Finite Group Databasebeta

← C11×#32879 #14610072

Subgroups — C11×#32879 #14610072

Order 2816.

3876 conjugacy classes of subgroups; only the 438 normal subgroups are shown.

normal subgroups only

This group has 3876 conjugacy classes of subgroups — too many to draw. Only its 438 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
1C24×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#448C216yesmaximal, complemented
3C11×#2847C211yesmaximal, characteristic
4C11×#1787C216yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic, complemented
6C23×Q8×C11—224no—
7C23×Q8×C11—23no—
8C23×Q8×C11C2216yes—
9C24×C4×C11—21no—
10C24×C4×C11C2211yescharacteristic
11C22×C11×SD16C2214yescomplemented
12C2×C11×#121C2213yes—
13C2×C11×#120—21no—
14C11×#448—224no—
15C2×C11×#103C22112yescomplemented
16C2×C11×C22⋊C8C2216yes—
17C11×#386—23no—
18C11×#380C2213yes—
19C25×C11D411yescharacteristic
20C22×Q8×C11—2128no—
21C22×Q8×C11—248no—
22C22×Q8×C11—224no—
23C22×Q8×C11—248no—
24C22×Q8×C11—212no—
25C22×Q8×C11—26no—
26C22×Q8×C11D4124yescomplemented
27C22×Q8×C11C2314yes—
28C22×D4×C11—23no—
29C22×D4×C11C2311yescharacteristic
30C23×C4×C11—224no—
31C23×C4×C11—26no—
32C23×C4×C11—212no—
33C23×C4×C11D413yes—
34C23×C4×C11C2313yes—
35C2×C11×SD16—224no—
36C22×C8×C11C2314yes—
37C11×#121—212no—
38C11×#120—44no—
39C2×C11×C4⋊C4C2313yes—
40C2×C11×C22⋊C4—23no—
41C2×C11×C22⋊C4—23no—
42C11×#103—224no—
43C11×C22⋊C8—212no—
44C11×#95—23no—
45#32879C1111yesmaximal, characteristic, direct product factor, Sylow
46C24×C11—26no—
47C24×C11—26no—
48C24×C11—21no—
49C24×C11SD1614yescomplemented
50C24×C11C2×D413yes—
51C2×Q8×C11—2192no—
52C2×Q8×C11—296no—
53C2×Q8×C11—248no—
54C2×Q8×C11—296no—
55C2×Q8×C11—224no—
56C2×Q8×C11—212no—
57C2×Q8×C11C2×D4124yes—
58C2×D4×C11—26no—
59C2×D4×C11—46no—
60C2×D4×C11—46no—
61C2×D4×C11—46no—
62C22×C4×C11—264no—
63C22×C4×C11—248no—
64C22×C4×C11—232no—
65C22×C4×C11—224no—
66C22×C4×C11—26no—
67C22×C4×C11—24no—
68C22×C4×C11—212no—
69C22×C4×C11—212no—
70C22×C4×C11—23no—
71C22×C4×C11C2×D413yes—
72C22×C4×C11C2×D4112yes—
73C22×C4×C11C2411yescharacteristic
74C11×SD16—416no—
75C2×C8×C11—212no—
76C11×C4⋊C4—26no—
77C11×C22⋊C4—46no—
78C11×C22⋊C4—46no—
79C24×Q8C2×C1111yescharacteristic, complemented
80C2×#448C2×C1116yescomplemented
81#2847C2×C1111yescharacteristic
82#1787C2×C1116yescomplemented
83#1779C2×C1111yescharacteristic, complemented
84C23×C11—28no—
85C23×C11—224no—
86C23×C11—26no—
87C23×C11—26no—
88C23×C11—224no—
89C23×C11—43no—
90C23×C11—41no—
91C23×C11—43no—
92C23×C11#12016yes—
93C23×C11C2×SD1616yes—
94C23×C11#13716yes—
95C23×C11C22×D411yescharacteristic
96Q8×C11—296no—
97Q8×C11—224no—
98Q8×C11#120116yescomplemented
99D4×C11—44no—
100D4×C11—812no—
101C2×C4×C11—296no—
102C2×C4×C11—224no—
103C2×C4×C11—224no—
104C2×C4×C11—26no—
105C2×C4×C11—224no—
106C2×C4×C11—43no—
107C2×C4×C11—43no—
108C2×C4×C11—43no—
109C2×C4×C11#12016yes—
110C2×C4×C11C22×D416yes—
111C8×C11—44no—
112C23×Q8—224no—
113C23×Q8—23no—
114C23×Q8C22×C1116yes—
115C24×C4—21no—
116C24×C4C22×C1111yescharacteristic
117C22×SD16C22×C1114yescomplemented
118C2×#121C22×C1113yes—
119C2×#120—21no—
120#448—224no—
121C2×#103C22×C11112yescomplemented
122C2×C22⋊C8C22×C1116yes—
123#386—23no—
124#380C22×C1113yes—
125C22×C11—232no—
126C22×C11—26no—
