Finite Group Databasebeta

← C11×#21946 #14599139

Subgroups — C11×#21946 #14599139

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#408C211yesmaximal, characteristic
2C11×#2311C212yesmaximal
3C11×#1854C214yesmaximal, complemented
4C11×#1853C214yesmaximal, complemented
5C11×#1809C212yesmaximal, complemented
6C11×#1807C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C22×C11×M16C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C2×C11×#117C2212yes—
11C22×C11×C4⋊C4C2212yes—
12C2×C11×#107C2212yes—
13C2×C11×#106C2212yes—
14C2×C11×#106C2212yes—
15C2×C11×#106C2212yes—
16C11×#408C418yescomplemented
17C2×C11×C22⋊C8C2214yes—
18C11×#391—22no—
19C11×#390—22no—
20C11×#386—22no—
21C11×#386—22no—
22C11×#380C2214yes—
23C11×#380C2214yes—
24C11×#340C2214yes—
25C11×#340C2214yes—
26C2×C11×#41—41no—
27C2×C11×#41—41no—
28C2×C11×#41—41no—
29C2×C11×#41—41no—
30C2×C11×#41C2×C414yes—
31C2×C11×#41Q814yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D412yes—
35C23×C4×C11—22no—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C2×C11×M16—41no—
39C2×C11×M16—41no—
40C2×C11×M16C2×C414yescomplemented
41C22×C8×C11—41no—
42C22×C8×C11—41no—
43C22×C8×C11C2×C414yescomplemented
44C22×C8×C11C2312yes—
45C22×C8×C11C2312yes—
46C11×#117—42no—
47C11×#117—42no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4—42no—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C42×C11—22no—
57C11×#107—42no—
58C11×#106—42no—
59C11×#106—42no—
60C11×#106—42no—
61C11×C22⋊C8C2×C4116yescomplemented
62C11×#95—24no—
63C11×#95—24no—
64#21946C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11C2×D411yescharacteristic
66C24×C11C2×D412yes—
67C11×#41—44no—
68C11×#41—44no—
69C11×#41—44no—
70C11×#41—44no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11C4⋊C414yes—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11C4⋊C414yes—
79C2×D4×C11C4⋊C418yes—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—44no—
91C22×C4×C11—84no—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×Q814yes—
97C22×C4×C11C2×Q812yes—
98C22×C4×C11C2411yescharacteristic
99C11×M16—44no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—44no—
105C2×C8×C11C22×C414yes—
106C2×C8×C11C22×C414yes—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—44no—
112C11×C22⋊C4—44no—
113C11×C22⋊C4—84no—
114C11×C22⋊C4—84no—
115C42×C11—44no—
116C2×#408C2×C1111yescharacteristic
117#2311C2×C1112yes—
118#1854C2×C1114yescomplemented
119#1853C2×C1114yescomplemented
120#1809C2×C1112yescomplemented
121#1807C2×C1112yescomplemented
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—24no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11C2×C4⋊C414yes—
130C23×C11C2×C4⋊C412yes—
131C23×C11C22×D411yescharacteristic
132Q8×C11—44no—
133D4×C11—48no—
134D4×C11—44no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—88no—
154C2×C4×C11C2×C4⋊C414yes—
155C2×C4×C11C2×C4⋊C412yes—
156C2×C4×C11C23×C411yescharacteristic
157C2×C4×C11C22×Q811yescharacteristic
158C2×C4×C11H(5,𝔽2)11yescharacteristic
159C2×C4×C11H(5,𝔽2)11yescharacteristic
160C2×C4×C11H(5,𝔽2)11yescharacteristic
161C2×C4×C11H(5,𝔽2)11yescharacteristic
162C8×C11—24no—
163C8×C11—24no—
164C22×#41C22×C1111yescharacteristic
165C22×M16C22×C1111yescharacteristic
166C23×C8C22×C1111yescharacteristic
167C2×#117C22×C1112yes—
168C22×C4⋊C4C22×C1112yes—
169C2×#107C22×C1112yes—
170C2×#106C22×C1112yes—
171C2×#106C22×C1112yes—
172C2×#106C22×C1112yes—
173#408C4×C1118yescomplemented
174C2×C22⋊C8C22×C1114yes—
175#391—22no—
176#390—22no—
177#386—22no—
178#386—22no—
179#380C22×C1114yes—
180#380C22×C1114yes—
181#340C22×C1114yes—
182#340C22×C1114yes—
183C22×C11—22no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11—28no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—44no—
191C22×C11—42no—
192C22×C11C22×C4⋊C411yescharacteristic
193C22×C11#53411yescharacteristic
194C22×C11#53411yescharacteristic
