Finite Group Databasebeta

← #15682228

Subgroups — #15682228

Order 2944.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625085C211yesmaximal, characteristic
2#13092899C211yesmaximal, characteristic, complemented
3#13092889C211yesmaximal, characteristic, complemented
4#13092530C211yesmaximal, characteristic, complemented
5#13092526C211yesmaximal, characteristic, complemented
6#13092520C211yesmaximal, characteristic, complemented
7SD16×Dic23C211yesmaximal, characteristic, complemented
8C4×#67274C211yesmaximal, characteristic, complemented
9#13092499C211yesmaximal, characteristic, complemented
10C4×#67272C211yesmaximal, characteristic, complemented
11#13092458C211yesmaximal, characteristic, complemented
12#13092412C211yesmaximal, characteristic, complemented
13#102×D23C211yesmaximal, characteristic, complemented
14#13092374C211yesmaximal, characteristic, complemented
15C23×#440C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic, complemented
20C4×D4×C23C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic, complemented
22C2×#67274C2211yescharacteristic
23D4×Dic23C2211yescharacteristic
24C2×#67272C2211yescharacteristic
25C4×C22⋊D23—21no—
26C2×(C2×D23)⋊C4—21no—
27#10625085C418yescomplemented
28C2×D184C2211yescharacteristic
29C2×#67262C2211yescharacteristic
30C2×C8×D23C2211yescharacteristic
31#10625064—21no—
32#10625064C2211yescharacteristic
33#10625064C2211yescharacteristic, complemented
34#10625063C2211yescharacteristic
35C4⋊C4×D23—21no—
36C4⋊C4×D23C2211yescharacteristic
37(C22⋊D23)⋊C4—21no—
38C22⋊C4×D23—21no—
39C4×D92—21no—
40C4×D92C2211yescharacteristic
41C4×D92C2211yescharacteristic, complemented
42#10625043—21no—
43#10625043C2211yescharacteristic
44C23×#107C2211yescharacteristic, complemented
45C23×#103C2211yescharacteristic, complemented
46C23×#102C2211yescharacteristic
47C23×#97C2211yescharacteristic, complemented
48#10625017C2211yescharacteristic, complemented
49#10625014C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic, complemented
52#10624999C2211yescharacteristic, complemented
53#10624997C2211yescharacteristic, complemented
54C8×Dic23C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic, complemented
57#10624990C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C4×C23⋊C8C2211yescharacteristic, complemented
60C23×D23—21no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23—21no—
64C2×C22⋊D23—21no—
65C22×Dic23—21no—
66#67292—22no—
67#67292C2×C414yescomplemented
68D4×D23—22no—
69D4×D23C2×C414yescomplemented
70C2×D92—21no—
71C2×D92C2311yescharacteristic
72C2×D92C2311yescharacteristic
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23—21no—
79C2×C4×D23C2311yescharacteristic
80SD16×C23C2×C414yescomplemented
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23—21no—
84C4⋊C4×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C22⋊C4×C23—21no—
87C42×C23—21no—
88C42×C23C2311yescharacteristic
89C22⋊Dic23—21no—
90#67274C2×C414yescomplemented
91#67272C2×C414yescomplemented
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4D411yescharacteristic
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23—21no—
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4D411yescharacteristic
104Dic23⋊C4D411yescharacteristic
