Finite Group Databasebeta

← #15676676

Subgroups — #15676676

Order 2944.

840 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 177 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×C4×D92C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D23C214yesmaximal, complemented
3#13092353C212yesmaximal, complemented
4#13092352C212yesmaximal, complemented
5#13092326C212yesmaximal, complemented
6#13092325C212yesmaximal, complemented
7#13092263C211yesmaximal, characteristic, complemented
8C2×C4×D4×C23C211yesmaximal, characteristic, complemented
9C22×D4×C23C2211yescharacteristic
10C23×C4×C23C2212yes—
11C22×C22⋊D23C2214yes—
12C22×D92C2211yescharacteristic
13C22×C4×D23C2212yes—
14C4×D4×C23—24no—
15C2×C4⋊C4×C23C2211yescharacteristic
16C2×C22⋊C4×C23C2212yes—
17C2×C42×C23C2211yescharacteristic
18C2×C22⋊Dic23C2214yes—
19C4×C22⋊D23—216no—
20C2×(C2×D23)⋊C4C2214yes—
21C2×(C2×D23)⋊C4C2212yes—
22C2×C4⋊Dic23C2211yescharacteristic
23C2×Dic23⋊C4C2214yes—
24C2×C4×Dic23C2212yes—
25C4×D92—24no—
26C23⋊#95C2212yes—
27C23⋊#95C2212yes—
28C24×C23C2312yes—
29C23×D23C2312yes—
30C2×D4×C23—24no—
31C2×D4×C23—22no—
32C22×C4×C23—28no—
33C22×C4×C23—24no—
34C22×C4×C23C2312yes—
35C22×C4×C23C2311yescharacteristic
36C22×C4×C23C2311yescharacteristic
37C22×C4×C23C2311yescharacteristic
38C2×C22⋊D23—28no—
39C2×C22⋊D23—28no—
40C2×C22⋊D23—28no—
41C22×Dic23C2312yes—
42C22×Dic23C2314yes—
43C2×D92—24no—
44C2×D92—22no—
45C2×C4×D23—24no—
46C2×C4×D23—28no—
47C4⋊C4×C23—22no—
48C22⋊C4×C23—24no—
49C42×C23D414yescomplemented
50C22⋊Dic23—28no—
51(C2×D23)⋊C4—24no—
52(C2×D23)⋊C4—28no—
53C4⋊Dic23—22no—
54Dic23⋊C4—28no—
55C4×Dic23D418yescomplemented
56C23×C23—24no—
57C23×C23—22no—
58C23×C23—24no—
59C23×C23—22no—
60C23×C23#4114yes—
61C23×C23C2411yescharacteristic
62C22×D23—22no—
63C22×D23—24no—
64C22×D23—22no—
65C22×D23—24no—
66C22×D23#4114yes—
67D4×C23—28no—
68C2×C4×C23—22no—
69C2×C4×C23—22no—
70C2×C4×C23—24no—
71C2×C4×C23—22no—
72C2×C4×C23—48no—
73C2×C4×C23C2×D414yes—
74C2×C4×C23C2×D412yes—
75C2×C4×C23C2×D412yes—
76C2×C4×C23C2×D412yes—
77C22⋊D23—232no—
78C2×Dic23—24no—
79C2×Dic23—24no—
80C2×Dic23—24no—
81C2×Dic23—22no—
82C2×Dic23C2×D418yes—
83D92—28no—
84C4×D23—48no—
85#2397—231nomaximal, Sylow
86C22×C23—28no—
87C22×C23—24no—
88C22×C23—42no—
89C22×C23—44no—
90C22×C23—42no—
91C22×C23C22×D412yes—
92C22×C23C22×D411yescharacteristic
93C22×C23C2×#4112yes—
94C22×C23C2×#4112yes—
95C2×D23—24no—
96C2×D23—28no—
97C2×D23—44no—
98C2×D23—42no—
99C2×D23—42no—
100C4×C23—22no—
101C4×C23—22no—
102C4×C23—42no—
103C4×C23#12714yes—
104Dic23—28no—
105Dic23—42no—
106C2×C4×D4—234no—
107C2×C4×D4—231no—
108C2×C4×D4D2311yescharacteristic, complemented
109#399—232no—
110#399—232no—
111#392—232no—
112#392—232no—
113#376—231no—
114C2×C23—44no—
