Finite Group Databasebeta

← #15683644

Subgroups — #15683644

Order 2944.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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#13092891C211yesmaximal, characteristic
2#13092755C212yesmaximal, complemented
3#13092714C212yesmaximal, complemented
4#13092619C212yesmaximal, complemented
5#13092567C212yesmaximal
6#13092515C212yesmaximal, complemented
7C4×#67274C212yesmaximal, complemented
8#13092478C211yesmaximal, characteristic, complemented
9C23×#541C211yesmaximal, characteristic, complemented
10C22×D92C2211yescharacteristic
11C23×C4⋊Q8C2211yescharacteristic, complemented
12C23×#126—22no—
13C23×#125—22no—
14C23×#125C2211yescharacteristic, complemented
15C23×C22⋊Q8C2212yes—
16C4×Q8×C23C2212yescomplemented
17C23×#117C2211yescharacteristic
18C2×#67274C2212yes—
19C2×#67274C2212yes—
20#10625097C2211yescharacteristic
21#10625064—22no—
22C22⋊C4×D23—22no—
23C4×D92C2212yes—
24C4×D92C2212yes—
25#10625017C2212yescomplemented
26#10625017C2212yescomplemented
27C22⋊(C23⋊C8)C2212yes—
28#10624991C2212yes—
29#10624991C2212yes—
30#10624990C2212yescomplemented
31#10624989C2212yescomplemented
32C4⋊(C23⋊C8)C2212yescomplemented
33#10624985C2211yescharacteristic, complemented
34C4×C23⋊C8C2211yescharacteristic, complemented
35C23×D23—21no—
36C2×Q8×C23C2312yes—
37C22×C4×C23C2311yescharacteristic
38C2×D92—21no—
39C2×D92—24no—
40C2×D92C2312yes—
41C2×C4×D23—22no—
42C2×C4×D23—22no—
43C4⋊C4×C23—22no—
44C4⋊C4×C23—22no—
45C4⋊C4×C23—22no—
46C4⋊C4×C23—22no—
47C4⋊C4×C23D412yes—
48C4⋊C4×C23C2312yes—
49C22⋊C4×C23—22no—
50C22⋊C4×C23D412yes—
51C42×C23—22no—
52C42×C23C2311yescharacteristic
53C42×C23C2311yescharacteristic
54C22⋊Dic23—21no—
55#67274—24no—
56#67274—24no—
57(C2×D23)⋊C4—22no—
58(C2×D23)⋊C4—22no—
59C4⋊Dic23C2312yes—
60C4×Dic23—21no—
61C2×C23⋊C8C2312yes—
62C2×C23⋊C8C2312yes—
63C23×C23C2×D411yescharacteristic
64C22×D23—22no—
65C22×D23—24no—
66C22×D23—82no—
67Q8×C23—22no—
68Q8×C23—22no—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23—22no—
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D412yes—
74C2×C4×C23C2×D412yes—
75C2×C4×C23C2411yescharacteristic
76C2×Dic23—22no—
77D92—24no—
78D92—22no—
79D92#4114yes—
80C4×D23—82no—
81C4×D23—82no—
82C23⋊C8—22no—
83C23⋊C8—22no—
84#3123—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—22no—
87C22×C23C22×D411yescharacteristic
88C2×D23—24no—
89C2×D23—42no—
90C2×D23—42no—
91C2×D23—84no—
92C4×C23—21no—
93C4×C23—22no—
94C4×C23—22no—
95C4×C23—42no—
96C4×C23—42no—
97C4×C23C2×#4112yes—
98Dic23—42no—
99#541D2311yescharacteristic, complemented
100#518—231no—
101#485—232no—
102#478—232no—
103#461—232no—
104#450—232no—
105#440—232no—
106C4×SD16—232no—
107#433—231no—
108C2×C23—41no—
109C2×C23#52511yescharacteristic
110C2×C23#57712yes—
111D23—44no—
112C22×D4—231no—
113C2×SD16—232no—
114C2×SD16—232no—
115C4⋊Q8C2×D2311yescharacteristic, complemented
116#126—22no—
117#125—22no—
118#125C2×D2311yescharacteristic, complemented
119C22⋊Q8C2×D2312yes—
120C4×Q8C2×D2312yescomplemented
121C4×D4—232no—
122C4×D4—232no—
123C4×D4—462no—
124#117—231no—
125#117C2×D2311yescharacteristic
126C2×C22⋊C4—462no—
127#107—232no—
128#106—232no—
129C4⋊C8—232no—
130#103—232no—
131#103—232no—
132#102—232no—
133#102—232no—
134C22⋊C8—232no—
135#97—231no—
136C4×C8—231no—
137C23#312311yescharacteristic, complemented, Sylow
138C24—461no—
139C2×Q8C22×D2312yes—
140C2×D4—232no—
141C2×D4—464no—
142C2×D4—461no—
143C22×C4—462no—
144C22×C4—462no—
145C22×C4C22×D2311yescharacteristic
146SD16—464no—
147SD16—464no—
148C2×C8—232no—
149C2×C8—232no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—232no—
155C4⋊C4C22⋊D2312yes—
156C4⋊C4C22×D2312yes—
157C22⋊C4—22no—
158C22⋊C4—461no—
159C22⋊C4—462no—
160C22⋊C4—462no—
161C22⋊C4C22⋊D2312yes—
162C42—22no—
163C42—461no—
164C42C22×D2311yescharacteristic
165C42C22×D2311yescharacteristic
166C23—464no—
167C23—462no—
168C23—1842no—
169C23C2×C22⋊D2311yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—234no—
173D4—464no—
174D4—462no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—462no—
179C2×C4—1842no—
180C2×C4—1842no—
181C2×C4C2×C22⋊D2312yes—
182C2×C4C2×C22⋊D2311yescharacteristic
183C2×C4C2×C22⋊D2312yes—
184C2×C4C23×D2311yescharacteristic
185C8—462no—
186C8—462no—
187C22—21no—
188C22—22no—
189C22—464no—
190C22—922no—
191C22—922no—
192C22—1844no—
193C22C22×C22⋊D2311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—922no—
200C4#41×D2312yes—
201C2—41no—
202C2—924no—
203C2#1309292411yescharacteristic
204C2#1309322512yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#541C2
socleC22×C23C22×D4
prime radicalC22×D92C22
hypercenter#541D23
hypocenterC23#3123
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #13092755C2semidirect
3. #13092714C2semidirect
4. #13092619C2semidirect
6. #13092515C2semidirect
7. C4×#67274C2semidirect
8. #13092478C2semidirect
9. C23×#541C2semidirect
11. C23×C4⋊Q8C22semidirect
14. C23×#125C22semidirect
16. C4×Q8×C23C22semidirect
25. #10625017C22semidirect
26. #10625017C22semidirect
30. #10624990C22semidirect
31. #10624989C22semidirect
32. C4⋊(C23⋊C8)C22semidirect
33. #10624985C22semidirect
34. C4×C23⋊C8C22semidirect
99. #541D23semidirect
115. C4⋊Q8C2×D23semidirect
118. #125C2×D23semidirect
120. C4×Q8C2×D23semidirect
137. C23#3123semidirect

Maximal subgroups

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

subgroupindex
#130928912
#130927552
#130927142
#130926192
#130925672
#130925152
C4×#672742
#130924782
C23×#5412
#312323