Finite Group Databasebeta

← #15682644

Subgroups — #15682644

Order 2944.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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×#67290C211yesmaximal, characteristic, complemented
2C2×#10625082C212yesmaximal, complemented
3#121×D23C211yesmaximal, characteristic, complemented
4#13092563C212yesmaximal, complemented
5#13092559C212yesmaximal, complemented
6#13092558C211yesmaximal, characteristic, complemented
7#13092555C211yesmaximal, characteristic, complemented
8#13092551C211yesmaximal, characteristic, complemented
9#13092415C212yesmaximal, complemented
10#13092379C211yesmaximal, characteristic, complemented
11C23×#447C211yesmaximal, characteristic, complemented
12C22×D4×C23C2211yescharacteristic, complemented
13C22×C22⋊D23—21no—
14C23×Dic23—21no—
15C2×#67290—28no—
16C2×#67290—21no—
17C2×#67290—21no—
18C2×#67290C2212yes—
19C2×#67290C2212yescomplemented
20C2×D4×D23—21no—
21C2×D4×D23C2211yescharacteristic, complemented
22C22×C4×D23C2211yescharacteristic
23C22×Dic46C2211yescharacteristic, complemented
24C2×D8×C23C2212yescomplemented
25C23×#121C2211yescharacteristic
26#10625110—21no—
27#10625109C2211yescharacteristic, complemented
28C2×#67273C2212yescomplemented
29C2×#67272C2212yescomplemented
30#10625101C2211yescharacteristic
31#10625082—28no—
32C2×#67263C2212yescomplemented
33C2×#67262C2212yescomplemented
34#10625066C2211yescharacteristic, complemented
35C4⋊C4×D23C2211yescharacteristic, complemented
36#10625055—21no—
37C22⋊C4×D23—21no—
38C23×#102C2212yescomplemented
39C23×C22⋊C8C2211yescharacteristic, complemented
40#10625014C2212yescomplemented
41C22⋊(C23⋊C8)C2211yescharacteristic, complemented
42(C2×D23)⋊C8C2212yescomplemented
43#10624998C2212yescomplemented
44#10624992C2212yescomplemented
45C24×C23—21no—
46C23×D23—21no—
47C23×D23D411yescharacteristic
48C2×D4×C23—24no—
49C2×D4×C23—21no—
50C2×D4×C23—21no—
51C2×D4×C23C2311yescharacteristic
52C2×D4×C23C2312yes—
53C22×C4×C23C2311yescharacteristic
54C2×C22⋊D23—28no—
55C2×C22⋊D23—22no—
56C2×C22⋊D23—22no—
57C2×C22⋊D23—21no—
58C2×C22⋊D23—21no—
59C2×C22⋊D23—21no—
60C22×Dic23—28no—
61C22×Dic23—21no—
62C22×Dic23—22no—
63C22×Dic23—22no—
64C22×Dic23D411yescharacteristic
65#67290—28no—
66#67290—28no—
67#67290—24no—
68#67290—24no—
69#67290—24no—
70#67290D418yescomplemented
71D4×D23—24no—
72D4×D23—44no—
73C2×D92—21no—
74C2×D92C2311yescharacteristic
75C2×C4×D23—24no—
76C2×C4×D23—21no—
77C2×C4×D23D411yescharacteristic
78C2×C4×D23D411yescharacteristic
79C2×C4×D23C2311yescharacteristic
80C2×C4×D23C2311yescharacteristic
81C2×Dic46—21no—
82C2×Dic46—24no—
83C2×Dic46C2312yes—
84D8×C23—24no—
85C2×C8×C23C2312yes—
86C4⋊C4×C23C2311yescharacteristic
87C22⋊C4×C23—21no—
88C22⋊Dic23—21no—
89#67273—24no—
90#67272—24no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93C4⋊Dic23C2311yescharacteristic
94Dic23⋊C4—21no—
95C2×C23⋊C8C2312yes—
96#67263—24no—
97#67262—24no—
98C23×C23—24no—
99C23×C23—22no—
100C23×C23—21no—
101C23×C23—42no—
102C23×C23—42no—
103C23×C23C2×D411yescharacteristic
104C22×D23—22no—
105C22×D23—22no—
106C22×D23—21no—
107C22×D23—41no—
