Finite Group Databasebeta

← #15683718

Subgroups — #15683718

Order 2944.

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

normal subgroups only

This group has 400 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#13092973C211yesmaximal, characteristic, complemented
2#13092966C211yesmaximal, characteristic
3#13092774C211yesmaximal, characteristic, complemented
4#13092772C211yesmaximal, characteristic, complemented
5#13092771C211yesmaximal, characteristic, complemented
6#13092766C212yesmaximal, complemented
7#13092762C212yesmaximal, complemented
8#13092412C212yesmaximal, complemented
9#13092410C212yesmaximal, complemented
10C4×C8×D23C211yesmaximal, characteristic, complemented
11C23×#488C211yesmaximal, characteristic, complemented
12C2×#67292C2211yescharacteristic
13C2×#67290C2211yescharacteristic
14C23×#125C2211yescharacteristic
15C23×#124C2211yescharacteristic
16#10625115C2211yescharacteristic
17#10625111C2211yescharacteristic
18C2×C8×D23C2212yes—
19#10625067—22no—
20#10625063C2212yes—
21#10625059C2212yes—
22#10625058—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—
35C8×Dic23C2212yes—
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—21no—
49C2×C4×D23D412yes—
50C2×C4×D23C2311yescharacteristic
51C2×Dic46—22no—
52C2×Dic46C2311yescharacteristic
53C2×C8×C23C2312yes—
54C4⋊C4×C23—22no—
55C4⋊C4×C23C2312yes—
56C22⋊C4×C23—22no—
57C42×C23C2311yescharacteristic
58(C2×D23)⋊C4—22no—
59(C2×D23)⋊C4—22no—
60C4⋊Dic23C2312yes—
61Dic23⋊C4—22no—
62Dic23⋊C4—22no—
63Dic23⋊C4—22no—
64C4×Dic23—22no—
65C4×Dic23D412yes—
66C4×Dic23C2311yescharacteristic
67C2×C23⋊C8C2312yes—
68C8×D23—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—42no—
79C22⋊D23—44no—
80C2×Dic23—22no—
81C2×Dic23—21no—
82C2×Dic23—42no—
83C2×Dic23C2×D411yescharacteristic
84C2×Dic23C2×D412yes—
85D92—22no—
86D92—42no—
87C4×D23—24no—
88C4×D23—42no—
89C4×D23#4114yes—
90Dic46—22no—
91Dic46—44no—
92C8×C23—22no—
93C23⋊C8—22no—
94#3131—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—41no—
107Dic23—42no—
108Dic23#12412yes—
109Dic23#13514yes—
110#533—231no—
111#532—231no—
112#488—231no—
113#488—231no—
114#488—231no—
115#488D2311yescharacteristic, complemented
116#487—232no—
117#486—232no—
118#416—232no—
119#416—232no—
120C2×C4×C8—231no—
121C2×C23—81no—
122C2×C23C2×#12411yescharacteristic
123C2×C23C2×#13512yes—
124D23—22no—
125D23—81no—
126C2×#41—231no—
127C2×#41—231no—
128C22×C8—232no—
129C4⋊Q8—232no—
130C4⋊Q8—231no—
131#127—231no—
132#125—231no—
133#125C2×D2311yescharacteristic
134#124—231no—
135#124C2×D2311yescharacteristic
136C22⋊Q8—462no—
137#121—462no—
138C4×Q8—462no—
139C4×D4—462no—
140#117—232no—
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—
150C4×C8—232no—
151C4×C8—231no—
152C4×C8C2×D2311yescharacteristic
153C23#313111yescharacteristic, complemented, Sylow
154#41—464no—
155#41—464no—
156C2×Q8—231no—
157C2×Q8—462no—
158C2×Q8C22×D2311yescharacteristic
159C2×D4—231no—
160C2×D4—461no—
161C2×D4—462no—
162C2×D4—461no—
163C2×D4C22×D2311yescharacteristic
164C22×C4—231no—
165C22×C4—232no—
166C22×C4—461no—
167C22×C4—461no—
168C2×C8—232no—
169C2×C8—464no—
170C2×C8C22×D2312yes—
171C4⋊C4—22no—
172C4⋊C4—232no—
173C4⋊C4—462no—
174C4⋊C4—462no—
175C4⋊C4—462no—
176C4⋊C4C22×D2312yes—
177C22⋊C4—22no—
178C22⋊C4—462no—
179C22⋊C4—462no—
180C42—232no—
181C42—231no—
182C42—462no—
183C42C22×D2311yescharacteristic
184C23—21no—
185C23—231no—
186C23—461no—
187Q8—22no—
188Q8—462no—
189Q8—924no—
190D4—22no—
191D4—462no—
192D4—922no—
193D4—924no—
194D4—922no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—231no—
198C2×C4—232no—
199C2×C4—234no—
200C2×C4—464no—
201C2×C4—462no—
202C2×C4—461no—
203C2×C4—922no—
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—234no—
221C4—921no—
222C4—922no—
223C4#41×D2312yes—
224C2—81no—
225C2—462no—
226C2—1841no—
227C2#124×D2311yescharacteristic
228C2#135×D2312yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#488C2
socleC22×C23C22×D4
prime radical#13092966C2
hypercenter#488D23
hypocenterC23#3131
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
1. #13092973C2semidirect
3. #13092774C2semidirect
4. #13092772C2semidirect
5. #13092771C2semidirect
6. #13092766C2semidirect
7. #13092762C2semidirect
8. #13092412C2semidirect
9. #13092410C2semidirect
10. C4×C8×D23C2semidirect
11. C23×#488C2semidirect
115. #488D23semidirect
153. C23#3131semidirect

Maximal subgroups

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

subgroupindex
#130929732
#130929662
#130927742
#130927722
#130927712
#130927662
#130927622
#130924122
#130924102
C4×C8×D232
C23×#4882
#313123