Finite Group Databasebeta

← #15683580

Subgroups — #15683580

Order 2944.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093036C211yesmaximal, characteristic, complemented
2#13092889C211yesmaximal, characteristic, complemented
3#13092756C211yesmaximal, characteristic, complemented
4#13092740C211yesmaximal, characteristic, complemented
5#13092708C211yesmaximal, characteristic, complemented
6#13092697C211yesmaximal, characteristic, complemented
7#13092629C211yesmaximal, characteristic, complemented
8#13092566C211yesmaximal, characteristic, complemented
9#13092549C211yesmaximal, characteristic
10#13092529C211yesmaximal, characteristic, complemented
11#13092520C211yesmaximal, characteristic, complemented
12SD16×Dic23C211yesmaximal, characteristic, complemented
13#13092497C211yesmaximal, characteristic, complemented
14#13092477C211yesmaximal, characteristic, complemented
15C23×#463C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C23×#124C2211yescharacteristic, complemented
20C4×D4×C23C2211yescharacteristic
21#10625117C2211yescharacteristic
22Q8×Dic23C2211yescharacteristic, complemented
23C2×#67274C2211yescharacteristic
24#10625109C2211yescharacteristic
25D4×Dic23C2211yescharacteristic
26D4×Dic23C2211yescharacteristic, complemented
27C2×#67272C2211yescharacteristic
28C4×C22⋊D23—21no—
29C2×(C2×D23)⋊C4—21no—
30#10625064C2211yescharacteristic
31#10625063C2211yescharacteristic
32#10625057—21no—
33#10625056—21no—
34(C22⋊D23)⋊C4—21no—
35C22⋊C4×D23—21no—
36#10625050—21no—
37#10625049—21no—
38C4×D92C2211yescharacteristic
39#10625043C2211yescharacteristic
40#10625040C2211yescharacteristic, complemented
41C23×C4⋊C8C2211yescharacteristic, complemented
42C23×#103C2211yescharacteristic, complemented
43C23×#102C2211yescharacteristic, complemented
44#10625017C2211yescharacteristic, complemented
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic, complemented
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic
52#10624999C2211yescharacteristic, complemented
53#10624999C2211yescharacteristic, complemented
54#10624997C2211yescharacteristic, complemented
55C8×Dic23C2211yescharacteristic, complemented
56#10624989C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23—21no—
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C22×Dic23—21no—
67C22×Dic23—21no—
68D4×D23—22no—
69D4×D23—22no—
70C2×D92C2311yescharacteristic
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23C2311yescharacteristic
74C2×Dic46—21no—
75SD16×C23—22no—
76D8×C23—22no—
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C42×C23C2311yescharacteristic
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87#67274—22no—
88#67272—22no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4D411yescharacteristic
94(C2×D23)⋊C4D411yescharacteristic
95C4⋊Dic23—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101Dic23⋊C4D411yescharacteristic
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23—21no—
110C22×D23—21no—
111C22×D23—24no—
112C22×D23—81no—
113C22×D23—81no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23#4112yes—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—81no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2411yescharacteristic
127C22⋊D23—24no—
128C22⋊D23—81no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—81no—
133C2×Dic23—81no—
134C2×Dic23C2×D411yescharacteristic
135C2×Dic23C2×D411yescharacteristic
136C2×Dic23C2×D411yescharacteristic
137D92—21no—
138D92#4112yes—
139C4×D23—21no—
140C4×D23—21no—
141C4×D23—81no—
142C4×D23—81no—
143Dic46—81no—
144C8×C23—21no—
145C8×C23—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3118—231nomaximal, Sylow
149C22×C23—22no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23C22×D411yescharacteristic
156C2×D23—21no—
157C2×D23—22no—
158C2×D23—21no—
159C2×D23—21no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—84no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23C2×#4111yescharacteristic
168C4×C23C2×#4111yescharacteristic
169Dic23—21no—
170Dic23—21no—
171Dic23—21no—
172Dic23—41no—
173Dic23—41no—
174Dic23—41no—
175#542—231no—
176#518—231no—
177#485—231no—
178#482—231no—
179#476—231no—
180#474—231no—
181#463—231no—
