Finite Group Databasebeta

← C11×#13218 #14590411

Subgroups — C11×#13218 #14590411

Order 2816.

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

normal subgroups only

This group has 840 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×#1799C211yesmaximal, characteristic, complemented
4C4×C11×#100C211yesmaximal, characteristic, complemented
5C23×D4×C11C411yescharacteristic, complemented
6C2×C11×#121—21no—
7C2×C11×#120C2212yes—
8C2×C4×D4×C11C2211yescharacteristic
9C2×C11×#100C2212yes—
10C2×C11×#99C2212yes—
11C4×C11×M16—21no—
12C11×#394—21no—
13C11×#392—21no—
14C11×#390—21no—
15C11×#380—21no—
16C11×#380C411yescharacteristic, complemented
17C11×#379C412yescomplemented
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⋊C4—41no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4C2×C412yes—
45C2×C11×C22⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C11×#100—22no—
49C11×#100D414yescomplemented
50C11×#99—24no—
51C11×#97—41no—
52C4×C8×C11—41no—
53C11×#95—21no—
54C11×#95—41no—
55#13218C1111yesmaximal, 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—42no—
75C2×D4×C11—42no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—82no—
79C2×D4×C11C2×D412yes—
80C2×D4×C11#4112yes—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×M16—24no—
95C11×M16—42no—
96C2×C8×C11—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—82no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—44no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—82no—
108C42×C11—21no—
109C42×C11—21no—
110#2408C2×C1111yescharacteristic
111C2×AΣL(1,𝔽16)C2×C1114yescomplemented
112#1799C2×C1111yescharacteristic, complemented
113C4×#100C2×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#12411yescharacteristic
138C23×C11#12711yescharacteristic
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—44no—
142D4×C11—48no—
143D4×C11—44no—
144D4×C11—84no—
145D4×C11—84no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—81no—
162C2×C4×C11—82no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11#9911yescharacteristic
166C2×C4×C11#9911yescharacteristic
167C2×C4×C11#12112yes—
168C8×C11—44no—
169C23×D4C4×C1111yescharacteristic, complemented
170C2×#121—21no—
171C2×#120C22×C1112yes—
172C2×C4×D4C22×C1111yescharacteristic
173C2×#100C22×C1112yes—
174C2×#99C22×C1112yes—
175C4×M16—21no—
176#394—21no—
177#392—21no—
178#390—21no—
179#380—21no—
180#380C4×C1111yescharacteristic, complemented
181#379C4×C1112yescomplemented
182AΣL(1,𝔽16)—28no—
183#343—21no—
184#342—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—22no—
189C22×C11—21no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—44no—
195C22×C11—44no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—44no—
201C22×C11—81no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11—88no—
205C22×C11—88no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11#39011yescharacteristic
209C22×C11C2×#9911yescharacteristic
210C22×C11#41011yescharacteristic
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—41no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—82no—
217C4×C11—162no—
218C4×C11AΣL(1,𝔽16)12yescomplemented
219C25C2×C4×C1112yes—
220C22×D4—22no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—41no—
224C22×D4—41no—
225C22×D4—44no—
226C22×D4C23×C1111yescharacteristic
227C23×C4C2×C4×C1111yescharacteristic
228C23×C4D4×C1111yescharacteristic
229C2×M16—22no—
230#121—44no—
231#120—24no—
232#120—24no—
233C4×D4—41no—
234C4×D4—41no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4D4×C1111yescharacteristic
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4C2×C4×C1112yes—
243C2×C22⋊C4C2×C4×C1111yescharacteristic
244C2×C22⋊C4D4×C1111yescharacteristic
245C2×C42D4×C1111yescharacteristic
246#100—22no—
247#100D4×C1114yescomplemented
248#99—24no—
249#97—41no—
250C4×C8—41no—
251#95—21no—
252#95—41no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—42no—
257C2×C11—41no—
258C2×C11—84no—
259C2×C11#196411yescharacteristic
260C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
261C2×C11#212211yescharacteristic
262C24—22no—
263C24—24no—
264C24—42no—
265C24—44no—
266C24—42no—
267C24—82no—
268C24C22×C4×C1111yescharacteristic
269C24C2×D4×C1111yescharacteristic
270C2×D4—24no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—44no—
276C2×D4—48no—
277C2×D4—44no—
278C2×D4—44no—
279C2×D4—44no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—82no—
285C2×D4C2×D4×C1112yes—
286C2×D4C11×#4112yes—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C11×C22⋊C411yescharacteristic
296C22×C4C11×C22⋊C411yescharacteristic
297C22×C4C11×C22⋊C411yescharacteristic
298C22×C4C11×C22⋊C411yescharacteristic
299C22×C4C2×D4×C1111yescharacteristic
300M16—24no—
301M16—42no—
302C2×C8—42no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—82no—
306C22⋊C4—24no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—44no—
310C22⋊C4—44no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—82no—
314C42—21no—
315C42—21no—
316C11#1321811yescharacteristic, direct product factor, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—24no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23—44no—
330C23—44no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—84no—
335C23—88no—
336C23—88no—
337C23—84no—
338C23C2×C11×C22⋊C411yescharacteristic
339C23C4×D4×C1112yes—
340C23C11×#12411yescharacteristic
341C23C11×#12711yescharacteristic
342D4—42no—
343D4—42no—
344D4—44no—
345D4—48no—
346D4—44no—
347D4—84no—
348D4—84no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4C11×#9911yescharacteristic
369C2×C4C11×#9911yescharacteristic
370C2×C4C11×#12112yes—
371C8—44no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—22no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—42no—
380C22—42no—
381C22—44no—
382C22—44no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—44no—
388C22—81no—
389C22—82no—
390C22—82no—
391C22—88no—
392C22—88no—
393C22—82no—
394C22—82no—
395C22C11×#39011yescharacteristic
396C22C2×C11×#9911yescharacteristic
397C22C11×#41011yescharacteristic
398C4—22no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—82no—
404C4—162no—
405C4C11×AΣL(1,𝔽16)12yescomplemented
406C2—21no—
407C2—21no—
408C2—41no—
409C2—42no—
410C2—41no—
411C2—84no—
412C2C11×#196411yescharacteristic
413C2C2×C11×AΣL(1,𝔽16)11yescharacteristic
414C2C11×#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×#1799C2semidirect
4. C4×C11×#100C2semidirect
5. C23×D4×C11C4semidirect
16. C11×#380C4semidirect
17. C11×#379C4semidirect
49. C11×#100D4semidirect
55. #13218C11direct (N × H)
111. C2×AΣL(1,𝔽16)C2×C11semidirect
112. #1799C2×C11semidirect
113. C4×#100C2×C11semidirect
169. C23×D4C4×C11semidirect
180. #380C4×C11semidirect
181. #379C4×C11semidirect
218. C4×C11AΣL(1,𝔽16)semidirect
247. #100D4×C11semidirect
316. C11#13218direct (N × H)
405. 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×#17992
C4×C11×#1002
#1321811