Finite Group Databasebeta

← #15683794

Subgroups — #15683794

Order 2944.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#13092966C211yesmaximal, characteristic
2#125×D23C211yesmaximal, characteristic, complemented
3#13092784C212yesmaximal, complemented
4#13092780C212yesmaximal, complemented
5#13092774C211yesmaximal, characteristic, complemented
6#13092772C211yesmaximal, characteristic, complemented
7#13092771C211yesmaximal, characteristic, complemented
8#13092417C212yesmaximal, complemented
9#13092415C212yesmaximal, complemented
10C4×#67262C211yesmaximal, characteristic, complemented
11C23×#488C211yesmaximal, characteristic, complemented
12C2×#67292C2211yescharacteristic
13C2×#67290C2211yescharacteristic
14C23×#125C2211yescharacteristic
15C23×#124C2211yescharacteristic
16#10625115C2211yescharacteristic
17#10625111C2211yescharacteristic
18C2×#67262C2212yes—
19C4⋊C4×D23—22no—
20C4⋊C4×D23C2212yes—
21#10625061C2212yes—
22#10625060—22no—
23#10625055—22no—
24(C22⋊D23)⋊C4—22no—
25#10625046C2211yescharacteristic
26C42×D23C2211yescharacteristic
27#10625041C2211yescharacteristic
28C23×#103C2212yes—
29C23×#102C2212yes—
30C4×C8×C23C2211yescharacteristic
31#10625017C2212yes—
32#10625014C2212yes—
33#10625003C2212yes—
34#10624998C2212yes—
35#10624997C2212yes—
36#10624992C2212yes—
37#10624991C2212yes—
38C4×C23⋊C8C2211yescharacteristic
39C2×Q8×C23C2311yescharacteristic
40C2×D4×C23C2311yescharacteristic
41C2×C22⋊D23—21no—
42C2×C22⋊D23—22no—
43C22×Dic23—21no—
44#67292—24no—
45#67290—24no—
46C2×D92—21no—
47C2×D92C2311yescharacteristic
48C2×C4×D23—22no—
49C2×C4×D23—21no—
50C2×C4×D23D412yes—
51C2×C4×D23C2311yescharacteristic
52C2×Dic46C2311yescharacteristic
53C2×C8×C23C2312yes—
54C4⋊C4×C23—22no—
55C4⋊C4×C23C2312yes—
56C22⋊C4×C23—22no—
57C42×C23C2311yescharacteristic
58(C2×D23)⋊C4—22no—
59C4⋊Dic23—22no—
60C4⋊Dic23C2312yes—
61Dic23⋊C4—22no—
62Dic23⋊C4—22no—
63Dic23⋊C4—22no—
64Dic23⋊C4—22no—
65C4×Dic23D412yes—
66C4×Dic23C2311yescharacteristic
67C2×C23⋊C8C2312yes—
68#67262—24no—
69C23×C23—21no—
70C22×D23—21no—
71C22×D23C2×D411yescharacteristic
72Q8×C23—22no—
73D4×C23—22no—
74C2×C4×C23—22no—
75C2×C4×C23—21no—
76C2×C4×C23C2×D412yes—
77C2×C4×C23C2411yescharacteristic
78C22⋊D23—44no—
79C22⋊D23—42no—
80C2×Dic23—22no—
81C2×Dic23—21no—
82C2×Dic23—42no—
83C2×Dic23C2×D412yes—
84C2×Dic23C2×D411yescharacteristic
85D92—22no—
86D92—42no—
87C4×D23—42no—
88C4×D23—44no—
89C4×D23—42no—
90C4×D23#4114yes—
91Dic46—22no—
92C8×C23—22no—
93C23⋊C8—22no—
94#3142—231nomaximal, Sylow
95C22×C23—41no—
96C22×C23—42no—
97C22×C23C22×D411yescharacteristic
98C2×D23—22no—
99C2×D23—41no—
100C2×D23—42no—
101C2×D23#12412yes—
102C4×C23—22no—
103C4×C23—41no—
104C4×C23—42no—
105C4×C23C2×#4112yes—
106Dic23—22no—
107Dic23—41no—
108Dic23—42no—
109Dic23#12412yes—
110#532—231no—