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110D184C2×C414yescomplemented
111#67262C2×C414yescomplemented
112C8×D23—22no—
113C23×C23—21no—
114C22×D23—21no—
115C22×D23—21no—
116C22×D23—24no—
117C22×D23—81no—
118C22×D23—81no—
119C22×D23C2×D411yescharacteristic
120Q8×C23—21no—
121Q8×C23C22×C412yes—
122D4×C23—21no—
123D4×C23C22×C412yes—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—81no—
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—24no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—81no—
135C2×Dic23C2×D411yescharacteristic
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138D92—24no—
139D92—21no—
140D92—21no—
141D92C22×C412yes—
142D92C22×C412yes—
143C4×D23—24no—
144C4×D23—81no—
145C4×D23—81no—
146C4×D23—81no—
147C4×D23—81no—
148C4×D23—81no—
149C4×D23C22×C412yes—
150C4×D23#4112yes—
151C8×C23—21no—
152C8×C23C22×C412yes—
153C23⋊C8—21no—
154C23⋊C8C22×C412yes—
155#2946—231nomaximal, Sylow
156C22×C23—22no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23C22×D411yescharacteristic
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—22no—
163C2×D23—22no—
164C2×D23—41no—
165C2×D23—41no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—84no—
169C2×D23C4×D412yes—
170C4×C23—22no—
171C4×C23—21no—
172C4×C23—21no—
173C4×C23—41no—
174C4×C23—41no—
175C4×C23C23×C411yescharacteristic
176C4×C23C2×#4111yescharacteristic
177Dic23—21no—
178Dic23—21no—
179Dic23—41no—
180Dic23—41no—
181Dic23C4×D412yes—
182C2×AGL(1,ℤ/8)—231no—
183#520—231no—
184#518—231no—
185#442—231no—
186#442—231no—
187#440—231no—
188#440D2311yescharacteristic, complemented
189C4×SD16—231no—
190C4×SD16—231no—
191C4×D8—231no—
192C4×D8—231no—
193#428—231no—
194#416—231no—
195C2×#102—231no—
196#405—231no—
197C2×C23—42no—
198C2×C23C2×C4×D411yescharacteristic
199C2×C23#57611yescharacteristic
200C2×C23#57711yescharacteristic
201D23—22no—
202D23—42no—
203D23—42no—
204C2×#41—231no—
205C22×D4—231no—
206AGL(1,ℤ/8)—238no—
207C2×SD16—231no—
208C2×SD16C2×D2311yescharacteristic
209C2×D8—231no—
210C2×D8—231no—
211C2×M16—231no—
212C22×C8—231no—
213C4×Q8—231no—
214C4×Q8C2×D2311yescharacteristic, complemented
215C4×D4—231no—
216C4×D4—231no—
217C4×D4—231no—
218C4×D4—231no—
219C4×D4—231no—
220C4×D4—461no—
221C4×D4—461no—
222C4×D4—461no—
223C4×D4—461no—
224C4×D4C2×D2311yescharacteristic
225#117—231no—
226#117—231no—
227#117—461no—
228C2×C4⋊C4—231no—
229C2×C4⋊C4—461no—
230C2×C22⋊C4—461no—
231C2×C22⋊C4—461no—
232#107—231no—
233#107C2×D2311yescharacteristic, complemented
234#106—231no—
235#106—231no—
236#103—231no—
237#103C2×D2311yescharacteristic, complemented
238#102—231no—
239#102—231no—
240#102—231no—
241#102—231no—
242#102—231no—
243#102C2×D2311yescharacteristic
244#97—231no—
245#97C2×D2311yescharacteristic, complemented
246C4×C8—231no—
247C4×C8—231no—
248C23#294611yescharacteristic, complemented, Sylow
249C24—461no—
250#41—234no—
251#41—462no—
252C2×Q8C22×D2311yescharacteristic
253C2×D4—234no—
254C2×D4—231no—
255C2×D4—231no—
256C2×D4—461no—
257C2×D4—462no—
258C2×D4—461no—
259C2×D4C22×D2311yescharacteristic
260C22×C4—21no—
261C22×C4—231no—
262C22×C4—461no—
263C22×C4—461no—
264C22×C4—461no—
265C22×C4—461no—
266C22×C4—461no—
267C22×C4—461no—
268C22×C4—461no—
269SD16—234no—
270SD16C4×D2314yescomplemented
271D8—234no—
272D8—234no—
273M16—234no—
274C2×C8—231no—
