Finite Group Databasebeta

← C11×#14331 #14591524

Subgroups — C11×#14331 #14591524

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#396C211yesmaximal, characteristic
2C11×#1445C213yesmaximal, complemented
3C11×#1443C211yesmaximal, characteristic, complemented
4C11×#1440C213yesmaximal
5C11×#1437C213yesmaximal
6C11×#1436C213yesmaximal, complemented
7C4×C11×#95C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2213yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2213yes—
11C22×C11×C22⋊C4C2213yes—
12C22×C42×C11C2213yes—
13C11×#396C418yescomplemented
14C2×C11×#95C2213yes—
15C2×C11×#95C2213yes—
16C2×C11×#95C2213yes—
17C2×C11×#95C2213yes—
18C2×C11×#95C2213yes—
19C2×C11×#95C2213yes—
20C2×C11×#95C2213yes—
21C2×C11×#95C2211yescharacteristic
22C25×C11C2311yescharacteristic
23C23×C4×C11C2313yes—
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×C4×C11C2313yes—
27C23×C4×C11C2313yes—
28C23×C4×C11C2311yescharacteristic
29C2×C11×C4⋊C4—43no—
30C2×C11×C4⋊C4—43no—
31C2×C11×C4⋊C4C2×C4112yes—
32C2×C11×C22⋊C4—26no—
33C2×C11×C22⋊C4—26no—
34C2×C11×C22⋊C4—43no—
35C2×C11×C22⋊C4—43no—
36C2×C11×C22⋊C4—43no—
37C2×C11×C22⋊C4—43no—
38C2×C11×C22⋊C4C2×C4112yes—
39C2×C42×C11—26no—
40C2×C42×C11—43no—
41C2×C42×C11—43no—
42C11×#95—26no—
43C11×#95—26no—
44C11×#95—26no—
45C11×#95—43no—
46C11×#95—43no—
47C11×#95—43no—
48C11×#95—43no—
49C11×#95C2×C414yes—
50#14331C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11—23no—
52C24×C11—23no—
53C24×C11—23no—
54C24×C11—23no—
55C24×C11—21no—
56C24×C11—21no—
57C24×C11C22×C412yes—
58C24×C11C2411yescharacteristic
59C22×C4×C11—23no—
60C22×C4×C11—21no—
61C22×C4×C11—23no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11—23no—
67C22×C4×C11—23no—
68C22×C4×C11—23no—
69C22×C4×C11—23no—
70C22×C4×C11—23no—
71C22×C4×C11—23no—
72C22×C4×C11—23no—
73C22×C4×C11—23no—
74C22×C4×C11—23no—
75C22×C4×C11—23no—
76C22×C4×C11—23no—
77C22×C4×C11—23no—
78C22×C4×C11—23no—
79C22×C4×C11—23no—
80C22×C4×C11—23no—
81C22×C4×C11—23no—
82C22×C4×C11—23no—
83C22×C4×C11—23no—
84C22×C4×C11—23no—
85C22×C4×C11—23no—
86C22×C4×C11—23no—
87C22×C4×C11—23no—
88C22×C4×C11—21no—
89C22×C4×C11C22×C416yes—
90C22×C4×C11C22×C416yes—
91C22×C4×C11#4116yes—
92C22×C4×C11#4116yes—
93C11×C4⋊C4—412no—
94C11×C22⋊C4—412no—
95C11×C22⋊C4—412no—
96C11×C22⋊C4—44no—
97C42×C11—412no—
98C2×#396C2×C1111yescharacteristic
99#1445C2×C1113yescomplemented
100#1443C2×C1111yescharacteristic, complemented
101#1440C2×C1113yes—
102#1437C2×C1113yes—
103#1436C2×C1113yescomplemented
104C4×#95C2×C1111yescharacteristic, complemented
105C23×C11—26no—
106C23×C11—26no—
107C23×C11—22no—
108C23×C11—41no—
109C23×C11—43no—
110C23×C11—43no—
111C23×C11—43no—
112C23×C11—43no—
113C23×C11—43no—
114C23×C11—43no—
115C23×C11—43no—
116C23×C11—43no—
117C23×C11—43no—
118C23×C11C23×C411yescharacteristic
119C23×C11C2×#4113yes—
120C23×C11C2×#4113yes—
121C23×C11H(5,𝔽2)13yes—
122C23×C11H(5,𝔽2)13yes—
123C23×C112−1+411yescharacteristic
124C23×C112−1+411yescharacteristic
125C2×C4×C11—26no—
126C2×C4×C11—26no—
127C2×C4×C11—26no—
128C2×C4×C11—26no—
129C2×C4×C11—26no—
130C2×C4×C11—26no—
131C2×C4×C11—26no—
132C2×C4×C11—26no—
133C2×C4×C11—26no—
134C2×C4×C11—26no—
135C2×C4×C11—26no—
136C2×C4×C11—43no—
137C2×C4×C11—43no—
138C2×C4×C11—43no—
139C2×C4×C11—43no—
140C2×C4×C11—43no—
141C2×C4×C11—43no—
142C2×C4×C11—43no—
143C2×C4×C11—43no—
144C2×C4×C11—43no—
145C2×C4×C11—43no—
146C2×C4×C11—43no—
147C2×C4×C11—43no—
148C2×C4×C11—41no—
149C2×C4×C11—43no—
150C2×C4×C11—43no—
151C2×C4×C11—43no—
152C2×C4×C11—43no—
153C2×C4×C11—43no—
154C2×C4×C11—43no—
155C2×C4×C11—43no—
156C2×C4×C11—43no—
157C2×C4×C11—43no—
158C2×C4×C11#12614yes—
159C22×C4⋊C4C22×C1113yes—
160C22×C22⋊C4C22×C1111yescharacteristic
161C22×C22⋊C4C22×C1113yes—
162C22×C22⋊C4C22×C1113yes—
163C22×C42C22×C1113yes—
164#396C4×C1118yescomplemented
165C2×#95C22×C1113yes—
