Finite Group Databasebeta

← C11×#36700 #14613893

Subgroups — C11×#36700 #14613893

Order 2816.

1356 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2839C214yesmaximal, complemented
2C11×#2836C214yesmaximal
3C11×#2833C214yesmaximal, complemented
4C11×#2831C214yesmaximal
5C11×#2402C211yesmaximal, characteristic, complemented
6C11×#2402C214yesmaximal, complemented
7C11×#2401C214yesmaximal
8C11×#2399C211yesmaximal, characteristic, complemented
9C11×#2396C212yesmaximal
10C11×#2298C211yesmaximal, characteristic
11C11×#2295C212yesmaximal, complemented
12C2×C4×Q8×C11C2212yes—
13C2×C11×#117C2211yescharacteristic
14C11×#401C2214yes—
15C11×#400C2212yes—
16C11×#400C2214yes—
17C11×#400C2214yes—
18C11×#400C2214yes—
19C11×#400C2214yes—
20C11×#400C2214yes—
21C11×#400C2214yes—
22C11×#400C2214yes—
23C11×#400C2214yes—
24C11×#399C2212yes—
25C11×#398C2214yes—
26C11×#398C2214yes—
27C11×#398C2214yes—
28C11×#398C2214yes—
29C11×#398C2214yes—
30C11×#398C2214yes—
31C11×#398C2214yes—
32C11×#397C2214yes—
33C11×#397C2214yes—
34C11×#397C2214yes—
35C11×#396C2214yes—
36C11×#396C2214yes—
37C11×#395C2212yes—
38C11×#395C2214yes—
39C11×#393C2212yes—
40C11×#391C2214yes—
41C11×#389C2214yes—
42C11×#388C2214yes—
43C11×#387C2214yes—
44C11×#387C2214yes—
45C11×#387C2214yes—
46C4×C11×C4⋊C4C2214yes—
47C4×C11×C4⋊C4C2212yes—
48C4×C11×C4⋊C4C2214yes—
49C4×C11×C4⋊C4C2214yes—
50C4×C11×C4⋊C4C2214yes—
51C4×C11×C4⋊C4C2212yes—
52C4×C11×C22⋊C4C2214yes—
53C4×C11×C22⋊C4C2212yes—
54C11×#376C2211yescharacteristic
55C11×#376C2214yes—
56C43×C11C2211yescharacteristic
57C22×Q8×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C4×Q8×C11—28no—
60C11×#117—24no—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2314yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C22⋊C4C2312yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C42×C11C2312yes—
79C2×C42×C11C2312yes—
80C2×C42×C11C2314yes—
81C2×C42×C11C2314yes—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2314yes—
84C2×C42×C11C2311yescharacteristic
85C11×#95C2314yes—
86C11×#95C2314yes—
87C11×#95C2314yes—
88C11×#95C2314yes—
89C11×#95C2314yes—
90C11×#95C2314yes—
91C11×#95C2314yes—
92C11×#95C2314yes—
93C11×#95C2312yes—
94C11×#95C2312yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104#36700C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11C2411yescharacteristic
106C2×Q8×C11—24no—
107C2×Q8×C11—44no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11C2411yescharacteristic
111C22×C4×C11C2414yes—
112C22×C4×C11C2414yes—
113C22×C4×C11C2414yes—
114C22×C4×C11C2414yes—
115C22×C4×C11C2414yes—
116C22×C4×C11C2412yes—
117C22×C4×C11C2414yes—
118C22×C4×C11C2412yes—
119C22×C4×C11C2411yescharacteristic
120C11×C4⋊C4—24no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—28no—
123C11×C4⋊C4—44no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4—44no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4—44no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4—44no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—44no—
135C11×C22⋊C4—44no—
136C11×C22⋊C4—44no—
137C42×C11—22no—
138C42×C11—28no—
139C42×C11—24no—
140C42×C11—24no—
141C42×C11—28no—
142C42×C11—44no—
143C42×C11#4114yes—
144#2839C2×C1114yescomplemented
145#2836C2×C1114yes—
146#2833C2×C1114yescomplemented
147#2831C2×C1114yes—
148#2402C2×C1111yescharacteristic, complemented
149#2402C2×C1114yescomplemented
150#2401C2×C1114yes—
151#2399C2×C1111yescharacteristic, complemented
152#2396C2×C1112yes—
153#2298C2×C1111yescharacteristic
154#2295C2×C1112yescomplemented
155C23×C11—21no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11C2511yescharacteristic
159Q8×C11—48no—
160C2×C4×C11—24no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—21no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—44no—
184C2×C4×C11C2×#4114yes—
185C2×C4×C11C2×#4112yes—
186C2×C4×C112−1+414yes—
187C2×C4×Q8C22×C1112yes—
188C2×#117C22×C1111yescharacteristic
189#401C22×C1114yes—
190#400C22×C1114yes—
191#400C22×C1114yes—
192#400C22×C1114yes—
193#400C22×C1114yes—
194#400C22×C1114yes—
195#400C22×C1114yes—
196#400C22×C1114yes—
197#400C22×C1112yes—
198#400C22×C1114yes—
199#399C22×C1112yes—
200#398C22×C1114yes—
201#398C22×C1114yes—
202#398C22×C1114yes—
