Finite Group Databasebeta

← #15685265

Subgroups — #15685265

Order 2944.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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#13093082C211yesmaximal, characteristic, complemented
2#13093072C211yesmaximal, characteristic
3#13092767C211yesmaximal, characteristic, complemented
4#13092746C212yesmaximal, complemented
5#13092703C211yesmaximal, characteristic, complemented
6#13092643C212yesmaximal, complemented
7#13092554C212yesmaximal, complemented
8C4×#67273C211yesmaximal, characteristic, complemented
9#13092482C211yesmaximal, characteristic, complemented
10#103×D23C212yesmaximal, complemented
11C23×#461C211yesmaximal, characteristic, complemented
12C2×Q8×D23C2212yes—
13C2×#67288—21no—
14C2×SD16×C23C2212yes—
15C23×C4⋊Q8C2211yescharacteristic
16C4×D4×C23C2211yescharacteristic
17#10625117C2212yes—
18#10625109C2212yes—
19C2×#67273C2211yescharacteristic
20#10625095—21no—
21C2×C8×D23C2212yes—
22#10625067—22no—
23#10625064—21no—
24C4⋊C4×D23C2212yes—
25#10625059—21no—
26#10625054—22no—
27C4×D92C2211yescharacteristic
28#10625040C2211yescharacteristic
29C4×Dic46C2211yescharacteristic
30C23×C4⋊C8C2211yescharacteristic
31C23×#103C2212yes—
32#10625017C2212yes—
33#10625017C2212yes—
34#10625014C2211yescharacteristic
35(C2×D23)⋊C8C2212yes—
36#10624999C2212yes—
37#10624998C2212yes—
38#10624992C2211yescharacteristic
39#10624990C2211yescharacteristic
40C4×C23⋊C8C2211yescharacteristic
41C2×Q8×C23C2312yes—
42C2×D4×C23C2311yescharacteristic
43C22×C4×C23—21no—
44C2×C22⋊D23—22no—
45Q8×D23—24no—
46Q8×D23—42no—
47#67288—44no—
48C2×D92D411yescharacteristic
49C2×C4×D23—22no—
50C2×C4×D23—22no—
51C2×C4×D23C2312yes—
52C2×Dic46—21no—
53C2×Dic46—22no—
54C2×Dic46C2311yescharacteristic
55SD16×C23—42no—
56C2×C8×C23C2312yes—
57C4⋊C4×C23—21no—
58C4⋊C4×C23—21no—
59C4⋊C4×C23C2311yescharacteristic
60C22⋊C4×C23—21no—
61C42×C23C2311yescharacteristic
62C22⋊Dic23—22no—
63#67273—22no—
64(C2×D23)⋊C4—22no—
65(C2×D23)⋊C4D412yes—
66C4⋊Dic23—21no—
67C4⋊Dic23D411yescharacteristic
68C4⋊Dic23C2311yescharacteristic
69C4⋊Dic23C2312yes—
70Dic23⋊C4—21no—
71Dic23⋊C4—22no—
72Dic23⋊C4—22no—
73C4×Dic23—21no—
74C2×C23⋊C8C2311yescharacteristic
75C2×C23⋊C8C2311yescharacteristic
76C8×D23—42no—
77C23×C23—21no—
78C22×D23C2×D412yes—
79Q8×C23—22no—
80Q8×C23—22no—
81D4×C23—21no—
82D4×C23—21no—
83C2×C4×C23—21no—
84C2×C4×C23—22no—
85C2×C4×C23—42no—
86C2×C4×C23C2×D411yescharacteristic
87C2×C4×C23C2×D411yescharacteristic
88C2×C4×C23C2411yescharacteristic
89C22⋊D23—44no—
90C2×Dic23—21no—
91C2×Dic23—21no—
92C2×Dic23—22no—
93C2×Dic23C2×D412yes—
94D92SD1614yescomplemented
95C4×D23—22no—
96C4×D23—22no—
97C4×D23—44no—
98C4×D23—44no—
99Dic46—21no—
100Dic46—44no—
101Dic46—42no—
102Dic46#4112yescomplemented
103C8×C23—22no—
104C23⋊C8—21no—
105C23⋊C8—21no—
106#3298—231nomaximal, Sylow
107C22×C23—41no—
108C22×C23—41no—
109C22×C23—41no—
110C22×C23C22×D411yescharacteristic
111C2×D23—22no—
112C2×D23—22no—
113C2×D23C2×SD1614yes—
114C4×C23—21no—
115C4×C23—42no—
116C4×C23—41no—
117C4×C23C2×SD1612yes—
118C4×C23C2×#4111yescharacteristic
119C4×C23H(5,𝔽2)11yescharacteristic
120Dic23—22no—
121Dic23—22no—
122Dic23—42no—
123Dic23—41no—
124D4×Q8—231no—