166C2×#95C22×C1113yes—
167C2×#95C22×C1113yes—
168C2×#95C22×C1113yes—
169C2×#95C22×C1113yes—
170C2×#95C22×C1113yes—
171C2×#95C22×C1113yes—
172C2×#95C22×C1111yescharacteristic
173C22×C11—42no—
174C22×C11—46no—
175C22×C11—46no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—83no—
179C22×C11—83no—
180C22×C11C4×#4113yes—
181C22×C11#51813yes—
182C22×C11#51911yescharacteristic
183C22×C11C2×#12611yescharacteristic
184C22×C11#52913yes—
185C22×C11#53813yes—
186C22×C11#53813yes—
187C22×C11#53913yes—
188C22×C11#53913yes—
189C22×C11#54013yes—
190C22×C11#54013yes—
191C22×C11#54213yes—
192C22×C11#54213yes—
193C4×C11—24no—
194C4×C11—46no—
195C4×C11—46no—
196C4×C11—46no—
197C4×C11—81no—
198C4×C11—83no—
199C25C23×C1111yescharacteristic
200C23×C4C23×C1113yes—
201C23×C4C23×C1111yescharacteristic
202C23×C4C23×C1113yes—
203C23×C4C23×C1113yes—
204C23×C4C23×C1113yes—
205C23×C4C23×C1111yescharacteristic
206C2×C4⋊C4—43no—
207C2×C4⋊C4—43no—
208C2×C4⋊C4C2×C4×C11112yes—
209C2×C22⋊C4—26no—
210C2×C22⋊C4—26no—
211C2×C22⋊C4—43no—
212C2×C22⋊C4—43no—
213C2×C22⋊C4—43no—
214C2×C22⋊C4—43no—
215C2×C22⋊C4C2×C4×C11112yes—
216C2×C42—26no—
217C2×C42—43no—
218C2×C42—43no—
219#95—26no—
220#95—26no—
221#95—26no—
222#95—43no—
223#95—43no—
224#95—43no—
225#95—43no—
226#95C2×C4×C1114yes—
227C2×C11—82no—
228C2×C11C4×#12611yescharacteristic
229C2×C11#233213yes—
230C2×C11#233313yes—
231C2×C11#264311yescharacteristic
232C2×C11#264411yescharacteristic
233C2×C11#264913yes—
234C2×C11#265113yes—
235C24—23no—
236C24—23no—
237C24—23no—
238C24—23no—
239C24—21no—
240C24—21no—
241C24C22×C4×C1112yes—
242C24C24×C1111yescharacteristic
243C22×C4—23no—
244C22×C4—21no—
245C22×C4—23no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4—23no—
266C22×C4—23no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—21no—
273C22×C4C22×C4×C1116yes—
274C22×C4C22×C4×C1116yes—
275C22×C4C11×#4116yes—
276C22×C4C11×#4116yes—
277C4⋊C4—412no—
278C22⋊C4—412no—
279C22⋊C4—412no—
280C22⋊C4—44no—
281C42—412no—
282C11#1433111yescharacteristic, direct product factor, Sylow
283C23—26no—
284C23—26no—
285C23—22no—
286C23—41no—
287C23—43no—
288C23—43no—
289C23—43no—
290C23—43no—
291C23—43no—
292C23—43no—
293C23—43no—
294C23—43no—
295C23—43no—
296C23C23×C4×C1111yescharacteristic
297C23C2×C11×#4113yes—
298C23C2×C11×#4113yes—
299C23C11×H(5,𝔽2)13yes—
300C23C11×H(5,𝔽2)13yes—
301C23C11×2−1+411yescharacteristic
302C23C11×2−1+411yescharacteristic
303C2×C4—26no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—43no—
315C2×C4—43no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—41no—
327C2×C4—43no—
328C2×C4—43no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4C11×#12614yes—
337C22—42no—
338C22—46no—
339C22—46no—
340C22—81no—
341C22—81no—
342C22—83no—
343C22—83no—
344C22C4×C11×#4113yes—
345C22C11×#51813yes—
346C22C11×#51911yescharacteristic
347C22C2×C11×#12611yescharacteristic
348C22C11×#52913yes—
349C22C11×#53813yes—
350C22C11×#53813yes—
351C22C11×#53913yes—
352C22C11×#53913yes—
353C22C11×#54013yes—
354C22C11×#54013yes—
355C22C11×#54213yes—
356C22C11×#54213yes—
357C4—24no—
358C4—46no—
359C4—46no—
360C4—46no—
361C4—81no—
362C4—83no—
363C2—82no—
364C2C4×C11×#12611yescharacteristic
365C2C11×#233213yes—
366C2C11×#233313yes—
367C2C11×#264311yescharacteristic
368C2C11×#264411yescharacteristic
369C2C11×#264913yes—
370C2C11×#265113yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1445C2semidirect
3. C11×#1443C2semidirect
6. C11×#1436C2semidirect
7. C4×C11×#95C2semidirect
13. C11×#396C4semidirect
50. #14331C11direct (N × H)
99. #1445C2×C11semidirect
100. #1443C2×C11semidirect
103. #1436C2×C11semidirect
104. C4×#95C2×C11semidirect
164. #396C4×C11semidirect
282. C11#14331direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3962
C11×#14452
C11×#14432
C11×#14402
C11×#14372
C11×#14362
C4×C11×#952
#1433111