Finite Group Databasebeta

← C22×C11×#398 #14611731

Subgroups — C22×C11×#398 #14611731

Order 2816.

4158 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×C4⋊C4C211yesmaximal, characteristic
2C23×C11×C4⋊C4C212yesmaximal
3C23×C11×C4⋊C4C211yesmaximal, characteristic
4C2×C11×#398C2124yesmaximal, direct product factor
5C22×C11×#95C212yesmaximal
6C22×C11×#95C211yesmaximal, characteristic
7C24×C4×C11C2212yes—
8C24×C4×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×C4×C11C2212yes—
12C22×C11×C4⋊C4—28no—
13C22×C11×C4⋊C4—216no—
14C22×C11×C4⋊C4—28no—
15C22×C11×C4⋊C4C22112yes—
16C22×C11×C4⋊C4C22112yes—
17C22×C11×C4⋊C4C22124yes—
18C11×#398C22164yesdirect product factor
19C2×C11×#95C22124yes—
20C2×C11×#95C22112yes—
21C25×C11C2311yescharacteristic
22C23×C4×C11—24no—
23C23×C4×C11—28no—
24C23×C4×C11—24no—
25C23×C4×C11—28no—
26C23×C4×C11—28no—
27C23×C4×C11—28no—
28C23×C4×C11—28no—
29C23×C4×C11—24no—
30C23×C4×C11—28no—
31C23×C4×C11—28no—
32C23×C4×C11D418yes—
33C23×C4×C11D418yes—
34C23×C4×C11Q8116yes—
35C23×C4×C11C2316yes—
36C23×C4×C11C23112yes—
37C23×C4×C11C2316yes—
38C23×C4×C11C2316yes—
39C23×C4×C11C23112yes—
40C2×C11×C4⋊C4—248no—
41C2×C11×C4⋊C4—296no—
42C2×C11×C4⋊C4—248no—
43C2×C11×C4⋊C4C23116yes—
44C2×C11×C4⋊C4C23116yes—
45C2×C11×C4⋊C4C23132yes—
46C11×#95C23132yes—
47C11×#95C23116yes—
48C22×#398C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C2×D414yes—
50C24×C11C2×D414yes—
51C24×C11C2×Q818yes—
52C24×C11#4114yes—
53C24×C11#4118yes—
54C24×C11C2413yes—
55C22×C4×C11—232no—
56C22×C4×C11—264no—
57C22×C4×C11—232no—
58C22×C4×C11—212no—
59C22×C4×C11—224no—
60C22×C4×C11—212no—
61C22×C4×C11—224no—
62C22×C4×C11—224no—
63C22×C4×C11—224no—
64C22×C4×C11—224no—
65C22×C4×C11—212no—
66C22×C4×C11—224no—
67C22×C4×C11—224no—
68C22×C4×C11—432no—
69C22×C4×C11—416no—
70C22×C4×C11C2×D4124yes—
71C22×C4×C11C2×D4124yes—
72C22×C4×C11C2×Q8148yes—
73C22×C4×C11C2414yes—
74C22×C4×C11C2418yes—
75C22×C4×C11C2414yes—
76C22×C4×C11C2414yes—
77C22×C4×C11C2418yes—
78C11×C4⋊C4—232no—
79C11×C4⋊C4—264no—
80C11×C4⋊C4—232no—
81C23×C4⋊C4C2×C1111yescharacteristic
82C23×C4⋊C4C2×C1112yes—
83C23×C4⋊C4C2×C1111yescharacteristic
84C2×#398C2×C11124yesdirect product factor
85C22×#95C2×C1112yes—
86C22×#95C2×C1111yescharacteristic
87C23×C11#121116yes—
88C23×C11C22⋊Q8132yes—
89C23×C11#123116yes—
90C23×C11#125132yes—
91C23×C11C4⋊Q8116yes—
92C23×C11C22×D416yes—
93C23×C11C22×D416yes—
94C23×C11C22×Q8112yes—
95C23×C11C2×#4116yes—
96C23×C11C2×#41112yes—
97C23×C11C2511yescharacteristic
98C2×C4×C11—248no—
99C2×C4×C11—296no—
100C2×C4×C11—248no—
101C2×C4×C11—24no—
102C2×C4×C11—28no—
103C2×C4×C11—24no—
104C2×C4×C11—28no—
105C2×C4×C11—28no—
106C2×C4×C11—28no—
107C2×C4×C11—28no—
108C2×C4×C11—24no—
109C2×C4×C11—28no—
110C2×C4×C11—28no—
111C2×C4×C11—448no—
112C2×C4×C11—424no—
113C2×C4×C11C22×D418yes—
114C2×C4×C11C22×D418yes—
115C2×C4×C11C22×Q8116yes—
116C24×C4C22×C1112yes—
117C24×C4C22×C1111yescharacteristic
118C24×C4C22×C1111yescharacteristic
119C24×C4C22×C1111yescharacteristic
120C24×C4C22×C1112yes—
121C22×C4⋊C4—28no—
122C22×C4⋊C4—216no—
123C22×C4⋊C4—28no—
124C22×C4⋊C4C22×C11112yes—
125C22×C4⋊C4C22×C11124yes—
126C22×C4⋊C4C22×C11112yes—
127#398C22×C11164yesdirect product factor
128C2×#95C22×C11124yes—
129C2×#95C22×C11112yes—
130C22×C11#398164yesdirect product factor
131C22×C11C2×#121112yes—
132C22×C11C2×C22⋊Q8124yes—
133C22×C11C2×#123112yes—
134C22×C11C2×#125124yes—
