Finite Group Databasebeta

← C2×#13074335 #14920686

Subgroups — C2×#13074335 #14920686

Order 2816.

5194 conjugacy classes of subgroups; only the 907 normal subgroups are shown.

normal subgroups only

This group has 5194 conjugacy classes of subgroups — too many to draw. Only its 907 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
1C22×#66982C213yesmaximal
2#13074335C2116yesmaximal, direct product factor
3C2×#10622842C214yesmaximal, complemented
4C2×#10622844C214yesmaximal, complemented
5C2×#10622824C213yesmaximal, complemented
6C24×Q8×C11C211yesmaximal, characteristic, complemented
7C23×Q8×C11—224no—
8C23×Q8×C11C2214yes—
9C23×Q8×C11C2218yescomplemented
10C24×C4×C11C2213yes—
11C23×C22⋊D11C2211yescharacteristic
12C22×C22⋊Dic11C2213yes—
13C2×#66982—224no—
14C2×#66982C22124yes—
15C22×(C2×D11)⋊C4C2216yes—
16C22×Dic11⋊C4C2216yes—
17#10622844C22132yescomplemented
18#10622842C22132yescomplemented
19#10622824C22124yescomplemented
20C2×C11⋊#95C22112yes—
21C25×C11C2311yescharacteristic
22C24×D11C2311yescharacteristic
23C22×Q8×C11—2128no—
24C22×Q8×C11—248no—
25C22×Q8×C11—296no—
26C22×Q8×C11C23116yes—
27C23×C4×C11—224no—
28C23×C4×C11D4124yes—
29C23×C4×C11C2316yes—
30C23×C4×C11C23112yes—
31C22×C22⋊D11—212no—
32C22×C22⋊D11C2314yes—
33C23×Dic11C2311yescharacteristic
34C23×Dic11C2316yes—
35C2×C22⋊Dic11—212no—
36C2×C22⋊Dic11C23112yes—
37#66982—296no—
38C2×(C2×D11)⋊C4—224no—
39C2×(C2×D11)⋊C4C23124yes—
40C2×Dic11⋊C4—224no—
41C2×Dic11⋊C4C23124yes—
42C11⋊#95C23148yes—
43C2×#2614—111nomaximal, Sylow
44C24×C11—28no—
45C24×C11C2×D4112yes—
46C24×C11C2412yes—
47C24×C11C2411yescharacteristic
48C23×D11—26no—
49C23×D11—28no—
50C23×D11C2412yes—
51C2×Q8×C11—2128no—
52C2×Q8×C11—2256no—
53C2×Q8×C11—296no—
54C22×C4×C11—296no—
55C22×C4×C11—248no—
56C22×C4×C11—224no—
57C22×C4×C11C2×D4124yes—
58C22×C4×C11C2×D4148yes—
59C22×C4×C11C24112yes—
60C2×C22⋊D11—224no—
61C2×C22⋊D11—416no—
62C22×Dic11—26no—
63C22×Dic11—212no—
64C22×Dic11—224no—
65C22×Dic11C24112yes—
66C22×Dic11C2412yes—
67C22⋊Dic11—224no—
68(C2×D11)⋊C4—248no—
69Dic11⋊C4—248no—
70C24×Q8D1111yescharacteristic, complemented
71C22×#123—113no—
72#2614—1116no—
73C2×#395—114no—
74C2×#393—114no—
75C2×#381—113no—
76C23×C11—248no—
77C23×C11—28no—
78C23×C11#120116yes—
79C23×C11C22×D4112yes—
80C23×C11C22×D416yes—
81C23×C112−1+418yes—
82C23×C11C2511yescharacteristic
83C22×D11—26no—
84C22×D11—28no—
85C22×D11—44no—
86C22×D11—424no—
87Q8×C11—2128no—
88C2×C4×C11—296no—
89C2×C4×C11—248no—
90C2×C4×C11—224no—
91C2×C4×C11C22×D4124yes—
92C22⋊D11—416no—
93C2×Dic11—26no—
94C2×Dic11—212no—
95C2×Dic11—224no—
96C2×Dic11—44no—
97C2×Dic11—424no—
98C23×Q8—224no—
99C23×Q8C2×D1114yes—
100C23×Q8C2×D1118yescomplemented
101C23×D4—111no—
102C24×C4C2×D1113yes—
103C2×#123—1124no—
104C2×#123—2224no—
105C22×C4⋊C4—116no—
106C22×C22⋊C4—113no—
107C22×C22⋊C4—116no—
108#395—1132no—
109#393—1132no—
110#381—1124no—
111C2×#95—1112no—
