Finite Group Databasebeta

← #15674438

Subgroups — #15674438

Order 2944.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10625103C212yesmaximal, complemented
2#13092998C211yesmaximal, characteristic, complemented
3C2×#10624987C212yesmaximal, complemented
4#13092186C211yesmaximal, characteristic, complemented
5C23×#390C211yesmaximal, characteristic, complemented
6C22×D4×C23C2211yescharacteristic
7C2×#67288C2212yes—
8C2×C4⋊C4×C23C2211yescharacteristic
9C2×C22⋊C4×C23—22no—
10C2×C42×C23C2211yescharacteristic
11C2×#67273—22no—
12#10625103—24no—
13#10625103—24no—
14C2×#67272—22no—
15#10625101—22no—
16C2×#67267C2212yes—
17#10625068—22no—
18#10625066—22no—
19#10624987—24no—
20C24×C23—21no—
21C2×D4×C23—22no—
22C2×D4×C23—22no—
23C2×D4×C23—21no—
24C2×D4×C23D412yescomplemented
25C22×C4×C23—21no—
26C22×C4×C23D412yes—
27C22×C4×C23C2311yescharacteristic
28C2×C22⋊D23—22no—
29#67288—22no—
30#67288—22no—
31#67288—22no—
32#67288—22no—
33C2×D92—22no—
34C2×D92D412yes—
35C2×C4×D23—22no—
36C2×Dic46D412yes—
37C4⋊C4×C23—22no—
38C22⋊C4×C23—44no—
39C42×C23—22no—
40#67273—28no—
41#67272—28no—
42(C2×D23)⋊C4—24no—
43C4⋊Dic23—22no—
44#67267—22no—
45#67267D414yescomplemented
46C2×C23⋊C8—22no—
47C23×C23—22no—
48C23×C23—42no—
49C23×C23—42no—
50C23×C23—41no—
51C23×C23—41no—
52C23×C23C2×D411yescharacteristic
53C22×D23—22no—
54D4×C23—24no—
55D4×C23—42no—
56C2×C4×C23—22no—
57C2×C4×C23—22no—
58C2×C4×C23—41no—
59C2×C4×C23—41no—
60C2×C4×C23—42no—
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D412yes—
63C2×C4×C23C2×D412yes—
64C2×C4×C23#4111yescharacteristic
65C22⋊D23—42no—
66C22⋊D23—42no—
67C2×Dic23—22no—
68D92—22no—
69D92—22no—
70D92—82no—
71C4×D23—42no—
72C4×D23—42no—
73Dic46—22no—
74Dic46—22no—
75C23⋊C8—24no—
76#2006—231nomaximal, Sylow
77C22×C23—21no—
78C22×C23—21no—
79C22×C23—44no—
80C22×C23—42no—
81C22×C23—82no—
82C22×C23—81no—
83C22×C23—81no—
84C22×C23#12011yescharacteristic
85C22×C23#12111yescharacteristic
86C22×C23#12711yescharacteristic
87C2×D23—42no—
88C2×D23—42no—
89C2×D23—42no—
90C4×C23—42no—
91C4×C23—42no—
92C4×C23#12012yes—
93C4×C23#12112yes—
94Dic23—42no—
95C2×AGL(1,ℤ/8)—232no—
96#537—231no—
97C2×#104—232no—
98#390D2311yescharacteristic, complemented
99#343—231no—
100C2×C23—21no—
101C2×C23—21no—
102C2×C23—82no—
103C2×C23#39211yescharacteristic
104C2×C23#45311yescharacteristic
105C2×C23#45411yescharacteristic
106D23—82no—
107C2×#41—232no—
108C22×D4C2×D2311yescharacteristic
109AGL(1,ℤ/8)—464no—
110AGL(1,ℤ/8)—464no—
111C2×SD16—462no—
112C2×D8—462no—
113C2×M16—232no—
114C22⋊Q8—462no—
115#121—462no—
116#121—462no—
117C2×C4⋊C4C2×D2311yescharacteristic
118C2×C22⋊C4—22no—
119C2×C42C2×D2311yescharacteristic
120#104—464no—
121C23#200611yescharacteristic, complemented, Sylow
122C24—21no—
123#41—462no—
124#41—462no—
125#41—462no—
126#41—462no—
127C2×Q8—232no—
128C2×D4—21no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—232no—
132C2×D4—462no—
133C2×D4—462no—
134C2×D4D9212yescomplemented
135C22×C4—21no—
136C22×C4—462no—
137C22×C4C22⋊D2312yes—
138C22×C4C22×D2311yescharacteristic
139SD16—468no—
140D8—468no—
141M16—234no—
142M16—462no—
143C2×C8—462no—
144C4⋊C4—22no—
145C4⋊C4—462no—
146C22⋊C4—44no—
147C22⋊C4—464no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—462no—
155C23C2×C22⋊D2311yescharacteristic
156Q8—462no—
157Q8—462no—
158D4—24no—
159D4—42no—
160D4—462no—
161D4—462no—
162D4—922no—
163D4—922no—
164D4—1842no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—462no—
171C2×C4—922no—
172C2×C4—922no—
173C2×C4C2×D9211yescharacteristic
174C2×C4#6728811yescharacteristic
175C2×C4D4×D2312yes—
176C2×C4D4×D2312yes—
177C8—464no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—922no—
186C22—922no—
187C22—922no—
188C22#1062510111yescharacteristic
189C22#1062510811yescharacteristic
190C22#1062511111yescharacteristic
191C4—42no—
192C4—42no—
193C4—922no—
194C4#1062505312yes—
195C4#1062505512yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—1842no—
200C2#1309232611yescharacteristic
201C2#1309258411yescharacteristic
202C2#1309258911yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#390C2
socleC22×C23#120
hypercenter#390D23
hypocenterC23#2006
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. #13092998C2semidirect
3. C2×#10624987C2semidirect
4. #13092186C2semidirect
5. C23×#390C2semidirect
24. C2×D4×C23D4semidirect
45. #67267D4semidirect
98. #390D23semidirect
121. C23#2006semidirect
134. C2×D4D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
#130929982
C2×#106249872
#130921862
C23×#3902
#200623