Finite Group Databasebeta

← #15673697

Subgroups — #15673697

Order 2944.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#67267C211yesmaximal, characteristic, complemented
2#13092928C211yesmaximal, characteristic
3C2×#10624987C212yesmaximal, complemented
4#13092177C212yesmaximal, complemented
5C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C2×#67288C2211yescharacteristic
8C2×C22⋊C4×C23—21no—
9C2×C42×C23C2212yes—
10#10625124—21no—
11#10625101C411yescharacteristic, complemented
12#10625101C411yescharacteristic, complemented
13#10625100—21no—
14C4×C22⋊D23—21no—
15C4×C22⋊D23—21no—
16#10625097C2211yescharacteristic
17#10625095C411yescharacteristic, complemented
18#10625095C411yescharacteristic, complemented
19C2×#67267—21no—
20C2×#67267—24no—
21C2×#67267C2212yes—
22C22×C23⋊C8—21no—
23C23×#95—21no—
24#10624987—24no—
25C24×C23D411yescharacteristic
26C22×C4×C23—22no—
27C22×C4×C23—22no—
28C22×C4×C23—22no—
29C22×C4×C23C2×C411yescharacteristic
30C22×C4×C23C2×C411yescharacteristic
31C22×C4×C23D411yescharacteristic
32C22×C4×C23D411yescharacteristic
33C22×C4×C23D411yescharacteristic
34C22×C4×C23C2311yescharacteristic
35C2×C22⋊D23—21no—
36C2×C22⋊D23—21no—
37C2×C22⋊D23—21no—
38#67288—22no—
39#67288—22no—
40C2×D92C2×C411yescharacteristic
41C2×C4×D23—21no—
42C2×Dic46C2×C411yescharacteristic
43C22⋊C4×C23—24no—
44C42×C23—22no—
45C42×C23—22no—
46C22⋊Dic23—21no—
47C22⋊Dic23—21no—
48C22⋊Dic23—21no—
49(C2×D23)⋊C4—21no—
50(C2×D23)⋊C4—21no—
51C4⋊Dic23C2×C411yescharacteristic
52C4⋊Dic23C2×C411yescharacteristic
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55C4×Dic23—21no—
56#67267—24no—
57#67267—22no—
58#67267D414yescomplemented
59C2×C23⋊C8—24no—
60C2×C23⋊C8—22no—
61C23×C23—22no—
62C23×C23—22no—
63C23×C23—41no—
64C23×C23C22⋊C411yescharacteristic
65C23×C23C22⋊C411yescharacteristic
66C23×C23C2×D411yescharacteristic
67C22×D23—21no—
68C2×C4×C23—22no—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23—21no—
72C2×C4×C23—21no—
73C2×C4×C23—21no—
74C2×C4×C23—21no—
75C2×C4×C23—24no—
76C2×C4×C23—42no—
77C2×C4×C23—42no—
78C2×C4×C23C22⋊C411yescharacteristic
79C2×C4×C23C22⋊C411yescharacteristic
80C2×C4×C23C22×C411yescharacteristic
81C2×C4×C23C2×D411yescharacteristic
82C2×C4×C23C2×D412yes—
83C2×C4×C23#4112yes—
84C22⋊D23—42no—
85C22⋊D23—42no—
86C22⋊D23—42no—
87C2×Dic23—21no—
88C2×Dic23—21no—
89C2×Dic23—21no—
90D92—22no—
91C4×D23—41no—
92C4×D23—41no—
93Dic46—22no—
94C23⋊C8—24no—
95#1871—231nomaximal, Sylow
96C22×C23—21no—
97C22×C23—21no—
98C22×C23—21no—
99C22×C23—21no—
100C22×C23—21no—
101C22×C23—21no—
102C22×C23—21no—
103C22×C23—44no—
104C22×C23#10412yescomplemented
105C22×C23C2×C22⋊C411yescharacteristic
106C22×C23#12112yes—
107C2×D23—41no—
108C2×D23—41no—
109C2×D23—41no—
110C4×C23—21no—
111C4×C23—21no—
112C4×C23—44no—
113C4×C23C4×D412yes—
114C4×C23#12011yescharacteristic
115C4×C23#12311yescharacteristic
116Dic23—41no—
117Dic23—41no—
118Dic23—41no—
119C22×M16—231no—
120#525—231no—
121C2×#104—232no—
122C4×C22⋊C4D2311yescharacteristic, complemented
123#339—232no—
124C2×C23—22no—
125C2×C23—22no—