203#398C22×C1114yes—
204#398C22×C1114yes—
205#398C22×C1114yes—
206#398C22×C1114yes—
207#397C22×C1114yes—
208#397C22×C1114yes—
209#397C22×C1114yes—
210#396C22×C1114yes—
211#396C22×C1114yes—
212#395C22×C1114yes—
213#395C22×C1112yes—
214#393C22×C1112yes—
215#391C22×C1114yes—
216#389C22×C1114yes—
217#388C22×C1114yes—
218#387C22×C1114yes—
219#387C22×C1114yes—
220#387C22×C1114yes—
221C4×C4⋊C4C22×C1114yes—
222C4×C4⋊C4C22×C1112yes—
223C4×C4⋊C4C22×C1114yes—
224C4×C4⋊C4C22×C1114yes—
225C4×C4⋊C4C22×C1114yes—
226C4×C4⋊C4C22×C1112yes—
227C4×C22⋊C4C22×C1114yes—
228C4×C22⋊C4C22×C1112yes—
229#376C22×C1111yescharacteristic
230#376C22×C1114yes—
231C43C22×C1111yescharacteristic
232C22×C11—41no—
233C22×C11—42no—
234C22×C11—44no—
235C22×C11C22×#4111yescharacteristic
236C22×C11C2×2−1+412yes—
237C22×C11#58514yes—
238C4×C11—24no—
239C4×C11—41no—
240C4×C11—42no—
241C4×C11—44no—
242C4×C11—44no—
243C4×C11—44no—
244C4×C11—44no—
245C4×C11—44no—
246C4×C11—44no—
247C4×C11#54114yes—
248C22×Q8C23×C1112yes—
249C23×C4C23×C1111yescharacteristic
250C4×Q8—28no—
251#117—24no—
252C2×C4⋊C4C23×C1112yes—
253C2×C4⋊C4C23×C1114yes—
254C2×C4⋊C4C23×C1112yes—
255C2×C4⋊C4C23×C1114yes—
256C2×C4⋊C4C23×C1114yes—
257C2×C4⋊C4C23×C1114yes—
258C2×C4⋊C4C23×C1114yes—
259C2×C4⋊C4C23×C1114yes—
260C2×C4⋊C4C23×C1114yes—
261C2×C4⋊C4C23×C1114yes—
262C2×C4⋊C4C23×C1114yes—
263C2×C4⋊C4C23×C1114yes—
264C2×C4⋊C4C23×C1114yes—
265C2×C22⋊C4C23×C1112yes—
266C2×C22⋊C4C23×C1114yes—
267C2×C22⋊C4C23×C1114yes—
268C2×C22⋊C4C23×C1114yes—
269C2×C42C23×C1111yescharacteristic
270C2×C42C23×C1114yes—
271C2×C42C23×C1112yes—
272C2×C42C23×C1112yes—
273C2×C42C23×C1114yes—
274C2×C42C23×C1114yes—
275C2×C42C23×C1111yescharacteristic
276#95C23×C1114yes—
277#95C23×C1114yes—
278#95C23×C1114yes—
279#95C23×C1114yes—
280#95C23×C1114yes—
281#95C23×C1114yes—
282#95C23×C1114yes—
283#95C23×C1114yes—
284#95C23×C1112yes—
285#95C23×C1112yes—
286#95C23×C1114yes—
287#95C23×C1114yes—
288#95C23×C1114yes—
289#95C23×C1114yes—
290#95C23×C1114yes—
291#95C23×C1114yes—
292#95C23×C1114yes—
293#95C23×C1114yes—
294#95C23×C1114yes—
295C2×C11—81no—
296C2×C11C2×#54111yescharacteristic
297C2×C11#345512yes—
298C2×C11#353114yes—
299C24C24×C1111yescharacteristic
300C2×Q8—24no—
301C2×Q8—44no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4C24×C1111yescharacteristic
305C22×C4C24×C1114yes—
306C22×C4C24×C1114yes—
307C22×C4C24×C1114yes—
308C22×C4C24×C1114yes—
309C22×C4C24×C1114yes—
310C22×C4C24×C1112yes—
311C22×C4C24×C1114yes—
312C22×C4C24×C1112yes—
313C22×C4C24×C1111yescharacteristic
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—28no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—44no—
320C4⋊C4—44no—
321C4⋊C4—44no—
322C4⋊C4—44no—
323C4⋊C4—44no—
324C4⋊C4—44no—
325C4⋊C4—44no—
326C4⋊C4—44no—
327C22⋊C4—24no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C42—22no—
332C42—28no—
333C42—24no—
334C42—24no—
335C42—28no—
336C42—44no—
337C42C11×#4114yes—
338C11#3670011yescharacteristic, direct product factor, Sylow
339C23—21no—
340C23—22no—
341C23—24no—
342C23C25×C1111yescharacteristic
343Q8—48no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—44no—
368C2×C4C2×C11×#4114yes—
369C2×C4C2×C11×#4112yes—
370C2×C4C11×2−1+414yes—
371C22—41no—
372C22—42no—
373C22—44no—
374C22C22×C11×#4111yescharacteristic
375C22C2×C11×2−1+412yes—
376C22C11×#58514yes—
377C4—24no—
378C4—41no—
379C4—44no—
380C4—42no—
381C4—44no—
382C4—44no—
383C4—44no—
384C4—44no—
385C4—44no—
386C4C11×#54114yes—
387C2—81no—
388C2C2×C11×#54111yescharacteristic
389C2C11×#345512yes—
390C2C11×#353114yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC24×C11C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2839C2semidirect
3. C11×#2833C2semidirect
5. C11×#2402C2semidirect
6. C11×#2402C2semidirect
8. C11×#2399C2semidirect
11. C11×#2295C2semidirect
104. #36700C11direct (N × H)
144. #2839C2×C11semidirect
146. #2833C2×C11semidirect
148. #2402C2×C11semidirect
149. #2402C2×C11semidirect
151. #2399C2×C11semidirect
154. #2295C2×C11semidirect
338. C11#36700direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28392
C11×#28362
C11×#28332
C11×#28312
C11×#24022
C11×#24012
C11×#23992
C11×#23962
C11×#22982
C11×#22952
#3670011