Finite Group Databasebeta

← #15673413

Subgroups — #15673413

Order 2944.

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

normal subgroups only

This group has 292 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
1C2×C4×Dic46C211yesmaximal, characteristic
2C2×#10624998C212yesmaximal
3#13092283C211yesmaximal, characteristic
4#13092180C212yesmaximal
5C2×C23×C4⋊C8C211yesmaximal, characteristic
6C22×Dic46C2211yescharacteristic
7C22×C8×C23C2212yes—
8C2×C42×C23C2211yescharacteristic
9C2×C4⋊Dic23C2212yes—
10C2×C4⋊Dic23C2211yescharacteristic
11C2×Dic23⋊C4—21no—
12C2×C4×Dic23—21no—
13C4×Dic46—22no—
14C4×Dic46C414yescomplemented
15C23×C4⋊C8—22no—
16C23⋊#95—21no—
17C23⋊#95—21no—
18#10624998—24no—
19C22×C4×C23D411yescharacteristic
20C22×C4×C23D411yescharacteristic
21C22×C4×C23C2311yescharacteristic
22C22×Dic23—21no—
23C22×Dic23—21no—
24C22×Dic23—22no—
25C2×Dic46—21no—
26C2×Dic46—21no—
27C2×Dic46—21no—
28C2×Dic46C2×C412yes—
29C2×Dic46D412yes—
30C2×Dic46Q812yes—
31C2×C8×C23—22no—
32C2×C8×C23—22no—
33C2×C8×C23—22no—
34C42×C23C2×C412yes—
35C42×C23D412yes—
36C4⋊Dic23—21no—
37C4⋊Dic23—22no—
38C4⋊Dic23—22no—
39C4⋊Dic23C2×C412yes—
40Dic23⋊C4—24no—
41C4×Dic23—24no—
42C23×C23C2×D411yescharacteristic
43C2×C4×C23—22no—
44C2×C4×C23—22no—
45C2×C4×C23C22⋊C412yes—
46C2×C4×C23C22⋊C412yes—
47C2×C4×C23C22×C411yescharacteristic
48C2×C4×C23C2×D411yescharacteristic
49C2×C4×C23C2×D411yescharacteristic
50C2×C4×C23C2×Q811yescharacteristic
51C2×C4×C23#4111yescharacteristic
52C2×C4×C23#4111yescharacteristic
53C2×Dic23—22no—
54C2×Dic23—22no—
55C2×Dic23—22no—
56C2×Dic23—22no—
57C2×Dic23—42no—
58C2×Dic23—42no—
59C2×Dic23—42no—
60C2×Dic23—42no—
61Dic46—22no—
62Dic46—22no—
63Dic46—22no—
64Dic46C4⋊C414yes—
65C8×C23—42no—
66#1805—231nomaximal, Sylow
67C22×C23C2×C22⋊C411yescharacteristic
68C22×C23#12111yescharacteristic
69C22×C23C22⋊Q811yescharacteristic
70C22×C23#13512yes—
71C22×C23#13712yes—
72C4×C23—22no—
73C4×C23—22no—
74C4×C23C2×C4⋊C411yescharacteristic
75C4×C23#11711yescharacteristic
76C4×C23#12111yescharacteristic
77C4×C23C22⋊Q811yescharacteristic
78Dic23—24no—
79Dic23—42no—
80Dic23—82no—
81C2×C4×Q8—231no—
82C2×C4⋊C8D2311yescharacteristic
83C2×#103—232no—
84#382—231no—
85#340—232no—
86C2×C23#38011yescharacteristic
87C2×C23#41611yescharacteristic
88C2×C23#41911yescharacteristic
89C2×C23#46412yes—
90C2×C23#47912yes—
91C22×Q8—231no—
92C22×C8C2×D2312yes—
93C4×Q8—234no—
94C4×Q8—462no—
95C2×C4⋊C4—231no—
96C2×C4⋊C4—232no—
97C2×C4⋊C4—461no—
98C2×C42—461no—
99C2×C42C2×D2311yescharacteristic
100C4⋊C8—22no—
101#103—464no—
102#95—461no—
103#95—461no—
104C23#180511yescharacteristic, complemented, Sylow
105C2×Q8—232no—
106C2×Q8—232no—
107C2×Q8—232no—
108C2×Q8—461no—
109C2×Q8—461no—
110C2×Q8—461no—
111C22×C4—461no—
112C22×C4—461no—
113C22×C4—462no—
114C22×C4D9211yescharacteristic
115C22×C4D9211yescharacteristic
116C22×C4C22×D2311yescharacteristic
117C2×C8—22no—
118C2×C8—22no—
119C2×C8—22no—
120C4⋊C4—232no—
121C4⋊C4—464no—
122C4⋊C4—461no—
123C4⋊C4—462no—
124C4⋊C4—462no—
125C42—464no—
126C42C4×D2312yes—
127C42C22⋊D2312yes—
128C23C2×D9211yescharacteristic
129Q8—234no—
130Q8—462no—
131Q8—462no—
132Q8—462no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—462no—
136C2×C4—462no—
137C2×C4—462no—
138C2×C4—462no—
139C2×C4—922no—
140C2×C4—922no—
141C2×C4—922no—
142C2×C4—922no—
143C2×C4(C2×D23)⋊C412yes—
144C2×C4(C2×D23)⋊C412yes—
145C2×C4C2×C4×D2311yescharacteristic
146C2×C4D4×D2311yescharacteristic
147C2×C4#6729011yescharacteristic
148C2×C4Q8×D2311yescharacteristic
149C2×C4#6729211yescharacteristic
150C2×C4C2×C22⋊D2311yescharacteristic
151C8—42no—
152C22#1062506611yescharacteristic
153C22#1062506811yescharacteristic
154C22#1062507512yes—
155C22#1062508012yes—
156C22C2×(C2×D23)⋊C411yescharacteristic
157C4—22no—
158C4—22no—
159C4—464no—
160C4—922no—
161C4—1842no—
162C4C4⋊C4×D2311yescharacteristic
163C4#1062506311yescharacteristic
164C4#1062510911yescharacteristic
165C4#1062511711yescharacteristic
166C2#1309227411yescharacteristic
167C2#1309241411yescharacteristic
168C2#1309242711yescharacteristic
169C2#1309264012yes—
170C2#1309272512yes—
subgroupG/H
centerC23C2×D92
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×C4⋊C8C2
socle, prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenterC2×C4⋊C8D23
hypocenterC23#1805
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
14. C4×Dic46C4semidirect
104. C23#1805semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic462
C2×#106249982
#130922832
#130921802
C2×C23×C4⋊C82
#180523