Finite Group Databasebeta

← C11×#12184 #14589377

Subgroups — C11×#12184 #14589377

Order 2816.

372 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2844C211yesmaximal, characteristic, complemented
2C11×#2040C211yesmaximal, characteristic
3C11×#1604C212yesmaximal
4C11×#1354C212yesmaximal, complemented
5C11×#1324C211yesmaximal, characteristic, complemented
6C11×#537C2211yescharacteristic
7C11×#448—22no—
8C2×C11×#104—21no—
9C11×#417—21no—
10C11×#400—21no—
11C11×#400—22no—
12C11×#395—22no—
13C11×#395C2212yes—
14C11×#382—21no—
15C11×#382C2211yescharacteristic
16C11×#343C2211yescharacteristic
17C11×#327—22no—
18C11×#324C2212yes—
19C2×C11×#41—21no—
20C22×Q8×C11D412yes—
21C2×C11×SD16—42no—
22C2×C11×M16—21no—
23C11×C22⋊Q8—41no—
24C11×#121—22no—
25C11×#121—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11D411yescharacteristic
33C11×#104—42no—
34C11×#103—42no—
35C11×#103—41no—
36C11×#102—41no—
37C11×C22⋊C8—22no—
38C11×#95—22no—
39C11×#95—22no—
40C11×#95—21no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95D412yes—
44#12184C1111yesmaximal, characteristic, direct product factor, Sylow
45C11×#41—41no—
46C11×#41—41no—
47C11×#41—41no—
48C11×#41—41no—
49C2×Q8×C11—21no—
50C2×Q8×C11—42no—
51C2×Q8×C11—82no—
52C2×D4×C11—21no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C11×SD16—84no—
63C11×M16—41no—
64C11×M16—41no—
65C2×C8×C11—42no—
66C2×C8×C11—41no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—81no—
71C11×C4⋊C4—81no—
72C11×C4⋊C4—82no—
73C11×C4⋊C4—81no—
74C11×C22⋊C4—42no—
75C42×C11—21no—
76C42×C11SD1612yescomplemented
77#2844C2×C1111yescharacteristic, complemented
78#2040C2×C1111yescharacteristic
79#1604C2×C1112yes—
80#1354C2×C1112yescomplemented
81#1324C2×C1111yescharacteristic, complemented
82C23×C11—41no—
83C23×C11#12011yescharacteristic
84Q8×C11—41no—
85Q8×C11—41no—
86Q8×C11—44no—
87Q8×C11—82no—
88D4×C11—41no—
89D4×C11—41no—
90D4×C11—82no—
91D4×C11—81no—
92D4×C11—81no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11C2×SD1611yescharacteristic
112C2×C4×C11#13711yescharacteristic
113C8×C11—81no—
114C8×C11—82no—
115#537C22×C1111yescharacteristic
116#448—22no—
117C2×#104—21no—
118#417—21no—
119#400—21no—
120#400—22no—
121#395—22no—
122#395C22×C1112yes—
123#382—21no—
124#382C22×C1111yescharacteristic
125#343C22×C1111yescharacteristic
126#327—22no—
127#324C22×C1112yes—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—81no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11#44811yescharacteristic
134C22×C11#45411yescharacteristic
135C22×C11B(4,𝔽2)11yescharacteristic
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—42no—
139C4×C11—42no—
140C4×C11—82no—
141C4×C11—81no—
142C4×C11—82no—
143C4×C11—81no—
144C2×#41—21no—
145C22×Q8D4×C1112yes—
146C2×SD16—42no—
147C2×M16—21no—
148C22⋊Q8—41no—
149#121—22no—
150#121—41no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4D4×C1111yescharacteristic
156C2×C4⋊C4C23×C1111yescharacteristic
157C2×C42D4×C1111yescharacteristic
158#104—42no—
159#103—42no—
160#103—41no—
161#102—41no—
162C22⋊C8—22no—
163#95—22no—
164#95—22no—
165#95—21no—
166#95—22no—
167#95—22no—
168#95D4×C1112yes—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11—161no—
172C2×C11#159911yescharacteristic
173C2×C11#219911yescharacteristic
174C2×C11#220311yescharacteristic
175#41—41no—
176#41—41no—
177#41—41no—
178#41—41no—
179C2×Q8—21no—
180C2×Q8—42no—
181C2×Q8—82no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—41no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—41no—
190C22×C4C2×D4×C1111yescharacteristic
191C22×C4C2×D4×C1112yes—
192SD16—84no—
193M16—41no—
194M16—41no—
195C2×C8—42no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—82no—
203C4⋊C4—81no—
204C22⋊C4—42no—
205C42—21no—
206C42C11×SD1612yescomplemented
207C11#1218411yescharacteristic, direct product factor, Sylow
208C23—41no—
209C23C11×#12011yescharacteristic
210Q8—41no—
211Q8—41no—
212Q8—44no—
213Q8—82no—
214D4—41no—
215D4—41no—
216D4—82no—
217D4—81no—
218D4—81no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4C2×C11×SD1611yescharacteristic
238C2×C4C11×#13711yescharacteristic
239C8—81no—
240C8—82no—
241C22—21no—
242C22—21no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22C11×#44811yescharacteristic
247C22C11×#45411yescharacteristic
248C22C11×B(4,𝔽2)11yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—161no—
260C2C11×#159911yescharacteristic
261C2C11×#219911yescharacteristic
262C2C11×#220311yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#537C22
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
1. C11×#2844C2semidirect
4. C11×#1354C2semidirect
5. C11×#1324C2semidirect
44. #12184C11direct (N × H)
76. C42×C11SD16semidirect
77. #2844C2×C11semidirect
80. #1354C2×C11semidirect
81. #1324C2×C11semidirect
206. C42C11×SD16semidirect
207. C11#12184direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28442
C11×#20402
C11×#16042
C11×#13542
C11×#13242
#1218411