Finite Group Databasebeta

← #15674537

Subgroups — #15674537

Order 2944.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10625059C211yesmaximal, characteristic
2C2×#10624998C211yesmaximal, characteristic
3C2×#10624992C211yesmaximal, characteristic
4#13092322C211yesmaximal, characteristic
5#13092179C211yesmaximal, characteristic
6#13092171C211yesmaximal, characteristic
7C23×#340C211yesmaximal, characteristic
8C22×Dic46—21no—
9C22×Dic46C2211yescharacteristic
10C22×C8×C23C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×C4⋊Dic23C2211yescharacteristic
14C2×Dic23⋊C4—21no—
15C2×C4×Dic23C2211yescharacteristic
16C22×C23⋊C8C2211yescharacteristic
17#10625059—22no—
18#10625059—22no—
19C23⋊#95—21no—
20C23⋊#95—21no—
21#10624998—22no—
22#10624992—22no—
23C22×C4×C23—21no—
24C22×C4×C23—21no—
25C22×C4×C23C2311yescharacteristic
26C22×Dic23—21no—
27C22×Dic23—21no—
28C22×Dic23D411yescharacteristic
29C22×Dic23D411yescharacteristic
30C2×Dic46—21no—
31C2×Dic46—21no—
32C2×Dic46—21no—
33C2×Dic46—21no—
34C2×Dic46—24no—
35C2×Dic46—21no—
36C2×Dic46—42no—
37C2×Dic46—42no—
38C2×Dic46Q812yescomplemented
39C2×C8×C23—21no—
40C2×C8×C23—21no—
41C2×C8×C23—21no—
42C4⋊C4×C23—21no—
43C4⋊C4×C23—21no—
44C4⋊C4×C23—21no—
45C4⋊C4×C23D412yes—
46C4⋊Dic23—21no—
47C4⋊Dic23D412yes—
48Dic23⋊C4—24no—
49C4×Dic23—21no—
50C4×Dic23—21no—
51C2×C23⋊C8—21no—
52C2×C23⋊C8—21no—
53C2×C23⋊C8—21no—
54C23×C23C2×D411yescharacteristic
55C2×C4×C23—22no—
56C2×C4×C23—41no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C2×C4×C23C2×Q811yescharacteristic
64C2×C4×C23#4111yescharacteristic
65C2×C4×C23#4111yescharacteristic
66C2×C4×C23#4111yescharacteristic
67C2×Dic23—21no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—41no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C2×Dic23SD1612yes—
78C2×Dic23Q1612yes—
79Dic46—22no—
80Dic46—22no—
81Dic46—48no—
82Dic46—41no—
83Dic46—41no—
84C8×C23—41no—
85C23⋊C8—41no—
86#2024—231nomaximal, Sylow
87C22×C23#12011yescharacteristic
88C22×C23C22⋊Q811yescharacteristic
89C22×C23#12411yescharacteristic
90C22×C23C2×SD1611yescharacteristic
91C22×C23C2×Q1611yescharacteristic
92C22×C23AGL(1,ℤ/8)11yescharacteristic
93C22×C23#13711yescharacteristic
94C4×C23—42no—
95C4×C23—81no—
96C4×C23C22⋊Q811yescharacteristic
97C4×C23C22⋊Q811yescharacteristic
98C4×C23#12411yescharacteristic
99C4×C23#12411yescharacteristic
100Dic23—22no—
101Dic23—22no—
102Dic23—42no—
103Dic23—42no—
104C2×C4⋊Q8—231no—
105C2×#103—231no—
106C2×#103—231no—
107#391—231no—
108#340—231no—
109#340D2311yescharacteristic
110#336—231no—
111C2×C23#39311yescharacteristic
112C2×C23#45011yescharacteristic
113C2×C23#45111yescharacteristic
114C2×C23#47511yescharacteristic
115C2×C23#47711yescharacteristic
116C2×C23#48711yescharacteristic
117C2×C23#48911yescharacteristic
118C22×Q8—231no—
119C22×Q8—461no—
120C22×C8—231no—
121C22×C8C2×D2311yescharacteristic
122C4⋊Q8—462no—
123C4⋊Q8—462no—
124C2×C4⋊C4—231no—
125C2×C4⋊C4—461no—
126C2×C4⋊C4C2×D2311yescharacteristic
127C2×C4⋊C4C2×D2311yescharacteristic
128C2×C42—231no—
129#103—462no—
130#103—462no—
131#95—461no—
132#95—461no—
133C23#202411yescharacteristic, complemented, Sylow
134C2×Q8—232no—
135C2×Q8—464no—
136C2×Q8—461no—
137C2×Q8—461no—
138C2×Q8—461no—
139C2×Q8—461no—
140C2×Q8—461no—
141C2×Q8—922no—
142C2×Q8—922no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—231no—
146C22×C4—231no—
147C22×C4—461no—
148C22×C4—461no—
149C22×C4C22×D2311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—461no—
154C2×C8—461no—
155C2×C8—461no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—232no—
160C4⋊C4—464no—
161C4⋊C4—461no—
162C4⋊C4D9212yes—
163C42—461no—
164C42—461no—
165C23D4×D2311yescharacteristic
166Q8—462no—
167Q8—462no—
168Q8—928no—
169Q8—921no—
170Q8—921no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—232no—
178C2×C4—232no—
179C2×C4—461no—
180C2×C4—461no—
181C2×C4—461no—
182C2×C4—461no—
183C2×C4—462no—
184C2×C4—462no—
185C2×C4—921no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4—921no—
189C2×C4C2×D9211yescharacteristic
190C2×C4#6728811yescharacteristic
191C2×C4#6728811yescharacteristic
192C2×C4D4×D2311yescharacteristic
193C2×C4#6729011yescharacteristic
194C2×C4Q8×D2311yescharacteristic
195C8—41no—
196C8—921no—
197C22#1062505311yescharacteristic
198C22#1062505611yescharacteristic
199C22#1062506711yescharacteristic
200C22#1062508211yescharacteristic
201C22SD16×D2311yescharacteristic
202C22#1062508611yescharacteristic
203C22Q16×D2311yescharacteristic
204C4—42no—
205C4—81no—
206C4—462no—
207C4—462no—
208C4—922no—
209C4—922no—
210C4#1062504611yescharacteristic
211C4#1062505611yescharacteristic
212C4#1062506711yescharacteristic
213C4#1062506811yescharacteristic
214C2#1309233011yescharacteristic
215C2#1309256911yescharacteristic
216C2#1309257411yescharacteristic
217C2#1309270111yescharacteristic
218C2#1309271111yescharacteristic
219C2#1309276611yescharacteristic
220C2#1309277511yescharacteristic
subgroupG/H
centerC23D4×D23
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#340C2
socle, prime radicalC23×C23C2×D4
hypercenter#340D23
hypocenterC23#2024
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
38. C2×Dic46Q8semidirect
133. C23#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#106250592
C2×#106249982
C2×#106249922
#130923222
#130921792
#130921712
C23×#3402
#202423