Finite Group Databasebeta

← #15683574

Subgroups — #15683574

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#13093034C211yesmaximal, characteristic, complemented
2#13092892C211yesmaximal, characteristic, complemented
3#13092759C211yesmaximal, characteristic, complemented
4#13092738C211yesmaximal, characteristic, complemented
5#13092705C211yesmaximal, characteristic, complemented
6#13092695C211yesmaximal, characteristic, complemented
7#13092630C211yesmaximal, characteristic, complemented
8#13092630C211yesmaximal, characteristic, complemented
9#13092568C211yesmaximal, characteristic, complemented
10#13092529C211yesmaximal, characteristic, complemented
11#13092514C211yesmaximal, characteristic, complemented
12#13092508C211yesmaximal, characteristic, complemented
13D8×Dic23C211yesmaximal, characteristic, complemented
14#13092475C211yesmaximal, characteristic, complemented
15C23×#447C211yesmaximal, characteristic
16C22×D4×C23C2211yescharacteristic
17C2×D8×C23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C23×#121C2211yescharacteristic
20C2×C22⋊Dic23—21no—
21C2×C22⋊Dic23—21no—
22#10625107—21no—
23#10625107C2211yescharacteristic, complemented
24#10625106—21no—
25D4×Dic23—21no—
26D4×Dic23—21no—
27D4×Dic23C2211yescharacteristic
28D4×Dic23C2211yescharacteristic
29D4×Dic23C2211yescharacteristic
30D4×Dic23C2211yescharacteristic
31D4×Dic23C2211yescharacteristic, complemented
32C2×#67273C2211yescharacteristic
33C2×#67273C2211yescharacteristic
34#10625097C2211yescharacteristic
35#10625097C2211yescharacteristic
36#10625095C2211yescharacteristic
37#10625059C2211yescharacteristic, complemented
38#10625058C2211yescharacteristic, complemented
39#10625050—21no—
40#10625049—21no—
41C23×#102C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44#10625014C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic, complemented
47#10625014C2211yescharacteristic, complemented
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625000C2211yescharacteristic, complemented
50#10624999C2211yescharacteristic, complemented
51#10624998C2211yescharacteristic, complemented
52#10624998C2211yescharacteristic, complemented
53#10624997C2211yescharacteristic, complemented
54Dic23⋊C8C2211yescharacteristic, complemented
55Dic23⋊C8C2211yescharacteristic, complemented
56C8×Dic23C2211yescharacteristic, complemented
57#10624990C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C24×C23—21no—
60C2×D4×C23—22no—
61C2×D4×C23—22no—
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23C2311yescharacteristic
68C22×Dic23—21no—
69C22×Dic23—21no—
70C22×Dic23—21no—
71C22×Dic23—21no—
72C22×Dic23—21no—
73C2×Dic46—21no—
74C2×Dic46C2311yescharacteristic
75D8×C23—22no—
76D8×C23—22no—
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊Dic23—21no—
82C22⋊Dic23—21no—
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23D411yescharacteristic
91C22⋊Dic23D411yescharacteristic
92#67273—22no—
93#67273—22no—
94C4⋊Dic23D411yescharacteristic
95C4⋊Dic23D411yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—24no—
109C23×C23—21no—
110C23×C23—21no—
111C23×C23—21no—
112C23×C23—81no—
113C23×C23—81no—
114C23×C23C2×D411yescharacteristic
115D4×C23—24no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—81no—
121D4×C23#4112yes—
122D4×C23#4112yes—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2411yescharacteristic
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—81no—
133C2×Dic23—81no—
134C2×Dic23—81no—
135C2×Dic23—81no—
136C2×Dic23—81no—
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139C2×Dic23C2×D411yescharacteristic
140C2×Dic23C2×D411yescharacteristic
141Dic46—21no—
142Dic46—21no—
143Dic46—81no—
144C8×C23—21no—
145C8×C23—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3118—231nomaximal, Sylow
149C22×C23—21no—
150C22×C23—22no—
151C22×C23—22no—
152C22×C23—21no—
153C22×C23—21no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—84no—
