Finite Group Databasebeta

← #15683689

Subgroups — #15683689

Order 2944.

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

normal subgroups only

This group has 382 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#13093022C211yesmaximal, characteristic
2#13092894C211yesmaximal, characteristic, complemented
3#13092742C212yesmaximal, complemented
4#13092725C212yesmaximal, complemented
5#13092618C212yesmaximal, complemented
6#13092558C212yesmaximal, complemented
7#13092519C212yesmaximal, complemented
8C4×#67263C212yesmaximal, complemented
9C23×#433C211yesmaximal, characteristic, complemented
10C22×Dic46C2211yescharacteristic
11C23×#117C2211yescharacteristic
12#10625101C2212yes—
13#10625097C2211yescharacteristic
14C2×#67263C2212yes—
15C2×#67263C2212yes—
16#10625065—22no—
17#10625058—22no—
18#10625055—22no—
19#10625048—22no—
20#10625045C2211yescharacteristic
21C4×D92C2212yes—
22#10625041C2211yescharacteristic
23C4×Dic46C2212yes—
24C4×Dic46C2212yes—
25C23×C4⋊C8C2212yes—
26C23×C22⋊C8C2212yes—
27C23×#97C2211yescharacteristic
28C4×C8×C23C2211yescharacteristic
29#10625003C2212yes—
30#10625003C2212yes—
31#10625000C2212yes—
32#10624999C2212yes—
33#10624998C2212yes—
34#10624998C2212yes—
35C22×C4×C23C2311yescharacteristic
36C2×C22⋊D23—22no—
37C22×Dic23—21no—
38C2×D92—22no—
39C2×D92C2312yes—
40C2×C4×D23—22no—
41C2×Dic46—21no—
42C2×Dic46—24no—
43C2×Dic46C2312yes—
44C2×C8×C23C2312yes—
45C2×C8×C23C2312yes—
46C4⋊C4×C23D412yes—
47C22⋊C4×C23D412yes—
48C42×C23C2311yescharacteristic
49C42×C23C2311yescharacteristic
50C22⋊Dic23—21no—
51(C2×D23)⋊C4—22no—
52(C2×D23)⋊C4—22no—
53C4⋊Dic23C2312yes—
54C4⋊Dic23C2312yes—
55Dic23⋊C4—22no—
56Dic23⋊C4—22no—
57Dic23⋊C4—22no—
58C4×Dic23—22no—
59C4×Dic23—22no—
60C4×Dic23—21no—
61#67263—24no—
62#67263—24no—
63C23×C23C2×D411yescharacteristic
64C22×D23—22no—
65C2×C4×C23—22no—
66C2×C4×C23C2×D412yes—
67C2×C4×C23C2×D412yes—
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2411yescharacteristic
70C22⋊D23—82no—
71C2×Dic23—24no—
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75D92—22no—
76D92—22no—
77D92—82no—
78C4×D23—82no—
79Dic46—24no—
80Dic46—22no—
81Dic46#4114yes—
82C8×C23—22no—
83C8×C23—22no—
84#3126—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—22no—
87C22×C23C22×D411yescharacteristic
88C2×D23—42no—
89C2×D23—42no—
90C2×D23—42no—
91C4×C23—21no—
92C4×C23—22no—
93C4×C23—22no—
94C4×C23C2×#4112yes—
95Dic23—24no—
96Dic23—42no—
97Dic23—42no—
98#540—231no—
99#519—231no—
100#482—232no—
101#479—232no—
102#460—232no—
103#448—232no—
104#440—232no—
105C4×SD16—232no—
106#433D2311yescharacteristic, complemented
107C2×C23—41no—
108C2×C23#52511yescharacteristic
109C2×C23#57712yes—
110D23—82no—
111C22×Q8—231no—
112C2×SD16—232no—
113C2×SD16—232no—
114#127—231no—
115#125—231no—
116#123—462no—
117#121—232no—
118#121—462no—
119C4×Q8—232no—
120C4×Q8—232no—
121C4×Q8—462no—
122C4×D4—232no—
123#117—231no—
124#117—462no—
125#117C2×D2311yescharacteristic
126#107—232no—
127#106—232no—
128C4⋊C8C2×D2312yes—
129#103—232no—
130#103—232no—
131#102—232no—
132#102—232no—
133C22⋊C8C2×D2312yes—
134#97C2×D2311yescharacteristic
135C4×C8C2×D2311yescharacteristic
136C23#312611yescharacteristic, complemented, Sylow
137C2×Q8—232no—
138C2×Q8—464no—
139C2×Q8—461no—
140C2×D4—232no—
141C2×D4—462no—
142C2×D4—462no—
143C22×C4—461no—
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⋊C4D9212yes—
156C22⋊C4—461no—
157C22⋊C4—462no—
158C22⋊C4—462no—
159C22⋊C4D9212yes—
160C42—461no—
161C42—462no—
162C42—462no—
163C42C22×D2311yescharacteristic
164C42C22×D2311yescharacteristic
165C23—462no—
166C23C2×D9211yescharacteristic
167Q8—234no—
168Q8—464no—
169Q8—462no—
170D4—462no—
171D4—462no—
172D4—1842no—
173D4—1842no—
174C2×C4—22no—
175C2×C4—464no—
176C2×C4—462no—
177C2×C4—462no—
178C2×C4—462no—
179C2×C4—1842no—
180C2×C4C2×D9212yes—
181C2×C4C2×D9212yes—
182C2×C4C2×D9211yescharacteristic
183C2×C4C23×D2311yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—922no—
189C22—922no—
190C22—922no—
191C22C22×D9211yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—464no—
196C4—922no—
197C4—922no—
198C4#41×D2312yes—
199C2—41no—
200C2—1842no—
201C2#1309292911yescharacteristic
202C2#1309322912yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#433C2
socleC22×C23C22×D4
prime radical#13093022C2
hypercenter#433D23
hypocenterC23#3126
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
2. #13092894C2semidirect
3. #13092742C2semidirect
4. #13092725C2semidirect
5. #13092618C2semidirect
6. #13092558C2semidirect
7. #13092519C2semidirect
8. C4×#67263C2semidirect
9. C23×#433C2semidirect
106. #433D23semidirect
136. C23#3126semidirect

Maximal subgroups

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

subgroupindex
#130930222
#130928942
#130927422
#130927252
#130926182
#130925582
#130925192
C4×#672632
C23×#4332
#312623