Finite Group Databasebeta

← #15683787

Subgroups — #15683787

Order 2944.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 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#13092965C211yesmaximal, characteristic
2C4⋊Q8×D23C211yesmaximal, characteristic, complemented
3#13092775C214yesmaximal, complemented
4#13092769C211yesmaximal, characteristic, complemented
5#13092768C211yesmaximal, characteristic, complemented
6#13092763C211yesmaximal, characteristic, complemented
7#13092415C214yesmaximal, complemented
8C4×#67262C211yesmaximal, characteristic, complemented
9C23×#486C211yesmaximal, characteristic, complemented
10C2×Q8×D23—21no—
11C2×#67290C2212yes—
12C23×C4⋊Q8C2211yescharacteristic
13C23×#127C2211yescharacteristic
14#10625115—21no—
15#10625109—21no—
16#10625109—21no—
17#10625107C2212yes—
18D4×Dic23—21no—
19D4×Dic23—21no—
20C2×#67262C2212yes—
21C4⋊C4×D23—21no—
22C4⋊C4×D23C2212yes—
23#10625059—21no—
24#10625059C2212yes—
25C42×D23C2211yescharacteristic
26#10625040C2211yescharacteristic
27#10625040C2211yescharacteristic
28C23×#102C2214yes—
29C4×C8×C23C2211yescharacteristic
30#10625014C2214yes—
31#10624998C2214yes—
32#10624997C2212yes—
33#10624992C2214yes—
34C4×C23⋊C8C2211yescharacteristic
35C2×Q8×C23—21no—
36C2×D4×C23—21no—
37C2×D4×C23—21no—
38C2×D4×C23C2312yes—
39C2×C22⋊D23—22no—
40C22×Dic23—22no—
41Q8×D23—44no—
42#67290—28no—
43C2×C4×D23—22no—
44C2×C4×D23D411yescharacteristic
45C2×C4×D23D411yescharacteristic
46C2×C4×D23C2311yescharacteristic
47C2×Dic46—21no—
48C2×Dic46—22no—
49C2×Dic46C2312yes—
50C2×C8×C23C2312yes—
51C4⋊C4×C23—21no—
52C4⋊C4×C23C2312yes—
53C42×C23C2311yescharacteristic
54C22⋊Dic23—22no—
55C22⋊Dic23—22no—
56C4⋊Dic23—21no—
57C4⋊Dic23—21no—
58C4⋊Dic23—21no—
59C4⋊Dic23C2312yes—
60Dic23⋊C4—22no—
61Dic23⋊C4—22no—
62C4×Dic23D411yescharacteristic
63C4×Dic23D411yescharacteristic
64C4×Dic23C2311yescharacteristic
65C2×C23⋊C8C2312yes—
66#67262—24no—
67C23×C23—22no—
68C22×D23C2×D411yescharacteristic
69Q8×C23—42no—
70D4×C23—24no—
71D4×C23—42no—
72D4×C23—42no—
73C2×C4×C23—22no—
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23C2×D411yescharacteristic
76C2×C4×C23C2411yescharacteristic
77C22⋊D23—44no—
78C2×Dic23—22no—
79C2×Dic23—22no—
80C2×Dic23—44no—
81C2×Dic23C2×D411yescharacteristic
82C2×Dic23C2×D411yescharacteristic
83C2×Dic23C2×D411yescharacteristic
84C4×D23—22no—
85C4×D23—22no—
86C4×D23—44no—
87C4×D23#4114yes—
88Dic46—24no—
89Dic46—44no—
90Dic46—42no—
91C8×C23—22no—
92C23⋊C8—22no—
93#3141—231nomaximal, Sylow
94C22×C23—42no—
95C22×C23—42no—
96C22×C23—42no—
97C22×C23C22×D411yescharacteristic
98C2×D23—21no—
99C2×D23—21no—
100C2×D23#12412yes—
101C4×C23—42no—
102C4×C23AGL(1,ℤ/8)12yes—
103C4×C23#13712yes—
104C4×C23C2×#4112yes—
105Dic23—21no—
106Dic23—21no—
107Dic23—42no—
108Dic23—42no—
109Dic23#12412yes—
110#532—231no—
111C2×C4⋊Q8—231no—
