented
353C42—24no—
354C11#2389511yescharacteristic, direct product factor, Sylow
355C23—22no—
356C23—22no—
357C23—21no—
358C23—22no—
359C23—22no—
360C23—24no—
361C23—21no—
362C23—28no—
363C23—42no—
364C23—44no—
365C23—44no—
366C23—48no—
367C23—48no—
368C23—44no—
369C23—44no—
370C23—82no—
371C23—81no—
372C23—81no—
373C23—82no—
374C23—84no—
375C23—82no—
376C23—84no—
377C23—84no—
378C23—84no—
379C23—82no—
380C23C11×#12014yes—
381C23C22×D4×C1111yescharacteristic
382C23C22×D4×C1114yes—
383C23C11×H(5,𝔽2)12yes—
384Q8—44no—
385D4—216no—
386D4—48no—
387D4—44no—
388D4—48no—
389D4—416no—
390D4—44no—
391D4—44no—
392D4—48no—
393D4—88no—
394D4—88no—
395D4—164no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—28no—
399C2×C4—24no—
400C2×C4—28no—
401C2×C4—44no—
402C2×C4—48no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—84no—
406C2×C4—84no—
407C2×C4—84no—
408C2×C4C11×#12014yes—
409C22—24no—
410C22—22no—
411C22—24no—
412C22—42no—
413C22—44no—
414C22—41no—
415C22—44no—
416C22—44no—
417C22—42no—
418C22—41no—
419C22—48no—
420C22—44no—
421C22—42no—
422C22—41no—
423C22—44no—
424C22—41no—
425C22—82no—
426C22—88no—
427C22—88no—
428C22—88no—
429C22—164no—
430C22C2×C11×#12012yes—
431C22C11×#53411yescharacteristic
432C22D42×C1114yes—
433C4—24no—
434C4—48no—
435C4—44no—
436C4—84no—
437C2—22no—
438C2—24no—
439C2—21no—
440C2—42no—
441C2—44no—
442C2—81no—
443C2—84no—
444C2C11×#240311yescharacteristic
subgroupG/H
center, socleC2×C11#2403
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3484C2semidirect
2. C11×#3026C2semidirect
3. C11×#2021C2semidirect
4. C11×#1913C2semidirect
5. C11×#1781C2semidirect
6. C2×C11×H(5,𝔽2)C22semidirect
13. C11×#534C22semidirect
16. C2×C11×#120C22semidirect
17. C11×#518C22semidirect
20. C2×C11×#99C22semidirect
21. C2×C11×#99C22semidirect
22. C11×#379C22semidirect
23. C11×#342C22semidirect
24. C25×C11D4semidirect
36. C22×D4×C11D4semidirect
39. C23×C4×C11D4semidirect
45. C11×#123D4semidirect
59. C11×#120D4semidirect
71. #23895C11direct (N × H)
82. C24×C11C2×D4semidirect
118. C22×C4×C11C2×D4semidirect
131. C11×C22⋊C4C2×D4semidirect
133. #3484C2×C11semidirect
134. #3026C2×C11semidirect
135. #2021C2×C11semidirect
136. #1913C2×C11semidirect
137. #1781C2×C11semidirect
192. C2×H(5,𝔽2)C22×C11semidirect
199. #534C22×C11semidirect
202. C2×#120C22×C11semidirect
203. #518C22×C11semidirect
206. C2×#99C22×C11semidirect
207. C2×#99C22×C11semidirect
208. #379C22×C11semidirect
209. #342C22×C11semidirect
238. C25D4×C11semidirect
250. C22×D4D4×C11semidirect
253. C23×C4D4×C11semidirect
259. #123D4×C11semidirect
273. #120D4×C11semidirect
303. C24C2×D4×C11semidirect
339. C22×C4C2×D4×C11semidirect
352. C22⋊C4C2×D4×C11semidirect
354. C11#23895direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34842
C11×#30262
C11×#20212
C11×#19132
C11×#17812
#2389511