108C22×D23—42no—
109C22×D23—42no—
110C22×D23—42no—
111C22×D23C2×D411yescharacteristic
112C22×D23C2×D411yescharacteristic
113D4×C23—24no—
114D4×C23—22no—
115D4×C23—22no—
116D4×C23—42no—
117D4×C23C2×D414yescomplemented
118C2×C4×C23—22no—
119C2×C4×C23—21no—
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2411yescharacteristic
122C22⋊D23—28no—
123C22⋊D23—28no—
124C22⋊D23—42no—
125C22⋊D23—42no—
126C22⋊D23—42no—
127C2×Dic23—24no—
128C2×Dic23—28no—
129C2×Dic23—22no—
130C2×Dic23—22no—
131C2×Dic23—28no—
132C2×Dic23—21no—
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135D92—22no—
136D92—42no—
137C4×D23—22no—
138C4×D23—22no—
139C4×D23—22no—
140C4×D23—42no—
141C4×D23C2×D414yes—
142Dic46—24no—
143Dic46—22no—
144Dic46C2×D414yescomplemented
145C8×C23—22no—
146C23⋊C8—22no—
147#3006—231nomaximal, Sylow
148C22×C23—21no—
149C22×C23—21no—
150C22×C23—24no—
151C22×C23—48no—
152C22×C23—42no—
153C22×C23—42no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23AGL(1,ℤ/8)12yescomplemented
158C22×C23C22×D411yescharacteristic
159C2×D23—21no—
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—21no—
163C2×D23—21no—
164C2×D23—44no—
165C2×D23—41no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—84no—
169C2×D23#12012yes—
170C4×C23—21no—
171C4×C23—41no—
172C4×C23C22×D412yes—
173Dic23—24no—
174Dic23—21no—
175Dic23—41no—
176Dic23#12012yes—
177C22×#41—231no—
178C2×AGL(1,ℤ/8)—232no—
179C2×#121—231no—
180#449—232no—
181#449—232no—
182#448—231no—
183#448—231no—
184#447—231no—
185#447D2311yescharacteristic, complemented
186#417—232no—
187#407—231no—
188C2×C23—22no—
189C2×C23—44no—
190C2×C23—81no—
191C2×C23C2×#12011yescharacteristic
192C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C23#57511yescharacteristic
194D23—22no—
195D23—41no—
196D23—81no—
197C2×#41—232no—
198C2×#41—232no—
199C2×#41—461no—
200C2×#41—461no—
201C2×#41—468no—
202C22×Q8—231no—
203C22×D4—231no—
204C22×D4—461no—
205C22×D4—461no—
206C22×D4C2×D2311yescharacteristic, complemented
207C23×C4—231no—
208C23×C4—461no—
209AGL(1,ℤ/8)—468no—
210C2×SD16—232no—
211C2×SD16—232no—
212C2×D8—232no—
213C2×D8C2×D2312yescomplemented
214C2×M16—232no—
215#121—231no—
216#121—231no—
217#121—231no—
218#121—461no—
219#121—461no—
220#121C2×D2311yescharacteristic
221C2×C4⋊C4—231no—
222C2×C22⋊C4—461no—
223#103—232no—
224#103—232no—
225#102—232no—
226#102C2×D2312yescomplemented
227C22⋊C8—231no—
228C22⋊C8—232no—
229C22⋊C8C2×D2311yescharacteristic, complemented
230C23#300611yescharacteristic, complemented, Sylow
231C24—21no—
232C24—231no—
233C24—461no—
234#41—238no—
235#41—464no—
236#41—464no—
237#41—468no—
238#41—468no—
239#41—464no—
240C2×Q8—232no—
241C2×Q8—464no—
242C2×Q8—461no—
243C2×D4—24no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—231no—
247C2×D4—461no—
248C2×D4—464no—
249C2×D4—461no—
250C2×D4—462no—
251C2×D4—462no—
252C2×D4—468no—
253C2×D4—461no—
254C2×D4—461no—
255C2×D4—924no—
256C2×D4C22×D2311yescharacteristic
257C2×D4C22×D2312yes—
258C22×C4—231no—
259C22×C4—231no—
260C22×C4—231no—
261C22×C4—231no—
262C22×C4—231no—
263C22×C4—464no—
264C22×C4—461no—
265C22×C4—462no—
266C22×C4—462no—
