Finite Group Databasebeta

← #15686788

Subgroups — #15686788

Order 2944.

1040 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093040C212yesmaximal, complemented
2#13093039C212yesmaximal, complemented
3#13093028C211yesmaximal, characteristic, complemented
4#13093023C211yesmaximal, characteristic, complemented
5#13093022C211yesmaximal, characteristic, complemented
6#13093015C214yesmaximal, complemented
7#13093006C214yesmaximal, complemented
8#13092973C211yesmaximal, characteristic, complemented
9#13092968C211yesmaximal, characteristic, complemented
10#13092952C214yesmaximal, complemented
11#13092950C214yesmaximal, complemented
12#13092930C212yesmaximal, complemented
13C4×#67292C212yesmaximal, complemented
14#117×D23C211yesmaximal, characteristic, complemented
15C23×#541C211yesmaximal, characteristic, complemented
16C2×#67292C2212yes—
17C22×C4×D23C2211yescharacteristic
18C23×C4⋊Q8C2211yescharacteristic, complemented
19C23×#126C2214yes—
20C23×#125C2214yescomplemented
21C23×#125C2211yescharacteristic, complemented
22C23×C22⋊Q8C2212yes—
23C4×Q8×C23C2212yescomplemented
24C23×#117C2211yescharacteristic
25#10625118C2212yescomplemented
26#10625117C2212yes—
27Q8×Dic23C2212yescomplemented
28#10625101C2212yes—
29#10625097C2211yescharacteristic
30#10625069C2214yes—
31#10625069C2214yescomplemented
32#10625068C2214yescomplemented
33#10625067C2214yes—
34#10625067C2214yescomplemented
35#10625066C2212yes—
36#10625066C2214yes—
37#10625066C2214yes—
38#10625065C2214yes—
39#10625065C2214yes—
40#10625065C2214yescomplemented
41#10625065C2214yescomplemented
42#10625064C2214yes—
43#10625064C2214yes—
44#10625064C2212yescomplemented
45#10625064C2214yescomplemented
46#10625063C2212yes—
47#10625063C2212yes—
48#10625063C2214yescomplemented
49C4⋊C4×D23C2212yes—
50#10625060C2214yescomplemented
51#10625059C2212yescomplemented
52#10625058C2214yescomplemented
53#10625056C2214yes—
54#10625055C2214yes—
55#10625054C2214yes—
56#10625053C2214yes—
57(C22⋊D23)⋊C4C2214yes—
58C22⋊C4×D23C2212yes—
59#10625048C2212yes—
60#10625047C2214yescomplemented
61#10625046C2214yes—
62#10625045C2211yescharacteristic, complemented
63C4×D92C2214yes—
64C4×D92C2212yescomplemented
65#10625043C2211yescharacteristic
66#10625043C2211yescharacteristic
67C42×D23C2211yescharacteristic
68C42×D23C2211yescharacteristic
69C42×D23C2214yescomplemented
70#10625041C2211yescharacteristic, complemented
71C23×D23C2311yescharacteristic
72C2×Q8×C23C2312yes—
73C22×C4×C23C2311yescharacteristic
74C2×C22⋊D23C2314yes—
75C22×Dic23C2311yescharacteristic
76#67292—28no—
77C2×D92C2314yes—
78C2×D92C2312yes—
79C2×D92C2314yes—
80C2×D92C2314yes—
81C2×C4×D23—24no—
82C2×C4×D23C2314yes—
83C2×C4×D23C2311yescharacteristic
84C2×C4×D23C2311yescharacteristic
85C2×C4×D23C2311yescharacteristic
86C2×C4×D23C2312yes—
87C2×C4×D23C2312yes—
88C2×C4×D23C2314yes—
89C2×C4×D23C2314yes—
90C2×C4×D23C2311yescharacteristic
91C2×Dic46C2314yes—
92C4⋊C4×C23C2314yes—
93C4⋊C4×C23C2312yes—
94C4⋊C4×C23C2314yes—
95C4⋊C4×C23C2312yes—
96C4⋊C4×C23C2314yes—
97C4⋊C4×C23C2314yes—
98C22⋊C4×C23C2312yes—
99C22⋊C4×C23C2314yes—
100C42×C23C2311yescharacteristic
101C42×C23C2311yescharacteristic
102C42×C23C2314yes—
103C22⋊Dic23C2312yes—
104(C2×D23)⋊C4C2312yes—
105(C2×D23)⋊C4C2312yes—
106(C2×D23)⋊C4C2314yes—
107(C2×D23)⋊C4C2314yes—
108(C2×D23)⋊C4C2314yes—
109(C2×D23)⋊C4C2314yes—
