Finite Group Databasebeta

← #15683683

Subgroups — #15683683

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#13092894C211yesmaximal, characteristic, complemented
2#13092738C212yesmaximal, complemented
3#13092721C212yesmaximal, complemented
4#13092614C212yesmaximal, complemented
5#13092555C212yesmaximal, complemented
6#13092517C212yesmaximal, complemented
7C4×#67273C212yesmaximal, complemented
8#13092478C211yesmaximal, characteristic, complemented
9C23×#540C211yesmaximal, characteristic
10C22×Dic46C2211yescharacteristic
11C23×#127C2211yescharacteristic
12C23×#125C2211yescharacteristic
13C23×#123—22no—
14C23×#121—22no—
15C23×#121C2212yes—
16C4×D4×C23C2212yes—
17C23×#117C2211yescharacteristic
18C2×#67273C2212yes—
19C2×#67273C2212yes—
20#10625097C2211yescharacteristic
21#10625058—22no—
22#10625048—22no—
23C4×Dic46C2212yes—
24C4×Dic46C2212yes—
25#10625014C2212yes—
26#10625014C2212yes—
27C22⋊(C23⋊C8)C2212yes—
28#10624992C2212yes—
29#10624992C2212yes—
30#10624990C2212yes—
31#10624989C2212yes—
32C4⋊(C23⋊C8)C2212yes—
33#10624985C2211yescharacteristic
34C4×C23⋊C8C2211yescharacteristic
35C2×D4×C23—22no—
36C2×D4×C23—22no—
37C2×D4×C23C2312yes—
38C22×C4×C23—22no—
39C22×C4×C23C2311yescharacteristic
40C22×Dic23—21no—
41C2×Dic46—21no—
42C2×Dic46—24no—
43C2×Dic46C2312yes—
44C4⋊C4×C23—22no—
45C4⋊C4×C23D412yes—
46C4⋊C4×C23C2312yes—
47C22⋊C4×C23—22no—
48C22⋊C4×C23—22no—
49C22⋊C4×C23D412yes—
50C42×C23C2311yescharacteristic
51C42×C23C2311yescharacteristic
52C22⋊Dic23—21no—
53#67273—24no—
54#67273—24no—
55C4⋊Dic23C2312yes—
56Dic23⋊C4—22no—
57Dic23⋊C4—22no—
58C4×Dic23—22no—
59C4×Dic23—22no—
60C4×Dic23—21no—
61C2×C23⋊C8C2312yes—
62C2×C23⋊C8C2312yes—
63C23×C23—22no—
64C23×C23C2×D411yescharacteristic
65D4×C23—22no—
66D4×C23—22no—
67D4×C23—82no—
68D4×C23—82no—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23—82no—
72C2×C4×C23C2×D412yes—
73C2×C4×C23C2×D412yes—
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23C2411yescharacteristic
76C2×Dic23—24no—
77C2×Dic23—22no—
78C2×Dic23—22no—
79Dic46—24no—
80Dic46—22no—
81Dic46#4114yes—
82C23⋊C8—22no—
83C23⋊C8—22no—
84#3126—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—22no—
87C22×C23—42no—
88C22×C23—42no—
89C22×C23—42no—
90C22×C23C22×D411yescharacteristic
91C4×C23—21no—
92C4×C23—22no—
93C4×C23—22no—
94C4×C23—42no—
95C4×C23C2×#4112yes—
96Dic23—24no—
97Dic23—42no—
98#540D2311yescharacteristic
99#519—231no—
100#482—232no—
101#479—232no—
102#460—232no—
103#448—232no—
104#440—232no—
105C4×SD16—232no—
106#433—231no—
107C2×C23—41no—
108C2×C23—82no—
109C2×C23#52511yescharacteristic
110C2×C23#57712yes—
111C22×Q8—231no—
112C2×SD16—232no—
113C2×SD16—232no—
114#127C2×D2311yescharacteristic
115#125C2×D2311yescharacteristic
116#123—22no—
117#121—22no—
118#121C2×D2312yes—
119C4×Q8—232no—
120C4×Q8—232no—
121C4×Q8—462no—
122C4×D4C2×D2312yes—
123#117—231no—
124#117—462no—
125#117C2×D2311yescharacteristic
126#107—232no—
127#106—232no—
128C4⋊C8—232no—
129#103—232no—
130#103—232no—
131#102—232no—
132#102—232no—
133C22⋊C8—232no—
134#97—231no—
135C4×C8—231no—
136C23#312611yescharacteristic, complemented, Sylow
137C2×Q8—232no—
138C2×Q8—464no—
139C2×Q8—461no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D2312yes—
143C22×C4—22no—
144C22×C4—461no—
145C22×C4C22×D2311yescharacteristic
146SD16—464no—
147SD16—464no—
148C2×C8—232no—
149C2×C8—232no—
150C4⋊C4—22no—
151C4⋊C4—232no—
152C4⋊C4—462no—
153C4⋊C4—462no—
154C4⋊C4C22⋊D2312yes—
155C4⋊C4C22×D2312yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—461no—
159C22⋊C4C22⋊D2312yes—
160C42—461no—
161C42—462no—
162C42—462no—
163C42C22×D2311yescharacteristic
164C42C22×D2311yescharacteristic
165C23—22no—
166C23C2×C22⋊D2311yescharacteristic
167Q8—234no—
168Q8—464no—
169Q8—462no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—464no—
178C2×C4—462no—
179C2×C4—462no—
180C2×C4C2×C22⋊D2312yes—
181C2×C4C2×C22⋊D2312yes—
182C2×C4C2×C22⋊D2311yescharacteristic
183C2×C4C23×D2311yescharacteristic
184C8—462no—
185C8—462no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D2311yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—464no—
197C4—922no—
198C4#41×D2312yes—
199C2—41no—
200C2—82no—
201C2#1309292411yescharacteristic
202C2#1309322812yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
Fitting, prime radicalC23×#540C2
socleC22×C23C22×D4
hypercenter#540D23
hypocenterC23#3126
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #13092894C2semidirect
2. #13092738C2semidirect
3. #13092721C2semidirect
4. #13092614C2semidirect
5. #13092555C2semidirect
6. #13092517C2semidirect
7. C4×#67273C2semidirect
8. #13092478C2semidirect
136. C23#3126semidirect

Maximal subgroups

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

subgroupindex
#130928942
#130927382
#130927212
#130926142
#130925552
#130925172
C4×#672732
#130924782
C23×#5402
#312623