Finite Group Databasebeta

← #15674446

Subgroups — #15674446

Order 2944.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10625080C212yesmaximal, complemented
2#13092998C211yesmaximal, characteristic
3C2×#10625007C212yesmaximal, complemented
4#13092322C211yesmaximal, characteristic, complemented
5C23×#343C211yesmaximal, characteristic, complemented
6C2×#67288C2212yes—
7C22×Dic46C2211yescharacteristic
8C2×M16×C23C2212yes—
9C2×C4⋊C4×C23C2211yescharacteristic
10#10625101—22no—
11C2×C4×Dic23C2211yescharacteristic
12#10625080—24no—
13#10625080—24no—
14C2×Dic92—22no—
15C2×#67263—22no—
16#10625068—22no—
17#10625066—22no—
18C23⋊#95—22no—
19#10625007—24no—
20C22×C4×C23D412yes—
21C22×C4×C23C2311yescharacteristic
22C2×C22⋊D23—22no—
23C22×Dic23—21no—
24C22×Dic23—21no—
25#67288—22no—
26#67288—22no—
27#67288—22no—
28#67288—22no—
29C2×D92—22no—
30C2×D92D412yes—
31C2×C4×D23—22no—
32C2×Dic46—22no—
33C2×Dic46—22no—
34C2×Dic46—21no—
35C2×Dic46D412yes—
36C2×Dic46D412yescomplemented
37M16×C23—22no—
38M16×C23D414yescomplemented
39C2×C8×C23—22no—
40C4⋊C4×C23—22no—
41(C2×D23)⋊C4—24no—
42C4⋊Dic23—22no—
43C4×Dic23—22no—
44Dic92—28no—
45#67263—28no—
46C23×C23C2×D411yescharacteristic
47C22×D23—22no—
48C2×C4×C23—22no—
49C2×C4×C23—42no—
50C2×C4×C23C2×D412yes—
51C2×C4×C23C2×D411yescharacteristic
52C2×C4×C23C2×D412yes—
53C2×C4×C23#4111yescharacteristic
54C22⋊D23—42no—
55C22⋊D23—42no—
56C2×Dic23—22no—
57C2×Dic23—22no—
58C2×Dic23—22no—
59C2×Dic23—41no—
60C2×Dic23—41no—
61C2×Dic23—41no—
62C2×Dic23—41no—
63D92—22no—
64D92—22no—
65D92—82no—
66C4×D23—42no—
67C4×D23—42no—
68Dic46—24no—
69Dic46—22no—
70Dic46—22no—
71Dic46—42no—
72C8×C23—24no—
73#2007—231nomaximal, Sylow
74C22×C23—21no—
75C22×C23—21no—
76C22×C23#12011yescharacteristic
77C22×C23#12111yescharacteristic
78C22×C23#12711yescharacteristic
79C2×D23—42no—
80C2×D23—42no—
81C2×D23—42no—
82C4×C23—42no—
83C4×C23#12012yes—
84C4×C23#12112yes—
85Dic23—42no—
86Dic23—42no—
87Dic23—42no—
88C2×#137—232no—
89#537—231no—
90C2×#104—232no—
91#391—231no—
92#343D2311yescharacteristic, complemented
93C2×C23—21no—
94C2×C23—21no—
95C2×C23#39211yescharacteristic
96C2×C23#45511yescharacteristic
97C2×C23#45611yescharacteristic
98D23—82no—
99C2×#41—232no—
100C22×Q8—231no—
101#137—464no—
102#137—464no—
103C2×Q16—462no—
104C2×SD16—462no—
105C2×M16C2×D2312yes—
106C22⋊Q8—462no—
107#121—462no—
108#121—462no—
109C2×C4⋊C4C2×D2311yescharacteristic
110C2×C42—231no—
111#104—464no—
112#95—462no—
113C23#200711yescharacteristic, complemented, Sylow
114#41—462no—
115#41—462no—
116#41—462no—
117#41—462no—
118C2×Q8—232no—
119C2×Q8—232no—
120C2×Q8—461no—
121C2×Q8—462no—
122C2×Q8—462no—
123C2×D4—232no—
124C2×D4—462no—
125C2×D4—462no—
126C22×C4—461no—
127C22×C4—461no—
128C22×C4—462no—
129C22×C4D9212yes—
130C22×C4C22×D2311yescharacteristic
131Q16—468no—
132SD16—468no—
133M16—22no—
134M16D9214yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—462no—
138C22⋊C4—464no—
139C42—462no—
140C23—462no—
141C23C2×D9211yescharacteristic
142Q8—464no—
143Q8—462no—
144Q8—462no—
145Q8—922no—
146D4—462no—
147D4—462no—
148D4—922no—
149D4—922no—
150D4—1842no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—462no—
154C2×C4—462no—
155C2×C4—462no—
156C2×C4—921no—
157C2×C4—921no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4—922no—
161C2×C4—922no—
162C2×C4C2×D9212yes—
163C2×C4D4×D2311yescharacteristic
164C2×C4D4×D2312yes—
165C2×C4#6729211yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—922no—
170C22—922no—
171C22—922no—
172C22#1062504511yescharacteristic
173C22#1062505311yescharacteristic
174C22#1062506611yescharacteristic
175C4—42no—
176C4—922no—
177C4—922no—
178C4—922no—
179C4#1062505312yes—
180C4#1062506612yes—
181C2—21no—
182C2—21no—
183C2—1842no—
184C2#1309232711yescharacteristic
185C2#1309259711yescharacteristic
186C2#1309260211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#343C2
socleC22×C23#120
prime radical#13092998C2
hypercenter#343D23
hypocenterC23#2007
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#10625080C2semidirect
3. C2×#10625007C2semidirect
4. #13092322C2semidirect
5. C23×#343C2semidirect
36. C2×Dic46D4semidirect
38. M16×C23D4semidirect
92. #343D23semidirect
113. C23#2007semidirect
134. M16D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
#130929982
C2×#106250072
#130923222
C23×#3432
#200723