Finite Group Databasebeta

← C11×#21481 #14598674

Subgroups — C11×#21481 #14598674

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×H(5,𝔽2)C211yesmaximal, characteristic
2C2×C11×#458C211yesmaximal, characteristic
3C11×#2322C213yesmaximal, complemented
4C11×#1890C213yesmaximal, complemented
5C11×#1867C213yesmaximal, complemented
6C11×#1790C211yesmaximal, characteristic
7C4×C11×#99C213yesmaximal, complemented
8C2×C11×H(5,𝔽2)C2211yescharacteristic
9C2×C11×#123C2213yes—
10C11×#520—23no—
11C11×#518—23no—
12C11×#518C2213yes—
13C4×C11×#41—23no—
14C2×C4×D4×C11—23no—
15C2×C4×D4×C11C2213yes—
16C22×C11×C4⋊C4C2211yescharacteristic, complemented
17C11×#458C418yescomplemented
18C2×C11×#99C2213yes—
19C2×C11×#99C2213yes—
20C11×#389—23no—
21C11×#388—23no—
22C11×#387—23no—
23C11×#386C2213yes—
24C11×#385—23no—
25C11×#385C2213yescomplemented
26C11×#381C2213yescomplemented
27C4×C11×C22⋊C4C2213yescomplemented
28C11×#342C2216yescomplemented
29C11×H(5,𝔽2)—26no—
30C11×H(5,𝔽2)C2×C414yes—
31C2×C11×#41—23no—
32C22×D4×C11—23no—
33C22×D4×C11C2313yes—
34C23×C4×C11—21no—
35C23×C4×C11D413yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C11×#123—26no—
40C11×#123C2×C4112yescomplemented
41C4×Q8×C11—21no—
42C4×Q8×C11—23no—
43C4×D4×C11—23no—
44C4×D4×C11—26no—
45C4×D4×C11—23no—
46C4×D4×C11—26no—
47C4×D4×C11—26no—
48C4×D4×C11—26no—
49C4×D4×C11—26no—
50C11×#117—26no—
51C11×#117—23no—
52C2×C11×C4⋊C4—23no—
53C2×C11×C4⋊C4—23no—
54C2×C11×C4⋊C4—23no—
55C2×C11×C4⋊C4—23no—
56C2×C11×C4⋊C4—23no—
57C2×C11×C4⋊C4D413yes—
58C2×C11×C22⋊C4—23no—
59C2×C11×C22⋊C4—23no—
60C2×C11×C22⋊C4—23no—
61C2×C11×C22⋊C4—23no—
62C2×C11×C22⋊C4D413yes—
63C2×C11×C22⋊C4C2313yes—
64C2×C11×C22⋊C4C2313yes—
65C2×C11×C22⋊C4C2313yes—
66C2×C42×C11—23no—
67C2×C42×C11—23no—
68C2×C42×C11D413yes—
69C11×#99—26no—
70C11×#99C2×C4112yescomplemented
71C11×#95—23no—
72C11×#95—23no—
73C11×#95—23no—
74C11×#95—23no—
75C11×#95—23no—
76#21481C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—21no—
78C24×C11C2×D413yes—
79C24×C11C2411yescharacteristic
80C11×#41—212no—
81C11×#41—212no—
82C2×Q8×C11—21no—
83C2×D4×C11—23no—
84C2×D4×C11—212no—
85C2×D4×C11—212no—
86C2×D4×C11—26no—
87C2×D4×C11—26no—
88C2×D4×C11C22×C416yes—
89C2×D4×C11#4116yes—
90C22×C4×C11—23no—
91C22×C4×C11—23no—
92C22×C4×C11—23no—
93C22×C4×C11—23no—
94C22×C4×C11—23no—
95C22×C4×C11—23no—
96C22×C4×C11—23no—
97C22×C4×C11—23no—
98C22×C4×C11—23no—
99C22×C4×C11—23no—
100C22×C4×C11—81no—
101C22×C4×C11—81no—
102C22×C4×C11—83no—
103C22×C4×C11—82no—
104C22×C4×C11C22×C412yescomplemented
105C22×C4×C11C2×D413yes—
106C22×C4×C11C2×D413yes—
107C22×C4×C11C2×D413yes—
108C22×C4×C11C2×D413yes—
109C22×C4×C11C2×D413yes—
110C11×C4⋊C4—23no—
111C11×C4⋊C4—23no—
112C11×C4⋊C4—212no—
113C11×C4⋊C4—26no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—43no—
116C11×C4⋊C4—83no—
117C11×C22⋊C4—26no—
118C11×C22⋊C4—212no—
119C11×C22⋊C4—26no—
120C11×C22⋊C4—23no—
121C11×C22⋊C4—26no—
122C11×C22⋊C4—26no—
123C11×C22⋊C4—83no—
124C11×C22⋊C4C22×C416yescomplemented
125C42×C11—26no—
126C42×C11—23no—
127C42×C11—23no—
128C42×C11—83no—
129C4×H(5,𝔽2)C2×C1111yescharacteristic
130C2×#458C2×C1111yescharacteristic
131#2322C2×C1113yescomplemented
