Finite Group Databasebeta

← #15686529

Subgroups — #15686529

Order 2944.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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×#10625083C211yesmaximal, characteristic, complemented
2#135×D23C211yesmaximal, characteristic, complemented
3#13092860C211yesmaximal, characteristic, complemented
4#13092857C211yesmaximal, characteristic, complemented
5#13092856C212yesmaximal, complemented
6#13092853C211yesmaximal, characteristic, complemented
7#13092851C212yesmaximal, complemented
8#13092848C212yesmaximal, complemented
9#13092846C212yesmaximal, complemented
10M32×D23C211yesmaximal, characteristic, complemented
11C23×#509C211yesmaximal, characteristic, complemented
12#41×D23—21no—
13C2×#67290—21no—
14C23×#135C2211yescharacteristic
15C2×D8×C23C2211yescharacteristic, complemented
16#10625121—21no—
17C2×#67273—21no—
18#10625090C2211yescharacteristic, complemented
19Q16×D23C2211yescharacteristic, complemented
20#10625087—21no—
21SD16×D23—21no—
22#10625083—21no—
23#10625083—21no—
24#10625083C2212yes—
25#10625083C2211yescharacteristic, complemented
26#10625083C2212yescomplemented
27D8×D23C2211yescharacteristic, complemented
28C2×Dic92C2211yescharacteristic, complemented
29#10625075C2211yescharacteristic
30C2×C8×D23C2211yescharacteristic
31C23×SD32C2212yescomplemented
32C23×D16C2212yescomplemented
33C23×M32C2211yescharacteristic, complemented
34#10625011C2212yescomplemented
35#10625009C2212yescomplemented
36#10625009C2212yescomplemented
37#10625008C2212yescomplemented
38#10624994C2211yescharacteristic, complemented
39Dic184C2212yescomplemented
40#10624982C2212yescomplemented
41#10624980C2212yescomplemented
42C16×D23C2212yescomplemented
43#41×C23—21no—
44C2×D4×C23—21no—
45C2×C22⋊D23—41no—
46C22×Dic23—41no—
47#67292—21no—
48Q8×D23—21no—
49#67290—22no—
50#67290—22no—
51#67290—21no—
52#67290—41no—
53#67290—41no—
54#67290—41no—
55D4×D23—21no—
56D4×D23—41no—
57#67288—21no—
58#67288—41no—
59C2×C4×D23—41no—
60C2×C4×D23D411yescharacteristic
61C2×Dic46—21no—
62Q16×C23C2311yescharacteristic
63SD16×C23—21no—
64D8×C23—21no—
65D8×C23C2311yescharacteristic
66D8×C23C2312yes—
67C2×C8×C23C2311yescharacteristic
68#67275—21no—
69#67274—21no—
70#67273—22no—
71#67273—22no—
72#67273—21no—
73#67272—21no—
74C2×C23⋊C8D411yescharacteristic
75Dic92—21no—
76Dic92C2311yescharacteristic
77Dic92C2312yes—
78D184C2311yescharacteristic
79#67263—21no—
80C8×D23D411yescharacteristic
81C8×D23D411yescharacteristic
82C8×D23C2311yescharacteristic
83C8×D23C2311yescharacteristic
84C16×C23C2312yes—
85C23⋊C16C2312yes—
86C23×C23—41no—
87C22×D23—41no—
88C22×D23D811yescharacteristic
89Q8×C23—21no—
90D4×C23—21no—
91D4×C23—22no—
92D4×C23—41no—
93D4×C23—41no—
94C2×C4×C23—41no—
95C2×C4×C23C2×D411yescharacteristic
96C22⋊D23—41no—
97C22⋊D23—41no—
98C22⋊D23—42no—
99C22⋊D23—42no—
100C22⋊D23—41no—
101C2×Dic23—41no—
102C2×Dic23—41no—
103C2×Dic23—42no—
104C2×Dic23—42no—
105C2×Dic23D811yescharacteristic
106D92—21no—
107D92—41no—
108C4×D23—41no—
109C4×D23—41no—
110C4×D23—41no—
111C4×D23D811yescharacteristic
112C4×D23D811yescharacteristic
113C4×D23C2×D411yescharacteristic
114C4×D23C2×D411yescharacteristic
115Dic46—21no—
116Dic46—22no—
117Dic46—41no—
118Dic46—41no—
119C8×C23C2×D411yescharacteristic
120C8×C23C2411yescharacteristic
121C23⋊C8C2×D411yescharacteristic
122C23⋊C8C2×D411yescharacteristic
123#3414—231nomaximal, Sylow
124C22×C23—42no—
125C22×C23—41no—
126C22×C23—82no—
127C22×C23C2×D811yescharacteristic
128C2×D23—41no—
129C2×D23—41no—
130C2×D23—82no—
131C2×D23C2×D811yescharacteristic
132C2×D23C2×D811yescharacteristic
133C4×C23—41no—
134C4×C23C2×D811yescharacteristic
135C4×C23C22×D411yescharacteristic
136Dic23—41no—
137Dic23—42no—
138Dic23C2×D811yescharacteristic
139Dic23C2×D811yescharacteristic
140C2×#135—231no—
141C2×#135—231no—
142#510—231no—
143#510—232no—
144#510—231no—
145#509—231no—
146#509—232no—