275C2×C8—231no—
276C2×C8—462no—
277C2×C8C22×D2311yescharacteristic
278C2×C8C22×D2311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—231no—
281C4⋊C4—231no—
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—461no—
285C4⋊C4—461no—
286C4⋊C4C22×D2311yescharacteristic
287C4⋊C4C22×D2311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—231no—
290C22⋊C4—231no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C42—21no—
298C42—231no—
299C42—461no—
300C42—461no—
301C42C22×D2311yescharacteristic
302C23—21no—
303C23—231no—
304C23—464no—
305C23—461no—
306C23—461no—
307C23—1841no—
308C23—1841no—
309Q8—21no—
310Q8C2×C4×D2312yes—
311D4—21no—
312D4—232no—
313D4—232no—
314D4—464no—
315D4—464no—
316D4—461no—
317D4—461no—
318D4C2×C4×D2312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—231no—
324C2×C4—232no—
325C2×C4—232no—
326C2×C4—231no—
327C2×C4—231no—
328C2×C4—464no—
329C2×C4—461no—
330C2×C4—461no—
331C2×C4—1841no—
332C2×C4—1841no—
333C2×C4—1841no—
334C2×C4—1841no—
335C2×C4—1841no—
336C2×C4—1841no—
337C2×C4D4×D2311yescharacteristic
338C2×C4D4×D2311yescharacteristic
339C2×C4C23×D2311yescharacteristic
340C8—21no—
341C8—232no—
342C8—461no—
343C8C2×C4×D2312yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—232no—
348C22—461no—
349C22—461no—
350C22—462no—
351C22—462no—
352C22—921no—
353C22—921no—
354C22—921no—
355C22—921no—
356C22—1844no—
357C22C2×D4×D2311yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—232no—
364C4—461no—
365C4—461no—
366C4—921no—
367C4—921no—
368C4C22×C4×D2311yescharacteristic
369C4#41×D2311yescharacteristic
370C2—42no—
371C2—462no—
372C2—922no—
373C2—922no—
374C2C4×D4×D2311yescharacteristic
375C2#1309322111yescharacteristic
376C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
prime radicalC2×#10625085C2
cosocleC2×C4×C23C24
hypercenter#440D23
hypocenterC23#2946
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #13092899C2semidirect
3. #13092889C2semidirect
4. #13092530C2semidirect
5. #13092526C2semidirect
6. #13092520C2semidirect
7. SD16×Dic23C2semidirect
8. C4×#67274C2semidirect
9. #13092499C2semidirect
10. C4×#67272C2semidirect
11. #13092458C2semidirect
12. #13092412C2semidirect
13. #102×D23C2semidirect
14. #13092374C2semidirect
15. C23×#440C2semidirect
19. C4×Q8×C23C22semidirect
21. Q8×Dic23C22semidirect
27. #10625085C4semidirect
33. #10625064C22semidirect
41. C4×D92C22semidirect
44. C23×#107C22semidirect
45. C23×#103C22semidirect
47. C23×#97C22semidirect
48. #10625017C22semidirect
51. #10625003C22semidirect
52. #10624999C22semidirect
53. #10624997C22semidirect
54. C8×Dic23C22semidirect
56. #10624991C22semidirect
57. #10624990C22semidirect
58. #10624989C22semidirect
59. C4×C23⋊C8C22semidirect
67. #67292C2×C4semidirect
69. D4×D23C2×C4semidirect
80. SD16×C23C2×C4semidirect
90. #67274C2×C4semidirect
91. #67272C2×C4semidirect
110. D184C2×C4semidirect
111. #67262C2×C4semidirect
188. #440D23semidirect
214. C4×Q8C2×D23semidirect
233. #107C2×D23semidirect
237. #103C2×D23semidirect
245. #97C2×D23semidirect
248. C23#2946semidirect
270. SD16C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
#130928992
#130928892
#130925302
#130925262
#130925202
SD16×Dic232
C4×#672742
#130924992
C4×#672722
#130924582
#130924122
#102×D232
#130923742
C23×#4402
#294623