Finite Group Databasebeta

← C11×#23203 #14600396

Subgroups — C11×#23203 #14600396

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#497C211yesmaximal, characteristic
2C11×#2950C212yesmaximal, complemented
3C11×#2949C212yesmaximal
4C11×#1979C212yesmaximal, complemented
5C11×#1977C212yesmaximal
6C11×#1888C211yesmaximal, characteristic
7C11×#1886C212yesmaximal, complemented
8C11×#1885C211yesmaximal, characteristic
9C11×#1773C212yesmaximal, complemented
10C22×C11×Q16C2212yes—
11C22×C11×SD16C2212yes—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#124C2211yescharacteristic
14C11×#519C2212yes—
15C11×#519C2211yescharacteristic
16C11×#518C2211yescharacteristic
17C11×#497C418yescomplemented
18C11×#441—24no—
19C11×#440—24no—
20C4×C11×Q16—24no—
21C4×C11×SD16—24no—
22C2×C11×#108C2212yes—
23C11×#427C2212yes—
24C11×#419C2212yes—
25C11×#419C2212yes—
26C11×#419C2212yes—
27C11×#418C2212yes—
28C2×C11×#101C2212yes—
29C2×C11×#101C2211yescharacteristic
30C2×C11×#100C2211yescharacteristic
31C11×#405C2212yes—
32C11×#405C2212yes—
33C2×C11×#97C2211yescharacteristic
34C11×#339C2212yes—
35C11×#339C2212yes—
36C22×Q8×C11C2311yescharacteristic
37C22×Q8×C11C2312yes—
38C22×D4×C11C2311yescharacteristic
39C2×C11×Q16—22no—
40C2×C11×Q16—22no—
41C2×C11×Q16—24no—
42C2×C11×Q16C2×C418yescomplemented
43C2×C11×SD16—22no—
44C2×C11×SD16—22no—
45C2×C11×SD16—24no—
46C2×C11×SD16C2×C418yes—
47C2×C11×M16C2312yes—
48C2×C11×M16C2312yes—
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—41no—
51C11×C4⋊Q8C2×C414yescomplemented
52C11×#124—41no—
53C11×#124C2×C414yes—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—24no—
57C4×D4×C11—24no—
58C11×#117—42no—
59C11×#117—41no—
60C11×#117C2312yes—
61C11×#117C2312yes—
62C2×C11×C4⋊C4—41no—
63C2×C11×C22⋊C4—41no—
64C2×C11×C22⋊C4—41no—
65C2×C42×C11C2311yescharacteristic
66C11×#108—24no—
67C11×#107D414yes—
68C11×#106D414yes—
69C11×#103—24no—
70C11×#103—24no—
71C11×#103—24no—
72C11×#102—24no—
73C11×#101—42no—
74C11×#101—41no—
75C11×#100—41no—
76C11×#97—22no—
77C11×#97—22no—
78C11×#97C2×C414yescomplemented
79C4×C8×C11—22no—
80C4×C8×C11—22no—
81#23203C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11C22×C412yes—
92C2×Q8×C11C22×C414yes—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11C22×C412yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—42no—
101C22×C4×C11C2411yescharacteristic
102C11×Q16—28no—
103C11×Q16—28no—
104C11×SD16—28no—
105C11×SD16—28no—
106C11×M16—22no—
107C11×M16—22no—
108C11×M16—22no—
109C11×M16—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11C22×C414yes—
113C2×C8×C11C2×D412yes—
114C2×C8×C11C2×D412yes—
115C2×C8×C11#4114yes—
116C11×C4⋊C4—44no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—44no—
119C11×C4⋊C4C2×D414yes—
120C11×C4⋊C4C2×D414yes—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—44no—
124C11×C22⋊C4—42no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11—21no—
128C42×C11—42no—
129C42×C11—44no—
130C42×C11C22×C412yes—
131C2×#497C2×C1111yescharacteristic
132#2950C2×C1112yescomplemented
133#2949C2×C1112yes—
134#1979C2×C1112yescomplemented
135#1977C2×C1112yes—
136#1888C2×C1111yescharacteristic
137#1886C2×C1112yescomplemented
138#1885C2×C1111yescharacteristic
139#1773C2×C1112yescomplemented
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—82no—
144C23×C11H(5,𝔽2)11yescharacteristic
145Q8×C11—24no—
146Q8×C11—24no—
147Q8×C11—24no—
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—42no—
151D4×C11—24no—
152D4×C11—42no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—162no—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D412yes—
166C2×C4×C11C2×#4112yes—
167C2×C4×C11H(5,𝔽2)11yescharacteristic
168C8×C11—42no—
169C8×C11—42no—
170C8×C11C4×D414yes—
171C8×C11C4×D414yes—
172C22×Q16C22×C1112yes—
173C22×SD16C22×C1112yes—
174C2×C4⋊Q8C22×C1111yescharacteristic
175C2×#124C22×C1111yescharacteristic
176#519C22×C1112yes—
177#519C22×C1111yescharacteristic
178#518C22×C1111yescharacteristic
179#497C4×C1118yescomplemented
180#441—24no—
181#440—24no—
182C4×Q16—24no—
183C4×SD16—24no—
