Finite Group Databasebeta

← C11×#13221 #14590414

Subgroups — C11×#13221 #14590414

Order 2816.

844 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2408C211yesmaximal, characteristic
2C2×C11×AΣL(1,𝔽16)C214yesmaximal, complemented
3C11×#1800C211yesmaximal, characteristic, complemented
4C4×C11×#99C211yesmaximal, characteristic, complemented
5C23×D4×C11C411yescharacteristic, complemented
6C2×C11×#121—21no—
7C2×C11×#120C2212yes—
8C2×C4×D4×C11C2211yescharacteristic
9C11×#423—21no—
10C2×C11×#100C2212yes—
11C2×C11×#99C2212yes—
12C11×#394—21no—
13C11×#392—21no—
14C11×#390—21no—
15C11×#380C411yescharacteristic, complemented
16C11×#379C412yescomplemented
17C4×C11×C22⋊C4—21no—
18C11×AΣL(1,𝔽16)—28no—
19C11×#343—21no—
20C11×#342—21no—
21C25×C11C2×C412yes—
22C22×D4×C11—22no—
23C22×D4×C11—21no—
24C22×D4×C11—21no—
25C22×D4×C11—41no—
26C22×D4×C11—41no—
27C22×D4×C11—44no—
28C22×D4×C11C2311yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C2×C11×M16—22no—
32C11×#121—44no—
33C11×#120—24no—
34C11×#120—24no—
35C4×D4×C11—41no—
36C4×D4×C11—41no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4C2×C412yes—
44C2×C11×C22⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C42×C11—41no—
47C2×C42×C11D411yescharacteristic
48C11×C4⋊C8—41no—
49C11×C4⋊C8—41no—
50C11×#100—24no—
51C11×#99—22no—
52C11×#99D414yescomplemented
53C11×#95—21no—
54C11×#95—41no—
55#13221C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—22no—
57C24×C11—24no—
58C24×C11—42no—
59C24×C11—44no—
60C24×C11—42no—
61C24×C11—82no—
62C24×C11C22×C411yescharacteristic
63C24×C11C2×D411yescharacteristic
64C2×D4×C11—24no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—44no—
70C2×D4×C11—48no—
71C2×D4×C11—44no—
72C2×D4×C11—44no—
73C2×D4×C11—44no—
74C2×D4×C11—44no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—82no—
78C2×D4×C11C2×D412yes—
79C2×D4×C11#4112yes—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C11×M16—42no—
94C11×M16—42no—
95C2×C8×C11—42no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—42no—
98C11×C22⋊C4—24no—
99C11×C22⋊C4—24no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—82no—
107C42×C11—21no—
108C42×C11—21no—
109C42×C11—82no—
110#2408C2×C1111yescharacteristic
111C2×AΣL(1,𝔽16)C2×C1114yescomplemented
112#1800C2×C1111yescharacteristic, complemented
113C4×#99C2×C1111yescharacteristic, complemented
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—24no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—44no—
127C23×C11—44no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—84no—
132C23×C11—88no—
133C23×C11—88no—
134C23×C11—84no—
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11C4×D412yes—
137C23×C11#12112yes—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—44no—
141D4×C11—48no—
142D4×C11—44no—
143D4×C11—88no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—44no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—81no—
161C2×C4×C11—82no—
162C2×C4×C11—82no—
163C2×C4×C11#9911yescharacteristic
164C2×C4×C11#9911yescharacteristic
165C2×C4×C11#12411yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C8×C11—82no—
168C23×D4C4×C1111yescharacteristic, complemented
169C2×#121—21no—
170C2×#120C22×C1112yes—
171C2×C4×D4C22×C1111yescharacteristic
172#423—21no—
173C2×#100C22×C1112yes—
174C2×#99C22×C1112yes—
175#394—21no—
176#392—21no—
177#390—21no—
178#380C4×C1111yescharacteristic, complemented
179#379C4×C1112yescomplemented
180C4×C22⋊C4—21no—
181AΣL(1,𝔽16)—28no—
182#343—21no—
183#342—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—44no—
192C22×C11—44no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—44no—
198C22×C11—81no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—88no—
202C22×C11—88no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11#39011yescharacteristic
206C22×C11C2×#9911yescharacteristic
207C22×C11#41011yescharacteristic
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—82no—