112C22×C11—232no—
113C22×C11—224no—
114C22×C11C2×#12018yes—
115C22×C11C2×#12014yes—
116C22×C11#536124yes—
117C22×C11C23×D413yes—
118C22×C11C2×2−1+414yes—
119C2×D11—42no—
120C2×D11—412no—
121C2×D11—88no—
122C4×C11—224no—
123Dic11—42no—
124Dic11—412no—
125C25—111no—
126C25C22×D1111yescharacteristic
127C22×Q8—2128no—
128C22×Q8—248no—
129C22×Q8—296no—
130C22×Q8C22×D11116yes—
131C22×D4—114no—
132C22×D4—2212no—
133C23×C4—224no—
134C23×C4—116no—
135C23×C4—111no—
136C23×C4C22⋊D11124yes—
137C23×C4C22×D11112yes—
138C23×C4C22×D1116yes—
139#123—2296no—
140C2×C4⋊C4—1124no—
141C2×C4⋊C4—2224no—
142C2×C22⋊C4—1112no—
143C2×C22⋊C4—1124no—
144C2×C22⋊C4—2212no—
145C2×C22⋊C4—2224no—
146#95—1148no—
147C2×C11—28no—
148C2×C11#261418yescomplemented
149C2×C11C22×#12011yescharacteristic
150C2×C11C2×#53616yes—
151D11—82no—
152C24—28no—
153C24—112no—
154C24—228no—
155C24—226no—
156C24C2×C22⋊D11112yes—
157C24C23×D1112yes—
158C24C23×D1111yescharacteristic
159C2×Q8—2128no—
160C2×Q8—2256no—
161C2×Q8—296no—
162C2×D4—2224no—
163C2×D4—4416no—
164C22×C4—296no—
165C22×C4—248no—
166C22×C4—224no—
167C22×C4—1112no—
168C22×C4—112no—
169C22×C4—2224no—
170C22×C4—2212no—
171C22×C4—226no—
172C22×C4C2×C22⋊D11124yes—
173C22×C4C2×C22⋊D11148yes—
174C22×C4C23×D11112yes—
175C4⋊C4—2248no—
176C22⋊C4—2224no—
177C22⋊C4—2248no—
178C11C2×#261411yescharacteristic, complemented, Sylow
179C23—248no—
180C23—28no—
181C23—228no—
182C23—226no—
183C23—4424no—
184C23—444no—
185C23#67006116yes—
186C23#6704018yes—
187C23C22×C22⋊D11112yes—
188C23C22×C22⋊D1116yes—
189C23C24×D1111yescharacteristic
190Q8—2128no—
191D4—4416no—
192C2×C4—296no—
193C2×C4—248no—
194C2×C4—224no—
195C2×C4—2224no—
196C2×C4—2212no—
197C2×C4—226no—
198C2×C4—4424no—
199C2×C4—444no—
200C2×C4C22×C22⋊D11124yes—
201C22—224no—
202C22—232no—
203C22—4412no—
204C22—442no—
205C22—888no—
206C22#10623347124yes—
207C22C2×#6700618yes—
208C22C2×#6700614yes—
209C22C2×#6704014yes—
210C22C23×C22⋊D1113yes—
211C4—224no—
212C4—4412no—
213C4—442no—
214C2—28no—
215C2—882no—
216C2#1307433518yesdirect product factor
217C2C22×#6700611yescharacteristic
218C2C2×#1062334716yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC24×Q8×C11C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC24×Q8D11
hypocenterC11C2×#2614
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×Q8

Complements

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

NH ≅ G/Ntype
2. #13074335C2direct (N × H)
3. C2×#10622842C2semidirect
4. C2×#10622844C2semidirect
5. C2×#10622824C2semidirect
6. C24×Q8×C11C2semidirect
9. C23×Q8×C11C22semidirect
17. #10622844C22semidirect
18. #10622842C22semidirect
19. #10622824C22semidirect
70. C24×Q8D11semidirect
100. C23×Q8C2×D11semidirect
148. C2×C11#2614semidirect
178. C11C2×#2614semidirect
216. C2#13074335direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
#130743352
C2×#106228422
C2×#106228442
C2×#106228242
C24×Q8×C112
C2×#261411