Finite Group Databasebeta

← #15683650

Subgroups — #15683650

Order 2944.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#13093029C211yesmaximal, characteristic, complemented
2#13092891C211yesmaximal, characteristic
3#13092759C212yesmaximal, complemented
4#13092718C212yesmaximal, complemented
5#13092623C212yesmaximal, complemented
6#13092570C212yesmaximal
7#13092519C212yesmaximal, complemented
8C4×#67263C212yesmaximal, complemented
9C23×#433C211yesmaximal, characteristic, complemented
10C22×D92C2211yescharacteristic
11C23×#117C2211yescharacteristic
12#10625097C2211yescharacteristic
13#10625095C2212yes—
14C2×#67263C2212yes—
15C2×#67263C2212yes—
16#10625064—22no—
17#10625060—22no—
18C22⋊C4×D23—22no—
19#10625050—22no—
20C4×D92C2212yes—
21C4×D92C2212yes—
22#10625041C2211yescharacteristic, complemented
23#10625040C2211yescharacteristic, complemented
24C4×Dic46C2212yescomplemented
25C23×C4⋊C8C2212yescomplemented
26C23×C22⋊C8C2212yes—
27C23×#97C2211yescharacteristic, complemented
28C4×C8×C23C2211yescharacteristic, complemented
29#10625003C2212yes—
30#10625003C2212yes—
31#10625000C2212yescomplemented
32#10624999C2212yescomplemented
33#10624998C2212yescomplemented
34#10624998C2212yescomplemented
35C23×D23—21no—
36C22×C4×C23C2311yescharacteristic
37C2×D92—21no—
38C2×D92—24no—
39C2×D92C2312yes—
40C2×C4×D23—22no—
41C2×C4×D23—22no—
42C2×Dic46C2312yes—
43C2×C8×C23C2312yes—
44C2×C8×C23C2312yes—
45C4⋊C4×C23D412yes—
46C22⋊C4×C23D412yes—
47C42×C23C2311yescharacteristic
48C42×C23C2311yescharacteristic
49C22⋊Dic23—22no—
50C22⋊Dic23—21no—
51(C2×D23)⋊C4—22no—
52(C2×D23)⋊C4—22no—
53C4⋊Dic23—22no—
54C4⋊Dic23C2312yes—
55C4⋊Dic23C2312yes—
56Dic23⋊C4—22no—
57Dic23⋊C4—22no—
58Dic23⋊C4—22no—
59C4×Dic23—22no—
60C4×Dic23—21no—
61#67263—24no—
62#67263—24no—
63C23×C23C2×D411yescharacteristic
64C22×D23—22no—
65C22×D23—24no—
66C22×D23—82no—
67C2×C4×C23—22no—
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×D412yes—
70C2×C4×C23C2×D412yes—
71C2×C4×C23C2411yescharacteristic
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75D92—24no—
76D92—22no—
77D92#4114yes—
78C4×D23—82no—
79C4×D23—82no—
80Dic46—22no—
81Dic46—22no—
82C8×C23—22no—
83C8×C23—22no—
84#3123—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—22no—
87C22×C23C22×D411yescharacteristic
88C2×D23—24no—
89C2×D23—42no—
90C2×D23—42no—
91C2×D23—84no—
92C4×C23—21no—
93C4×C23—22no—
94C4×C23—22no—
95C4×C23C2×#4112yes—
96Dic23—42no—
97Dic23—42no—
98Dic23—42no—
99#541—231no—
100#518—231no—
101#485—232no—
102#478—232no—
103#461—232no—
104#450—232no—
105#440—232no—
106C4×SD16—232no—
107#433D2311yescharacteristic, complemented
108C2×C23—41no—
109C2×C23#52511yescharacteristic
110C2×C23#57712yes—
111D23—44no—
112C22×D4—231no—
113C2×SD16—232no—
114C2×SD16—232no—
115C4⋊Q8—231no—
116#126—462no—
117#125—231no—
118#125—462no—
119C22⋊Q8—232no—
120C4×Q8—232no—
121C4×D4—232no—
122C4×D4—232no—
123C4×D4—462no—
124#117—231no—
125#117C2×D2311yescharacteristic
126C2×C22⋊C4—462no—
127#107—232no—
128#106—232no—
129C4⋊C8C2×D2312yescomplemented
130#103—232no—
131#103—232no—
132#102—232no—
133#102—232no—
134C22⋊C8C2×D2312yes—
135#97C2×D2311yescharacteristic, complemented
136C4×C8C2×D2311yescharacteristic, complemented
137C23#312311yescharacteristic, complemented, Sylow
138C24—461no—
139C2×Q8—232no—
140C2×D4—232no—
141C2×D4—464no—
142C2×D4—461no—
143C22×C4—462no—
144C22×C4—462no—
145C22×C4C22×D2311yescharacteristic
146SD16—464no—
147SD16—464no—
148C2×C8C22×D2312yes—
149C2×C8C22×D2312yes—
150C4⋊C4—232no—
151C4⋊C4—232no—
152C4⋊C4—462no—
153C4⋊C4—462no—
154C4⋊C4—462no—
155C4⋊C4—462no—
156C4⋊C4D9212yes—
157C22⋊C4—461no—
158C22⋊C4—462no—
159C22⋊C4—462no—
160C22⋊C4—462no—
161C22⋊C4D9212yes—
162C42—461no—
163C42—462no—
164C42C22×D2311yescharacteristic
165C42C22×D2311yescharacteristic
166C23—464no—
167C23—462no—
168C23—1842no—
169C23C2×D9211yescharacteristic
170Q8—462no—
171Q8—462no—
172D4—234no—
173D4—464no—
174D4—462no—
175C2×C4—22no—
176C2×C4—462no—
177C2×C4—462no—
178C2×C4—462no—
179C2×C4—1842no—
180C2×C4—1842no—
181C2×C4C2×D9212yes—
182C2×C4C2×D9211yescharacteristic
183C2×C4C2×D9212yes—
184C2×C4C23×D2311yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—22no—
189C22—464no—
190C22—922no—
191C22—922no—
192C22—1844no—
193C22C22×D9211yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—922no—
198C4—922no—
199C4—922no—
200C4#41×D2312yes—
201C2—41no—
202C2—924no—
203C2#1309292911yescharacteristic
204C2#1309322912yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#433C2
socleC22×C23C22×D4
prime radicalC22×D92C22
hypercenter#433D23
hypocenterC23#3123
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #13093029C2semidirect
3. #13092759C2semidirect
4. #13092718C2semidirect
5. #13092623C2semidirect
7. #13092519C2semidirect
8. C4×#67263C2semidirect
9. C23×#433C2semidirect
22. #10625041C22semidirect
23. #10625040C22semidirect
24. C4×Dic46C22semidirect
25. C23×C4⋊C8C22semidirect
27. C23×#97C22semidirect
28. C4×C8×C23C22semidirect
31. #10625000C22semidirect
32. #10624999C22semidirect
33. #10624998C22semidirect
34. #10624998C22semidirect
107. #433D23semidirect
129. C4⋊C8C2×D23semidirect
135. #97C2×D23semidirect
136. C4×C8C2×D23semidirect
137. C23#3123semidirect

Maximal subgroups

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

subgroupindex
#130930292
#130928912
#130927592
#130927182
#130926232
#130925702
#130925192
C4×#672632
C23×#4332
#312323