Finite Group Databasebeta

← #14680938

Subgroups — #14680938

Order 2816.

4390 conjugacy classes of subgroups; only the 651 normal subgroups are shown.

normal subgroups only

This group has 4390 conjugacy classes of subgroups — too many to draw. Only its 651 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
1C2×#10622825C216yesmaximal, complemented
2#13066887C212yesmaximal, complemented
3#13066857C216yesmaximal, complemented
4C23×C11×#41C211yesmaximal, characteristic
5C22×C11×#41—224no—
6C22×C11×#41C418yescomplemented
7C23×Q8×C11C2211yescharacteristic
8C23×D4×C11C2213yes—
9C24×C4×C11C2213yes—
10C22×C22⋊Dic11C22112yes—
11C22×C4⋊Dic11C2214yes—
12#10622825—224no—
13C2×C11⋊#95C22112yes—
14C25×C11C2313yes—
15C2×C11×#41—2128no—
16C2×C11×#41—296no—
17C22×Q8×C11—212no—
18C22×Q8×C11C2×C414yes—
19C22×D4×C11—224no—
20C22×D4×C11—212no—
21C22×D4×C11C2×C4112yes—
22C23×C4×C11—224no—
23C23×C4×C11C2×C4112yes—
24C23×C4×C11D4124yes—
25C23×C4×C11C2313yes—
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2318yes—
28C2×C22⋊Dic11—224no—
29C2×C22⋊Dic11—424no—
30C2×C4⋊Dic11—224no—
31C11⋊#95—224no—
32#14337—111nomaximal, Sylow
33C24×C11—212no—
34C24×C11—212no—
35C24×C11—212no—
36C24×C11C22×C416yes—
37C24×C11C2×D4112yes—
38C24×C11C2411yescharacteristic
39C11×#41—2256no—
40C2×Q8×C11—232no—
41C2×Q8×C11—224no—
42C2×D4×C11—296no—
43C2×D4×C11—248no—
44C2×D4×C11—224no—
45C22×C4×C11—212no—
46C22×C4×C11—248no—
47C22×C4×C11—296no—
48C22×C4×C11C22⋊C4148yescomplemented
49C22×C4×C11C22×C416yes—
50C22×C4×C11C22×C412yes—
51C22×C4×C11C2×D4112yes—
52C22×C4×C11C2×D4112yes—
53C22×Dic11—224no—
54C22×Dic11—224no—
55C22×Dic11—28no—
56C22⋊Dic11—448no—
57C4⋊Dic11—416no—
58C23×#41D1111yescharacteristic
59C2×#380—116no—
60#1446—112no—
61#1438—116no—
62C23×C11—212no—
63C23×C11—224no—
64C23×C11—224no—
65C23×C11—212no—
66C23×C11—212no—
67C23×C11—224no—
68C23×C11—412no—
69C23×C11—412no—
70C23×C11—424no—
71C23×C11C2×C22⋊C4112yes—
72C23×C11C23×C411yescharacteristic
73C23×C11C22×D416yes—
74C23×C11H(5,𝔽2)14yes—
75C23×C112−1+414yes—
76Q8×C11—232no—
77D4×C11—296no—
78C2×C4×C11—212no—
79C2×C4×C11—224no—
80C2×C4×C11—296no—
81C2×C4×C11C2×C22⋊C4112yes—
82C2×C4×C11C2×C22⋊C4112yes—
83C2×C4×C11#120116yes—
84C2×Dic11—48no—
85C2×Dic11—424no—
86C2×Dic11—424no—
87C22×#41—224no—
88C22×#41Dic1118yescomplemented
89C23×Q8C2×D1111yescharacteristic
90C23×D4C2×D1113yes—
91C24×C4C2×D1113yes—
92C22×C4⋊C4—114no—
93C22×C22⋊C4—1112no—
94#380—2224no—
95C2×#95—1112no—
96C22×C11—224no—
97C22×C11—212no—
98C22×C11—424no—
99C22×C11—424no—
100C22×C11—424no—
