Finite Group Databasebeta

← C11×#12240 #14589433

Subgroups — C11×#12240 #14589433

Order 2816.

350 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2792C211yesmaximal, characteristic
2C11×#2060C211yesmaximal, characteristic
3C11×#1611C211yesmaximal, characteristic
4C11×#1605C211yesmaximal, characteristic
5C11×#1354C211yesmaximal, characteristic
6C11×#1346C211yesmaximal, characteristic
7C11×#1325C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#483—21no—
10C11×#451—21no—
11C11×#428—21no—
12C11×#398—21no—
13C11×#398C2211yescharacteristic
14C11×#395—21no—
15C11×#395C2211yescharacteristic
16C11×#389—21no—
17C11×#389—21no—
18C11×#387—21no—
19C11×#387—21no—
20C11×#384C2211yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23C11×#328—21no—
24C11×#328—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C2×C11×Q16—41no—
29C2×C11×M16—21no—
30C11×C4⋊Q8—41no—
31C11×#125—41no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×#117—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11D411yescharacteristic
47C11×#107—41no—
48C11×#106—41no—
49C11×#106—41no—
50C11×#103—41no—
51C11×#103—41no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95D411yescharacteristic
61C11×#95D411yescharacteristic
62#12240C1111yesmaximal, characteristic, direct product factor, Sylow
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—81no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C11×Q16—82no—
77C11×M16—22no—
78C11×M16—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—24no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C11×C4⋊C4—81no—
98C11×C4⋊C4—81no—
99C11×C22⋊C4—41no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11—41no—
103C42×C11—81no—
104#2792C2×C1111yescharacteristic
105#2060C2×C1111yescharacteristic
106#1611C2×C1111yescharacteristic
107#1605C2×C1111yescharacteristic
108#1354C2×C1111yescharacteristic
109#1346C2×C1111yescharacteristic
110#1325C2×C1111yescharacteristic
111C23×C11#12011yescharacteristic
112Q8×C11—42no—
113Q8×C11—81no—
114Q8×C11—81no—
115Q8×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C8×C11—42no—
145C8×C11—81no—
146C8×C11—81no—
147#544C22×C1111yescharacteristic
148#483—21no—
149#451—21no—
150#428—21no—
151#398—21no—
152#398C22×C1111yescharacteristic
153#395—21no—
154#395C22×C1111yescharacteristic
155#389—21no—
156#389—21no—
157#387—21no—
158#387—21no—
159#384C22×C1111yescharacteristic
160#343C22×C1111yescharacteristic
161#339—21no—
162#328—21no—
163#328—21no—
164#324C22×C1111yescharacteristic
165#324C22×C1111yescharacteristic
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#45211yescharacteristic
169C22×C11#45611yescharacteristic
170C22×C11B(4,𝔽2)11yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11—42no—
175C4×C11—42no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182C4×C11—81no—
183C22×Q8D4×C1111yescharacteristic
184C2×Q16—41no—
185C2×M16—21no—
186C4⋊Q8—41no—
187#125—41no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190#117—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4D4×C1111yescharacteristic
199C2×C4⋊C4D4×C1111yescharacteristic
200C2×C4⋊C4C23×C1111yescharacteristic
201C2×C42—21no—
202C2×C42D4×C1111yescharacteristic
203#107—41no—
204#106—41no—
205#106—41no—
206#103—41no—
207#103—41no—
208C22⋊C8—21no—
209C22⋊C8—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95D4×C1111yescharacteristic
217#95D4×C1111yescharacteristic
218C2×C11—21no—
219C2×C11—21no—
220C2×C11#160311yescharacteristic
221C2×C11#220011yescharacteristic
222C2×C11#220511yescharacteristic
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—81no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C2×D4×C1111yescharacteristic
235C22×C4C2×D4×C1111yescharacteristic
236Q16—82no—
237M16—22no—
238M16—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C4⋊C4—24no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C22⋊C4—41no—
260C42—21no—
261C42—21no—
262C42—41no—
263C42—81no—
264C11#1224011yescharacteristic, direct product factor, Sylow
265C23C11×#12011yescharacteristic
266Q8—42no—
267Q8—81no—
268Q8—81no—
269Q8—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4C11×#13511yescharacteristic
297C2×C4C11×#13711yescharacteristic
298C8—42no—
299C8—81no—
300C8—81no—
301C22—21no—
302C22—21no—
303C22C11×#45211yescharacteristic
304C22C11×#45611yescharacteristic
305C22C11×B(4,𝔽2)11yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—42no—
310C4—42no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4—81no—
316C4—81no—
317C4—81no—
318C2—21no—
319C2—21no—
320C2C11×#160311yescharacteristic
321C2C11×#220011yescharacteristic
322C2C11×#220511yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×C11#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
62. #12240C11direct (N × H)
264. C11#12240direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27922
C11×#20602
C11×#16112
C11×#16052
C11×#13542
C11×#13462
C11×#13252
#1224011