Finite Group Databasebeta

← #15673610

Subgroups — #15673610

Order 2944.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#13092894C211yesmaximal, characteristic
2#13092457C211yesmaximal, characteristic
3C2×#10625006C211yesmaximal, characteristic
4#13092322C211yesmaximal, characteristic
5#13092178C211yesmaximal, characteristic
6#13092176C211yesmaximal, characteristic
7C23×#428C211yesmaximal, characteristic
8C22×Dic46C2211yescharacteristic
9C2×M16×C23C2211yescharacteristic
10C23×#117C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12#10625097C2211yescharacteristic
13C2×C4×Dic23C2211yescharacteristic
14C2×#67267C2211yescharacteristic
15#10625058—21no—
16#10625058—21no—
17#10625048—22no—
18C4×Dic46—21no—
19C4×Dic46—21no—
20C23×#107—21no—
21C23×#106—21no—
22C23⋊#95—22no—
23#10625006C414yescomplemented
24#10624990—21no—
25#10624989—21no—
26C22×C4×C23—21no—
27C22×C4×C23C2311yescharacteristic
28C22×Dic23—21no—
29C22×Dic23D412yes—
30C2×Dic46—21no—
31C2×Dic46—21no—
32C2×Dic46—21no—
33C2×Dic46—21no—
34C2×Dic46C2×C412yes—
35C2×Dic46Q812yes—
36M16×C23—21no—
37M16×C23C2×C412yes—
38C2×C8×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23—21no—
41C4⋊C4×C23D411yescharacteristic
42C4⋊C4×C23D411yescharacteristic
43C22⋊C4×C23—21no—
44C42×C23—21no—
45C22⋊Dic23—21no—
46C4⋊Dic23D411yescharacteristic
47C4⋊Dic23D411yescharacteristic
48Dic23⋊C4—22no—
49Dic23⋊C4—22no—
50C4×Dic23—22no—
51C4×Dic23—22no—
52C4×Dic23—21no—
53C4×Dic23—21no—
54C4×Dic23—21no—
55#67267—21no—
56#67267C2×C412yes—
57C2×C23⋊C8—21no—
58C23×C23C2×D411yescharacteristic
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—42no—
62C2×C4×C23—41no—
63C2×C4×C23C22×C411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×Q811yescharacteristic
67C2×C4×C23#4111yescharacteristic
68C2×C4×C23#4111yescharacteristic
69C2×Dic23—22no—
70C2×Dic23—22no—
71C2×Dic23—22no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23C4⋊C414yes—
77Dic46—22no—
78Dic46—22no—
79Dic46—22no—
80Dic46—22no—
81C8×C23—22no—
82C23⋊C8—22no—
83#1857—231nomaximal, Sylow
84C22×C23—21no—
85C22×C23—21no—
86C22×C23C2×C4⋊C411yescharacteristic
87C22×C23#12011yescharacteristic
88C22×C23#12311yescharacteristic
89C4×C23—41no—
90C4×C23—41no—
91C4×C23—81no—
92C4×C23C4×D411yescharacteristic
93C4×C23C4×D411yescharacteristic
94C4×C23C22⋊Q811yescharacteristic
95C4×C23C22⋊Q811yescharacteristic
96Dic23—24no—
97Dic23—42no—
98Dic23—41no—
99Dic23—41no—
100#519—231no—
101#428—231no—
102#428D2311yescharacteristic
103C2×#101—231no—
104#391—231no—
105#339—231no—
106#339—231no—
107C2×C23—21no—
108C2×C23—21no—
109C2×C23#38511yescharacteristic
110C2×C23#45411yescharacteristic
111C2×C23#45611yescharacteristic
112C22×Q8—231no—
113C2×M16—231no—
114C2×M16C2×D2311yescharacteristic
115C4×Q8—461no—
116C4×Q8—461no—
117C4×Q8—461no—
118C4×Q8—461no—
119#117—231no—
120#117—462no—
121#117C2×D2311yescharacteristic
122C2×C4⋊C4C2×D2311yescharacteristic
123C2×C42—231no—
124#107—21no—
125#107—461no—
126#106—21no—
127#106—461no—
128#101—234no—
129#95—462no—
130C23#185711yescharacteristic, complemented, Sylow
131C2×Q8—232no—
132C2×Q8—232no—
133C2×Q8—461no—
134C2×Q8—461no—
135C2×Q8—461no—
136C2×Q8—461no—
137C22×C4—21no—
138C22×C4—232no—
139C22×C4—461no—
140C22×C4C22×D2311yescharacteristic
141M16—21no—
142M16—232no—
143M16—461no—
144M16C4×D2312yes—
145C2×C8—21no—
146C2×C8—461no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—231no—
150C4⋊C4—231no—
151C4⋊C4—462no—
152C4⋊C4—462no—
153C4⋊C4C22⋊D2311yescharacteristic
154C4⋊C4C22⋊D2311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—461no—
157C42—21no—
158C42—462no—
159C42—462no—
160C42—461no—
161C42—461no—
162C42—461no—
163C23D4×D2311yescharacteristic
164Q8—462no—
165Q8—462no—
166Q8—462no—
167Q8—462no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—234no—
173C2×C4—462no—
174C2×C4—462no—
175C2×C4—462no—
176C2×C4—461no—
177C2×C4—461no—
178C2×C4—921no—
179C2×C4—921no—
180C2×C4C2×C4×D2311yescharacteristic
181C2×C4#6728811yescharacteristic
182C2×C4D4×D2311yescharacteristic
183C2×C4Q8×D2311yescharacteristic
184C2×C4#6729211yescharacteristic
185C2×C4C2×C22⋊D2311yescharacteristic
186C8—22no—
187C8—462no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D2311yescharacteristic
191C22#1062506511yescharacteristic
192C22#1062510811yescharacteristic
193C4—41no—
194C4—41no—
195C4—81no—
196C4—464no—
197C4—922no—
198C4—921no—
199C4—921no—
200C4#1062506411yescharacteristic
201C4#1062506711yescharacteristic
202C4C4×C22⋊D2311yescharacteristic
203C4#1062511711yescharacteristic
204C2—21no—
205C2—21no—
206C2#1309228811yescharacteristic
207C2#1309258811yescharacteristic
208C2#1309259811yescharacteristic
subgroupG/H
centerC22#10625108
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#428C2
socleC22×C23#120
prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenter#428D23
hypocenterC23#1857
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
23. #10625006C4semidirect
130. C23#1857semidirect

Maximal subgroups

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

subgroupindex
#130928942
#130924572
C2×#106250062
#130923222
#130921782
#130921762
C23×#4282
#185723