135C22×C11C2×C4⋊Q8112yes—
136C22×C11C23×D411yescharacteristic
137C22×C11C23×D411yescharacteristic
138C22×C11C23×Q812yes—
139C22×C11C22×#4111yescharacteristic
140C22×C11C22×#4112yes—
141C4×C11—28no—
142C4×C11—216no—
143C4×C11—28no—
144C4×C11—48no—
145C4×C11—44no—
146C25C23×C1111yescharacteristic
147C23×C4—24no—
148C23×C4—28no—
149C23×C4—24no—
150C23×C4—28no—
151C23×C4—28no—
152C23×C4—28no—
153C23×C4—28no—
154C23×C4—24no—
155C23×C4—28no—
156C23×C4—28no—
157C23×C4D4×C1118yes—
158C23×C4D4×C1118yes—
159C23×C4Q8×C11116yes—
160C23×C4C23×C11112yes—
161C23×C4C23×C1116yes—
162C23×C4C23×C1116yes—
163C23×C4C23×C1116yes—
164C23×C4C23×C11112yes—
165C2×C4⋊C4—248no—
166C2×C4⋊C4—296no—
167C2×C4⋊C4—248no—
168C2×C4⋊C4C23×C11116yes—
169C2×C4⋊C4C23×C11116yes—
170C2×C4⋊C4C23×C11132yes—
171#95C23×C11132yes—
172#95C23×C11116yes—
173C2×C11C2×#398124yesdirect product factor
174C2×C11C22×#12111yescharacteristic
175C2×C11C22×C22⋊Q812yes—
176C2×C11C22×#12311yescharacteristic
177C2×C11C22×#12512yes—
178C2×C11C22×C4⋊Q811yescharacteristic
179C24C2×D4×C1114yes—
180C24C2×D4×C1114yes—
181C24C2×Q8×C1118yes—
182C24C11×#4114yes—
183C24C11×#4118yes—
184C24C24×C1113yes—
185C22×C4—232no—
186C22×C4—264no—
187C22×C4—232no—
188C22×C4—212no—
189C22×C4—224no—
190C22×C4—212no—
191C22×C4—224no—
192C22×C4—224no—
193C22×C4—224no—
194C22×C4—224no—
195C22×C4—212no—
196C22×C4—224no—
197C22×C4—224no—
198C22×C4—432no—
199C22×C4—416no—
200C22×C4C2×D4×C11124yes—
201C22×C4C2×D4×C11124yes—
202C22×C4C2×Q8×C11148yes—
203C22×C4C24×C1114yes—
204C22×C4C24×C1118yes—
205C22×C4C24×C1114yes—
206C22×C4C24×C1114yes—
207C22×C4C24×C1118yes—
208C4⋊C4—232no—
209C4⋊C4—264no—
210C4⋊C4—232no—
211C11C22×#39811yescharacteristic, direct product factor, Sylow
212C23C11×#121116yes—
213C23C11×C22⋊Q8132yes—
214C23C11×#123116yes—
215C23C11×#125132yes—
216C23C11×C4⋊Q8116yes—
217C23C22×D4×C1116yes—
218C23C22×D4×C1116yes—
219C23C22×Q8×C11112yes—
220C23C2×C11×#4116yes—
221C23C2×C11×#41112yes—
222C23C25×C1111yescharacteristic
223C2×C4—248no—
224C2×C4—296no—
225C2×C4—248no—
226C2×C4—24no—
227C2×C4—28no—
228C2×C4—24no—
229C2×C4—28no—
230C2×C4—28no—
231C2×C4—28no—
232C2×C4—28no—
233C2×C4—24no—
234C2×C4—28no—
235C2×C4—28no—
236C2×C4—448no—
237C2×C4—424no—
238C2×C4C22×D4×C1118yes—
239C2×C4C22×D4×C1118yes—
240C2×C4C22×Q8×C11116yes—
241C22C11×#398164yesdirect product factor
242C22C2×C11×#121112yes—
243C22C2×C11×C22⋊Q8124yes—
244C22C2×C11×#123112yes—
245C22C2×C11×#125124yes—
246C22C2×C11×C4⋊Q8112yes—
247C22C23×D4×C1111yescharacteristic
248C22C23×D4×C1111yescharacteristic
249C22C23×Q8×C1112yes—
250C22C22×C11×#4111yescharacteristic
251C22C22×C11×#4112yes—
252C4—28no—
253C4—216no—
254C4—28no—
255C4—48no—
256C4—44no—
257C2C2×C11×#398124yesdirect product factor
258C2C22×C11×#12111yescharacteristic
259C2C22×C11×C22⋊Q812yes—
260C2C22×C11×#12311yescharacteristic
261C2C22×C11×#12512yes—
262C2C22×C11×C4⋊Q811yescharacteristic
subgroupG/H
center, socle, prime radicalC25×C11C23
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#398C2direct (N × H)
18. C11×#398C22direct (N × H)
48. C22×#398C11direct (N × H)
84. C2×#398C2×C11direct (N × H)
127. #398C22×C11direct (N × H)
130. C22×C11#398direct (N × H)
173. C2×C11C2×#398direct (N × H)
211. C11C22×#398direct (N × H)
241. C22C11×#398direct (N × H)
257. C2C2×C11×#398direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×C4⋊C42
C2×C11×#3982
C22×C11×#952
C22×#39811