Finite Group Databasebeta

← #15673608

Subgroups — #15673608

Order 2944.

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

normal subgroups only

This group has 324 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#13092891C211yesmaximal, characteristic
2#13092460C211yesmaximal, characteristic, complemented
3#13092459C211yesmaximal, characteristic, complemented
4C2×#10625005C211yesmaximal, characteristic
5#13092319C211yesmaximal, characteristic
6#13092177C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C22×D92C2211yescharacteristic
9C2×M16×C23C2211yescharacteristic
10C23×#117C2211yescharacteristic
11C2×C42×C23C2211yescharacteristic
12C2×(C2×D23)⋊C4—22no—
13#10625097C2211yescharacteristic
14C2×C4⋊Dic23C2211yescharacteristic
15C2×#67267C2211yescharacteristic
16#10625064—21no—
17#10625064—21no—
18C22⋊C4×D23—22no—
19C4×D92—21no—
20C4×D92—21no—
21#10625005C414yescomplemented
22#10625000—21no—
23#10624999—21no—
24#10624990—21no—
25#10624989—21no—
26C23×D23D412yes—
27C22×C4×C23—21no—
28C22×C4×C23C2311yescharacteristic
29C22×Dic23—21no—
30C2×D92—21no—
31C2×D92—21no—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92C2×C412yes—
35C2×D92Q812yes—
36C2×C4×D23—22no—
37C2×C4×D23—22no—
38M16×C23—21no—
39M16×C23C2×C412yescomplemented
40C2×C8×C23—21no—
41C4⋊C4×C23D411yescharacteristic
42C4⋊C4×C23D411yescharacteristic
43C22⋊C4×C23—21no—
44C42×C23—21no—
45C42×C23—21no—
46C42×C23—21no—
47C22⋊Dic23—21no—
48(C2×D23)⋊C4—22no—
49(C2×D23)⋊C4—22no—
50(C2×D23)⋊C4—44no—
51C4⋊Dic23—21no—
52C4⋊Dic23—21no—
53C4⋊Dic23D411yescharacteristic
54C4⋊Dic23D411yescharacteristic
55C4×Dic23—21no—
56#67267—21no—
57#67267C2×C412yescomplemented
58C2×C23⋊C8—21no—
59C23×C23C2×D411yescharacteristic
60C22×D23—22no—
61C22×D23—22no—
62C22×D23—42no—
63C22×D23—42no—
64C22×D23C4⋊C414yes—
65C2×C4×C23—22no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23C22×C411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×Q811yescharacteristic
74C2×C4×C23#4111yescharacteristic
75C2×C4×C23#4111yescharacteristic
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—42no—
79C2×Dic23—41no—
80D92—22no—
81D92—22no—
82D92—22no—
83D92—22no—
84C4×D23—82no—
85C4×D23—82no—
86C8×C23—22no—
87C23⋊C8—22no—
88#1856—231nomaximal, Sylow
89C22×C23—21no—
90C22×C23—21no—
91C22×C23C2×C4⋊C411yescharacteristic
92C22×C23#12011yescharacteristic
93C22×C23#12311yescharacteristic
94C2×D23—24no—
95C2×D23—42no—
96C2×D23—42no—
97C2×D23—44no—
98C2×D23—82no—
99C4×C23—42no—
100C4×C23—41no—
101C4×C23—41no—
102C4×C23C4×D411yescharacteristic
103C4×C23C4×D411yescharacteristic
104C4×C23C22⋊Q811yescharacteristic
105C4×C23C22⋊Q811yescharacteristic
106Dic23—41no—
107Dic23—41no—
108Dic23—81no—
109#518—231no—
110#428—231no—
111#428—231no—
112C2×#100—231no—
113#390—231no—
114#339—231no—
115#339D2311yescharacteristic, complemented
116C2×C23—21no—
117C2×C23—21no—
118C2×C23#38511yescharacteristic
119C2×C23#45311yescharacteristic
120C2×C23#45511yescharacteristic
121D23—44no—
122C22×D4—231no—
123C2×M16—231no—
124C2×M16C2×D2311yescharacteristic
125C4×D4—461no—
126C4×D4—461no—
127C4×D4—461no—
128C4×D4—461no—
129#117—231no—
130#117C2×D2311yescharacteristic
131C2×C4⋊C4—231no—
132C2×C22⋊C4—462no—
133C2×C22⋊C4—462no—
134C2×C42C2×D2311yescharacteristic
135#107—461no—
136#107—461no—
137#106—461no—
138#106—461no—
139#100—234no—
140C23#185611yescharacteristic, complemented, Sylow
141C24—232no—
142C2×D4—232no—
143C2×D4—232no—
144C2×D4—461no—
145C2×D4—461no—
146C2×D4—461no—
147C2×D4—461no—
148C22×C4—21no—
149C22×C4—462no—
150C22×C4—462no—
151C22×C4—461no—
152C22×C4C22×D2311yescharacteristic
153M16—21no—
154M16—232no—
155M16—461no—
156M16C4×D2312yescomplemented
157C2×C8—21no—
158C2×C8—461no—
159C4⋊C4—231no—
160C4⋊C4—231no—
161C4⋊C4—461no—
162C4⋊C4—461no—
163C4⋊C4D9211yescharacteristic
164C4⋊C4D9211yescharacteristic
165C22⋊C4—21no—
166C22⋊C4—462no—
167C22⋊C4—462no—
168C22⋊C4—461no—
169C22⋊C4—924no—
170C42—21no—
171C42—21no—
172C42—21no—
173C42—461no—
174C23—234no—
175C23—462no—
176C23—462no—
177C23—922no—
178C23—922no—
179C23D4×D2311yescharacteristic
180D4—462no—
181D4—462no—
182D4—462no—
183D4—462no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—461no—
190C2×C4—461no—
191C2×C4—922no—
192C2×C4—921no—
193C2×C4—1842no—
194C2×C4—1842no—
195C2×C4C2×C4×D2311yescharacteristic
196C2×C4C2×D9211yescharacteristic
197C2×C4#6728811yescharacteristic
198C2×C4D4×D2311yescharacteristic
199C2×C4#6729011yescharacteristic
200C2×C4Q8×D2311yescharacteristic
201C8—22no—
202C8—462no—
203C22—21no—
204C22—21no—
205C22—464no—
206C22—924no—
207C22—922no—
208C22—922no—
209C22—1842no—
210C22#1062505311yescharacteristic
211C22#1062505411yescharacteristic
212C22C4⋊C4×D2311yescharacteristic
213C4—42no—
214C4—41no—
215C4—41no—
216C4—921no—
217C4—921no—
218C4—1841no—
219C4C4×D9211yescharacteristic
220C4(C22⋊D23)⋊C411yescharacteristic
221C4#1062506711yescharacteristic
222C4#1062506811yescharacteristic
223C2—21no—
224C2—21no—
225C2—924no—
226C2#1309229111yescharacteristic
227C2#1309258611yescharacteristic
228C2#1309259611yescharacteristic
subgroupG/H
centerC22#10625053
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23#120
prime radicalC22×D92C22
cosocleC22×C4×C23C23
hypercenter#339D23
hypocenterC23#1856
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #13092460C2semidirect
3. #13092459C2semidirect
6. #13092177C2semidirect
7. C23×#339C2semidirect
21. #10625005C4semidirect
39. M16×C23C2×C4semidirect
57. #67267C2×C4semidirect
115. #339D23semidirect
140. C23#1856semidirect
156. M16C4×D23semidirect

Maximal subgroups

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

subgroupindex
#130928912
#130924602
#130924592
C2×#106250052
#130923192
#130921772
C23×#3392
#185623