Finite Group Databasebeta

← #15674268

Subgroups — #15674268

Order 2944.

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

normal subgroups only

This group has 304 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×Dic92C211yesmaximal, characteristic
2C2×#10624999C211yesmaximal, characteristic
3C2×#10624998C212yesmaximal
4#13092323C212yesmaximal
5C2×C23×#97C211yesmaximal, characteristic
6C22×Dic46C2212yes—
7C22×C8×C23C2211yescharacteristic
8C22×C8×C23C2211yescharacteristic
9C2×C42×C23C2211yescharacteristic
10C2×C4⋊Dic23C2212yes—
11C2×Dic92—22no—
12C2×Dic92—22no—
13C2×Dic92C414yescomplemented
14C23×#97—22no—
15C23⋊#95—24no—
16#10624999—22no—
17#10624998—24no—
18C22×C4×C23D412yes—
19C22×C4×C23C2311yescharacteristic
20C22×Dic23—22no—
21C22×Dic23—22no—
22C2×Dic46—22no—
23C2×Dic46—22no—
24C2×Dic46—22no—
25C2×Dic46—22no—
26C2×Dic46—22no—
27C2×Dic46C2×C414yes—
28C2×C8×C23—21no—
29C2×C8×C23—21no—
30C2×C8×C23C2×C412yes—
31C2×C8×C23D412yes—
32C2×C8×C23D412yes—
33C2×C8×C23D412yes—
34C42×C23—21no—
35C42×C23—21no—
36C4⋊Dic23—22no—
37C4⋊Dic23—22no—
38Dic92—28no—
39C23×C23C2×D411yescharacteristic
40C2×C4×C23—22no—
41C2×C4×C23—24no—
42C2×C4×C23C22×C411yescharacteristic
43C2×C4×C23C2×D411yescharacteristic
44C2×C4×C23C2×D411yescharacteristic
45C2×C4×C23C2×D411yescharacteristic
46C2×C4×C23#4111yescharacteristic
47C2×C4×C23#4111yescharacteristic
48C2×Dic23—24no—
49C2×Dic23—42no—
50C2×Dic23—42no—
51C2×Dic23—42no—
52C2×Dic23—44no—
53Dic46—24no—
54Dic46—24no—
55Dic46—42no—
56Dic46—42no—
57C8×C23—22no—
58C8×C23C22⋊C414yes—
59#1971—231nomaximal, Sylow
60C22×C23C4×D411yescharacteristic
61C22×C23#12111yescharacteristic
62C22×C23#12711yescharacteristic
63C22×C23#13714yes—
64C4×C23—42no—
65C4×C23C2×C22⋊C411yescharacteristic
66C4×C23C4×D411yescharacteristic
67C4×C23#12111yescharacteristic
68C4×C23#12411yescharacteristic
69Dic23—44no—
70Dic23—82no—
71C22×Q16—231no—
72C2×#106—231no—
73C2×#103—232no—
74C2×#97D2311yescharacteristic
75#391—232no—
76C2×C23#39011yescharacteristic
77C2×C23#44112yes—
78C2×C23#47012yes—
79C2×C23#49712yes—
80C22×Q8—232no—
81C2×Q16—234no—
82C2×Q16—462no—
83C2×Q16—462no—
84C22×C8C2×D2311yescharacteristic
85C22×C8C2×D2311yescharacteristic
86C2×C4⋊C4—232no—
87C2×C42C2×D2311yescharacteristic
88#106—462no—
89#103—464no—
90#97—22no—
91#95—464no—
92C23#197111yescharacteristic, complemented, Sylow
93C2×Q8—234no—
94C2×Q8—462no—
95C2×Q8—462no—
96C2×Q8—462no—
97C2×Q8—462no—
98C2×Q8—462no—
99C22×C4—462no—
100C22×C4—462no—
101C22×C4D9212yes—
102C22×C4C22×D2311yescharacteristic
103Q16—468no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8C4×D2312yes—
107C2×C8D9212yes—
108C2×C8D9212yes—
109C2×C8C22⋊D2312yes—
110C4⋊C4—462no—
111C4⋊C4—462no—
112C42—21no—
113C42—21no—
114C23C2×D9211yescharacteristic
115Q8—464no—
116Q8—464no—
117Q8—922no—
118Q8—922no—
119C2×C4—24no—
120C2×C4—22no—
121C2×C4—464no—
122C2×C4—922no—
123C2×C4—922no—
124C2×C4—922no—
125C2×C4—924no—
126C2×C4C2×C4×D2311yescharacteristic
127C2×C4C2×D9211yescharacteristic
128C2×C4C2×D9211yescharacteristic
129C2×C4#6728811yescharacteristic
130C2×C4#6728811yescharacteristic
131C2×C4C2×C22⋊D2311yescharacteristic
132C8—22no—
133C8(C2×D23)⋊C414yes—
134C22C4×D9211yescharacteristic
135C22#1062504511yescharacteristic
136C22#1062508014yes—
137C22#1062510111yescharacteristic
138C4—42no—
139C4—924no—
140C4—1842no—
141C4C4×D9211yescharacteristic
142C4#1062504611yescharacteristic
143C4C2×(C2×D23)⋊C411yescharacteristic
144C4#1062510111yescharacteristic
145C2#1309231911yescharacteristic
146C2#1309252512yes—
147C2#1309267512yes—
148C2#1309281112yes—
subgroupG/H
centerC23C2×D92
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#97C2
socle, prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenterC2×#97D23
hypocenterC23#1971
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
13. C2×Dic92C4semidirect
92. C23#1971semidirect

Maximal subgroups

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

subgroupindex
C22×Dic922
C2×#106249992
C2×#106249982
#130923232
C2×C23×#972
#197123