147#509D2311yescharacteristic, complemented
148#508—232no—
149#508—232no—
150C2×M32—231no—
151C2×C23—21no—
152C2×C23—81no—
153C2×C23—82no—
154C2×C23C22×D811yescharacteristic
155D23—21no—
156D23—21no—
157D23—81no—
158C2×#41—461no—
159C2×#41—461no—
160#135—231no—
161#135—232no—
162#135—232no—
163#135—231no—
164#135—231no—
165#135—461no—
166#135—461no—
167#135—461no—
168#135—461no—
169#135C2×D2311yescharacteristic
170C2×Q16—231no—
171C2×Q16—231no—
172C2×SD16—461no—
173C2×SD16—461no—
174C2×D8—231no—
175C2×D8C2×D2311yescharacteristic, complemented
176C22×C8—231no—
177Q32—232no—
178Q32—232no—
179SD32—232no—
180SD32—232no—
181SD32—232no—
182SD32C2×D2312yescomplemented
183D16—232no—
184D16C2×D2312yescomplemented
185M32—231no—
186M32—232no—
187M32C2×D2311yescharacteristic, complemented
188C2×C16—232no—
189C23#341411yescharacteristic, complemented, Sylow
190#41—21no—
191#41—462no—
192#41—462no—
193#41—461no—
194#41—461no—
195#41—461no—
196#41—921no—
197#41—921no—
198#41—921no—
199#41—921no—
200C2×Q8—461no—
201C2×Q8—461no—
202C2×D4—21no—
203C2×D4—461no—
204C2×D4—921no—
205C2×D4—921no—
206C22×C4—231no—
207C22×C4—921no—
208C22×C4—921no—
209Q16—231no—
210Q16—232no—
211Q16—461no—
212Q16—461no—
213Q16C22×D2311yescharacteristic
214SD16—21no—
215SD16—462no—
216SD16—462no—
217SD16—461no—
218SD16—461no—
219SD16—461no—
220D8—21no—
221D8—231no—
222D8—461no—
223D8C22×D2312yes—
224D8C22×D2311yescharacteristic
225C2×C8—231no—
226C2×C8—231no—
227C2×C8—231no—
228C2×C8—231no—
229C2×C8—231no—
230C2×C8C22×D2311yescharacteristic
231C16—232no—
232C16C22×D2312yes—
233C23—41no—
234C23—231no—
235C23—921no—
236Q8—21no—
237Q8—462no—
238Q8—461no—
239Q8—921no—
240Q8—921no—
241D4—22no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—461no—
246D4—921no—
247D4—921no—
248D4—921no—
249D4—922no—
250D4—922no—
251D4—921no—
252C2×C4—41no—
253C2×C4—231no—
254C2×C4—231no—
255C2×C4—231no—
256C2×C4—231no—
257C2×C4—231no—
258C2×C4—921no—
259C2×C4—921no—
260C2×C4—921no—
261C2×C4—922no—
262C2×C4—922no—
263C2×C4—921no—
264C2×C4—921no—
265C2×C4D4×D2311yescharacteristic
266C8—231no—
267C8—231no—
268C8D4×D2311yescharacteristic
269C8C23×D2311yescharacteristic
270C22—41no—
271C22—42no—
272C22—82no—
273C22—231no—
274C22—231no—
275C22—921no—
276C22—921no—
277C22—1842no—
278C22D8×D2311yescharacteristic
279C4—41no—
280C4—231no—
281C4—231no—
282C4—921no—
283C4—922no—
284C4D8×D2311yescharacteristic
285C4C2×D4×D2311yescharacteristic
286C2—21no—
287C2—82no—
288C2—81no—
289C2—461no—
290C2—461no—
291C2—1841no—
292C2C2×D8×D2311yescharacteristic
subgroupG/H
centerC2C2×D8×D23
commutator, cosocleC8×C23C24
FrattiniC8C23×D23
FittingC23×#509C2
socleC2×C23C22×D8
hypercenter#509D23
hypocenterC23#3414
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. C2×#10625083C2semidirect
2. #135×D23C2semidirect
3. #13092860C2semidirect
4. #13092857C2semidirect
5. #13092856C2semidirect
6. #13092853C2semidirect
7. #13092851C2semidirect
8. #13092848C2semidirect
9. #13092846C2semidirect
10. M32×D23C2semidirect
11. C23×#509C2semidirect
15. C2×D8×C23C22semidirect
18. #10625090C22semidirect
19. Q16×D23C22semidirect
25. #10625083C22semidirect
26. #10625083C22semidirect
27. D8×D23C22semidirect
28. C2×Dic92C22semidirect
31. C23×SD32C22semidirect
32. C23×D16C22semidirect
33. C23×M32C22semidirect
34. #10625011C22semidirect
35. #10625009C22semidirect
36. #10625009C22semidirect
37. #10625008C22semidirect
38. #10624994C22semidirect
39. Dic184C22semidirect
40. #10624982C22semidirect
41. #10624980C22semidirect
42. C16×D23C22semidirect
147. #509D23semidirect
175. C2×D8C2×D23semidirect
182. SD32C2×D23semidirect
184. D16C2×D23semidirect
187. M32C2×D23semidirect
189. C23#3414semidirect

Maximal subgroups

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

subgroupindex
C2×#106250832
#135×D232
#130928602
#130928572
#130928562
#130928532
#130928512
#130928482
#130928462
M32×D232
C23×#5092
#341423