Finite Group Databasebeta

← #15682764

Subgroups — #15682764

Order 2944.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#10625158C211yesmaximal, characteristic, complemented
2#13093217C212yesmaximal, complemented
3#13092991C211yesmaximal, characteristic, complemented
4#13092602C214yesmaximal, complemented
5#13092592C214yesmaximal, complemented
6#13092433C212yesmaximal, complemented
7C2×C23×#101C211yesmaximal, characteristic, complemented
8C22×Q8×C23C2211yescharacteristic
9#10625158—22no—
10#10625158—24no—
11#10625158C2214yes—
12C2×#67292—22no—
13C2×Q8×D23—22no—
14C2×#67288—22no—
15C2×#67288C2212yes—
16C2×#67288C2211yescharacteristic
17C2×M16×C23C2212yes—
18#10625118C2212yescomplemented
19#10625117—22no—
20#10625115C2212yescomplemented
21#10625100—22no—
22#10625097C2211yescharacteristic
23#10625080—22no—
24#10625080C2214yescomplemented
25#10625079—22no—
26#10625079C2214yescomplemented
27#10625075—24no—
28C23×#101C2214yescomplemented
29#10625007C2218yescomplemented
30C2×Q8×C23—22no—
31C2×Q8×C23—22no—
32C2×Q8×C23D412yes—
33C2×Q8×C23C2312yes—
34C22×C4×C23D412yes—
35C22×C4×C23C2311yescharacteristic
36C2×C22⋊D23—22no—
37C2×C22⋊D23—21no—
38#67292—28no—
39#67292—28no—
40Q8×D23—28no—
41Q8×D23—28no—
42#67288—28no—
43#67288—28no—
44#67288—22no—
45#67288—22no—
46#67288—22no—
47#67288—22no—
48#67288D414yes—
49#67288C2314yes—
50C2×D92—22no—
51C2×D92D412yes—
52C2×D92C2311yescharacteristic
53C2×C4×D23—24no—
54C2×C4×D23—22no—
55C2×C4×D23—21no—
56C2×Dic46—22no—
57C2×Dic46D412yes—
58C2×Dic46C2311yescharacteristic
59M16×C23—22no—
60M16×C23C2314yes—
61C2×C8×C23—22no—
62C22⋊Dic23—21no—
63(C2×D23)⋊C4—24no—
64C4⋊Dic23—21no—
65Dic23⋊C4—24no—
66C4×Dic23C2312yes—
67Dic92—24no—
68D184—24no—
69#67263—24no—
70#67263—24no—
71C23×C23C2×D411yescharacteristic
72C22×D23—22no—
73C22×D23—21no—
74Q8×C23—24no—
75Q8×C23—24no—
76C2×C4×C23—22no—
77C2×C4×C23—22no—
78C2×C4×C23C2×D414yes—
79C2×C4×C23C2×D411yescharacteristic
80C2×C4×C23C2×D412yes—
81C2×C4×C23C2×D412yes—
82C2×C4×C23C2411yescharacteristic
83C22⋊D23—24no—
84C22⋊D23—24no—
85C22⋊D23—41no—
86C22⋊D23—41no—
87C2×Dic23—22no—
88C2×Dic23—22no—
89C2×Dic23—21no—
90D92—28no—
91D92—22no—
92D92—22no—
93D92C2×D414yes—
94C4×D23—216no—
95C4×D23—24no—
96C4×D23—24no—
97C4×D23—42no—
98Dic46—28no—
99Dic46—22no—
100Dic46—22no—
101Dic46C2×D414yes—
102C8×C23—24no—
103#3020—231nomaximal, Sylow
104C22×C23—41no—
105C22×C23#12011yescharacteristic
106C22×C23#12011yescharacteristic
107C22×C23C22×D411yescharacteristic
108C2×D23—24no—
109C2×D23—44no—
110C2×D23—42no—
111C2×D23—41no—
112C4×C23—24no—
113C4×C23#12012yes—
114C4×C23C22×D412yes—
115Dic23—24no—
116Dic23—42no—
117Dic23—41no—
118C2×2−1+4—231no—
119#575—232no—
120#536—231no—
121#456—234no—
122#454—234no—
123#421—232no—
124C2×#101D2311yescharacteristic, complemented
125C2×C23—21no—
126C2×C23—21no—
127C2×C23—21no—
128C2×C23C2×#12011yescharacteristic
129D23—44no—
