Finite Group Databasebeta

← #15674439

Subgroups — #15674439

Order 2944.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10625120C212yesmaximal, complemented
2C2×#10625019C212yesmaximal, complemented
3#13092318C211yesmaximal, characteristic, complemented
4#13092186C211yesmaximal, characteristic, complemented
5C23×#537C211yesmaximal, characteristic, complemented
6C2×#41×C23C2212yes—
7C22×D92C2211yescharacteristic
8C23×C22⋊Q8—22no—
9C23×#121—22no—
10C23×#121—22no—
11C2×C4⋊C4×C23C2211yescharacteristic
12#10625120—24no—
13#10625120—24no—
14C2×#67274—22no—
15C2×#67272—22no—
16C2×(C2×D23)⋊C4—22no—
17C2×C4×Dic23C2211yescharacteristic
18C2×#67267C2212yes—
19#10625019—24no—
20C23×D23—21no—
21#41×C23—22no—
22#41×C23—22no—
23#41×C23—22no—
24#41×C23—22no—
25C2×Q8×C23D412yes—
26C2×D4×C23—22no—
27C2×D4×C23—22no—
28C2×D4×C23D412yes—
29C22×C4×C23—22no—
30C22×C4×C23D412yes—
31C22×C4×C23C2311yescharacteristic
32C22×Dic23—21no—
33C2×D92—22no—
34C2×D92—22no—
35C2×D92—21no—
36C2×D92D412yescomplemented
37C4⋊C4×C23—22no—
38C4⋊C4×C23—22no—
39C22⋊C4×C23—24no—
40#67274—28no—
41#67272—28no—
42(C2×D23)⋊C4—44no—
43C4×Dic23—22no—
44#67267—22no—
45#67267D414yescomplemented
46C2×C23⋊C8—22no—
47C23×C23—22no—
48C23×C23C2×D411yescharacteristic
49C22×D23—22no—
50C22×D23—42no—
51C22×D23—42no—
52C22×D23—41no—
53C22×D23—41no—
54Q8×C23—22no—
55Q8×C23—22no—
56D4×C23—22no—
57D4×C23—22no—
58D4×C23—42no—
59D4×C23—42no—
60D4×C23—82no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—42no—
64C2×C4×C23—42no—
65C2×C4×C23—42no—
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D412yes—
68C2×C4×C23C2×D412yes—
69C2×C4×C23#4111yescharacteristic
70C2×Dic23—22no—
71C2×Dic23—41no—
72C2×Dic23—41no—
73D92—24no—
74D92—42no—
75C23⋊C8—24no—
76#2006—231nomaximal, Sylow
77C22×C23—21no—
78C22×C23—21no—
79C22×C23—42no—
80C22×C23—42no—
81C22×C23—42no—
82C22×C23#12011yescharacteristic
83C22×C23#12111yescharacteristic
84C22×C23#12711yescharacteristic
85C2×D23—44no—
86C2×D23—42no—
87C2×D23—82no—
88C2×D23—81no—
89C2×D23—81no—
90C4×C23—42no—
91C4×C23—42no—
92C4×C23#12012yes—
93C4×C23#12112yes—
94Dic23—42no—
95C2×AGL(1,ℤ/8)—232no—
96#537D2311yescharacteristic, complemented
97C2×#104—232no—
98#390—231no—
99#343—231no—
100C2×C23—21no—
101C2×C23—21no—
102C2×C23—82no—
103C2×C23#39211yescharacteristic
104C2×C23#45311yescharacteristic
105C2×C23#45411yescharacteristic
106D23—82no—
107C2×#41C2×D2312yes—
108C22×D4—231no—
109AGL(1,ℤ/8)—464no—
110AGL(1,ℤ/8)—464no—
111C2×SD16—462no—
112C2×D8—462no—
113C2×M16—232no—
114C22⋊Q8—22no—
115#121—22no—
116#121—22no—
117C2×C4⋊C4C2×D2311yescharacteristic
118C2×C22⋊C4—462no—
119C2×C42—231no—
120#104—464no—
121C23#200611yescharacteristic, complemented, Sylow
122C24—461no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D2312yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—232no—
131C2×D4—462no—
132C2×D4—461no—
133C2×D4—462no—
134C2×D4C22⋊D2312yes—
135C22×C4—22no—
136C22×C4—461no—
137C22×C4C22⋊D2312yes—
138C22×C4C22×D2311yescharacteristic
139SD16—468no—
140D8—468no—
141M16—234no—
142M16—462no—
143C2×C8—462no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—924no—
148C42—462no—
149C23—22no—
150C23—462no—
151C23—922no—
152C23—922no—
153C23—921no—
154C23—921no—
155C23C2×C22⋊D2311yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—464no—
164D4—922no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—462no—
171C2×C4—921no—
172C2×C4—921no—
173C2×C4D4×D2311yescharacteristic
174C2×C4D4×D2312yes—
175C2×C4#6729011yescharacteristic
176C2×C4C2×C22⋊D2312yes—
177C8—464no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—924no—
184C22—922no—
185C22—1842no—
186C22—1841no—
187C22—1841no—
188C22#1062510911yescharacteristic
189C22#1062511111yescharacteristic
190C22#1062512411yescharacteristic
191C4—42no—
192C4—42no—
193C4—922no—
194C4#1062510812yes—
195C4#1062511012yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—1842no—
200C2#1309232511yescharacteristic
201C2#1309258511yescharacteristic
202C2#1309259011yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#537C2
socleC22×C23#120
hypercenter#537D23
hypocenterC23#2006
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#10625120C2semidirect
2. C2×#10625019C2semidirect
3. #13092318C2semidirect
4. #13092186C2semidirect
5. C23×#537C2semidirect
36. C2×D92D4semidirect
45. #67267D4semidirect
96. #537D23semidirect
121. C23#2006semidirect

Maximal subgroups

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

subgroupindex
C2×#106251202
C2×#106250192
#130923182
#130921862
C23×#5372
#200623