112#489—234no—
113#487—231no—
114#487—231no—
115#486—231no—
116#486D2311yescharacteristic, complemented
117#417—234no—
118C4×M16—231no—
119C2×C23—82no—
120C2×C23C2×#12411yescharacteristic
121C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
122C2×C23C2×#13711yescharacteristic
123D23—22no—
124C2×#41—232no—
125C22×Q8—461no—
126C2×M16—232no—
127C4⋊Q8—232no—
128C4⋊Q8—231no—
129C4⋊Q8—231no—
130C4⋊Q8—461no—
131C4⋊Q8—461no—
132C4⋊Q8C2×D2311yescharacteristic
133#127C2×D2311yescharacteristic
134#124—232no—
135#121—461no—
136#121—461no—
137C4×D4—461no—
138C4×D4—461no—
139C2×C4⋊C4—232no—
140C2×C4⋊C4—461no—
141C2×C42—231no—
142#103—234no—
143#103—234no—
144#102—234no—
145#102C2×D2314yes—
146#97—232no—
147C4×C8—231no—
148C4×C8C2×D2311yescharacteristic
149C23#314111yescharacteristic, complemented, Sylow
150#41—468no—
151C2×Q8—21no—
152C2×Q8—232no—
153C2×Q8—462no—
154C2×Q8—461no—
155C2×Q8—924no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—462no—
159C2×D4C22×D2312yes—
160C22×C4—231no—
161C22×C4—231no—
162C22×C4—231no—
163C22×C4—462no—
164C22×C4—462no—
165M16—464no—
166C2×C8—232no—
167C2×C8C22×D2312yes—
168C4⋊C4—21no—
169C4⋊C4—232no—
170C4⋊C4—462no—
171C4⋊C4—462no—
172C4⋊C4—461no—
173C4⋊C4—461no—
174C4⋊C4—461no—
175C4⋊C4C22×D2312yes—
176C22⋊C4—462no—
177C22⋊C4—462no—
178C42—231no—
179C42—231no—
180C42—231no—
181C42C22×D2311yescharacteristic
182C23—22no—
183C23—231no—
184Q8—42no—
185Q8—464no—
186Q8—924no—
187Q8—922no—
188D4—24no—
189D4—42no—
190D4—42no—
191D4—924no—
192C2×C4—22no—
193C2×C4—231no—
194C2×C4—234no—
195C2×C4—231no—
196C2×C4—231no—
197C2×C4—462no—
198C2×C4—462no—
199C2×C4—462no—
200C2×C4—462no—
201C2×C4—924no—
202C2×C4—924no—
203C2×C4D4×D2311yescharacteristic
204C2×C4D4×D2311yescharacteristic
205C2×C4C23×D2311yescharacteristic
206C8—22no—
207C8—462no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—232no—
212C22—461no—
213C22—461no—
214C22C2×D4×D2311yescharacteristic
215C4—42no—
216C4—232no—
217C4—461no—
218C4—461no—
219C4—922no—
220C4—922no—
221C4#1062508212yes—
222C4#1062508612yes—
223C4#41×D2312yes—
224C2—82no—
225C2—462no—
226C2#124×D2311yescharacteristic
227C2C2×#1062508211yescharacteristic
228C2C2×#1062508611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#486C2
socleC22×C23C22×D4
prime radical#13092965C2
hypercenter#486D23
hypocenterC23#3141
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D23C2semidirect
3. #13092775C2semidirect
4. #13092769C2semidirect
5. #13092768C2semidirect
6. #13092763C2semidirect
7. #13092415C2semidirect
8. C4×#67262C2semidirect
9. C23×#486C2semidirect
116. #486D23semidirect
149. C23#3141semidirect

Maximal subgroups

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

subgroupindex
#130929652
C4⋊Q8×D232
#130927752
#130927692
#130927682
#130927632
#130924152
C4×#672622
C23×#4862
#314123