115C2×C23#52511yescharacteristic
116C2×C23#52514yes—
117C2×C23#52511yescharacteristic
118C2×C23C2×#12711yescharacteristic
119D23—44no—
120C22×D4—234no—
121C22×D4—231no—
122C22×D4C2×D2311yescharacteristic
123C23×C4—232no—
124C23×C4C2×D2312yes—
125C4×D4—24no—
126C4×D4—4616no—
127C4×D4—464no—
128C2×C4⋊C4—234no—
129C2×C4⋊C4—231no—
130C2×C4⋊C4C2×D2311yescharacteristic
131C2×C22⋊C4—234no—
132C2×C22⋊C4—234no—
133C2×C22⋊C4—232no—
134C2×C22⋊C4C2×D2312yes—
135C2×C42—232no—
136C2×C42C2×D2311yescharacteristic
137#95—232no—
138#95—232no—
139C23#239711yescharacteristic, complemented, Sylow
140C24—232no—
141C24C22×D2312yes—
142C2×D4—24no—
143C2×D4—22no—
144C2×D4—464no—
145C2×D4—468no—
146C2×D4—468no—
147C2×D4—468no—
148C2×D4—462no—
149C22×C4—28no—
150C22×C4—24no—
151C22×C4—234no—
152C22×C4—232no—
153C22×C4—468no—
154C22×C4—464no—
155C22×C4C22×D2312yes—
156C22×C4C22×D2311yescharacteristic
157C22×C4C22×D2311yescharacteristic
158C22×C4C22×D2311yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—468no—
161C4⋊C4—462no—
162C22⋊C4—24no—
163C22⋊C4—468no—
164C22⋊C4—468no—
165C22⋊C4—464no—
166C42—238no—
167C42C22⋊D2314yescomplemented
168C23—22no—
169C23—24no—
170C23—24no—
171C23—22no—
172C23—234no—
173C23—464no—
174C23—464no—
175C23—462no—
176C23—462no—
177C23#6728814yes—
178C23C23×D2311yescharacteristic
179D4—28no—
180D4—468no—
181D4—4632no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—238no—
188C2×C4—464no—
189C2×C4—464no—
190C2×C4—464no—
191C2×C4—462no—
192C2×C4—928no—
193C2×C4D4×D2314yes—
194C2×C4C2×C22⋊D2312yes—
195C2×C4C2×C22⋊D2312yes—
196C2×C4C2×C22⋊D2312yes—
197C22—28no—
198C22—24no—
199C22—42no—
200C22—44no—
201C22—42no—
202C22—464no—
203C22—468no—
204C22—924no—
205C22—922no—
206C22—922no—
207C22C2×#6728812yes—
208C22C2×D4×D2312yes—
209C22#41×D2312yes—
210C22C22×C22⋊D2311yescharacteristic
211C4—22no—
212C4—22no—
213C4—42no—
214C4—468no—
215C4—922no—
216C4#1062511114yes—
217C2—44no—
218C2—924no—
219C2#1309292411yescharacteristic
220C2#1309292614yes—
221C2#1309292811yescharacteristic
222C2C2×#1062511111yescharacteristic
subgroupG/H
centerC22×C4C22×D23
commutator, socle, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC2×C4×D4×C23C2
hypercenterC2×C4×D4D23
hypocenterC23#2397
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D92C2semidirect
2. C2×C4×C22⋊D23C2semidirect
3. #13092353C2semidirect
4. #13092352C2semidirect
5. #13092326C2semidirect
6. #13092325C2semidirect
7. #13092263C2semidirect
8. C2×C4×D4×C23C2semidirect
49. C42×C23D4semidirect
55. C4×Dic23D4semidirect
108. C2×C4×D4D23semidirect
139. C23#2397semidirect
167. C42C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D922
C2×C4×C22⋊D232
#130923532
#130923522
#130923262
#130923252
#130922632
C2×C4×D4×C232
#239723