Finite Group Databasebeta

← #15683641

Subgroups — #15683641

Order 2944.

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

normal subgroups only

This group has 418 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#13093022C211yesmaximal, characteristic, complemented
2#13092891C211yesmaximal, characteristic, complemented
3#13092742C212yesmaximal, complemented
4#13092718C212yesmaximal, complemented
5#13092613C212yesmaximal, complemented
6#13092553C212yesmaximal, complemented
7#13092530C212yesmaximal, complemented
8C4×D184C212yesmaximal, complemented
9C23×#433C211yesmaximal, characteristic, complemented
10C22×D92C2211yescharacteristic
11C23×#117C2211yescharacteristic
12#10625101C2212yes—
13#10625097C2211yescharacteristic
14C2×D184C2212yes—
15C2×D184C2212yes—
16#10625065—22no—
17#10625064—22no—
18#10625055—22no—
19C22⋊C4×D23—22no—
20#10625045C2211yescharacteristic, complemented
21C4×D92C2212yes—
22C4×D92C2212yes—
23C4×D92C2212yescomplemented
24#10625041C2211yescharacteristic, complemented
25C23×C4⋊C8C2212yescomplemented
26C23×C22⋊C8C2212yes—
27C23×#97C2211yescharacteristic, complemented
28C4×C8×C23C2211yescharacteristic, complemented
29#10625003C2212yes—
30#10625003C2212yes—
31#10625003C2212yescomplemented
32#10625003C2212yescomplemented
33#10625000C2212yescomplemented
34#10624999C2212yescomplemented
35C23×D23—21no—
36C22×C4×C23C2311yescharacteristic
37C2×C22⋊D23—22no—
38C2×D92—21no—
39C2×D92—24no—
40C2×D92—22no—
41C2×D92C2312yes—
42C2×D92C2312yes—
43C2×C4×D23—22no—
44C2×C4×D23—22no—
45C2×C4×D23—22no—
46C2×C8×C23C2312yes—
47C2×C8×C23C2312yes—
48C4⋊C4×C23D412yes—
49C22⋊C4×C23D412yes—
50C42×C23C2311yescharacteristic
51C42×C23C2311yescharacteristic
52C22⋊Dic23—21no—
53(C2×D23)⋊C4—22no—
54(C2×D23)⋊C4—22no—
55(C2×D23)⋊C4—22no—
56(C2×D23)⋊C4—22no—
57C4⋊Dic23C2312yes—
58C4⋊Dic23C2312yes—
59Dic23⋊C4—22no—
60C4×Dic23—21no—
61D184—24no—
62D184—24no—
63C23×C23C2×D411yescharacteristic
64C22×D23—22no—
65C22×D23—24no—
66C22×D23—22no—
67C22×D23—82no—
68C2×C4×C23—22no—
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D412yes—
71C2×C4×C23C2×D412yes—
72C2×C4×C23C2411yescharacteristic
73C22⋊D23—82no—
74C2×Dic23—22no—
75C2×Dic23—22no—
76D92—24no—
77D92—22no—
78D92—22no—
79D92—22no—
80D92—82no—
81D92#4114yes—
82C4×D23—82no—
83C4×D23—82no—
84C4×D23—82no—
85C8×C23—22no—
86C8×C23—22no—
87#3122—231nomaximal, Sylow
88C22×C23—21no—
89C22×C23—22no—
90C22×C23C22×D411yescharacteristic
91C2×D23—24no—
92C2×D23—42no—
93C2×D23—42no—
94C2×D23—42no—
95C2×D23—42no—
96C2×D23—42no—
97C2×D23—84no—
98C4×C23—21no—
99C4×C23—22no—
100C4×C23—22no—
101C4×C23C2×#4112yes—
102Dic23—42no—
103Dic23—42no—
104#540—231no—
105#518—231no—
106#482—232no—
107#478—232no—
108#459—232no—
109#447—232no—
110#442—232no—
111C4×D8—232no—
112#433D2311yescharacteristic, complemented
113C2×C23—41no—
114C2×C23#52511yescharacteristic
