Finite Group Databasebeta

← C11×#10637 #14587830

Subgroups — C11×#10637 #14587830

Order 2816.

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

normal subgroups only

This group has 330 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×#1804C211yesmaximal, characteristic
2C11×#1800C211yesmaximal, characteristic
3C11×#1571C211yesmaximal, characteristic, complemented
4C11×#1478C211yesmaximal, characteristic
5C11×#1301C211yesmaximal, characteristic, complemented
6C11×#1286C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#102—21no—
15C2×C11×#100—21no—
16C11×#382C2211yescharacteristic
17C11×#343—21no—
18C11×#340—21no—
19C11×#335—22no—
20C11×D4⋊C8—22no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11—21no—
23C2×C11×M16—21no—
24C2×C11×M16—21no—
25C22×C8×C11—21no—
26C4×D4×C11—21no—
27C4×D4×C11—21no—
28C4×D4×C11—21no—
29C4×D4×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C42×C11C2311yescharacteristic
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×#102—42no—
43C11×#100—42no—
44C11×C22⋊C8—21no—
45C11×C22⋊C8—21no—
46C4×C8×C11—21no—
47C4×C8×C11D412yes—
48C11×#95—21no—
49C11×#95—21no—
50#10637C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11—21no—
52C2×D4×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—21no—
56C2×D4×C11—21no—
57C2×D4×C11D812yes—
58C22×C4×C11—21no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—82no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C11×M16—41no—
67C11×M16—41no—
68C11×M16—41no—
69C11×M16—41no—
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—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87#1804C2×C1111yescharacteristic
88#1800C2×C1111yescharacteristic
89#1571C2×C1111yescharacteristic, complemented
90#1478C2×C1111yescharacteristic
91#1301C2×C1111yescharacteristic, complemented
92#1286C2×C1111yescharacteristic, complemented
93#1286C2×C1111yescharacteristic, complemented
94C23×C11—22no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—81no—
98C23×C11—81no—
99C23×C11#12311yescharacteristic
100D4×C11—22no—
101D4×C11—22no—
102D4×C11—41no—
103D4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—82no—
108C2×C4×C11—82no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11—81no—
113C2×C4×C11#12111yescharacteristic
114C2×C4×C11#12311yescharacteristic
115C2×C4×C11#12311yescharacteristic
116C2×C4×C11#12411yescharacteristic
117C2×C4×C11#12611yescharacteristic
118C2×C4×C11#12611yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11#13511yescharacteristic
121C2×C4×C11#13711yescharacteristic
122C2×C4×C11#13711yescharacteristic
123C8×C11—42no—
124C8×C11—81no—
125C8×C11—81no—
126C8×C11—81no—
127C8×C11—81no—
128C2×C4×D4C22×C1111yescharacteristic
129#431C22×C1111yescharacteristic
130#431C22×C1111yescharacteristic
131#423C22×C1111yescharacteristic
132#423C22×C1111yescharacteristic
133C2×C4⋊C8C22×C1111yescharacteristic
134C2×#102—21no—
135C2×#100—21no—
136#382C22×C1111yescharacteristic
137#343—21no—
138#340—21no—
139#335—22no—
140D4⋊C8—22no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—42no—
144C22×C11—82no—
145C22×C11—82no—
146C22×C11—81no—
147C22×C11—81no—
148C22×C11#39711yescharacteristic
149C22×C11#48011yescharacteristic
150C22×C11#48511yescharacteristic
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—81no—
156C4×C11—161no—
157C4×C11#46611yescharacteristic
158C4×C11#47011yescharacteristic
159C4×C11#48011yescharacteristic
160C4×C11#48511yescharacteristic
161C22×D4D4×C1111yescharacteristic
162C23×C4—21no—
163C2×M16—21no—
164C2×M16—21no—
165C22×C8—21no—
166C4×D4—21no—
167C4×D4—21no—
168C4×D4—21no—
169C4×D4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4D4×C1111yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C23×C1111yescharacteristic
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8—21no—
182#102—42no—
183#100—42no—
184C22⋊C8—21no—
185C22⋊C8—21no—
186C4×C8—21no—
187C4×C8D4×C1112yes—
188#95—21no—
189#95—21no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11—82no—
193C2×C11#207511yescharacteristic
194C2×C11#208011yescharacteristic
195C2×C11#208111yescharacteristic
196C24—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4C11×D812yes—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—82no—
208C22×C4C2×D4×C1111yescharacteristic
209C22×C4C11×#4111yescharacteristic
210C22×C4C11×#4111yescharacteristic
211M16—41no—
212M16—41no—
213M16—41no—
214M16—41no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—41no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C42C2×D4×C1111yescharacteristic
229C42C11×#4111yescharacteristic
230C42C11×#4111yescharacteristic
231C42C11×#4111yescharacteristic
232C11#1063711yescharacteristic, direct product factor, Sylow
233C23—22no—
234C23—41no—
235C23—41no—
236C23—81no—
237C23—81no—
238C23C11×#12311yescharacteristic
239D4—22no—
240D4—22no—
241D4—41no—
242D4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4C11×#12111yescharacteristic
253C2×C4C11×#12311yescharacteristic
254C2×C4C11×#12311yescharacteristic
255C2×C4C11×#12411yescharacteristic
256C2×C4C11×#12611yescharacteristic
257C2×C4C11×#12611yescharacteristic
258C2×C4C2×C11×D811yescharacteristic
259C2×C4C11×#13511yescharacteristic
260C2×C4C11×#13711yescharacteristic
261C2×C4C11×#13711yescharacteristic
262C8—42no—
263C8—81no—
264C8—81no—
265C8—81no—
266C8—81no—
267C22—21no—
268C22—21no—
269C22—42no—
270C22—82no—
271C22—82no—
272C22—81no—
273C22—81no—
274C22C11×#39711yescharacteristic
275C22C11×#48011yescharacteristic
276C22C11×#48511yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—81no—
282C4—161no—
283C4C11×#46611yescharacteristic
284C4C11×#47011yescharacteristic
285C4C11×#48011yescharacteristic
286C4C11×#48511yescharacteristic
287C2—21no—
288C2—21no—
289C2—82no—
290C2C11×#207511yescharacteristic
291C2C11×#208011yescharacteristic
292C2C11×#208111yescharacteristic
subgroupG/H
center, socleC22×C11#397
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1571C2semidirect
5. C11×#1301C2semidirect
6. C11×#1286C2semidirect
7. C11×#1286C2semidirect
50. #10637C11direct (N × H)
89. #1571C2×C11semidirect
91. #1301C2×C11semidirect
92. #1286C2×C11semidirect
93. #1286C2×C11semidirect
232. C11#10637direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#18042
C11×#18002
C11×#15712
C11×#14782
C11×#13012
C11×#12862
#1063711