267C22×C4—468no—
268C22×C4—461no—
269C22×C4C22×D2311yescharacteristic
270SD16—464no—
271SD16—464no—
272D8—24no—
273D8—464no—
274M16—464no—
275C2×C8—232no—
276C2×C8C22×D2312yes—
277C4⋊C4—231no—
278C4⋊C4—461no—
279C4⋊C4C22×D2311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C23—24no—
285C23—22no—
286C23—21no—
287C23—42no—
288C23—42no—
289C23—231no—
290C23—231no—
291C23—462no—
292C23—462no—
293C23—461no—
294C23—921no—
295C23—922no—
296C23—922no—
297C23—922no—
298C23D4×D2311yescharacteristic
299Q8—234no—
300Q8—464no—
301Q8—462no—
302D4—24no—
303D4—22no—
304D4—22no—
305D4—42no—
306D4—468no—
307D4—468no—
308D4—462no—
309D4—922no—
310D4—922no—
311D4—922no—
312D4—922no—
313D4D4×D2314yescomplemented
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—231no—
317C2×C4—234no—
318C2×C4—231no—
319C2×C4—462no—
320C2×C4—462no—
321C2×C4—462no—
322C2×C4—468no—
323C2×C4—464no—
324C2×C4—468no—
325C2×C4—462no—
326C2×C4—462no—
327C2×C4—461no—
328C2×C4—922no—
329C2×C4D4×D2311yescharacteristic
330C2×C4C23×D2311yescharacteristic
331C8—22no—
332C8—462no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—48no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—232no—
343C22—461no—
344C22—461no—
345C22—461no—
346C22—461no—
347C22—461no—
348C22—924no—
349C22—921no—
350C22—921no—
351C22—921no—
352C22—1844no—
353C22#1062508212yescomplemented
354C22C2×D4×D2311yescharacteristic
355C4—21no—
356C4—41no—
357C4—232no—
358C4—461no—
359C4—464no—
360C4—921no—
361C4C2×D4×D2312yes—
362C2—22no—
363C2—44no—
364C2—81no—
365C2—462no—
366C2—921no—
367C2—1841no—
368C2#120×D2311yescharacteristic
369C2C2×#1062508211yescharacteristic
370C2#1309321311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3006
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×#67290C2semidirect
2. C2×#10625082C2semidirect
3. #121×D23C2semidirect
4. #13092563C2semidirect
5. #13092559C2semidirect
6. #13092558C2semidirect
7. #13092555C2semidirect
8. #13092551C2semidirect
9. #13092415C2semidirect
10. #13092379C2semidirect
11. C23×#447C2semidirect
12. C22×D4×C23C22semidirect
19. C2×#67290C22semidirect
21. C2×D4×D23C22semidirect
23. C22×Dic46C22semidirect
24. C2×D8×C23C22semidirect
27. #10625109C22semidirect
28. C2×#67273C22semidirect
29. C2×#67272C22semidirect
32. C2×#67263C22semidirect
33. C2×#67262C22semidirect
34. #10625066C22semidirect
35. C4⋊C4×D23C22semidirect
38. C23×#102C22semidirect
39. C23×C22⋊C8C22semidirect
40. #10625014C22semidirect
41. C22⋊(C23⋊C8)C22semidirect
42. (C2×D23)⋊C8C22semidirect
43. #10624998C22semidirect
44. #10624992C22semidirect
70. #67290D4semidirect
117. D4×C23C2×D4semidirect
144. Dic46C2×D4semidirect
157. C22×C23AGL(1,ℤ/8)semidirect
185. #447D23semidirect
206. C22×D4C2×D23semidirect
213. C2×D8C2×D23semidirect
226. #102C2×D23semidirect
229. C22⋊C8C2×D23semidirect
230. C23#3006semidirect
313. D4D4×D23semidirect
353. C22#10625082semidirect

Maximal subgroups

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

subgroupindex
C22×#672902
C2×#106250822
#121×D232
#130925632
#130925592
#130925582
#130925552
#130925512
#130924152
#130923792
C23×#4472
#300623