115C2×C23#57612yes—
116D23—44no—
117D23—82no—
118C22×D4—231no—
119C2×D8—232no—
120C2×D8—232no—
121#127—231no—
122#125—231no—
123#123—462no—
124#121—232no—
125#121—462no—
126C4×D4—232no—
127C4×D4—232no—
128C4×D4—232no—
129C4×D4—462no—
130#117—231no—
131#117C2×D2311yescharacteristic
132C2×C22⋊C4—462no—
133#107—232no—
134#106—232no—
135C4⋊C8C2×D2312yescomplemented
136#102—232no—
137#102—232no—
138#102—232no—
139#102—232no—
140C22⋊C8C2×D2312yes—
141#97C2×D2311yescharacteristic, complemented
142C4×C8C2×D2311yescharacteristic, complemented
143C23#312211yescharacteristic, complemented, Sylow
144C24—461no—
145C2×D4—232no—
146C2×D4—232no—
147C2×D4—464no—
148C2×D4—462no—
149C2×D4—461no—
150C2×D4—462no—
151C22×C4—462no—
152C22×C4—462no—
153C22×C4—462no—
154C22×C4C22×D2311yescharacteristic
155D8—464no—
156D8—464no—
157C2×C8C22×D2312yes—
158C2×C8C22×D2312yes—
159C4⋊C4—232no—
160C4⋊C4—232no—
161C4⋊C4—462no—
162C4⋊C4D9212yes—
163C22⋊C4—461no—
164C22⋊C4—462no—
165C22⋊C4—462no—
166C22⋊C4—462no—
167C22⋊C4—462no—
168C22⋊C4D9212yes—
169C42—461no—
170C42C22×D2311yescharacteristic
171C42C22×D2311yescharacteristic
172C23—464no—
173C23—462no—
174C23—462no—
175C23—1842no—
176C23C2×D9211yescharacteristic
177D4—234no—
178D4—464no—
179D4—462no—
180D4—462no—
181D4—462no—
182D4—1842no—
183D4—1842no—
184C2×C4—22no—
185C2×C4—462no—
186C2×C4—462no—
187C2×C4—1842no—
188C2×C4—1842no—
189C2×C4—1842no—
190C2×C4C2×D9211yescharacteristic
191C2×C4C2×D9212yes—
192C2×C4C2×D9212yes—
193C2×C4C23×D2311yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—464no—
199C22—922no—
200C22—922no—
201C22—922no—
202C22—922no—
203C22—922no—
204C22—1844no—
205C22C22×D9211yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—922no—
210C4—922no—
211C4#41×D2312yes—
212C2—41no—
213C2—924no—
214C2—1842no—
215C2#1309292911yescharacteristic
216C2#1309322212yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#433C2
socleC22×C23C22×D4
hypercenter#433D23
hypocenterC23#3122
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #13093022C2semidirect
2. #13092891C2semidirect
3. #13092742C2semidirect
4. #13092718C2semidirect
5. #13092613C2semidirect
6. #13092553C2semidirect
7. #13092530C2semidirect
8. C4×D184C2semidirect
9. C23×#433C2semidirect
20. #10625045C22semidirect
23. C4×D92C22semidirect
24. #10625041C22semidirect
25. C23×C4⋊C8C22semidirect
27. C23×#97C22semidirect
28. C4×C8×C23C22semidirect
31. #10625003C22semidirect
32. #10625003C22semidirect
33. #10625000C22semidirect
34. #10624999C22semidirect
112. #433D23semidirect
135. C4⋊C8C2×D23semidirect
141. #97C2×D23semidirect
142. C4×C8C2×D23semidirect
143. C23#3122semidirect

Maximal subgroups

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

subgroupindex
#130930222
#130928912
#130927422
#130927182
#130926132
#130925532
#130925302
C4×D1842
C23×#4332
#312223