Finite Group Databasebeta

← #15675046

Subgroups — #15675046

Order 2944.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092981C211yesmaximal, characteristic
2#13092401C211yesmaximal, characteristic, complemented
3#13092203C214yesmaximal, complemented
4C23×#410C211yesmaximal, characteristic, complemented
5C2×#41×C23C2211yescharacteristic
6C22×D92C411yescharacteristic, complemented
7C23×#117—21no—
8#10625118—21no—
9#10625111—21no—
10#10625108C412yescomplemented
11#10625108C2212yes—
12#10625101—21no—
13#10625101—21no—
14#10625097C411yescharacteristic, complemented
15C2×#67267—21no—
16C23×#99—21no—
17C23×#99C2212yes—
18#10625018—21no—
19#10625015C2212yes—
20C23×D23C2×C412yes—
21#41×C23—41no—
22#41×C23—41no—
23C2×Q8×C23D411yescharacteristic
24C2×D4×C23C2×C411yescharacteristic
25C2×D4×C23D411yescharacteristic
26C2×D4×C23C2311yescharacteristic
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C2×C22⋊D23—22no—
31C2×C22⋊D23—22no—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92—41no—
35C2×D92—41no—
36C4⋊C4×C23—41no—
37C22⋊C4×C23—22no—
38C42×C23—41no—
39C22⋊Dic23C2×C412yes—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—22no—
42C4⋊Dic23—21no—
43C4×Dic23—21no—
44#67267—22no—
45#67267—41no—
46C2×C23⋊C8—41no—
47C23×C23C22⋊C411yescharacteristic
48C23×C23C22×C411yescharacteristic
49C23×C23C2×D411yescharacteristic
50C22×D23—22no—
51C22×D23—42no—
52C22×D23—82no—
53Q8×C23—41no—
54D4×C23—41no—
55D4×C23—41no—
56D4×C23—41no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—42no—
64C2×C4×C23C22⋊C411yescharacteristic
65C2×C4×C23C22⋊C411yescharacteristic
66C2×C4×C23C22⋊C411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C22⋊D23—82no—
69C22⋊D23—82no—
70C2×Dic23—22no—
71D92—42no—
72D92—41no—
73D92—41no—
74C23⋊C8—42no—
75#2122—231nomaximal, Sylow
76C22×C23—21no—
77C22×C23—21no—
78C22×C23—21no—
79C22×C23—41no—
80C22×C23—41no—
81C22×C23—41no—
82C22×C23C2×C22⋊C411yescharacteristic
83C2×D23—42no—
84C2×D23—42no—
85C2×D23—42no—
86C2×D23—84no—
87C4×C23—21no—
88C4×C23—21no—
89C4×C23—21no—
90C4×C23—82no—
91C4×C23#9911yescharacteristic
92C4×C23#9911yescharacteristic
93Dic23—42no—
94#535—231no—
95#413—231no—
96#410D2311yescharacteristic, complemented
97AΣL(1,𝔽16)—234no—
98C2×C23—21no—
99C2×C23—41no—
100C2×C23—41no—
101C2×C23—41no—
102C2×C23C2×#9911yescharacteristic
103D23—82no—
104C2×#41C2×D2311yescharacteristic
105C22×D4—231no—
106C2×M16—461no—
107#127—461no—
108#124—461no—
109#121—461no—
110#121—461no—
111#120—232no—
112#120—232no—
113#117—21no—
114#117—231no—
115#101—461no—
116#100—232no—
117#99—21no—
118#99C2×D2312yes—
119C23#212211yescharacteristic, complemented, Sylow
120C24—232no—
121#41—41no—
122#41—41no—
123C2×Q8D9211yescharacteristic
124C2×D4—462no—
125C2×D4—462no—
126C2×D4—461no—
127C2×D4—461no—
128C2×D4—921no—
129C2×D4—921no—
130C2×D4C4×D2311yescharacteristic
131C2×D4C22⋊D2311yescharacteristic
132C2×D4C22×D2311yescharacteristic
133C22×C4C4×D2311yescharacteristic
134C22×C4D9211yescharacteristic
135C22×C4C22⋊D2311yescharacteristic
136M16—462no—
137M16—921no—
138C2×C8—921no—
139C4⋊C4—41no—
140C4⋊C4—461no—
141C22⋊C4—22no—
142C22⋊C4—232no—
143C22⋊C4—462no—
144C22⋊C4—462no—
145C42—41no—
146C42—461no—
147C23—462no—
148C23—922no—
149C23—1842no—
150C23(C2×D23)⋊C411yescharacteristic
151C23C2×C4×D2311yescharacteristic
152C23C2×C22⋊D2311yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—922no—
158D4—921no—
159D4—921no—
160D4—1842no—
161D4—1842no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—462no—
170C2×C4(C2×D23)⋊C411yescharacteristic
171C2×C4(C2×D23)⋊C411yescharacteristic
172C2×C4(C2×D23)⋊C411yescharacteristic
173C2×C4C2×D9211yescharacteristic
174C8—922no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—922no—
182C22—922no—
183C22—922no—
184C22—1844no—
185C22C2×(C2×D23)⋊C411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—82no—
190C4—922no—
191C4#1062498811yescharacteristic
192C4#1062498811yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—1842no—
198C2C2×#1062498811yescharacteristic
subgroupG/H
centerC2C2×#10624988
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#410C2
socleC2×C23C2×#99
prime radical#13092981C2
cosocleC2×D4×C23C23
hypercenter#410D23
hypocenterC23#2122
LCSG ▷ C23×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #13092401C2semidirect
3. #13092203C2semidirect
4. C23×#410C2semidirect
6. C22×D92C4semidirect
10. #10625108C4semidirect
14. #10625097C4semidirect
96. #410D23semidirect
119. C23#2122semidirect

Maximal subgroups

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

subgroupindex
#130929812
#130924012
#130922032
C23×#4102
#212223