Finite Group Databasebeta

← C11×#33800 #14610993

Subgroups — C11×#33800 #14610993

Order 2816.

502 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3169C211yesmaximal, characteristic
2C2×C11×#499C211yesmaximal, characteristic, complemented
3C11×#2255C212yesmaximal, complemented
4C11×#2244C212yesmaximal, complemented
5C11×#2233C212yesmaximal, complemented
6C11×#2232C212yesmaximal, complemented
7C11×#2228C214yesmaximal, complemented
8C11×#2163C211yesmaximal, characteristic, complemented
9C11×#532—21no—
10C2×C11×#125—21no—
11C11×#500C2211yescharacteristic
12C11×#499—21no—
13C11×#499—21no—
14C11×#499C2212yes—
15C11×#499C2212yes—
16C11×#493C2211yescharacteristic
17C11×#486—21no—
18C11×#466—21no—
19C11×#466C2212yes—
20C4×C11×D8—21no—
21C4×C11×D8C2212yes—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106—21no—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#367C2214yes—
27C11×#366C2214yes—
28C11×C4⋊C16C2212yes—
29C11×#357C2214yes—
30C11×#357C2214yes—
31C11×C22⋊C16C2212yes—
32C11×#346C2212yes—
33C2×C11×#41—41no—
34C2×C11×D8—21no—
35C2×C11×D8C2312yes—
36C22×C8×C11D411yescharacteristic
37C22×C8×C11C2311yescharacteristic
38C11×C4⋊Q8—21no—
39C11×#127—21no—
40C11×#125—22no—
41C11×#125—22no—
42C11×#125—41no—
43C11×#125—41no—
44C11×#124—41no—
45C11×#121—22no—
46C11×#121—41no—
47C4×D4×C11—22no—
48C4×D4×C11—41no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—41no—
52C2×C11×C4⋊C4—41no—
53C2×C42×C11D411yescharacteristic
54C2×C11×C16C2314yes—
55C11×#107—21no—
56C11×#107—21no—
57C11×#107—21no—
58C11×#107C2312yes—
59C11×#107C2312yes—
60C11×#107C2312yes—
61C11×#106—22no—
62C11×#106—22no—
63C11×#102—22no—
64C11×#102—22no—
65C4×C8×C11D411yescharacteristic
66C4×C8×C11D411yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C4×C8×C11C2311yescharacteristic
69#33800C1111yesmaximal, characteristic, direct product factor, Sylow
70C11×#41—84no—
71C2×Q8×C11—41no—
72C2×D4×C11—22no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—42no—
79C22×C4×C11D811yescharacteristic
80C22×C4×C11D811yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C11×D8—24no—
83C11×D8—42no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2411yescharacteristic
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—42no—
102C42×C11D811yescharacteristic
103C42×C11D811yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C11×C16—24no—
107#3169C2×C1111yescharacteristic
108C2×#499C2×C1111yescharacteristic, complemented
109#2255C2×C1112yescomplemented
110#2244C2×C1112yescomplemented
111#2233C2×C1112yescomplemented
112#2232C2×C1112yescomplemented
113#2228C2×C1114yescomplemented
114#2163C2×C1111yescharacteristic, complemented
115C23×C11—42no—
116C23×C11C2×D811yescharacteristic
117Q8×C11—82no—
118D4×C11—42no—
119D4×C11—42no—
120D4×C11—82no—
121D4×C11—82no—
122D4×C11—84no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—84no—
131C2×C4×C11—82no—
132C2×C4×C11—82no—
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C8×C11—21no—
140C8×C11—21no—
141C8×C11#13712yes—
142C8×C112−1+412yes—
143#532—21no—
144C2×#125—21no—
145#500C22×C1111yescharacteristic
146#499—21no—
147#499—21no—
148#499C22×C1112yes—
149#499C22×C1112yes—
150#493C22×C1111yescharacteristic
151#486—21no—
152#466—21no—
153#466C22×C1112yes—
154C4×D8—21no—
155C4×D8C22×C1112yes—
156C2×#107C22×C1111yescharacteristic
157C2×#107C22×C1111yescharacteristic
158C2×#106—21no—
159C2×C4×C8C22×C1111yescharacteristic
160#367C22×C1114yes—
161#366C22×C1114yes—
162C4⋊C16C22×C1112yes—