111C2×#125—231no—
112#491—232no—
113#490—232no—
114#488—231no—
115#488—231no—
116#488—231no—
117#488D2311yescharacteristic, complemented
118#417—232no—
119#417—232no—
120C4×M16—231no—
121C2×C23—81no—
122C2×C23C2×#12411yescharacteristic
123C2×C23#57512yes—
124D23—22no—
125D23—81no—
126C2×#41—231no—
127C2×#41—231no—
128C2×M16—232no—
129C4⋊Q8—231no—
130#127—231no—
131#125—232no—
132#125—231no—
133#125—462no—
134#125C2×D2311yescharacteristic
135#124—231no—
136#124C2×D2311yescharacteristic
137#121—462no—
138C4×D4—462no—
139C2×C4⋊C4—232no—
140C2×C4⋊C4—462no—
141C2×C42—231no—
142#103—232no—
143#103—232no—
144#103—232no—
145#103C2×D2312yes—
146#102—232no—
147#102—232no—
148#102—232no—
149#102C2×D2312yes—
150#97—232no—
151C4×C8—231no—
152C4×C8C2×D2311yescharacteristic
153C23#314211yescharacteristic, complemented, Sylow
154#41—464no—
155#41—464no—
156C2×Q8—231no—
157C2×Q8C22×D2311yescharacteristic
158C2×D4—231no—
159C2×D4—461no—
160C2×D4—462no—
161C2×D4—461no—
162C2×D4C22×D2311yescharacteristic
163C22×C4—231no—
164C22×C4—232no—
165C22×C4—461no—
166C22×C4—462no—
167C22×C4—461no—
168M16—464no—
169C2×C8—232no—
170C2×C8C22×D2312yes—
171C4⋊C4—22no—
172C4⋊C4—232no—
173C4⋊C4—462no—
174C4⋊C4—462no—
175C4⋊C4—462no—
176C4⋊C4—462no—
177C4⋊C4—462no—
178C4⋊C4C22×D2312yes—
179C22⋊C4—22no—
180C22⋊C4—462no—
181C42—232no—
182C42—231no—
183C42C22×D2311yescharacteristic
184C23—21no—
185C23—231no—
186C23—461no—
187Q8—22no—
188Q8—462no—
189D4—22no—
190D4—462no—
191D4—922no—
192D4—924no—
193D4—922no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—231no—
197C2×C4—234no—
198C2×C4—232no—
199C2×C4—461no—
200C2×C4—462no—
201C2×C4—922no—
202C2×C4—922no—
203C2×C4—924no—
204C2×C4—922no—
205C2×C4D4×D2312yes—
206C2×C4C23×D2311yescharacteristic
207C8—22no—
208C8—462no—
209C22—41no—
210C22—42no—
211C22—232no—
212C22—462no—
213C22—921no—
214C22—922no—
215C22C2×D4×D2311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—232no—
220C4—462no—
221C4—921no—
222C4—922no—
223C4#41×D2312yes—
224C2—81no—
225C2—462no—
226C2—1841no—
227C2#124×D2311yescharacteristic
228C2#1309321412yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#488C2
socleC22×C23C22×D4
prime radical#13092966C2
hypercenter#488D23
hypocenterC23#3142
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D23C2semidirect
3. #13092784C2semidirect
4. #13092780C2semidirect
5. #13092774C2semidirect
6. #13092772C2semidirect
7. #13092771C2semidirect
8. #13092417C2semidirect
9. #13092415C2semidirect
10. C4×#67262C2semidirect
11. C23×#488C2semidirect
117. #488D23semidirect
153. C23#3142semidirect

Maximal subgroups

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

subgroupindex
#130929662
#125×D232
#130927842
#130927802
#130927742
#130927722
#130927712
#130924172
#130924152
C4×#672622
C23×#4882
#314223