Finite Group Databasebeta

← #15672415

Subgroups — #15672415

Order 2944.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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#13092975C211yesmaximal, characteristic
2#13092735C211yesmaximal, characteristic, complemented
3#13092352C211yesmaximal, characteristic, complemented
4#13092152C211yesmaximal, characteristic, complemented
5#13092151C211yesmaximal, characteristic, complemented
6#13092140C211yesmaximal, characteristic, complemented
7C23×#481C211yesmaximal, characteristic, complemented
8C2×D4×D23—21no—
9C23×#121C2211yescharacteristic
10C2×C4⋊C4×C23C2211yescharacteristic, complemented
11#10625110—21no—
12#10625108—21no—
13#10625101C2211yescharacteristic
14C2×(C2×D23)⋊C4—21no—
15C2×(C2×D23)⋊C4C2211yescharacteristic
16C2×Dic23⋊C4—21no—
17#10625065—21no—
18#10625054—21no—
19#10625053—21no—
20C23×#106—21no—
21C23×#102—21no—
22C23×C22⋊C8C2211yescharacteristic, complemented
23C23⋊#95C2211yescharacteristic, complemented
24C22⋊(C23⋊C8)C2211yescharacteristic, complemented
25#10624991—21no—
26#10624990—21no—
27C23×D23—21no—
28C23×D23D411yescharacteristic
29C2×D4×C23—21no—
30C2×D4×C23D411yescharacteristic
31C22×C4×C23—21no—
32C22×C4×C23C2311yescharacteristic
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C2×C22⋊D23—21no—
36C22×Dic23—21no—
37C22×Dic23D411yescharacteristic
38D4×D23—42no—
39D4×D23—42no—
40C2×D92—21no—
41C2×D92D411yescharacteristic
42C2×C4×D23—21no—
43C2×C8×C23—21no—
44C4⋊C4×C23—21no—
45C4⋊C4×C23—21no—
46C4⋊C4×C23D411yescharacteristic
47C22⋊C4×C23—21no—
48C22⋊Dic23—21no—
49(C2×D23)⋊C4—21no—
50(C2×D23)⋊C4—21no—
51(C2×D23)⋊C4—21no—
52(C2×D23)⋊C4—21no—
53(C2×D23)⋊C4—42no—
54C4⋊Dic23D411yescharacteristic
55Dic23⋊C4—21no—
56Dic23⋊C4—42no—
57C2×C23⋊C8—21no—
58C23×C23—21no—
59C23×C23C2×D411yescharacteristic
60C22×D23—21no—
61C22×D23—21no—
62C22×D23—21no—
63C22×D23—42no—
64C22×D23—41no—
65C22×D23—41no—
66C22×D23—81no—
67C22×D23—81no—
68C22×D23SD1612yes—
69D4×C23—41no—
70D4×C23—41no—
71D4×C23—41no—
72C2×C4×C23—21no—
73C2×C4×C23—41no—
74C2×C4×C23—41no—
75C2×C4×C23—41no—
76C2×C4×C23—41no—
77C2×C4×C23C2×D411yescharacteristic
78C2×C4×C23C2×D411yescharacteristic
79C22⋊D23—42no—
80C22⋊D23—41no—
81C22⋊D23—41no—
82C22⋊D23—81no—
83C2×Dic23—22no—
84C2×Dic23—21no—
85C2×Dic23—21no—
86C2×Dic23—41no—
87C2×Dic23—41no—
88C2×Dic23—41no—
89D92—41no—
90D92—42no—
91C4×D23—42no—
92C8×C23—41no—
93C23⋊C8—41no—
94#1613—231nomaximal, Sylow
95C22×C23—21no—
96C22×C23—21no—
97C22×C23—41no—
98C22×C23—41no—
99C22×C23—41no—
100C22×C23#12011yescharacteristic
101C22×C23C2×SD1611yescharacteristic
102C22×C23AGL(1,ℤ/8)11yescharacteristic
103C2×D23—22no—
104C2×D23—41no—
105C2×D23—41no—
106C2×D23—42no—
107C2×D23—41no—
108C2×D23—41no—
109C2×D23—41no—
110C2×D23—81no—
111C2×D23—84no—
112C4×C23—21no—
113C4×C23—21no—
114C4×C23—41no—
115C4×C23—81no—
116Dic23—42no—
117Dic23—41no—
118Dic23—41no—
119#534—231no—
120#481—231no—
121#481D2311yescharacteristic, complemented
122#399—231no—
123#327—231no—
124#327—231no—
