Finite Group Databasebeta

← #15673431

Subgroups — #15673431

Order 2944.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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×#67262C211yesmaximal, characteristic
2C2×#10624999C211yesmaximal, characteristic, complemented
3#13092274C212yesmaximal
4#13092179C212yesmaximal, complemented
5C2×C23×#107C211yesmaximal, characteristic, complemented
6C22×C4×D23C2211yescharacteristic
7C22×C8×C23C2211yescharacteristic
8C2×C4⋊C4×C23C2212yes—
9C2×(C2×D23)⋊C4—22no—
10C2×C4⋊Dic23C2212yes—
11C22×C23⋊C8C2211yescharacteristic
12C2×#67262—22no—
13C2×#67262—22no—
14C2×#67262C414yescomplemented
15C23×#107—22no—
16C23⋊#95—22no—
17#10624999—22no—
18C23×D23D411yescharacteristic
19C22×C4×C23—22no—
20C22×C4×C23C2311yescharacteristic
21C22×Dic23—22no—
22C22×Dic23D411yescharacteristic
23C2×C4×D23—21no—
24C2×C4×D23—21no—
25C2×C4×D23—21no—
26C2×C4×D23—21no—
27C2×C4×D23C2×C412yes—
28C2×C4×D23Q812yes—
29C2×C8×C23C2×C412yes—
30C2×C8×C23D412yes—
31C2×C8×C23D412yes—
32C4⋊C4×C23—22no—
33C4⋊C4×C23—22no—
34(C2×D23)⋊C4—44no—
35C4⋊Dic23—22no—
36C4⋊Dic23—22no—
37C2×C23⋊C8—21no—
38C2×C23⋊C8—21no—
39C2×C23⋊C8C2×C412yes—
40#67262—28no—
41C23×C23C2×D411yescharacteristic
42C22×D23—21no—
43C22×D23—21no—
44C22×D23—22no—
45C22×D23—22no—
46C22×D23C4⋊C412yes—
47C2×C4×C23—42no—
48C2×C4×C23—42no—
49C2×C4×C23—42no—
50C2×C4×C23C22×C411yescharacteristic
51C2×C4×C23C2×D411yescharacteristic
52C2×C4×C23C2×D411yescharacteristic
53C2×C4×C23C2×Q811yescharacteristic
54C2×C4×C23#4111yescharacteristic
55C2×C4×C23#4111yescharacteristic
56C2×Dic23—21no—
57C2×Dic23—21no—
58C2×Dic23—42no—
59C2×Dic23—42no—
60C2×Dic23—42no—
61C2×Dic23C4⋊C412yes—
62C4×D23—22no—
63C4×D23—22no—
64C4×D23—22no—
65C4×D23—22no—
66C8×C23C22⋊C414yescomplemented
67C23⋊C8—22no—
68#1809—231nomaximal, Sylow
69C22×C23C2×C4⋊C411yescharacteristic
70C22×C23#12111yescharacteristic
71C22×C23#12111yescharacteristic
72C22×C23AGL(1,ℤ/8)12yes—
73C22×C23#13712yes—
74C2×D23—22no—
75C2×D23—24no—
76C2×D23—42no—
77C2×D23—41no—
78C2×D23—41no—
79C4×C23—82no—
80C4×C23C2×C22⋊C411yescharacteristic
81C4×C23#11711yescharacteristic
82C4×C23C22⋊Q811yescharacteristic
83C4×C23C22⋊Q811yescharacteristic
84Dic23—22no—
85Dic23—82no—
86C22×M16—231no—
87C2×#107D2311yescharacteristic, complemented
88C2×#106—231no—
89#380—232no—
90#340—232no—
91C2×C23#38011yescharacteristic
92C2×C23#42812yes—
93C2×C23#46812yes—
94C2×C23#46911yescharacteristic
95C2×C23#47011yescharacteristic
96D23—42no—
97C23×C4—231no—
98C2×M16—234no—
99C2×M16—462no—
100C2×M16—462no—
101C22×C8—231no—
102C22×C8C2×D2311yescharacteristic
103C2×C4⋊C4—232no—
104C2×C4⋊C4C2×D2312yes—
105C2×C22⋊C4—462no—
106#107—22no—
107#106—462no—
108#95—462no—
109C23#180911yescharacteristic, complemented, Sylow
110C24—231no—
111C22×C4—22no—
112C22×C4—231no—
113C22×C4—232no—
114C22×C4—232no—
115C22×C4—461no—
116C22×C4—461no—
117C22×C4—461no—
118C22×C4—461no—
119C22×C4—462no—
120C22×C4C22×D2311yescharacteristic
121M16—468no—
122C2×C8—232no—
123C2×C8—461no—
124C2×C8—461no—
125C2×C8C4×D2312yes—
126C2×C8D9212yes—
127C2×C8C22⋊D2312yes—
128C4⋊C4—22no—
129C4⋊C4—22no—
130C4⋊C4—462no—
131C4⋊C4—462no—
132C22⋊C4—924no—
133C23—232no—
134C23—461no—
135C23—462no—
136C23—462no—
137C23—461no—
138C23D4×D2311yescharacteristic
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—232no—
143C2×C4—461no—
144C2×C4—461no—
145C2×C4—462no—
146C2×C4—462no—
147C2×C4—462no—
148C2×C4—462no—
149C2×C4—922no—
150C2×C4—922no—
151C2×C4—922no—
152C2×C4C2×C4×D2311yescharacteristic
153C2×C4C2×D9211yescharacteristic
154C2×C4#6729011yescharacteristic
155C2×C4Q8×D2311yescharacteristic
156C2×C4#6729211yescharacteristic
157C2×C4C2×C22⋊D2311yescharacteristic
158C8—462no—
159C8(C2×D23)⋊C414yescomplemented
160C22—464no—
161C22—462no—
162C22—922no—
163C22—921no—
164C22—921no—
165C22C4⋊C4×D2311yescharacteristic
166C22#1062506611yescharacteristic
167C22#1062508212yes—
168C22#1062508912yes—
169C22#1062510911yescharacteristic
170C4—82no—
171C4—462no—
172C4—1842no—
173C4#1062506311yescharacteristic
174C4#1062506811yescharacteristic
175C4C2×(C2×D23)⋊C411yescharacteristic
176C4#1062511711yescharacteristic
177C2—922no—
178C2#1309227411yescharacteristic
179C2#1309245812yes—
180C2#1309266412yes—
181C2#1309266711yescharacteristic
182C2#1309267211yescharacteristic
subgroupG/H
centerC23D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#107C2
socleC23×C23C2×D4
prime radicalC23×D23D4
cosocleC22×C4×C23C23
hypercenterC2×#107D23
hypocenterC23#1809
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#10624999C2semidirect
4. #13092179C2semidirect
5. C2×C23×#107C2semidirect
14. C2×#67262C4semidirect
66. C8×C23C22⋊C4semidirect
87. C2×#107D23semidirect
109. C23#1809semidirect
159. C8(C2×D23)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#672622
C2×#106249992
#130922742
#130921792
C2×C23×#1072
#180923