126C2×C23—41no—
127C2×C23#38611yescharacteristic
128C2×C23C2×#10411yescharacteristic
129C2×C23#42111yescharacteristic
130D23—81no—
131C2×#41—231no—
132C23×C4C2×D2311yescharacteristic
133C2×M16—232no—
134C2×M16—464no—
135C2×M16—461no—
136C22×C8—461no—
137#123—461no—
138C22⋊Q8—231no—
139C22⋊Q8—231no—
140#121—231no—
141#121—231no—
142#120—461no—
143C4×D4—461no—
144C4×D4—461no—
145#117—231no—
146C2×C22⋊C4—21no—
147C2×C42C2×D2312yes—
148#104—464no—
149#95—21no—
150C23#187111yescharacteristic, complemented, Sylow
151C24C22⋊D2311yescharacteristic
152#41—462no—
153#41—462no—
154C2×Q8—231no—
155C2×D4—231no—
156C2×D4—461no—
157C2×D4—461no—
158C2×D4—461no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—461no—
163C22×C4C4×D2311yescharacteristic
164C22×C4C4×D2311yescharacteristic
165C22×C4D9211yescharacteristic
166C22×C4D9211yescharacteristic
167C22×C4C22⋊D2311yescharacteristic
168C22×C4C22×D2311yescharacteristic
169M16—234no—
170M16—464no—
171M16—462no—
172C2×C8—464no—
173C2×C8—462no—
174C4⋊C4—231no—
175C4⋊C4—231no—
176C4⋊C4—461no—
177C4⋊C4—461no—
178C22⋊C4—24no—
179C22⋊C4—461no—
180C22⋊C4—461no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C22⋊C4—461no—
184C42—22no—
185C42—22no—
186C42—461no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—461no—
191C23(C2×D23)⋊C411yescharacteristic
192C23(C2×D23)⋊C411yescharacteristic
193C23C2×C22⋊D2311yescharacteristic
194Q8—462no—
195D4—462no—
196D4—922no—
197D4—922no—
198D4—922no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—461no—
210C2×C4—461no—
211C2×C4—461no—
212C2×C4—921no—
213C2×C4—921no—
214C2×C4(C2×D23)⋊C411yescharacteristic
215C2×C4(C2×D23)⋊C411yescharacteristic
216C2×C4C2×C4×D2311yescharacteristic
217C2×C4C2×D9211yescharacteristic
218C2×C4D4×D2312yes—
219C2×C4#6729012yes—
220C8—464no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—921no—
230C22—921no—
231C22—921no—
232C22#1062498712yescomplemented
233C22C2×(C2×D23)⋊C411yescharacteristic
234C22#1062511012yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—921no—
239C4—921no—
240C4—921no—
241C4(C22⋊D23)⋊C412yes—
242C4#1062505311yescharacteristic
243C4#1062505711yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—1841no—
248C2#1309229411yescharacteristic
249C2C2×#1062498711yescharacteristic
250C2#1309243511yescharacteristic
subgroupG/H
centerC2×C4C2×D92
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC4×C22⋊C4×C23C2
socleC22×C23C2×C22⋊C4
prime radical#13092928C2
cosocleC22×C4×C23C23
hypercenterC4×C22⋊C4D23
hypocenterC23#1871
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#67267C2semidirect
3. C2×#10624987C2semidirect
4. #13092177C2semidirect
5. C4×C22⋊C4×C23C2semidirect
11. #10625101C4semidirect
12. #10625101C4semidirect
17. #10625095C4semidirect
18. #10625095C4semidirect
58. #67267D4semidirect
104. C22×C23#104semidirect
122. C4×C22⋊C4D23semidirect
150. C23#1871semidirect
232. C22#10624987semidirect

Maximal subgroups

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

subgroupindex
C22×#672672
#130929282
C2×#106249872
#130921772
C4×C22⋊C4×C232
#187123