125#547—231no—
126#487—231no—
127#483—232no—
128#475—231no—
129#465—232no—
130#461D2311yescharacteristic, complemented
131#448—232no—
132C4×SD16—231no—
133C8×D4—231no—
134C2×#103—232no—
135C2×C23—81no—
136C2×C23#54611yescharacteristic
137C2×C23C22×SD1611yescharacteristic
138C2×C23#57811yescharacteristic
139D23—24no—
140C2×#41—461no—
141C22×Q8—232no—
142C2×SD16—231no—
143C2×SD16C2×D2312yes—
144C22×C8—232no—
145C4⋊Q8—231no—
146C4⋊Q8—461no—
147C4⋊Q8C2×D2311yescharacteristic
148#123—462no—
149C22⋊Q8—232no—
150C22⋊Q8—462no—
151C22⋊Q8—461no—
152#121—232no—
153C4×Q8—231no—
154C4×D4—231no—
155C4×D4—461no—
156C4×D4C2×D2311yescharacteristic
157C2×C4⋊C4—232no—
158#106—232no—
159#106—231no—
160C4⋊C8C2×D2311yescharacteristic
161#103—232no—
162#103—232no—
163#103—232no—
164#103—231no—
165#103C2×D2312yes—
166#102—231no—
167C22⋊C8—232no—
168C4×C8—231no—
169C23#329811yescharacteristic, complemented, Sylow
170#41—924no—
171C2×Q8—231no—
172C2×Q8—462no—
173C2×Q8—461no—
174C2×Q8—464no—
175C2×Q8—922no—
176C2×Q8C22×D2312yes—
177C2×D4—231no—
178C2×D4—462no—
179C2×D4C22×D2311yescharacteristic
180C22×C4—21no—
181C22×C4—232no—
182C22×C4—462no—
183C22×C4—462no—
184SD16—42no—
185SD16—462no—
186C2×C8—231no—
187C2×C8—231no—
188C2×C8—922no—
189C2×C8C22×D2312yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—231no—
193C4⋊C4—231no—
194C4⋊C4—232no—
195C4⋊C4—462no—
196C4⋊C4—462no—
197C4⋊C4—461no—
198C4⋊C4—461no—
199C4⋊C4C22×D2311yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—232no—
202C22⋊C4—462no—
203C22⋊C4—462no—
204C42—461no—
205C42C22×D2311yescharacteristic
206C23—21no—
207C23—232no—
208Q8—22no—
209Q8—22no—
210Q8—232no—
211Q8—461no—
212Q8—924no—
213Q8—922no—
214D4—21no—
215D4—21no—
216D4—234no—
217D4—924no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—232no—
222C2×C4—461no—
223C2×C4—462no—
224C2×C4—462no—
225C2×C4—461no—
226C2×C4—462no—
227C2×C4—924no—
228C2×C4—924no—
229C2×C4D4×D2311yescharacteristic
230C2×C4D4×D2311yescharacteristic
231C2×C4C23×D2311yescharacteristic
232C8—22no—
233C8—461no—
234C8—461no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—234no—
239C22—462no—
240C22—462no—
241C22C2×D4×D2311yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—462no—
246C4—462no—
247C4—922no—
248C4—921no—
249C4SD16×D2312yes—
250C4#1062515511yescharacteristic
251C4#41×D2311yescharacteristic
252C2—81no—
253C2—464no—
254C2#1309306411yescharacteristic
255C2C2×SD16×D2311yescharacteristic
256C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#461C2
socleC22×C23C22×D4
prime radical#13093072C2
hypercenter#461D23
hypocenterC23#3298
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #13093082C2semidirect
3. #13092767C2semidirect
4. #13092746C2semidirect
5. #13092703C2semidirect
6. #13092643C2semidirect
7. #13092554C2semidirect
8. C4×#67273C2semidirect
9. #13092482C2semidirect
10. #103×D23C2semidirect
11. C23×#461C2semidirect
94. D92SD16semidirect
102. Dic46#41semidirect
130. #461D23semidirect
169. C23#3298semidirect

Maximal subgroups

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

subgroupindex
#130930822
#130930722
#130927672
#130927462
#130927032
#130926432
#130925542
C4×#672732
#130924822
#103×D232
C23×#4612
#329823