125#323—231no—
126C2×C23—21no—
127C2×C23—21no—
128C2×C23—81no—
129C2×C23#45011yescharacteristic
130C2×C23#45311yescharacteristic
131C2×C23#45811yescharacteristic
132D23—42no—
133D23—81no—
134C22×D4—461no—
135#123—461no—
136#123—461no—
137#121—231no—
138#121—461no—
139#121C2×D2311yescharacteristic
140#120—461no—
141#120—461no—
142C2×C4⋊C4—461no—
143C2×C4⋊C4C2×D2311yescharacteristic, complemented
144C2×C22⋊C4—231no—
145C2×C22⋊C4—461no—
146#106—21no—
147#106—461no—
148#102—21no—
149#102—461no—
150C22⋊C8—231no—
151C22⋊C8C2×D2311yescharacteristic, complemented
152#95—231no—
153C23#161311yescharacteristic, complemented, Sylow
154C24—231no—
155C24—461no—
156C2×D4—21no—
157C2×D4—231no—
158C2×D4—461no—
159C2×D4—461no—
160C2×D4—461no—
161C2×D4—461no—
162C2×D4—922no—
163C2×D4—922no—
164C2×D4C22⋊D2311yescharacteristic
165C22×C4—21no—
166C22×C4—231no—
167C22×C4—461no—
168C22×C4—461no—
169C22×C4C22×D2311yescharacteristic
170C2×C8—21no—
171C2×C8—461no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—231no—
175C4⋊C4—461no—
176C4⋊C4—922no—
177C4⋊C4C22⋊D2311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—461no—
180C22⋊C4—461no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C22⋊C4—461no—
184C22⋊C4—922no—
185C23—21no—
186C23—232no—
187C23—461no—
188C23—461no—
189C23—461no—
190C23—921no—
191C23—921no—
192C23—922no—
193C23—1841no—
194C23—1841no—
195C23D4×D2311yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—921no—
200D4—922no—
201D4—922no—
202D4—921no—
203D4—921no—
204D4—1841no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—462no—
211C2×C4—461no—
212C2×C4—461no—
213C2×C4—922no—
214C2×C4—921no—
215C2×C4—921no—
216C2×C4—921no—
217C2×C4D4×D2311yescharacteristic
218C2×C4C2×C22⋊D2311yescharacteristic
219C8—41no—
220C8—921no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—462no—
227C22—922no—
228C22—921no—
229C22—921no—
230C22—921no—
231C22—921no—
232C22—921no—
233C22—1841no—
234C22—1844no—
235C22SD16×D2311yescharacteristic
236C22#1062508511yescharacteristic
237C22#1062510811yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—922no—
243C4—921no—
244C4—921no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—922no—
249C2—1841no—
250C2#1309256611yescharacteristic
251C2#1309258311yescharacteristic
252C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#481C2
socleC22×C23#120
prime radical#13092975C2
hypercenter#481D23
hypocenterC23#1613
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #13092735C2semidirect
3. #13092352C2semidirect
4. #13092152C2semidirect
5. #13092151C2semidirect
6. #13092140C2semidirect
7. C23×#481C2semidirect
10. C2×C4⋊C4×C23C22semidirect
22. C23×C22⋊C8C22semidirect
23. C23⋊#95C22semidirect
24. C22⋊(C23⋊C8)C22semidirect
121. #481D23semidirect
143. C2×C4⋊C4C2×D23semidirect
151. C22⋊C8C2×D23semidirect
153. C23#1613semidirect

Maximal subgroups

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

subgroupindex
#130929752
#130927352
#130923522
#130921522
#130921512
#130921402
C23×#4812
#161323