Finite Group Databasebeta

← C11×#11209 #14588402

Subgroups — C11×#11209 #14588402

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#423C211yesmaximal, characteristic
2C11×#2296C211yesmaximal, characteristic
3C2×C11×#339C212yesmaximal
4C2×C11×#339C212yesmaximal
5C4×C11×#95C211yesmaximal, characteristic
6C22×C11×M16C2212yes—
7C2×C11×#117C2211yescharacteristic
8C2×C11×#117C2211yescharacteristic
9C22×C42×C11C2212yes—
10C22×C42×C11C2211yescharacteristic
11C11×#423—24no—
12C2×C11×C4⋊C8—22no—
13C11×#389C412yescomplemented
14C11×#389C412yescomplemented
15C11×#385—22no—
16C4×C11×C4⋊C4—22no—
17C2×C11×#95—22no—
18C11×#339—24no—
19C11×#339—24no—
20C23×C4×C11—22no—
21C23×C4×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C2×C11×M16—22no—
24C2×C11×M16—22no—
25C2×C11×M16—22no—
26C2×C11×M16—22no—
27C2×C11×M16—22no—
28C2×C11×M16D414yes—
29C22×C8×C11—22no—
30C11×#117—21no—
31C11×#117—21no—
32C11×#117—22no—
33C11×#117—22no—
34C11×#117D412yes—
35C11×#117Q812yes—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4C2×C412yes—
39C2×C11×C4⋊C4C2×C412yes—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C42×C11—22no—
43C2×C42×C11—21no—
44C2×C42×C11—22no—
45C2×C42×C11—22no—
46C2×C42×C11—22no—
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11—21no—
50C2×C42×C11—22no—
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11D412yes—
54C2×C42×C11Q814yes—
55C11×C4⋊C8—28no—
56C11×#95—28no—
57C11×#95—22no—
58C11×#95—22no—
59#11209C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11C2×D411yescharacteristic
61C22×C4×C11—28no—
62C22×C4×C11—22no—
63C22×C4×C11—24no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—22no—
67C22×C4×C11—42no—
68C22×C4×C11—44no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C412yes—
72C22×C4×C11C22⋊C412yes—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×Q811yescharacteristic
78C22×C4×C11C2×Q812yes—
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4112yes—
82C22×C4×C11#4112yes—
83C11×M16—24no—
84C11×M16—24no—
85C11×M16—42no—
86C11×M16—42no—
87C2×C8×C11—24no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—44no—
93C11×C4⋊C4—44no—
94C11×C4⋊C4C4⋊C414yes—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—42no—
98C42×C11—22no—
99C42×C11—22no—
100C42×C11—22no—
101C42×C11—22no—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11—24no—
105C42×C11—24no—
106C42×C11—41no—
107C42×C11—42no—
108C42×C11—41no—
109C42×C11—42no—
110C2×#423C2×C1111yescharacteristic
111#2296C2×C1111yescharacteristic
112C2×#339C2×C1112yes—
113C2×#339C2×C1112yes—
114C4×#95C2×C1111yescharacteristic
115C23×C11—22no—
116C23×C11—22no—
117C23×C11C2×C22⋊C411yescharacteristic
118C23×C11#12111yescharacteristic
119C23×C11#12112yes—
120C23×C11C22⋊Q811yescharacteristic
121C23×C11C22⋊Q812yes—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—28no—
125C2×C4×C11—24no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—48no—
130C2×C4×C11—48no—
131C2×C4×C11—48no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11#10414yes—
140C2×C4×C11C2×C4⋊C411yescharacteristic
141C2×C4×C11#11711yescharacteristic
142C2×C4×C11C4×D412yes—
143C2×C4×C11C4×Q812yes—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12112yes—
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11C22⋊Q812yes—
148C2×C4×C11C22⋊Q812yes—
149C2×C4×C11C22⋊Q811yescharacteristic
150C2×C4×C11#12312yes—
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12411yescharacteristic
153C2×C4×C11#12512yes—
154C2×C4×C11#12512yes—
155C2×C4×C11#12612yes—
156C2×C4×C11C4⋊Q812yes—
157C2×C4×C11C4⋊Q811yescharacteristic
158C8×C11—44no—
159C22×M16C22×C1112yes—
160C2×#117C22×C1111yescharacteristic
161C2×#117C22×C1111yescharacteristic
162C22×C42C22×C1112yes—
163C22×C42C22×C1111yescharacteristic
164#423—24no—
165C2×C4⋊C8—22no—
166#389C4×C1112yescomplemented
167#389C4×C1112yescomplemented
168#385—22no—
169C4×C4⋊C4—22no—
170C2×#95—22no—
171#339—24no—
172#339—24no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—24no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11#38011yescharacteristic
179C22×C11#38611yescharacteristic
180C22×C11#39111yescharacteristic