195C22×C11#57714yes—
196C4×C11—24no—
197C4×C11—22no—
198C4×C11—84no—
199C4×C11—84no—
200C4×C11#51811yescharacteristic
201C4×C11#51811yescharacteristic
202C4×C11#54311yescharacteristic
203C4×C11#54311yescharacteristic
204C2×#41—41no—
205C2×#41—41no—
206C2×#41—41no—
207C2×#41—41no—
208C2×#41C2×C4×C1114yes—
209C2×#41Q8×C1114yes—
210C22×Q8D4×C1111yescharacteristic
211C22×D4D4×C1111yescharacteristic
212C22×D4D4×C1112yes—
213C23×C4—22no—
214C23×C4C23×C1112yes—
215C23×C4C23×C1111yescharacteristic
216C2×M16—41no—
217C2×M16—41no—
218C2×M16C2×C4×C1114yescomplemented
219C22×C8—41no—
220C22×C8—41no—
221C22×C8C2×C4×C1114yescomplemented
222C22×C8C23×C1112yes—
223C22×C8C23×C1112yes—
224#117—42no—
225#117—42no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—42no—
228C2×C4⋊C4—42no—
229C2×C4⋊C4C23×C1114yes—
230C2×C4⋊C4C23×C1114yes—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—24no—
234C2×C42—22no—
235#107—42no—
236#106—42no—
237#106—42no—
238#106—42no—
239C22⋊C8C2×C4×C11116yescomplemented
240#95—24no—
241#95—24no—
242C2×C11—44no—
243C2×C11—42no—
244C2×C11#231511yescharacteristic
245C2×C11#291212yes—
246C2×C11#320012yes—
247C2×C11#320412yes—
248C24C2×D4×C1111yescharacteristic
249C24C2×D4×C1112yes—
250#41—44no—
251#41—44no—
252#41—44no—
253#41—44no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8C11×C4⋊C414yes—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4C11×C4⋊C414yes—
262C2×D4C11×C4⋊C418yes—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—44no—
274C22×C4—84no—
275C22×C4C22×C4×C1114yes—
276C22×C4C22×C4×C1112yes—
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C2×D4×C1112yes—
279C22×C4C2×Q8×C1114yes—
280C22×C4C2×Q8×C1112yes—
281C22×C4C24×C1111yescharacteristic
282M16—44no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—44no—
288C2×C8C22×C4×C1114yes—
289C2×C8C22×C4×C1114yes—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—44no—
295C22⋊C4—44no—
296C22⋊C4—84no—
297C22⋊C4—84no—
298C42—44no—
299C11#2194611yescharacteristic, direct product factor, Sylow
300C23—22no—
301C23—22no—
302C23—21no—
303C23—21no—
304C23—24no—
305C23—24no—
306C23—24no—
307C23C2×C11×C4⋊C414yes—
308C23C2×C11×C4⋊C412yes—
309C23C22×D4×C1111yescharacteristic
310Q8—44no—
311D4—48no—
312D4—44no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—88no—
332C2×C4C2×C11×C4⋊C414yes—
333C2×C4C2×C11×C4⋊C412yes—
334C2×C4C23×C4×C1111yescharacteristic
335C2×C4C22×Q8×C1111yescharacteristic
336C2×C4C11×H(5,𝔽2)11yescharacteristic
337C2×C4C11×H(5,𝔽2)11yescharacteristic
338C2×C4C11×H(5,𝔽2)11yescharacteristic
339C2×C4C11×H(5,𝔽2)11yescharacteristic
340C8—24no—
341C8—24no—
342C22—24no—
343C22—28no—
344C22—22no—
345C22—24no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—44no—
350C22—42no—
351C22C22×C11×C4⋊C411yescharacteristic
352C22C11×#53411yescharacteristic
353C22C11×#53411yescharacteristic
354C22C11×#57714yes—
355C4—24no—
356C4—22no—
357C4—84no—
358C4—84no—
359C4C11×#51811yescharacteristic
360C4C11×#51811yescharacteristic
361C4C11×#54311yescharacteristic
362C4C11×#54311yescharacteristic
363C2—44no—
364C2—42no—
365C2C11×#231511yescharacteristic
366C2C11×#291212yes—
367C2C11×#320012yes—
368C2C11×#320412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1854C2semidirect
4. C11×#1853C2semidirect
5. C11×#1809C2semidirect
6. C11×#1807C2semidirect
16. C11×#408C4semidirect
40. C2×C11×M16C2×C4semidirect
43. C22×C8×C11C2×C4semidirect
61. C11×C22⋊C8C2×C4semidirect
64. #21946C11direct (N × H)
118. #1854C2×C11semidirect
119. #1853C2×C11semidirect
120. #1809C2×C11semidirect
121. #1807C2×C11semidirect
173. #408C4×C11semidirect
218. C2×M16C2×C4×C11semidirect
221. C22×C8C2×C4×C11semidirect
239. C22⋊C8C2×C4×C11semidirect
299. C11#21946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4082
C11×#23112
C11×#18542
C11×#18532
C11×#18092
C11×#18072
#2194611