101C22×C11C22×C22⋊C413yes—
102C22×C11#52014yes—
103C22×C11C2×#12014yes—
104C22×C11#53516yes—
105C22×C11#53616yes—
106C22×C11#537112yes—
107C4×C11—212no—
108C4×C11#37918yes—
109Dic11—88no—
110C25C22×D1113yes—
111C2×#41—2128no—
112C2×#41—296no—
113C22×Q8—212no—
114C22×Q8C2×Dic1114yes—
115C22×D4—224no—
116C22×D4—212no—
117C22×D4C2×Dic11112yes—
118C23×C4—224no—
119C23×C4—118no—
120C23×C4C2×Dic11112yes—
121C23×C4C22⋊D11124yes—
122C23×C4C22×D1113yes—
123C23×C4C22×D1111yescharacteristic
124C2×C4⋊C4—2224no—
125C2×C22⋊C4—2224no—
126C2×C22⋊C4—4424no—
127#95—2224no—
128C2×C11—412no—
129C2×C11C2×#37911yescharacteristic
130C2×C11#231116yes—
131C2×C11#261514yes—
132C2×C11#261614yes—
133C24—212no—
134C24—212no—
135C24—212no—
136C24C22×Dic1116yes—
137C24C2×C22⋊D11112yes—
138C24C23×D1111yescharacteristic
139#41—2256no—
140C2×Q8—232no—
141C2×Q8—224no—
142C2×D4—296no—
143C2×D4—248no—
144C2×D4—224no—
145C22×C4—212no—
146C22×C4—248no—
147C22×C4—296no—
148C22×C4—2224no—
149C22×C4—228no—
150C22×C4—2224no—
151C22×C4C22⋊Dic11148yescomplemented
152C22×C4C22×Dic1116yes—
153C22×C4C22×Dic1112yes—
154C22×C4C2×C22⋊D11112yes—
155C22×C4C2×C22⋊D11112yes—
156C4⋊C4—4416no—
157C22⋊C4—4448no—
158C11#1433711yescharacteristic, complemented, Sylow
159C23—212no—
160C23—224no—
161C23—212no—
162C23—224no—
163C23—212no—
164C23—224no—
165C23—412no—
166C23—412no—
167C23—424no—
168C23C2×C22⋊Dic11112yes—
169C23#6704214yes—
170C23#6704314yes—
171C23C23×Dic1111yescharacteristic
172C23C22×C22⋊D1116yes—
173Q8—232no—
174D4—296no—
175C2×C4—212no—
176C2×C4—224no—
177C2×C4—296no—
178C2×C4—4424no—
179C2×C4—4424no—
180C2×C4—448no—
181C2×C4C2×C22⋊Dic11112yes—
182C2×C4C2×C22⋊Dic11112yes—
183C2×C4#67006116yes—
184C22—224no—
185C22—212no—
186C22—424no—
187C22—424no—
188C22—424no—
189C22#1062335616yes—
190C22#1062335814yes—
191C22#1062336116yes—
192C22#10623364112yes—
193C22C22×C22⋊Dic1113yes—
194C22C2×#6700614yes—
195C4—212no—
196C4—888no—
197C4#1062286018yes—
198C2—412no—
199C2C2×#1062286011yescharacteristic
200C2#1307120816yes—
201C2#1307434014yes—
202C2#1307434514yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC23×C11×#41C2
socle, cosocleC24×C11C24
hypercenterC23×#41D11
hypocenterC11#14337
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10622825C2semidirect
2. #13066887C2semidirect
3. #13066857C2semidirect
6. C22×C11×#41C4semidirect
48. C22×C4×C11C22⋊C4semidirect
88. C22×#41Dic11semidirect
151. C22×C4C22⋊Dic11semidirect
158. C11#14337semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
#130668872
#130668572
C23×C11×#412
#1433711