162C22×C23C22×D411yescharacteristic
163C4×C23—21no—
164C4×C23—41no—
165C4×C23C2×#4111yescharacteristic
166C4×C23C2×#4111yescharacteristic
167Dic23—21no—
168Dic23—21no—
169Dic23—21no—
170Dic23—21no—
171Dic23—41no—
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#463—231no—
183#450—231no—
184#447D2311yescharacteristic
185#442—231no—
186#440—231no—
187C4×SD16—231no—
188C4×D8—231no—
189#433—231no—
190C2×C23—41no—
191C2×C23—42no—
192C2×C23—42no—
193C2×C23—81no—
194C2×C23#52511yescharacteristic
195C2×C23#57611yescharacteristic
196C2×C23#57711yescharacteristic
197C22×D4C2×D2311yescharacteristic
198C2×SD16—231no—
199C2×SD16—231no—
200C2×D8C2×D2311yescharacteristic
201C2×D8C2×D2311yescharacteristic
202C4⋊Q8—231no—
203#126—461no—
204#124—231no—
205#124—461no—
206#123—461no—
207C22⋊Q8—231no—
208C22⋊Q8—461no—
209#121C2×D2311yescharacteristic
210C4×Q8—231no—
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—231no—
216C4×D4—461no—
217C4×D4—461no—
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⋊C8—231no—
228#103—231no—
229#103—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102C2×D2311yescharacteristic
235#102C2×D2311yescharacteristic
236C22⋊C8—231no—
237C22⋊C8C2×D2311yescharacteristic
238#97—231no—
239C4×C8—231no—
240C23#311811yescharacteristic, complemented, Sylow
241C24—21no—
242C2×Q8—231no—
243C2×Q8—461no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D2311yescharacteristic
249C2×D4C22×D2311yescharacteristic
250C2×D4C22×D2311yescharacteristic
251C22×C4—461no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4C22×D2311yescharacteristic
257SD16—462no—
258SD16—462no—
259D8—22no—
260D8—22no—
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—231no—
276C22⋊C4—231no—
277C22⋊C4—461no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C42—231no—
287C42—231no—
288C42—461no—
289C42—461no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D2311yescharacteristic
297Q8—461no—
298Q8—461no—
299Q8—1841no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#6729012yes—
307D4#6729012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—231no—
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×C4—1841no—
324C2×C4D4×D2311yescharacteristic
325C2×C4C23×D2311yescharacteristic
326C8—21no—
327C8—21no—
328C8—461no—
329C8—461no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D2311yescharacteristic
344C4—21no—
345C4—41no—
346C4—461no—
347C4—461no—
348C4—461no—
349C4—461no—
350C4—921no—
351C4—921no—
352C4—921no—
353C4—921no—
354C4C2×#6729011yescharacteristic
355C4C2×#6729011yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#1309292311yescharacteristic
361C2#1309321811yescharacteristic
362C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
Fitting, prime radicalC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3118
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. #13093034C2semidirect
2. #13092892C2semidirect
3. #13092759C2semidirect
4. #13092738C2semidirect
5. #13092705C2semidirect
6. #13092695C2semidirect
7. #13092630C2semidirect
8. #13092630C2semidirect
9. #13092568C2semidirect
10. #13092529C2semidirect
11. #13092514C2semidirect
12. #13092508C2semidirect
13. D8×Dic23C2semidirect
14. #13092475C2semidirect
23. #10625107C22semidirect
31. D4×Dic23C22semidirect
37. #10625059C22semidirect
38. #10625058C22semidirect
46. #10625014C22semidirect
47. #10625014C22semidirect
49. #10625000C22semidirect
50. #10624999C22semidirect
51. #10624998C22semidirect
52. #10624998C22semidirect
53. #10624997C22semidirect
54. Dic23⋊C8C22semidirect
55. Dic23⋊C8C22semidirect
56. C8×Dic23C22semidirect
57. #10624990C22semidirect
58. #10624989C22semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130930342
#130928922
#130927592
#130927382
#130927052
#130926952
#130926302
#130925682
#130925292
#130925142
#130925082
D8×Dic232
#130924752
C23×#4472
#311823