110(C2×D23)⋊C4C2314yes—
111(C2×D23)⋊C4C2314yes—
112(C2×D23)⋊C4C2314yes—
113(C2×D23)⋊C4C2314yes—
114C4⋊Dic23C2312yes—
115C4⋊Dic23C2314yes—
116C4⋊Dic23C2312yes—
117Dic23⋊C4C2314yes—
118Dic23⋊C4C2312yes—
119Dic23⋊C4C2312yes—
120Dic23⋊C4C2314yes—
121Dic23⋊C4C2314yes—
122C4×Dic23C2312yes—
123C4×Dic23C2311yescharacteristic
124C4×Dic23C2311yescharacteristic
125C4×Dic23C2312yes—
126C4×Dic23C2314yes—
127C4×Dic23C2314yes—
128C23×C23C2411yescharacteristic
129C22×D23—22no—
130C22×D23—42no—
131C22×D23C2411yescharacteristic
132C22×D23C2414yes—
133C22×D23C2411yescharacteristic
134Q8×C23—24no—
135C2×C4×C23—22no—
136C2×C4×C23C2412yes—
137C2×C4×C23C2414yes—
138C2×C4×C23C2412yes—
139C2×C4×C23C2414yes—
140C2×C4×C23C2411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—44no—
143C2×Dic23—22no—
144C2×Dic23C2412yes—
145C2×Dic23C2414yes—
146C2×Dic23C2412yes—
147C2×Dic23C2411yescharacteristic
148C2×Dic23C2411yescharacteristic
149D92—28no—
150D92—24no—
151D92—44no—
152D92—44no—
153C4×D23—22no—
154C4×D23—22no—
155C4×D23—22no—
156C4×D23—28no—
157C4×D23—42no—
158C4×D23—44no—
159C4×D23—44no—
160C4×D23—42no—
161C4×D23#4114yes—
162Dic46—44no—
163#3455—231nomaximal, Sylow
164C22×C23—21no—
165C22×C23—22no—
166C22×C23C2511yescharacteristic
167C2×D23—22no—
168C2×D23—21no—
169C2×D23—24no—
170C2×D23—24no—
171C2×D23—24no—
172C2×D23—22no—
173C2×D23—44no—
174C2×D23C2×#4112yes—
175C4×C23—21no—
176C4×C23—24no—
177C4×C23—24no—
178C4×C23—22no—
179C4×C23—22no—
180C4×C23C2×#4112yes—
181Dic23—21no—
182Dic23—22no—
183Dic23—24no—
184Dic23—22no—
185Dic23C2×#4112yes—
186#542—232no—
187#542—232no—
188#541—231no—
189#541D2311yescharacteristic, complemented
190#540—231no—
191#540—231no—
192#539—234no—
193#538—234no—
194#533—231no—
195#532—231no—
196#529—234no—
197#529—234no—
198#525—232no—
199C4×#41—232no—
200C2×#117—231no—
201C2×C23—41no—
202C2×C23C22×#4111yescharacteristic
203C2×C23#58512yes—
204D23—22no—
205D23—44no—
206D23—41no—
207C2×#41—232no—
208C23×C4—231no—
209C4⋊Q8—232no—
210C4⋊Q8C2×D2311yescharacteristic, complemented
211#127—231no—
212#126—234no—
213#126—234no—
214#126—234no—
215#126C2×D2314yes—
216#125—234no—
217#125—231no—
218#125C2×D2314yescomplemented
219#125C2×D2311yescharacteristic, complemented
220#124—232no—
221#124—234no—
222#124—234no—
223#123—234no—
224#123—234no—
225#123—234no—
226#123—234no—
227#123—234no—
228C22⋊Q8—232no—
229C22⋊Q8—234no—
230C22⋊Q8—234no—
231C22⋊Q8—234no—
232C22⋊Q8C2×D2312yes—
233#121—232no—
234#121—232no—
235#121—234no—
236#121—234no—
237#121—234no—
238#120—234no—
239C4×Q8—232no—
240C4×Q8—234no—
241C4×Q8C2×D2312yescomplemented
242C4×D4—234no—
243C4×D4—232no—
244C4×D4—234no—
245C4×D4—234no—
246C4×D4—234no—
247C4×D4—234no—
248C4×D4—232no—
249#117—231no—
250#117—232no—
251#117—232no—
252#117—234no—
253#117—232no—
254#117—231no—
255#117—231no—
256#117C2×D2311yescharacteristic
257C2×C4⋊C4—232no—
258C2×C22⋊C4—232no—
259C2×C42—231no—
260C2×C42—231no—
261C2×C42—234no—
262C23#345511yescharacteristic, complemented, Sylow
263C24—231no—
264#41—468no—
265C2×Q8—234no—
266C2×Q8C22×D2312yes—
267C2×D4—234no—
268C2×D4—234no—
269C2×D4—232no—
270C2×D4—234no—
271C2×D4—234no—
272C22×C4—231no—
273C22×C4—231no—
274C22×C4—234no—
275C22×C4—231no—
276C22×C4—231no—
277C22×C4—231no—
278C22×C4—232no—
279C22×C4—232no—
280C22×C4—234no—
281C22×C4—234no—
282C22×C4—464no—