184C2×#108C22×C1112yes—
185#427C22×C1112yes—
186#419C22×C1112yes—
187#419C22×C1112yes—
188#419C22×C1112yes—
189#418C22×C1112yes—
190C2×#101C22×C1112yes—
191C2×#101C22×C1111yescharacteristic
192C2×#100C22×C1111yescharacteristic
193#405C22×C1112yes—
194#405C22×C1112yes—
195C2×#97C22×C1111yescharacteristic
196#339C22×C1112yes—
197#339C22×C1112yes—
198C22×C11—22no—
199C22×C11—42no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11—161no—
203C22×C11#51811yescharacteristic
204C22×C11D4211yescharacteristic
205C22×C11#55911yescharacteristic
206C4×C11—42no—
207C4×C11—42no—
208C4×C11—44no—
209C4×C11—44no—
210C4×C11—44no—
211C4×C11C2×C4×D412yes—
212C4×C11#55012yes—
213C22×Q8C23×C1111yescharacteristic
214C22×Q8C23×C1112yes—
215C22×D4C23×C1111yescharacteristic
216C2×Q16—22no—
217C2×Q16—22no—
218C2×Q16—24no—
219C2×Q16C2×C4×C1118yescomplemented
220C2×SD16—22no—
221C2×SD16—22no—
222C2×SD16—24no—
223C2×SD16C2×C4×C1118yes—
224C2×M16C23×C1112yes—
225C2×M16C23×C1112yes—
226C22×C8C23×C1112yes—
227C4⋊Q8—41no—
228C4⋊Q8C2×C4×C1114yescomplemented
229#124—41no—
230#124C2×C4×C1114yes—
231C4×Q8—24no—
232C4×Q8—24no—
233C4×Q8—24no—
234C4×D4—24no—
235#117—42no—
236#117—41no—
237#117C23×C1112yes—
238#117C23×C1112yes—
239C2×C4⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—41no—
242C2×C42C23×C1111yescharacteristic
243#108—24no—
244#107D4×C1114yes—
245#106D4×C1114yes—
246#103—24no—
247#103—24no—
248#103—24no—
249#102—24no—
250#101—42no—
251#101—41no—
252#100—41no—
253#97—22no—
254#97—22no—
255#97C2×C4×C1114yescomplemented
256C4×C8—22no—
257C4×C8—22no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—82no—
261C2×C11#236611yescharacteristic
262C2×C11#328912yes—
263C24—21no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8C22×C4×C1112yes—
273C2×Q8C22×C4×C1114yes—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—21no—
277C2×D4C22×C4×C1112yes—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4C24×C1111yescharacteristic
283Q16—28no—
284Q16—28no—
285SD16—28no—
286SD16—28no—
287M16—22no—
288M16—22no—
289M16—22no—
290M16—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8C22×C4×C1114yes—
294C2×C8C2×D4×C1112yes—
295C2×C8C2×D4×C1112yes—
296C2×C8C11×#4114yes—
297C4⋊C4—44no—
298C4⋊C4—42no—
299C4⋊C4—44no—
300C4⋊C4C2×D4×C1114yes—
301C4⋊C4C2×D4×C1114yes—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—44no—
305C22⋊C4—42no—
306C42—22no—
307C42—22no—
308C42—21no—
309C42—42no—
310C42—44no—
311C42C22×C4×C1112yes—
312C11#2320311yescharacteristic, direct product factor, Sylow
313C23—22no—
314C23—41no—
315C23—41no—
316C23—82no—
317C23C11×H(5,𝔽2)11yescharacteristic
318Q8—24no—
319Q8—24no—
320Q8—24no—
321Q8—42no—
322Q8—42no—
323Q8—42no—
324D4—24no—
325D4—42no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—162no—
337C2×C4C23×C4×C1111yescharacteristic
338C2×C4C22×D4×C1112yes—
339C2×C4C2×C11×#4112yes—
340C2×C4C11×H(5,𝔽2)11yescharacteristic
341C8—42no—
342C8—42no—
343C8C4×D4×C1114yes—
344C8C4×D4×C1114yes—
345C22—22no—
346C22—42no—
347C22—82no—
348C22—82no—
349C22—161no—
350C22C11×#51811yescharacteristic
351C22D42×C1111yescharacteristic
352C22C11×#55911yescharacteristic
353C4—42no—
354C4—44no—
355C4—44no—
356C4—42no—
357C4—44no—
358C4C2×C4×D4×C1112yes—
359C4C11×#55012yes—
360C2—21no—
361C2—21no—
362C2—82no—
363C2C11×#236611yescharacteristic
364C2C11×#328912yes—
subgroupG/H
center, socleC22×C11D42
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2950C2semidirect
4. C11×#1979C2semidirect
7. C11×#1886C2semidirect
9. C11×#1773C2semidirect
17. C11×#497C4semidirect
42. C2×C11×Q16C2×C4semidirect
51. C11×C4⋊Q8C2×C4semidirect
78. C11×#97C2×C4semidirect
81. #23203C11direct (N × H)
132. #2950C2×C11semidirect
134. #1979C2×C11semidirect
137. #1886C2×C11semidirect
139. #1773C2×C11semidirect
179. #497C4×C11semidirect
219. C2×Q16C2×C4×C11semidirect
228. C4⋊Q8C2×C4×C11semidirect
255. #97C2×C4×C11semidirect
312. C11#23203direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4972
C11×#29502
C11×#29492
C11×#19792
C11×#19772
C11×#18882
C11×#18862
C11×#18852
C11×#17732
#2320311