Finite Group Databasebeta

← #15683007

Subgroups — #15683007

Order 2944.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625075C211yesmaximal, characteristic, complemented
2C22×#67262C211yesmaximal, characteristic, complemented
3#13092929C212yesmaximal, complemented
4#13092676C212yesmaximal, complemented
5#13092671C212yesmaximal, complemented
6#13092664C214yesmaximal, complemented
7#13092411C212yesmaximal, complemented
8C23×#427C211yesmaximal, characteristic, complemented
9C2×#67288C2212yes—
10C22×C4×D23C2211yescharacteristic
11C22×C8×C23C2211yescharacteristic
12C23×#117C2212yes—
13C22×C23⋊C8C2211yescharacteristic
14C2×Dic92C2211yescharacteristic, complemented
15#10625075—24no—
16C2×D184C2211yescharacteristic, complemented
17C2×#67263C2212yescomplemented
18C2×#67262—24no—
19C2×#67262C2212yes—
20C2×#67262C2212yes—
21#10625068C2214yes—
22#10625066C2214yes—
23#10625057—22no—
24#10625053—22no—
25C4×D92—24no—
26C23×#107C2212yescomplemented
27C23×#106C2212yescomplemented
28#10624992C2214yescomplemented
29#10624991C2214yescomplemented
30C23×D23D411yescharacteristic
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—22no—
33C22×Dic23D411yescharacteristic
34#67288—24no—
35#67288—24no—
36C2×D92—24no—
37C2×D92C2312yes—
38C2×C4×D23—22no—
39C2×C4×D23—22no—
40C2×C4×D23—22no—
41C2×C4×D23D412yes—
42C2×C4×D23C2312yes—
43C2×Dic46C2312yes—
44C2×C8×C23D414yescomplemented
45C2×C8×C23C2311yescharacteristic
46C2×C8×C23C2311yescharacteristic
47C4⋊C4×C23C2314yes—
48C22⋊C4×C23—22no—
49C42×C23—22no—
50(C2×D23)⋊C4—24no—
51(C2×D23)⋊C4—24no—
52C4⋊Dic23—24no—
53C2×C23⋊C8—22no—
54C2×C23⋊C8C2312yes—
55Dic92—22no—
56D184—22no—
57#67263—24no—
58#67262—24no—
59#67262—24no—
60C23×C23C2×D411yescharacteristic
61C22×D23—22no—
62C22×D23—22no—
63C22×D23—42no—
64C22×D23C2×D412yes—
65C2×C4×C23—24no—
66C2×C4×C23C2×D412yes—
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23#4112yes—
69C2×C4×C23C2411yescharacteristic
70C22⋊D23—44no—
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23C2×D412yes—
74D92—22no—
75D92—22no—
76D92—48no—
77C4×D23—24no—
78C4×D23—22no—
79C4×D23—22no—
80C4×D23—44no—
81Dic46—22no—
82Dic46—22no—
83C8×C23C2×D412yes—
84C8×C23C2×D412yes—
85C23⋊C8—22no—
86#3054—231nomaximal, Sylow
87C22×C23—22no—
88C22×C23#12112yes—
89C22×C23C22×D411yescharacteristic
90C2×D23—22no—
91C2×D23—24no—
92C2×D23—44no—
93C2×D23—42no—
94C2×D23—44no—
95C4×C23—44no—
96C4×C23#12112yes—
97C4×C23C22×D411yescharacteristic
98C4×C23C2×#4111yescharacteristic
99Dic23—22no—
100Dic23—42no—
101C2×#135—231no—
102C22×M16—231no—
103#525—232no—
104#470—232no—
105#469—232no—
106#468—234no—
107#427D2311yescharacteristic, complemented
108#416—232no—
109C2×C23—22no—
110C2×C23C2×#12111yescharacteristic
111C2×C23#57512yes—
112D23—42no—
113D23—82no—
114C2×#41—232no—
115C23×C4—231no—
116#135—464no—
117C2×Q16—231no—
118C2×SD16—232no—
119C2×D8—231no—
120C2×M16—232no—
121C2×M16—232no—
122C2×M16—464no—
123C22×C8—231no—
124C22×C8C2×D2311yescharacteristic
125#123—462no—
126C22⋊Q8—234no—
127#121—234no—
128#120—462no—
129C4×D4—464no—
130#117C2×D2312yes—
131#107C2×D2312yescomplemented
132#106C2×D2312yescomplemented
133#103—234no—
134#102—234no—
135C23#305411yescharacteristic, complemented, Sylow
136C24—231no—
137#41—464no—
138#41—464no—
139C2×Q8—232no—
140C2×D4—232no—
141C2×D4—464no—
142C2×D4—462no—
143C22×C4—231no—
144C22×C4—232no—
145C22×C4—232no—
146C22×C4—462no—
147C22×C4—462no—
148C22×C4—462no—
149C22×C4C22×D2311yescharacteristic
150Q16—462no—
151SD16—464no—
152D8—462no—
153M16—464no—
154M16—464no—
155C2×C8—232no—
156C2×C8—462no—
157C2×C8D9214yescomplemented
158C2×C8C22×D2311yescharacteristic
159C2×C8C22×D2311yescharacteristic
160C4⋊C4—464no—
161C4⋊C4C22×D2314yes—
162C22⋊C4—22no—
163C22⋊C4—464no—
164C22⋊C4—464no—
165C42—22no—
166C23—232no—
167C23—462no—
168C23—462no—
169C23—922no—
170C23D4×D2311yescharacteristic
171Q8—462no—
172Q8—462no—
173D4—462no—
174D4—462no—
175D4—928no—
176D4—924no—
177C2×C4—24no—
178C2×C4—232no—
179C2×C4—462no—
180C2×C4—464no—
181C2×C4—462no—
182C2×C4—462no—
183C2×C4—462no—
184C2×C4—924no—
185C2×C4C2×D9212yes—
186C2×C4D4×D2311yescharacteristic
187C2×C4#6729212yes—
188C2×C4C23×D2311yescharacteristic
189C8—462no—
190C8C2×D9212yes—
191C8C2×D9212yes—
192C22—22no—
193C22—462no—
194C22—464no—
195C22—924no—
196C22—922no—
197C22—924no—
198C22#1062506612yes—
199C22C2×D4×D2311yescharacteristic
200C4—44no—
201C4—462no—
202C4—922no—
203C4#1062506612yes—
204C4C22×D9211yescharacteristic
205C4C2×#6729211yescharacteristic
206C2—22no—
207C2—922no—
208C2—1842no—
209C2C2×#1062506611yescharacteristic
210C2#1309321412yes—
subgroupG/H
centerC2×C4D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#427C2
socleC22×C23C22×D4
hypercenter#427D23
hypocenterC23#3054
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. C2×#10625075C2semidirect
2. C22×#67262C2semidirect
3. #13092929C2semidirect
4. #13092676C2semidirect
5. #13092671C2semidirect
6. #13092664C2semidirect
7. #13092411C2semidirect
8. C23×#427C2semidirect
14. C2×Dic92C22semidirect
16. C2×D184C22semidirect
17. C2×#67263C22semidirect
26. C23×#107C22semidirect
27. C23×#106C22semidirect
28. #10624992C22semidirect
29. #10624991C22semidirect
44. C2×C8×C23D4semidirect
107. #427D23semidirect
131. #107C2×D23semidirect
132. #106C2×D23semidirect
135. C23#3054semidirect
157. C2×C8D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250752
C22×#672622
#130929292
#130926762
#130926712
#130926642
#130924112
C23×#4272
#305423