182#463D2311yescharacteristic, complemented
183#450—231no—
184#447—231no—
185#442—231no—
186#440—231no—
187C4×SD16—231no—
188C4×D8—231no—
189#433—231no—
190C2×C23—42no—
191C2×C23—81no—
192C2×C23#52511yescharacteristic
193C2×C23#57611yescharacteristic
194C2×C23#57711yescharacteristic
195D23—41no—
196D23—42no—
197C22×D4—231no—
198C2×SD16—231no—
199C2×SD16C2×D2311yescharacteristic
200C2×D8—231no—
201C2×D8C2×D2311yescharacteristic
202C4⋊Q8—231no—
203#126—461no—
204#124—461no—
205#124C2×D2311yescharacteristic, complemented
206#123—461no—
207C22⋊Q8—231no—
208C22⋊Q8—461no—
209#121—231no—
210C4×Q8—231no—
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—461no—
216C4×D4—461no—
217C4×D4C2×D2311yescharacteristic
218#117—231no—
219#117—231no—
220C2×C22⋊C4—461no—
221C2×C22⋊C4—461no—
222#107—231no—
223#107—231no—
224#106—231no—
225#106—231no—
226C4⋊C8—231no—
227C4⋊C8C2×D2311yescharacteristic, complemented
228#103—231no—
229#103C2×D2311yescharacteristic, complemented
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102—231no—
235#102C2×D2311yescharacteristic, complemented
236C22⋊C8—231no—
237C22⋊C8—231no—
238#97—231no—
239C4×C8—231no—
240C23#311811yescharacteristic, complemented, Sylow
241C24—461no—
242C2×Q8—461no—
243C2×Q8C22×D2311yescharacteristic
244C2×D4—231no—
245C2×D4—461no—
246C2×D4—462no—
247C2×D4—462no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—231no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257SD16—22no—
258SD16—462no—
259D8—22no—
260D8—462no—
261C2×C8—231no—
262C2×C8—231no—
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4C22×D2311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—231no—
278C22⋊C4—231no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C42—231no—
287C42—461no—
288C42—461no—
289C42C22×D2311yescharacteristic
290C23—21no—
291C23—21no—
292C23—231no—
293C23—464no—
294C23—461no—
295C23—1841no—
296C23—1841no—
297Q8—21no—
298Q8—21no—
299Q8—1841no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—232no—
304D4—464no—
305D4—461no—
306D4—1841no—
307D4#6729012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—461no—
319C2×C4—1841no—
320C2×C4—1841no—
321C2×C4—1841no—
322C2×C4—1841no—
323C2×C4D4×D2311yescharacteristic
324C2×C4D4×D2311yescharacteristic
325C2×C4C23×D2311yescharacteristic
326C8—21no—
327C8—21no—
328C8—461no—
329C8—461no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—461no—
337C22—462no—
338C22—461no—
339C22—461no—
340C22—921no—
341C22—921no—
342C22—1844no—
343C22C2×D4×D2311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—461no—
349C4—461no—
350C4—461no—
351C4—921no—
352C4—921no—
353C4—921no—
354C4C2×#6729011yescharacteristic
355C4#41×D2311yescharacteristic
356C2—42no—
357C2—81no—
358C2—921no—
359C2—922no—
360C2#1309292711yescharacteristic
361C2#1309322111yescharacteristic
362C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#463C2
socleC22×C23C22×D4
prime radical#13092549C2
hypercenter#463D23
hypocenterC23#3118
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #13093036C2semidirect
2. #13092889C2semidirect
3. #13092756C2semidirect
4. #13092740C2semidirect
5. #13092708C2semidirect
6. #13092697C2semidirect
7. #13092629C2semidirect
8. #13092566C2semidirect
10. #13092529C2semidirect
11. #13092520C2semidirect
12. SD16×Dic23C2semidirect
13. #13092497C2semidirect
14. #13092477C2semidirect
15. C23×#463C2semidirect
19. C23×#124C22semidirect
22. Q8×Dic23C22semidirect
26. D4×Dic23C22semidirect
40. #10625040C22semidirect
41. C23×C4⋊C8C22semidirect
42. C23×#103C22semidirect
43. C23×#102C22semidirect
44. #10625017C22semidirect
47. #10625014C22semidirect
52. #10624999C22semidirect
53. #10624999C22semidirect
54. #10624997C22semidirect
55. C8×Dic23C22semidirect
56. #10624989C22semidirect
57. #10624989C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
182. #463D23semidirect
205. #124C2×D23semidirect
227. C4⋊C8C2×D23semidirect
229. #103C2×D23semidirect
235. #102C2×D23semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130930362
#130928892
#130927562
#130927402
#130927082
#130926972
#130926292
#130925662
#130925492
#130925292
#130925202
SD16×Dic232
#130924972
#130924772
C23×#4632
#311823