132#1890C2×C1113yescomplemented
133#1867C2×C1113yescomplemented
134#1790C2×C1111yescharacteristic
135C4×#99C2×C1113yescomplemented
136C23×C11—24no—
137C23×C11—23no—
138C23×C11—23no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—43no—
142C23×C11—43no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11C4×D416yes—
146C23×C11C23×C411yescharacteristic
147C23×C11C22×D413yes—
148C23×C11C2×#4113yes—
149Q8×C11—24no—
150D4×C11—212no—
151D4×C11—212no—
152D4×C11—212no—
153C2×C4×C11—212no—
154C2×C4×C11—23no—
155C2×C4×C11—23no—
156C2×C4×C11—26no—
157C2×C4×C11—26no—
158C2×C4×C11—23no—
159C2×C4×C11—23no—
160C2×C4×C11—43no—
161C2×C4×C11—43no—
162C2×C4×C11—46no—
163C2×C4×C11—43no—
164C2×C4×C11—43no—
165C2×C4×C11—41no—
166C2×C4×C11—43no—
167C2×C4×C11—43no—
168C2×C4×C11—43no—
169C2×C4×C11—43no—
170C2×C4×C11—43no—
171C2×C4×C11—43no—
172C2×C4×C11—43no—
173C2×C4×C11—41no—
174C2×C4×C11—43no—
175C2×C4×C11—83no—
176C2×C4×C11—83no—
177C2×C4×C11—83no—
178C2×C4×C11C4×D416yes—
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12013yes—
181C2×H(5,𝔽2)C22×C1111yescharacteristic
182C2×#123C22×C1113yes—
183#520—23no—
184#518—23no—
185#518C22×C1113yes—
186C4×#41—23no—
187C2×C4×D4—23no—
188C2×C4×D4C22×C1113yes—
189C22×C4⋊C4C22×C1111yescharacteristic, complemented
190#458C4×C1118yescomplemented
191C2×#99C22×C1113yes—
192C2×#99C22×C1113yes—
193#389—23no—
194#388—23no—
195#387—23no—
196#386C22×C1113yes—
197#385—23no—
198#385C22×C1113yescomplemented
199#381C22×C1113yescomplemented
200C4×C22⋊C4C22×C1113yescomplemented
201#342C22×C1116yescomplemented
202C22×C11—23no—
203C22×C11—23no—
204C22×C11—26no—
205C22×C11—41no—
206C22×C11—43no—
207C22×C11—46no—
208C22×C11—43no—
209C22×C11—43no—
210C22×C11—83no—
211C22×C11—84no—
212C22×C11C2×C4×D413yes—
213C22×C11C2×#12011yescharacteristic
214C22×C11#52513yes—
215C4×C11—21no—
216C4×C11—23no—
217C4×C11—26no—
218C4×C11—46no—
219C4×C11—43no—
220C4×C11—43no—
221C4×C11—42no—
222C4×C11—83no—
223C4×C11—81no—
224H(5,𝔽2)—26no—
225H(5,𝔽2)C2×C4×C1114yes—
226C2×#41—23no—
227C22×D4—23no—
228C22×D4C23×C1113yes—
229C23×C4—21no—
230C23×C4D4×C1113yes—
231C23×C4C23×C1111yescharacteristic
232C23×C4C23×C1111yescharacteristic
233C23×C4C23×C1111yescharacteristic
234#123—26no—
235#123C2×C4×C11112yescomplemented
236C4×Q8—21no—
237C4×Q8—23no—
238C4×D4—23no—
239C4×D4—26no—
240C4×D4—23no—
241C4×D4—26no—
242C4×D4—26no—
243C4×D4—26no—
244C4×D4—26no—
245#117—26no—
246#117—23no—
247C2×C4⋊C4—23no—
248C2×C4⋊C4—23no—
249C2×C4⋊C4—23no—
250C2×C4⋊C4—23no—
251C2×C4⋊C4—23no—
252C2×C4⋊C4D4×C1113yes—
253C2×C22⋊C4—23no—
254C2×C22⋊C4—23no—
255C2×C22⋊C4—23no—
256C2×C22⋊C4—23no—
257C2×C22⋊C4D4×C1113yes—
258C2×C22⋊C4C23×C1113yes—
259C2×C22⋊C4C23×C1113yes—
260C2×C22⋊C4C23×C1113yes—
261C2×C42—23no—
262C2×C42—23no—
263C2×C42D4×C1113yes—
264#99—26no—
265#99C2×C4×C11112yescomplemented
266#95—23no—
267#95—23no—
268#95—23no—
269#95—23no—
270#95—23no—
271C2×C11—23no—
272C2×C11—23no—
273C2×C11—46no—
274C2×C11C4×#12011yescharacteristic
275C2×C11#302611yescharacteristic
276C2×C11#302811yescharacteristic
277C24—21no—
278C24C2×D4×C1113yes—
279C24C24×C1111yescharacteristic
280#41—212no—
281#41—212no—
282C2×Q8—21no—