127C22×C11—212no—
128C22×C11—26no—
129C22×C11—212no—
130C22×C11—81no—
131C22×C11—83no—
132C22×C11—83no—
133C22×C11#448112yescomplemented
134C22×C11C2×#12013yes—
135C22×C11C22×SD1611yescharacteristic
136C22×C11C2×#13713yes—
137C4×C11—216no—
138C4×C11—26no—
139C4×C11—83no—
140C4×C11C2×#12014yes—
141C25D4×C1111yescharacteristic
142C22×Q8—2128no—
143C22×Q8—248no—
144C22×Q8—224no—
145C22×Q8—248no—
146C22×Q8—212no—
147C22×Q8—26no—
148C22×Q8D4×C11124yescomplemented
149C22×Q8C23×C1114yes—
150C22×D4—23no—
151C22×D4C23×C1111yescharacteristic
152C23×C4—224no—
153C23×C4—26no—
154C23×C4—212no—
155C23×C4D4×C1113yes—
156C23×C4C23×C1113yes—
157C2×SD16—224no—
158C22×C8C23×C1114yes—
159#121—212no—
160#120—44no—
161C2×C4⋊C4C23×C1113yes—
162C2×C22⋊C4—23no—
163C2×C22⋊C4—23no—
164#103—224no—
165C22⋊C8—212no—
166#95—23no—
167C2×C11—212no—
168C2×C11—161no—
169C2×C11#284611yescharacteristic
170C2×C11C2×#44813yes—
171C2×C11#300413yes—
172C24—26no—
173C24—26no—
174C24—21no—
175C24C11×SD1614yescomplemented
176C24C2×D4×C1113yes—
177C2×Q8—2192no—
178C2×Q8—296no—
179C2×Q8—248no—
180C2×Q8—296no—
181C2×Q8—224no—
182C2×Q8—212no—
183C2×Q8C2×D4×C11124yes—
184C2×D4—26no—
185C2×D4—46no—
186C2×D4—46no—
187C2×D4—46no—
188C22×C4—264no—
189C22×C4—248no—
190C22×C4—232no—
191C22×C4—224no—
192C22×C4—26no—
193C22×C4—24no—
194C22×C4—212no—
195C22×C4—212no—
196C22×C4—23no—
197C22×C4C2×D4×C1113yes—
198C22×C4C2×D4×C11112yes—
199C22×C4C24×C1111yescharacteristic
200SD16—416no—
201C2×C8—212no—
202C4⋊C4—26no—
203C22⋊C4—46no—
204C22⋊C4—46no—
205C11#3287911yescharacteristic, direct product factor, Sylow
206C23—28no—
207C23—224no—
208C23—26no—
209C23—26no—
210C23—224no—
211C23—43no—
212C23—41no—
213C23—43no—
214C23C11×#12016yes—
215C23C2×C11×SD1616yes—
216C23C11×#13716yes—
217C23C22×D4×C1111yescharacteristic
218Q8—296no—
219Q8—224no—
220Q8C11×#120116yescomplemented
221D4—44no—
222D4—812no—
223C2×C4—296no—
224C2×C4—224no—
225C2×C4—224no—
226C2×C4—26no—
227C2×C4—224no—
228C2×C4—43no—
229C2×C4—43no—
230C2×C4—43no—
231C2×C4C11×#12016yes—
232C2×C4C22×D4×C1116yes—
233C8—44no—
234C22—232no—
235C22—212no—
236C22—26no—
237C22—212no—
238C22—26no—
239C22—83no—
240C22—83no—
241C22—81no—
242C22C11×#448112yescomplemented
243C22C2×C11×#12013yes—
244C22C22×C11×SD1611yescharacteristic
245C22C2×C11×#13713yes—
246C4—216no—
247C4—26no—
248C4—83no—
249C4C2×C11×#12014yes—
250C2—212no—
251C2—161no—
252C2C11×#284611yescharacteristic
253C2C2×C11×#44813yes—
254C2C11×#300413yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×Q8×C11C2semidirect
2. C2×C11×#448C2semidirect
4. C11×#1787C2semidirect
5. C11×#1779C2semidirect
11. C22×C11×SD16C22semidirect
15. C2×C11×#103C22semidirect
26. C22×Q8×C11D4semidirect
45. #32879C11direct (N × H)
49. C24×C11SD16semidirect
79. C24×Q8C2×C11semidirect
80. C2×#448C2×C11semidirect
82. #1787C2×C11semidirect
83. #1779C2×C11semidirect
98. Q8×C11#120semidirect
117. C22×SD16C22×C11semidirect
121. C2×#103C22×C11semidirect
133. C22×C11#448semidirect
148. C22×Q8D4×C11semidirect
175. C24C11×SD16semidirect
205. C11#32879direct (N × H)
220. Q8C11×#120semidirect
242. C22C11×#448semidirect

Maximal subgroups

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

subgroupindex
C24×Q8×C112
C2×C11×#4482
C11×#28472
C11×#17872
C11×#17792
#3287911