163#357C22×C1114yes—
164#357C22×C1114yes—
165C22⋊C16C22×C1112yes—
166#346C22×C1112yes—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—82no—
170C22×C11—82no—
171C22×C11—82no—
172C22×C11#50912yes—
173C22×C11C22×D811yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—82no—
180C4×C11—82no—
181C4×C11—82no—
182C4×C11#53611yescharacteristic
183C4×C11C2×#13711yescharacteristic
184C2×#41—41no—
185C2×D8—21no—
186C2×D8C23×C1112yes—
187C22×C8D4×C1111yescharacteristic
188C22×C8C23×C1111yescharacteristic
189C4⋊Q8—21no—
190#127—21no—
191#125—22no—
192#125—22no—
193#125—41no—
194#125—41no—
195#124—41no—
196#121—22no—
197#121—41no—
198C4×D4—22no—
199C4×D4—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—41no—
204C2×C42D4×C1111yescharacteristic
205C2×C16C23×C1114yes—
206#107—21no—
207#107—21no—
208#107—21no—
209#107C23×C1112yes—
210#107C23×C1112yes—
211#107C23×C1112yes—
212#106—22no—
213#106—22no—
214#102—22no—
215#102—22no—
216C4×C8D4×C1111yescharacteristic
217C4×C8D4×C1111yescharacteristic
218C4×C8C23×C1111yescharacteristic
219C4×C8C23×C1111yescharacteristic
220C2×C11—22no—
221C2×C11—162no—
222C2×C11#322611yescharacteristic
223C2×C11C2×#50911yescharacteristic
224C2×C11#341411yescharacteristic
225#41—84no—
226C2×Q8—41no—
227C2×D4—22no—
228C2×D4—42no—
229C2×D4—41no—
230C2×D4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4C11×D811yescharacteristic
235C22×C4C11×D811yescharacteristic
236C22×C4C2×D4×C1111yescharacteristic
237D8—24no—
238D8—42no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8C2×D4×C1111yescharacteristic
242C2×C8C2×D4×C1111yescharacteristic
243C2×C8C2×D4×C1111yescharacteristic
244C2×C8C24×C1111yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C42C11×D811yescharacteristic
258C42C11×D811yescharacteristic
259C42C2×D4×C1111yescharacteristic
260C42C2×D4×C1111yescharacteristic
261C16—24no—
262C11#3380011yescharacteristic, direct product factor, Sylow
263C23—42no—
264C23C2×C11×D811yescharacteristic
265Q8—82no—
266D4—42no—
267D4—42no—
268D4—82no—
269D4—82no—
270D4—84no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—84no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4C2×C11×D811yescharacteristic
282C2×C4C2×C11×D811yescharacteristic
283C2×C4C2×C11×D811yescharacteristic
284C2×C4C2×C11×D811yescharacteristic
285C2×C4C2×C11×D811yescharacteristic
286C2×C4C22×D4×C1111yescharacteristic
287C8—21no—
288C8—21no—
289C8C11×#13712yes—
290C8C11×2−1+412yes—
291C22—21no—
292C22—21no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22C11×#50912yes—
297C22C22×C11×D811yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—82no—
305C4—82no—
306C4C11×#53611yescharacteristic
307C4C2×C11×#13711yescharacteristic
308C2—22no—
309C2—162no—
310C2C11×#322611yescharacteristic
311C2C2×C11×#50911yescharacteristic
312C2C11×#341411yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#3169C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#499C2semidirect
3. C11×#2255C2semidirect
4. C11×#2244C2semidirect
5. C11×#2233C2semidirect
6. C11×#2232C2semidirect
7. C11×#2228C2semidirect
8. C11×#2163C2semidirect
69. #33800C11direct (N × H)
108. C2×#499C2×C11semidirect
109. #2255C2×C11semidirect
110. #2244C2×C11semidirect
111. #2233C2×C11semidirect
112. #2232C2×C11semidirect
113. #2228C2×C11semidirect
114. #2163C2×C11semidirect
262. C11#33800direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31692
C2×C11×#4992
C11×#22552
C11×#22442
C11×#22332
C11×#22322
C11×#22282
C11×#21632
#3380011