Finite Group Databasebeta

← C11×#7815 #14585008

Subgroups — C11×#7815 #14585008

Order 2816.

374 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2726C211yesmaximal, characteristic
2C11×#2099C211yesmaximal, characteristic
3C11×#2084C211yesmaximal, characteristic
4C11×#2084C211yesmaximal, characteristic
5C11×#1271C211yesmaximal, characteristic
6C11×#1271C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×C11×#125—21no—
9C2×C11×#106—21no—
10C2×C11×#106—21no—
11C11×#398—21no—
12C11×#398—21no—
13C11×#398—21no—
14C11×#389—21no—
15C11×#389C2211yescharacteristic
16C11×#389C2211yescharacteristic
17C11×#389C2211yescharacteristic
18C11×#387—21no—
19C11×#384C2211yescharacteristic
20C11×#340—21no—
21C11×#340—21no—
22C11×#340—21no—
23C11×#340—21no—
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26C11×#336C2211yescharacteristic
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×#125—42no—
31C11×#125—42no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—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⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C11×#106—42no—
51C11×#106—42no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58#7815C1111yesmaximal, characteristic, direct product factor, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—81no—
100C11×C4⋊C4SD1612yes—
101C11×C4⋊C4SD1612yes—
102C42×C11—41no—
103C42×C11—42no—
104#2726C2×C1111yescharacteristic
105#2099C2×C1111yescharacteristic
106#2084C2×C1111yescharacteristic
107#2084C2×C1111yescharacteristic
108#1271C2×C1111yescharacteristic
109#1271C2×C1111yescharacteristic
110#1271C2×C1111yescharacteristic
111C23×C11#12011yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
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—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C8×C11—42no—
146C8×C11—42no—
147C8×C11—81no—
148C2×#125—21no—
149C2×#106—21no—
150C2×#106—21no—
151#398—21no—
152#398—21no—
153#398—21no—
154#389—21no—
155#389C22×C1111yescharacteristic
156#389C22×C1111yescharacteristic
157#389C22×C1111yescharacteristic
158#387—21no—
159#384C22×C1111yescharacteristic
160#340—21no—
161#340—21no—
162#340—21no—
163#340—21no—
164#336C22×C1111yescharacteristic
165#336C22×C1111yescharacteristic
166#336C22×C1111yescharacteristic
167C22×C11#44811yescharacteristic
168C22×C11#44911yescharacteristic
169C22×C11#45011yescharacteristic
170C22×C11#45411yescharacteristic
171C22×C11#45611yescharacteristic
172C22×C11#45611yescharacteristic
173C22×C11#45811yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—42no—
181C4×C11—42no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—161no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190#125—42no—
191#125—42no—
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⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4D4×C1111yescharacteristic
203C2×C4⋊C4D4×C1111yescharacteristic
204C2×C4⋊C4D4×C1111yescharacteristic
205C2×C4⋊C4D4×C1111yescharacteristic
206C2×C4⋊C4D4×C1111yescharacteristic
207C2×C4⋊C4D4×C1111yescharacteristic
208C2×C42—21no—
209C2×C42C23×C1111yescharacteristic
210#106—42no—
211#106—42no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C2×C11#160911yescharacteristic
219C2×C11#161111yescharacteristic
220C2×C11#161611yescharacteristic
221C2×C11#162611yescharacteristic
222C2×C11#165111yescharacteristic
223C2×C11#165411yescharacteristic
224C2×C11#166311yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4C2×D4×C1111yescharacteristic
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C2×D4×C1111yescharacteristic
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4C11×SD1612yes—
267C4⋊C4C11×SD1612yes—
268C42—41no—
269C42—42no—
270C11#781511yescharacteristic, direct product factor, Sylow
271C23C11×#12011yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
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×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4C2×C11×SD1611yescharacteristic
300C2×C4C2×C11×SD1611yescharacteristic
301C2×C4C11×#13511yescharacteristic
302C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
303C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
304C2×C4C11×#13711yescharacteristic
305C8—42no—
306C8—42no—
307C8—81no—
308C22C11×#44811yescharacteristic
309C22C11×#44911yescharacteristic
310C22C11×#45011yescharacteristic
311C22C11×#45411yescharacteristic
312C22C11×#45611yescharacteristic
313C22C11×#45611yescharacteristic
314C22C11×#45811yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—161no—
328C2C11×#160911yescharacteristic
329C2C11×#161111yescharacteristic
330C2C11×#161611yescharacteristic
331C2C11×#162611yescharacteristic
332C2C11×#165111yescharacteristic
333C2C11×#165411yescharacteristic
334C2C11×#166311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
58. #7815C11direct (N × H)
270. C11#7815direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27262
C11×#20992
C11×#20842
C11×#12712
#781511