181C22×C11#39612yes—
182C22×C11#39812yes—
183C22×C11C2×#10412yes—
184C22×C11#42112yes—
185C4×C11—24no—
186C4×C11—48no—
187C4×C11—44no—
188C4×C11—42no—
189C4×C11—82no—
190C4×C11#38712yes—
191C4×C11#38912yes—
192C4×C11#39411yescharacteristic
193C4×C11#39511yescharacteristic
194C4×C11#39811yescharacteristic
195C4×C11#40011yescharacteristic
196C23×C4—22no—
197C23×C4D4×C1112yes—
198C23×C4C23×C1111yescharacteristic
199C2×M16—22no—
200C2×M16—22no—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16D4×C1114yes—
205C22×C8—22no—
206#117—21no—
207#117—21no—
208#117—22no—
209#117—22no—
210#117D4×C1112yes—
211#117Q8×C1112yes—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4C2×C4×C1112yes—
215C2×C4⋊C4C2×C4×C1112yes—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C42—21no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—21no—
226C2×C42—22no—
227C2×C42C2×C4×C1111yescharacteristic
228C2×C42C2×C4×C1111yescharacteristic
229C2×C42D4×C1112yes—
230C2×C42Q8×C1114yes—
231C4⋊C8—28no—
232#95—28no—
233#95—22no—
234#95—22no—
235C2×C11—22no—
236C2×C11—22no—
237C2×C11#144111yescharacteristic
238C2×C11#180612yes—
239C2×C11#187112yes—
240C2×C11#199411yescharacteristic
241C2×C11#199511yescharacteristic
242C24C2×D4×C1111yescharacteristic
243C22×C4—28no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—44no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4C11×C22⋊C412yes—
254C22×C4C11×C22⋊C412yes—
255C22×C4C22×C4×C1111yescharacteristic
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×D4×C1112yes—
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C2×Q8×C1111yescharacteristic
260C22×C4C2×Q8×C1112yes—
261C22×C4C11×#4111yescharacteristic
262C22×C4C11×#4111yescharacteristic
263C22×C4C11×#4112yes—
264C22×C4C11×#4112yes—
265M16—24no—
266M16—24no—
267M16—42no—
268M16—42no—
269C2×C8—24no—
270C2×C8—42no—
271C2×C8—42no—
272C4⋊C4—22no—
273C4⋊C4—24no—
274C4⋊C4—44no—
275C4⋊C4—44no—
276C4⋊C4C11×C4⋊C414yes—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—42no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—22no—
286C42—24no—
287C42—24no—
288C42—41no—
289C42—42no—
290C42—41no—
291C42—42no—
292C11#1120911yescharacteristic, direct product factor, Sylow
293C23—22no—
294C23—22no—
295C23C2×C11×C22⋊C411yescharacteristic
296C23C11×#12111yescharacteristic
297C23C11×#12112yes—
298C23C11×C22⋊Q811yescharacteristic
299C23C11×C22⋊Q812yes—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—28no—
303C2×C4—24no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—48no—
308C2×C4—48no—
309C2×C4—44no—
310C2×C4—48no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4C11×#10414yes—
318C2×C4C2×C11×C4⋊C411yescharacteristic
319C2×C4C11×#11711yescharacteristic
320C2×C4C4×D4×C1112yes—
321C2×C4C4×Q8×C1112yes—
322C2×C4C11×#12011yescharacteristic
323C2×C4C11×#12112yes—
324C2×C4C11×#12111yescharacteristic
325C2×C4C11×C22⋊Q812yes—
326C2×C4C11×C22⋊Q812yes—
327C2×C4C11×C22⋊Q811yescharacteristic
328C2×C4C11×#12312yes—
329C2×C4C11×#12311yescharacteristic
330C2×C4C11×#12411yescharacteristic
331C2×C4C11×#12512yes—
332C2×C4C11×#12512yes—
333C2×C4C11×#12612yes—
334C2×C4C11×C4⋊Q812yes—
335C2×C4C11×C4⋊Q811yescharacteristic
336C8—44no—
337C22—24no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22C11×#38011yescharacteristic
343C22C11×#38611yescharacteristic
344C22C11×#39111yescharacteristic
345C22C11×#39612yes—
346C22C11×#39812yes—
347C22C2×C11×#10412yes—
348C22C11×#42112yes—
349C4—24no—
350C4—48no—
351C4—42no—
352C4—44no—
353C4—82no—
354C4C11×#38712yes—
355C4C11×#38912yes—
356C4C11×#39411yescharacteristic
357C4C11×#39511yescharacteristic
358C4C11×#39811yescharacteristic
359C4C11×#40011yescharacteristic
360C2—22no—
361C2—22no—
362C2C11×#144111yescharacteristic
363C2C11×#180612yes—
364C2C11×#187112yes—
365C2C11×#199411yescharacteristic
366C2C11×#199511yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
13. C11×#389C4semidirect
14. C11×#389C4semidirect
59. #11209C11direct (N × H)
166. #389C4×C11semidirect
167. #389C4×C11semidirect
292. C11#11209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4232
C11×#22962
C2×C11×#3392
C4×C11×#952
#1120911