Finite Group Databasebeta

← #15682760

Subgroups — #15682760

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#13093215C212yesmaximal, complemented
3#13092599C214yesmaximal, complemented
4#13092589C214yesmaximal, complemented
5#13092435C212yesmaximal, complemented
6C2×#10625018C211yesmaximal, characteristic, complemented
7C23×#536C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9C22×Q8×C23C2211yescharacteristic
10#10625158—22no—
11#10625158—24no—
12#10625158C2214yes—
13C2×#67292—22no—
14C2×Q8×D23—22no—
15C2×#67288—22no—
16C2×#67288C2212yes—
17C23×C4⋊Q8C2212yescomplemented
18C23×#124C2212yescomplemented
19C23×#123—22no—
20C23×C22⋊Q8—22no—
21C23×#117C2211yescharacteristic
22#10625122—22no—
23#10625121—24no—
24#10625120—22no—
25#10625113C2214yescomplemented
26#10625103C2214yescomplemented
27C2×#67267C2212yes—
28#10625018C2214yescomplemented
29#10624987C2218yescomplemented
30#41×C23—22no—
31#41×C23—22no—
32C2×Q8×C23—22no—
33C2×Q8×C23—22no—
34C2×Q8×C23D412yes—
35C2×Q8×C23C2311yescharacteristic
36C2×Q8×C23C2312yes—
37C2×D4×C23—21no—
38C2×D4×C23C2311yescharacteristic
39C22×C4×C23—21no—
40C22×C4×C23D412yes—
41C22×C4×C23C2311yescharacteristic
42C2×C22⋊D23—22no—
43#67292—28no—
44#67292—28no—
45Q8×D23—28no—
46Q8×D23—28no—
47#67288—28no—
48#67288—28no—
49#67288—22no—
50#67288—22no—
51#67288D414yes—
52#67288C2314yes—
53C2×D92—22no—
54C2×D92D412yes—
55C2×C4×D23—24no—
56C2×C4×D23—22no—
57C2×Dic46—22no—
58C2×Dic46D412yes—
59C4⋊C4×C23—21no—
60C4⋊C4×C23—24no—
61C22⋊C4×C23—21no—
62C22⋊C4×C23—24no—
63C42×C23C2312yes—
64#67275—24no—
65#67274—24no—
66#67273—24no—
67#67272—24no—
68#67267—22no—
69#67267C2314yes—
70C2×C23⋊C8—22no—
71C23×C23—21no—
72C23×C23C2×D411yescharacteristic
73C22×D23—22no—
74Q8×C23—24no—
75Q8×C23—24no—
76Q8×C23—22no—
77D4×C23—22no—
78D4×C23—41no—
79D4×C23—41no—
80C2×C4×C23—22no—
81C2×C4×C23—22no—
82C2×C4×C23—22no—
83C2×C4×C23—21no—
84C2×C4×C23—42no—
85C2×C4×C23C2×D412yes—
86C2×C4×C23C2×D412yes—
87C2×C4×C23C2×D414yes—
88C2×C4×C23C2×D411yescharacteristic
89C2×C4×C23C2411yescharacteristic
90C22⋊D23—24no—
91C22⋊D23—24no—
92C2×Dic23—22no—
93D92—28no—
94D92—22no—
95D92C2×D414yes—
96C4×D23—216no—
97C4×D23—24no—
98C4×D23—24no—
99Dic46—28no—
100Dic46—22no—
101Dic46C2×D414yes—
102C23⋊C8—24no—
103#3020—231nomaximal, Sylow
104C22×C23—41no—
105C22×C23—42no—
106C22×C23—41no—
107C22×C23#12011yescharacteristic
108C22×C23#12011yescharacteristic
109C22×C23C22×D411yescharacteristic
110C2×D23—24no—
111C2×D23—44no—
112C4×C23—24no—
113C4×C23—42no—
114C4×C23—41no—
115C4×C23#12012yes—
116C4×C23C22×D412yes—
117Dic23—24no—
118C2×2−1+4—231no—
119#575—232no—
120#536D2311yescharacteristic, complemented
121#456—234no—
122#454—234no—
123#421—232no—
124C2×#101—231no—
125C2×C23—21no—
126C2×C23—21no—
127C2×C23—21no—
128C2×C23—81no—
129C2×C23C2×#12011yescharacteristic
130D23—44no—
1312−1+4—234no—
1322−1+4—464no—
1332−1+4—462no—
134C2×#41—232no—
135C2×#41—462no—
136C2×#41—462no—
137C2×#41C2×D2311yescharacteristic
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×M16—232no—
146C4⋊Q8C2×D2312yescomplemented
147#124C2×D2312yescomplemented
148#123—22no—
149C22⋊Q8—22no—
150#117C2×D2311yescharacteristic
151#104—238no—
152#101—234no—
153C23#302011yescharacteristic, complemented, Sylow
154#41—22no—
155#41—22no—
156#41—234no—
157#41—234no—
158#41—468no—
159#41—468no—
160#41—468no—
161#41—462no—
162#41—462no—
163#41—468no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—232no—
167C2×Q8—462no—
168C2×Q8—468no—
169C2×Q8—468no—
170C2×Q8C22⋊D2312yes—
171C2×Q8C22×D2311yescharacteristic
172C2×Q8C22×D2312yes—
173C2×D4—21no—
174C2×D4—232no—
175C2×D4—462no—
176C2×D4—462no—
177C2×D4C22×D2311yescharacteristic
178C22×C4—21no—
179C22×C4—464no—
180C22×C4—462no—
181C22×C4C22⋊D2312yes—
182C22×C4C22×D2311yescharacteristic
183Q16—464no—
184SD16—464no—
185SD16—464no—
186D8—464no—
187M16—234no—
188M16—462no—
189C2×C8—462no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D2312yes—
195C23—21no—
196C23—462no—
197C23C2×C22⋊D2311yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—234no—
202Q8—468no—
203Q8—462no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—234no—
208D4—468no—
209D4—464no—
210D4—464no—
211D4—462no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—4616no—
218C2×C4—462no—
219C2×C4—464no—
220C2×C4—464no—
221C2×C4D4×D2312yes—
222C2×C4D4×D2312yes—
223C2×C4C2×C22⋊D2314yes—
224C2×C4C2×C22⋊D2311yescharacteristic
225C2×C4C23×D2311yescharacteristic
226C8—464no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—464no—
231C22—924no—
232C22#1062510811yescharacteristic
233C22#1062510811yescharacteristic
234C22C22×C22⋊D2311yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—464no—
239C4#1062510812yes—
240C4C2×D4×D2312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—924no—
246C2C2×#1062510811yescharacteristic
subgroupG/H
centerC2C2×#10625108
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#536C2
socleC2×C23C2×#120
hypercenter#536D23
hypocenterC23#3020
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#10625158C2semidirect
2. #13093215C2semidirect
3. #13092599C2semidirect
4. #13092589C2semidirect
5. #13092435C2semidirect
6. C2×#10625018C2semidirect
7. C23×#536C2semidirect
17. C23×C4⋊Q8C22semidirect
18. C23×#124C22semidirect
25. #10625113C22semidirect
26. #10625103C22semidirect
28. #10625018C22semidirect
29. #10624987C22semidirect
120. #536D23semidirect
146. C4⋊Q8C2×D23semidirect
147. #124C2×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
#130932152
#130925992
#130925892
#130924352
C2×#106250182
C23×#5362
#302023