130D23—81no—
1312−1+4—234no—
1322−1+4—464no—
1332−1+4—462no—
134C2×#41—232no—
135C2×#41—231no—
136C2×#41—462no—
137C2×#41—462no—
138C22×Q8—462no—
139C22×Q8C2×D2311yescharacteristic
140#137—234no—
141#137—462no—
142AGL(1,ℤ/8)—234no—
143AGL(1,ℤ/8)—462no—
144#135—464no—
145C2×M16C2×D2312yes—
146C4⋊Q8—232no—
147#124—232no—
148#123—462no—
149C22⋊Q8—462no—
150#117—231no—
151#104—238no—
152#101C2×D2314yescomplemented
153C23#302011yescharacteristic, complemented, Sylow
154#41—234no—
155#41—234no—
156#41—468no—
157#41—468no—
158#41—468no—
159#41—462no—
160#41—468no—
161#41—462no—
162#41—462no—
163#41—462no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—232no—
167C2×Q8—231no—
168C2×Q8—462no—
169C2×Q8—468no—
170C2×Q8—468no—
171C2×Q8D9212yes—
172C2×Q8C22×D2312yes—
173C2×D4—232no—
174C2×D4—231no—
175C2×D4—462no—
176C2×D4—462no—
177C2×D4—461no—
178C22×C4—464no—
179C22×C4—462no—
180C22×C4—461no—
181C22×C4D9212yes—
182C22×C4C22×D2311yescharacteristic
183Q16—464no—
184SD16—464no—
185SD16—464no—
186D8—464no—
187M16—22no—
188M16C22×D2314yes—
189C2×C8—22no—
190C4⋊C4—461no—
191C4⋊C4—464no—
192C22⋊C4—461no—
193C22⋊C4—464no—
194C42—232no—
195C23—462no—
196C23—461no—
197C23C2×D9211yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—234no—
201Q8—468no—
202Q8—462no—
203Q8—462no—
204D4—234no—
205D4—468no—
206D4—464no—
207D4—464no—
208D4—462no—
209D4—462no—
210D4—921no—
211D4—921no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—4616no—
215C2×C4—462no—
216C2×C4—464no—
217C2×C4—464no—
218C2×C4—462no—
219C2×C4—461no—
220C2×C4—922no—
221C2×C4C2×D9214yes—
222C2×C4C2×D9211yescharacteristic
223C2×C4D4×D2312yes—
224C2×C4D4×D2312yes—
225C2×C4C23×D2311yescharacteristic
226C8—24no—
227C22—41no—
228C22—464no—
229C22—924no—
230C22—922no—
231C22—921no—
232C22#1062505311yescharacteristic
233C22#1062505311yescharacteristic
234C22C22×D9211yescharacteristic
235C4—24no—
236C4—464no—
237C4—922no—
238C4—921no—
239C4#1062505312yes—
240C4C2×D4×D2312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—924no—
245C2—1841no—
246C2C2×#1062505311yescharacteristic
subgroupG/H
centerC2C2×#10625053
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#101C2
socleC2×C23C2×#120
hypercenterC2×#101D23
hypocenterC23#3020
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#10625158C2semidirect
2. #13093217C2semidirect
3. #13092991C2semidirect
4. #13092602C2semidirect
5. #13092592C2semidirect
6. #13092433C2semidirect
7. C2×C23×#101C2semidirect
18. #10625118C22semidirect
20. #10625115C22semidirect
24. #10625080C22semidirect
26. #10625079C22semidirect
28. C23×#101C22semidirect
29. #10625007C22semidirect
124. C2×#101D23semidirect
152. #101C2×D23semidirect
153. C23#3020semidirect

Maximal subgroups

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

subgroupindex
C2×#106251582
#130932172
#130929912
#130926022
#130925922
#130924332
C2×C23×#1012
#302023