Finite Group Databasebeta

← C11×#14637 #14591830

Subgroups — C11×#14637 #14591830

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#396C211yesmaximal, characteristic
2C11×#1445C213yesmaximal, complemented
3C11×#1444C211yesmaximal, characteristic, complemented
4C11×#1443C211yesmaximal, characteristic, complemented
5C11×#1441C213yesmaximal, complemented
6C11×#1439C213yesmaximal
7C11×C22⋊#95C213yesmaximal
8C24×C4×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2213yes—
10C22×C11×C4⋊C4C2213yes—
11C22×C11×C22⋊C4C2213yes—
12C22×C11×C22⋊C4C2213yes—
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×C11—43no—
24C23×C4×C11—43no—
25C23×C4×C11Q814yes—
26C23×C4×C11C2313yes—
27C23×C4×C11C2313yes—
28C23×C4×C11C2313yes—
29C23×C4×C11C2313yes—
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C2×C11×C4⋊C4—43no—
33C2×C11×C4⋊C4—43no—
34C2×C11×C4⋊C4—43no—
35C2×C11×C4⋊C4—43no—
36C2×C11×C4⋊C4—43no—
37C2×C11×C4⋊C4C2×C4112yescomplemented
38C2×C11×C22⋊C4—26no—
39C2×C11×C22⋊C4—43no—
40C2×C11×C22⋊C4—43no—
41C2×C11×C22⋊C4—43no—
42C2×C11×C22⋊C4—43no—
43C2×C11×C22⋊C4C2×C4112yes—
44C11×#95—43no—
45C11×#95—43no—
46C11×#95—43no—
47C11×#95—43no—
48C11×#95—43no—
49C11×#95—43no—
50C11×#95—43no—
51C11×#95C2×C414yescomplemented
52#14637C1111yesmaximal, characteristic, direct product factor, Sylow
53C24×C11—23no—
54C24×C11—23no—
55C24×C11—23no—
56C24×C11—23no—
57C24×C11C22×C412yes—
58C24×C11C2×Q812yes—
59C24×C11#4112yes—
60C24×C11C2411yescharacteristic
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—23no—
89C22×C4×C11—23no—
90C22×C4×C11—23no—
91C22×C4×C11—412no—
92C22×C4×C11—44no—
93C22×C4×C11—412no—
94C22×C4×C11C22×C416yes—
95C22×C4×C11C22×C416yes—
96C22×C4×C11C2×Q812yes—
97C22×C4×C11C2×Q812yes—
98C11×C4⋊C4—412no—
99C11×C4⋊C4—412no—
100C11×C22⋊C4—412no—
101C11×C22⋊C4—412no—
102C2×#396C2×C1111yescharacteristic
103#1445C2×C1113yescomplemented
104#1444C2×C1111yescharacteristic, complemented
105#1443C2×C1111yescharacteristic, complemented
106#1441C2×C1113yescomplemented
107#1439C2×C1113yes—
108C22⋊#95C2×C1113yes—
109C23×C11—26no—
110C23×C11—26no—
111C23×C11—26no—
112C23×C11—26no—
113C23×C11—26no—
114C23×C11—26no—
115C23×C11—41no—
116C23×C11—43no—
117C23×C11—43no—
118C23×C11—43no—
119C23×C11—43no—
120C23×C11—43no—
121C23×C11C4×Q814yes—
122C23×C11C23×C411yescharacteristic
123C23×C11C22×Q811yescharacteristic
124C23×C11C2×#4111yescharacteristic
125C23×C11H(5,𝔽2)13yes—
126C23×C11H(5,𝔽2)13yes—
127C23×C11H(5,𝔽2)13yes—
128C23×C112−1+413yes—
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—26no—
137C2×C4×C11—416no—
138C2×C4×C11—43no—
139C2×C4×C11—43no—
140C2×C4×C11—43no—
141C2×C4×C11—43no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—43no—
145C2×C4×C11—43no—
146C2×C4×C11—43no—
147C2×C4×C11—43no—
148C2×C4×C11—43no—
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—43no—
159C2×C4×C11—43no—
160C2×C4×C11—43no—
161C2×C4×C11—43no—
162C2×C4×C11—43no—
163C2×C4×C11—43no—
164C24×C4C22×C1111yescharacteristic
165C22×C4⋊C4C22×C1113yes—
166C22×C4⋊C4C22×C1113yes—
167C22×C22⋊C4C22×C1113yes—
168C22×C22⋊C4C22×C1113yes—
169#396C4×C1118yescomplemented
170C2×#95C22×C1113yes—
171C2×#95C22×C1113yes—
172C2×#95C22×C1113yes—
173C2×#95C22×C1113yes—
174C2×#95C22×C1113yes—
175C2×#95C22×C1113yes—
176C2×#95C22×C1113yes—
177C2×#95C22×C1111yescharacteristic
178C22×C11—212no—
179C22×C11—42no—
180C22×C11—46no—
181C22×C11—46no—
182C22×C11—42no—
183C22×C11—46no—
184C22×C11—42no—
185C22×C11C2×C4×Q811yescharacteristic
186C22×C11#51813yes—
187C22×C11#52013yes—
188C22×C11#53813yes—
189C22×C11#53913yes—
190C22×C11#54313yes—
191C22×C11#54413yes—
192C22×C11#56013yes—