283C22×C4C22×D2311yescharacteristic
284C4⋊C4—232no—
285C4⋊C4—232no—
286C4⋊C4—232no—
287C4⋊C4—232no—
288C4⋊C4—234no—
289C4⋊C4—234no—
290C4⋊C4—234no—
291C4⋊C4—234no—
292C4⋊C4C22×D2312yes—
293C4⋊C4C22×D2312yes—
294C4⋊C4C22×D2314yes—
295C4⋊C4C22×D2314yes—
296C4⋊C4C22×D2314yes—
297C4⋊C4C22×D2314yes—
298C22⋊C4—232no—
299C22⋊C4—232no—
300C22⋊C4—232no—
301C22⋊C4—234no—
302C22⋊C4—234no—
303C22⋊C4—234no—
304C22⋊C4—234no—
305C22⋊C4—234no—
306C22⋊C4—234no—
307C22⋊C4—234no—
308C22⋊C4—234no—
309C22⋊C4C22×D2312yes—
310C22⋊C4C22×D2314yes—
311C42—232no—
312C42—232no—
313C42—234no—
314C42—231no—
315C42—231no—
316C42—234no—
317C42C22×D2311yescharacteristic
318C42C22×D2311yescharacteristic
319C42C22×D2314yes—
320C23—231no—
321C23—231no—
322C23—234no—
323C23—462no—
324C23—922no—
325C23C23×D2311yescharacteristic
326Q8—24no—
327Q8—924no—
328D4—468no—
329D4—464no—
330D4—924no—
331D4—924no—
332D4—924no—
333C2×C4—22no—
334C2×C4—231no—
335C2×C4—234no—
336C2×C4—232no—
337C2×C4—232no—
338C2×C4—234no—
339C2×C4—231no—
340C2×C4—462no—
341C2×C4—468no—
342C2×C4—462no—
343C2×C4—462no—
344C2×C4—462no—
345C2×C4—922no—
346C2×C4—924no—
347C2×C4—922no—
348C2×C4—924no—
349C2×C4C23×D2312yes—
350C2×C4C23×D2314yes—
351C2×C4C23×D2314yes—
352C2×C4C23×D2312yes—
353C2×C4C23×D2311yescharacteristic
354C2×C4C23×D2311yescharacteristic
355C22—21no—
356C22—22no—
357C22—232no—
358C22—462no—
359C22—461no—
360C22—464no—
361C22—464no—
362C22—464no—
363C22—462no—
364C22—924no—
365C22C24×D2311yescharacteristic
366C4—21no—
367C4—24no—
368C4—22no—
369C4—22no—
370C4—24no—
371C4—232no—
372C4—461no—
373C4—462no—
374C4—464no—
375C4—462no—
376C4#41×D2312yes—
377C2—41no—
378C2—462no—
379C2—921no—
380C2—924no—
381C2C2×#41×D2311yescharacteristic
382C2#1309325412yes—
subgroupG/H
center, FrattiniC22C24×D23
commutator, socle, cosocleC22×C23C25
FittingC23×#541C2
hypercenter#541D23
hypocenterC23#3455
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #13093040C2semidirect
2. #13093039C2semidirect
3. #13093028C2semidirect
4. #13093023C2semidirect
5. #13093022C2semidirect
6. #13093015C2semidirect
7. #13093006C2semidirect
8. #13092973C2semidirect
9. #13092968C2semidirect
10. #13092952C2semidirect
11. #13092950C2semidirect
12. #13092930C2semidirect
13. C4×#67292C2semidirect
14. #117×D23C2semidirect
15. C23×#541C2semidirect
18. C23×C4⋊Q8C22semidirect
20. C23×#125C22semidirect
21. C23×#125C22semidirect
23. C4×Q8×C23C22semidirect
25. #10625118C22semidirect
27. Q8×Dic23C22semidirect
31. #10625069C22semidirect
32. #10625068C22semidirect
34. #10625067C22semidirect
40. #10625065C22semidirect
41. #10625065C22semidirect
44. #10625064C22semidirect
45. #10625064C22semidirect
48. #10625063C22semidirect
50. #10625060C22semidirect
51. #10625059C22semidirect
52. #10625058C22semidirect
60. #10625047C22semidirect
62. #10625045C22semidirect
64. C4×D92C22semidirect
69. C42×D23C22semidirect
70. #10625041C22semidirect
189. #541D23semidirect
210. C4⋊Q8C2×D23semidirect
218. #125C2×D23semidirect
219. #125C2×D23semidirect
241. C4×Q8C2×D23semidirect
262. C23#3455semidirect

Maximal subgroups

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

subgroupindex
#130930402
#130930392
#130930282
#130930232
#130930222
#130930152
#130930062
#130929732
#130929682
#130929522
#130929502
#130929302
C4×#672922
#117×D232
C23×#5412
#345523