Finite Group Databasebeta

← #15671914

Subgroups — #15671914

Order 2944.

346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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×#10625101C211yesmaximal, characteristic
2C4×C22⋊Dic23C211yesmaximal, characteristic, complemented
3#13092152C214yesmaximal, complemented
4C23×#407C211yesmaximal, characteristic, complemented
5C23×C4×C23C2211yescharacteristic
6C22×C22⋊D23—21no—
7C22×D92C411yescharacteristic, complemented
8C2×M16×C23—21no—
9C2×C22⋊Dic23—21no—
10#10625101—21no—
11#10625101—21no—
12#10625101C412yescomplemented
13#10625101C2212yes—
14C2×(C2×D23)⋊C4—21no—
15C2×C4⋊Dic23C411yescharacteristic, complemented
16C2×C4×Dic23—21no—
17C23×C22⋊C8—21no—
18C23×C22⋊C8C2212yescomplemented
19C23⋊#95C2212yescomplemented
20C24×C23D411yescharacteristic
21C23×D23—21no—
22C22×C4×C23—42no—
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23C2×C411yescharacteristic
25C22×C4×C23D411yescharacteristic
26C22×C4×C23D411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23C2311yescharacteristic
29C2×C22⋊D23—22no—
30C2×C22⋊D23—22no—
31C2×C22⋊D23—44no—
32C22×Dic23—21no—
33C22×Dic23—22no—
34C2×D92—21no—
35C2×D92—42no—
36C2×D92C2×C412yes—
37M16×C23—42no—
38C2×C8×C23—22no—
39C22⋊Dic23—24no—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—22no—
42C4⋊Dic23—21no—
43C4⋊Dic23C2×C412yes—
44C4×Dic23—42no—
45C23×C23—22no—
46C23×C23—22no—
47C23×C23—41no—
48C23×C23C22⋊C411yescharacteristic
49C23×C23C22⋊C411yescharacteristic
50C23×C23C2×D411yescharacteristic
51C22×D23—22no—
52C22×D23—42no—
53C22×D23—42no—
54C22×D23—42no—
55C2×C4×C23—22no—
56C2×C4×C23—22no—
57C2×C4×C23—22no—
58C2×C4×C23—41no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23C22⋊C411yescharacteristic
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C22×C411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C22⋊D23—44no—
66C22⋊D23—44no—
67C2×Dic23—24no—
68C2×Dic23—22no—
69C2×Dic23—42no—
70C2×Dic23—42no—
71C2×Dic23—42no—
72D92—42no—
73D92—42no—
74C8×C23—42no—
75#1507—231nomaximal, Sylow
76C22×C23—21no—
77C22×C23—21no—
78C22×C23—21no—
79C22×C23—21no—
80C22×C23—21no—
81C22×C23—21no—
82C22×C23—21no—
83C22×C23—44no—
84C22×C23#10412yes—
85C22×C23C2×C22⋊C411yescharacteristic
86C22×C23AGL(1,ℤ/8)12yes—
87C2×D23—42no—
88C2×D23—42no—
89C2×D23—42no—
90C2×D23—84no—
91C4×C23—21no—
92C4×C23—21no—
93C4×C23—21no—
94C4×C23#9912yes—
95Dic23—44no—
96Dic23—42no—
97C2×#121—231no—
98#407D2311yescharacteristic, complemented
99C4×C22⋊C4—231no—
100#327—234no—
101C2×C23—22no—
102C2×C23—22no—
103C2×C23—41no—
104C2×C23C2×#9911yescharacteristic
105C2×C23#41811yescharacteristic
106C2×C23C2×#10411yescharacteristic
107D23—82no—
108C22×D4—231no—
109C22×D4—461no—
110C23×C4C2×D2311yescharacteristic
111C2×M16—21no—
112#121—232no—
113#121—232no—
114#121—461no—
115#121—461no—
116C2×C4⋊C4—231no—
117C2×C22⋊C4—461no—
118C2×C22⋊C4—461no—
119C2×C42—461no—
120C22⋊C8—21no—
121C22⋊C8C2×D2312yescomplemented
122#95—232no—
123C23#150711yescharacteristic, complemented, Sylow
124C24—461no—
125C24D9211yescharacteristic
126C2×D4—232no—
127C2×D4—462no—
128C2×D4—462no—
129C2×D4—461no—
130C2×D4—922no—
131C2×D4—924no—
132C22×C4—42no—
133C22×C4—461no—
134C22×C4—462no—
135C22×C4C4×D2311yescharacteristic
136C22×C4C4×D2311yescharacteristic
137C22×C4D9211yescharacteristic
138C22×C4C22⋊D2311yescharacteristic
139C22×C4C22⋊D2311yescharacteristic
140C22×C4C22×D2311yescharacteristic
141M16—42no—
142C2×C8—22no—
143C4⋊C4—232no—
144C4⋊C4—461no—
145C22⋊C4—464no—
146C22⋊C4—462no—
147C22⋊C4—462no—
148C42—922no—
149C23—22no—
150C23—22no—
151C23—41no—
152C23—462no—
153C23—922no—
154C23—922no—
155C23—922no—
156C23(C2×D23)⋊C411yescharacteristic
157C23(C2×D23)⋊C411yescharacteristic
158C23C2×D9211yescharacteristic
159D4—922no—
160D4—924no—
161D4—924no—
162D4—922no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—464no—
170C2×C4—462no—
171C2×C4—922no—
172C2×C4—922no—
173C2×C4—922no—
174C2×C4(C2×D23)⋊C411yescharacteristic
175C2×C4(C2×D23)⋊C411yescharacteristic
176C2×C4C2×C4×D2311yescharacteristic
177C2×C4C2×C22⋊D2311yescharacteristic
178C8—42no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—922no—
188C22—922no—
189C22—922no—
190C22—1844no—
191C22#1062500712yes—
192C22#1062507912yes—
193C22C2×(C2×D23)⋊C411yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—924no—
198C4—922no—
199C4#1062498812yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—1842no—
204C2C2×#1062498811yescharacteristic
205C2#1309242311yescharacteristic
206C2C2×#1062500711yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#407C2
socleC22×C23C2×C22⋊C4
prime radicalC2×#10625101C2
cosocleC22×C4×C23C23
hypercenter#407D23
hypocenterC23#1507
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Dic23C2semidirect
3. #13092152C2semidirect
4. C23×#407C2semidirect
7. C22×D92C4semidirect
12. #10625101C4semidirect
15. C2×C4⋊Dic23C4semidirect
18. C23×C22⋊C8C22semidirect
19. C23⋊#95C22semidirect
98. #407D23semidirect
121. C22⋊C8C2×D23semidirect
123. C23#1507semidirect

Maximal subgroups

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

subgroupindex
C2×#106251012
C4×C22⋊Dic232
#130921522
C23×#4072
#150723