193C22×C11#56011yescharacteristic
194C22×C11#56013yes—
195C22×C11#56213yes—
196C22×C11#56213yes—
197C22×C11#56313yes—
198C4×C11—42no—
199C4×C11—42no—
200C4×C11—46no—
201C4×C11—46no—
202C4×C11—83no—
203C4×C11—83no—
204C25C23×C1111yescharacteristic
205C23×C4—43no—
206C23×C4—43no—
207C23×C4Q8×C1114yes—
208C23×C4C23×C1113yes—
209C23×C4C23×C1113yes—
210C23×C4C23×C1113yes—
211C23×C4C23×C1113yes—
212C23×C4C23×C1111yescharacteristic
213C23×C4C23×C1111yescharacteristic
214C2×C4⋊C4—43no—
215C2×C4⋊C4—43no—
216C2×C4⋊C4—43no—
217C2×C4⋊C4—43no—
218C2×C4⋊C4—43no—
219C2×C4⋊C4C2×C4×C11112yescomplemented
220C2×C22⋊C4—26no—
221C2×C22⋊C4—43no—
222C2×C22⋊C4—43no—
223C2×C22⋊C4—43no—
224C2×C22⋊C4—43no—
225C2×C22⋊C4C2×C4×C11112yes—
226#95—43no—
227#95—43no—
228#95—43no—
229#95—43no—
230#95—43no—
231#95—43no—
232#95—43no—
233#95C2×C4×C1114yescomplemented
234C2×C11—44no—
235C2×C11#232913yes—
236C2×C11#237713yes—
237C2×C11#238311yescharacteristic
238C2×C11#282511yescharacteristic
239C2×C11#282713yes—
240C2×C11#284113yes—
241C2×C11#284211yescharacteristic
242C24—23no—
243C24—23no—
244C24—23no—
245C24—23no—
246C24C22×C4×C1112yes—
247C24C2×Q8×C1112yes—
248C24C11×#4112yes—
249C24C24×C1111yescharacteristic
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—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—23no—
276C22×C4—23no—
277C22×C4—23no—
278C22×C4—23no—
279C22×C4—23no—
280C22×C4—412no—
281C22×C4—44no—
282C22×C4—412no—
283C22×C4C22×C4×C1116yes—
284C22×C4C22×C4×C1116yes—
285C22×C4C2×Q8×C1112yes—
286C22×C4C2×Q8×C1112yes—
287C4⋊C4—412no—
288C4⋊C4—412no—
289C22⋊C4—412no—
290C22⋊C4—412no—
291C11#1463711yescharacteristic, direct product factor, Sylow
292C23—26no—
293C23—26no—
294C23—26no—
295C23—26no—
296C23—26no—
297C23—26no—
298C23—41no—
299C23—43no—
300C23—43no—
301C23—43no—
302C23—43no—
303C23—43no—
304C23C4×Q8×C1114yes—
305C23C23×C4×C1111yescharacteristic
306C23C22×Q8×C1111yescharacteristic
307C23C2×C11×#4111yescharacteristic
308C23C11×H(5,𝔽2)13yes—
309C23C11×H(5,𝔽2)13yes—
310C23C11×H(5,𝔽2)13yes—
311C23C11×2−1+413yes—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—416no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—41no—
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×C4—43no—
337C2×C4—43no—
338C2×C4—43no—
339C2×C4—43no—
340C2×C4—43no—
341C2×C4—43no—
342C2×C4—43no—
343C2×C4—43no—
344C2×C4—43no—
345C2×C4—43no—
346C2×C4—43no—
347C22—212no—
348C22—42no—
349C22—42no—
350C22—46no—
351C22—46no—
352C22—42no—
353C22—46no—
354C22C2×C4×Q8×C1111yescharacteristic
355C22C11×#51813yes—
356C22C11×#52013yes—
357C22C11×#53813yes—
358C22C11×#53913yes—
359C22C11×#54313yes—
360C22C11×#54413yes—
361C22C11×#56011yescharacteristic
362C22C11×#56013yes—
363C22C11×#56013yes—
364C22C11×#56213yes—
365C22C11×#56213yes—
366C22C11×#56313yes—
367C4—42no—
368C4—42no—
369C4—46no—
370C4—46no—
371C4—83no—
372C4—83no—
373C2—44no—
374C2C11×#232913yes—
375C2C11×#237713yes—
376C2C11×#238311yescharacteristic
377C2C11×#282511yescharacteristic
378C2C11×#282713yes—
379C2C11×#284113yes—
380C2C11×#284211yescharacteristic
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×#1444C2semidirect
4. C11×#1443C2semidirect
5. C11×#1441C2semidirect
13. C11×#396C4semidirect
37. C2×C11×C4⋊C4C2×C4semidirect
51. C11×#95C2×C4semidirect
52. #14637C11direct (N × H)
103. #1445C2×C11semidirect
104. #1444C2×C11semidirect
105. #1443C2×C11semidirect
106. #1441C2×C11semidirect
169. #396C4×C11semidirect
219. C2×C4⋊C4C2×C4×C11semidirect
233. #95C2×C4×C11semidirect
291. C11#14637direct (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×#14442
C11×#14432
C11×#14412
C11×#14392
C11×C22⋊#952
#1463711