215C4×C11—84no—
216C4×C11AΣL(1,𝔽16)12yescomplemented
217C25C2×C4×C1112yes—
218C22×D4—22no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—41no—
222C22×D4—41no—
223C22×D4—44no—
224C22×D4C23×C1111yescharacteristic
225C23×C4C2×C4×C1111yescharacteristic
226C23×C4D4×C1111yescharacteristic
227C2×M16—22no—
228#121—44no—
229#120—24no—
230#120—24no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C1111yescharacteristic
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4C2×C4×C1112yes—
240C2×C22⋊C4C2×C4×C1111yescharacteristic
241C2×C22⋊C4D4×C1111yescharacteristic
242C2×C42—41no—
243C2×C42D4×C1111yescharacteristic
244C4⋊C8—41no—
245C4⋊C8—41no—
246#100—24no—
247#99—22no—
248#99D4×C1114yescomplemented
249#95—21no—
250#95—41no—
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—42no—
254C2×C11—42no—
255C2×C11—84no—
256C2×C11#196411yescharacteristic
257C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
258C2×C11#212211yescharacteristic
259C24—22no—
260C24—24no—
261C24—42no—
262C24—44no—
263C24—42no—
264C24—82no—
265C24C22×C4×C1111yescharacteristic
266C24C2×D4×C1111yescharacteristic
267C2×D4—24no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—44no—
273C2×D4—48no—
274C2×D4—44no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4—44no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—82no—
281C2×D4C2×D4×C1112yes—
282C2×D4C11×#4112yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4C11×C22⋊C411yescharacteristic
292C22×C4C11×C22⋊C411yescharacteristic
293C22×C4C11×C22⋊C411yescharacteristic
294C22×C4C11×C22⋊C411yescharacteristic
295C22×C4C2×D4×C1111yescharacteristic
296M16—42no—
297M16—42no—
298C2×C8—42no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C22⋊C4—24no—
302C22⋊C4—24no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—44no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—82no—
310C42—21no—
311C42—21no—
312C42—82no—
313C11#1322111yescharacteristic, direct product factor, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—24no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—44no—
327C23—44no—
328C23—42no—
329C23—42no—
330C23—42no—
331C23—84no—
332C23—88no—
333C23—88no—
334C23—84no—
335C23C2×C11×C22⋊C411yescharacteristic
336C23C4×D4×C1112yes—
337C23C11×#12112yes—
338D4—42no—
339D4—42no—
340D4—44no—
341D4—48no—
342D4—44no—
343D4—88no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4C11×#9911yescharacteristic
364C2×C4C11×#9911yescharacteristic
365C2×C4C11×#12411yescharacteristic
366C2×C4C11×#12711yescharacteristic
367C8—82no—
368C22—21no—
369C22—21no—
370C22—22no—
371C22—22no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—44no—
376C22—44no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—44no—
382C22—81no—
383C22—82no—
384C22—82no—
385C22—88no—
386C22—88no—
387C22—82no—
388C22—82no—
389C22C11×#39011yescharacteristic
390C22C2×C11×#9911yescharacteristic
391C22C11×#41011yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—82no—
399C4—84no—
400C4C11×AΣL(1,𝔽16)12yescomplemented
401C2—21no—
402C2—21no—
403C2—42no—
404C2—42no—
405C2—84no—
406C2C11×#196411yescharacteristic
407C2C2×C11×AΣL(1,𝔽16)11yescharacteristic
408C2C11×#212211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC22×D4C23×C11
prime radicalC11×#2408C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×AΣL(1,𝔽16)C2semidirect
3. C11×#1800C2semidirect
4. C4×C11×#99C2semidirect
5. C23×D4×C11C4semidirect
15. C11×#380C4semidirect
16. C11×#379C4semidirect
52. C11×#99D4semidirect
55. #13221C11direct (N × H)
111. C2×AΣL(1,𝔽16)C2×C11semidirect
112. #1800C2×C11semidirect
113. C4×#99C2×C11semidirect
168. C23×D4C4×C11semidirect
178. #380C4×C11semidirect
179. #379C4×C11semidirect
216. C4×C11AΣL(1,𝔽16)semidirect
248. #99D4×C11semidirect
313. C11#13221direct (N × H)
400. C4C11×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C11×#24082
C2×C11×AΣL(1,𝔽16)2
C11×#18002
C4×C11×#992
#1322111