283C2×D4—23no—
284C2×D4—212no—
285C2×D4—212no—
286C2×D4—26no—
287C2×D4—26no—
288C2×D4C22×C4×C1116yes—
289C2×D4C11×#4116yes—
290C22×C4—23no—
291C22×C4—23no—
292C22×C4—23no—
293C22×C4—23no—
294C22×C4—23no—
295C22×C4—23no—
296C22×C4—23no—
297C22×C4—23no—
298C22×C4—23no—
299C22×C4—23no—
300C22×C4—81no—
301C22×C4—81no—
302C22×C4—83no—
303C22×C4—82no—
304C22×C4C22×C4×C1112yescomplemented
305C22×C4C2×D4×C1113yes—
306C22×C4C2×D4×C1113yes—
307C22×C4C2×D4×C1113yes—
308C22×C4C2×D4×C1113yes—
309C22×C4C2×D4×C1113yes—
310C4⋊C4—23no—
311C4⋊C4—23no—
312C4⋊C4—212no—
313C4⋊C4—26no—
314C4⋊C4—41no—
315C4⋊C4—43no—
316C4⋊C4—83no—
317C22⋊C4—26no—
318C22⋊C4—212no—
319C22⋊C4—26no—
320C22⋊C4—23no—
321C22⋊C4—26no—
322C22⋊C4—26no—
323C22⋊C4—83no—
324C22⋊C4C22×C4×C1116yescomplemented
325C42—26no—
326C42—23no—
327C42—23no—
328C42—83no—
329C11#2148111yescharacteristic, direct product factor, Sylow
330C23—24no—
331C23—23no—
332C23—23no—
333C23—41no—
334C23—41no—
335C23—43no—
336C23—43no—
337C23—81no—
338C23—81no—
339C23C4×D4×C1116yes—
340C23C23×C4×C1111yescharacteristic
341C23C22×D4×C1113yes—
342C23C2×C11×#4113yes—
343Q8—24no—
344D4—212no—
345D4—212no—
346D4—212no—
347C2×C4—212no—
348C2×C4—23no—
349C2×C4—23no—
350C2×C4—26no—
351C2×C4—26no—
352C2×C4—23no—
353C2×C4—23no—
354C2×C4—43no—
355C2×C4—43no—
356C2×C4—46no—
357C2×C4—43no—
358C2×C4—43no—
359C2×C4—41no—
360C2×C4—43no—
361C2×C4—43no—
362C2×C4—43no—
363C2×C4—43no—
364C2×C4—43no—
365C2×C4—43no—
366C2×C4—43no—
367C2×C4—41no—
368C2×C4—43no—
369C2×C4—83no—
370C2×C4—83no—
371C2×C4—83no—
372C2×C4C4×D4×C1116yes—
373C2×C4C11×#12011yescharacteristic
374C2×C4C11×#12013yes—
375C22—23no—
376C22—23no—
377C22—26no—
378C22—41no—
379C22—43no—
380C22—46no—
381C22—43no—
382C22—43no—
383C22—83no—
384C22—84no—
385C22C2×C4×D4×C1113yes—
386C22C2×C11×#12011yescharacteristic
387C22C11×#52513yes—
388C4—21no—
389C4—23no—
390C4—26no—
391C4—46no—
392C4—43no—
393C4—43no—
394C4—42no—
395C4—83no—
396C4—81no—
397C2—23no—
398C2—23no—
399C2—46no—
400C2C4×C11×#12011yescharacteristic
401C2C11×#302611yescharacteristic
402C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×H(5,𝔽2)C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2322C2semidirect
4. C11×#1890C2semidirect
5. C11×#1867C2semidirect
7. C4×C11×#99C2semidirect
16. C22×C11×C4⋊C4C22semidirect
17. C11×#458C4semidirect
25. C11×#385C22semidirect
26. C11×#381C22semidirect
27. C4×C11×C22⋊C4C22semidirect
28. C11×#342C22semidirect
40. C11×#123C2×C4semidirect
70. C11×#99C2×C4semidirect
76. #21481C11direct (N × H)
104. C22×C4×C11C22×C4semidirect
124. C11×C22⋊C4C22×C4semidirect
131. #2322C2×C11semidirect
132. #1890C2×C11semidirect
133. #1867C2×C11semidirect
135. C4×#99C2×C11semidirect
189. C22×C4⋊C4C22×C11semidirect
190. #458C4×C11semidirect
198. #385C22×C11semidirect
199. #381C22×C11semidirect
200. C4×C22⋊C4C22×C11semidirect
201. #342C22×C11semidirect
235. #123C2×C4×C11semidirect
265. #99C2×C4×C11semidirect
304. C22×C4C22×C4×C11semidirect
324. C22⋊C4C22×C4×C11semidirect
329. C11#21481direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×H(5,𝔽2)2
C2×C11×#4582
C11×#23222
C11×#18902
C11×#18672
C11×#17902
C4×C11×#992
#2148111