Finite Group Databasebeta

← #15683583

Subgroups — #15683583

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#13093038C211yesmaximal, characteristic, complemented
2#13092891C211yesmaximal, characteristic, complemented
3#13092759C211yesmaximal, characteristic, complemented
4#13092742C211yesmaximal, characteristic, complemented
5#13092708C211yesmaximal, characteristic, complemented
6#13092698C211yesmaximal, characteristic, complemented
7#13092633C211yesmaximal, characteristic, complemented
8#13092633C211yesmaximal, characteristic, complemented
9#13092570C211yesmaximal, characteristic, complemented
10#13092553C211yesmaximal, characteristic
11#13092530C211yesmaximal, characteristic, complemented
12#13092519C211yesmaximal, characteristic, complemented
13C4×#67263C211yesmaximal, characteristic, complemented
14C4×D184C211yesmaximal, characteristic, complemented
15C23×#433C211yesmaximal, characteristic, complemented
16C22×D92C2211yescharacteristic
17C23×#117C2211yescharacteristic
18#10625101C2211yescharacteristic
19#10625097C2211yescharacteristic
20#10625095C2211yescharacteristic
21C2×D184C2211yescharacteristic
22C2×D184C2211yescharacteristic
23C2×#67263C2211yescharacteristic
24C2×#67263C2211yescharacteristic
25#10625069—21no—
26#10625067—21no—
27#10625064—21no—
28#10625064—21no—
29#10625056—21no—
30#10625054—21no—
31C22⋊C4×D23—21no—
32C22⋊C4×D23—21no—
33#10625046C2211yescharacteristic, complemented
34C4×D92C2211yescharacteristic
35C4×D92C2211yescharacteristic
36C4×D92C2211yescharacteristic
37C4×D92C2211yescharacteristic
38C4×D92C2211yescharacteristic, complemented
39#10625040C2211yescharacteristic, complemented
40C4×Dic46C2211yescharacteristic, complemented
41C23×C4⋊C8C2211yescharacteristic, complemented
42C23×C4⋊C8C2211yescharacteristic, complemented
43C23×C22⋊C8C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45C23×#97C2211yescharacteristic, complemented
46C4×C8×C23C2211yescharacteristic, complemented
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic, complemented
52#10625003C2211yescharacteristic, complemented
53#10625000C2211yescharacteristic, complemented
54#10625000C2211yescharacteristic, complemented
55#10624999C2211yescharacteristic, complemented
56#10624999C2211yescharacteristic, complemented
57#10624998C2211yescharacteristic, complemented
58#10624998C2211yescharacteristic, complemented
59C23×D23—21no—
60C22×C4×C23C2311yescharacteristic
61C2×C22⋊D23—21no—
62C2×D92—21no—
63C2×D92—22no—
64C2×D92—22no—
65C2×D92C2311yescharacteristic
66C2×D92C2311yescharacteristic
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×Dic46—21no—
74C2×Dic46C2311yescharacteristic
75C2×C8×C23C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23D411yescharacteristic
80C4⋊C4×C23D411yescharacteristic
81C22⋊C4×C23D411yescharacteristic
82C22⋊C4×C23D411yescharacteristic
83C42×C23C2311yescharacteristic
84C42×C23C2311yescharacteristic
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104D184—22no—
105D184—22no—
106#67263—22no—
107#67263—22no—
108C23×C23C2×D411yescharacteristic
109C22×D23—21no—
110C22×D23—21no—
111C22×D23—24no—
112C22×D23—21no—
113C22×D23—81no—
114C22×D23—81no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23C2×D411yescharacteristic
118C2×C4×C23C2×D411yescharacteristic
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2×D411yescharacteristic
122C2×C4×C23C2411yescharacteristic
123C22⋊D23—81no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129D92—24no—
130D92—21no—
131D92—21no—
132D92—21no—
133D92—21no—
134D92#4112yes—
135D92#4112yes—
136C4×D23—81no—
137C4×D23—81no—
138C4×D23—81no—
139C4×D23—81no—
140C4×D23—81no—
141Dic46—21no—
142Dic46—21no—
143Dic46—81no—
144C8×C23—21no—
145C8×C23—21no—
146C8×C23—21no—
147C8×C23—21no—
148#3118—231nomaximal, Sylow
149C22×C23—21no—
150C22×C23—21no—
151C22×C23—21no—
152C22×C23C22×D411yescharacteristic
153C2×D23—22no—
154C2×D23—22no—
155C2×D23—41no—
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—84no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23C2×#4111yescharacteristic
169C4×C23C2×#4111yescharacteristic
170Dic23—41no—
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#447—231no—
185#442—231no—
186#440—231no—
187C4×SD16—231no—
188C4×D8—231no—
189#433D2311yescharacteristic, complemented
190C2×C23—41no—
191C2×C23#52511yescharacteristic
192C2×C23#57611yescharacteristic
193C2×C23#57711yescharacteristic
194D23—42no—
195D23—42no—
196D23—81no—
197C22×D4—231no—
198C2×SD16—231no—
199C2×SD16—231no—
200C2×D8—231no—
201C2×D8—231no—
202C4⋊Q8—231no—
203#126—461no—
204#124—231no—
205#124—461no—
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—231no—
216C4×D4—461no—
217C4×D4—461no—
218#117—231no—
219#117C2×D2311yescharacteristic
220C2×C22⋊C4—461no—
221C2×C22⋊C4—461no—
222#107—231no—
223#107—231no—
224#106—231no—
225#106—231no—
226C4⋊C8C2×D2311yescharacteristic, complemented
227C4⋊C8C2×D2311yescharacteristic, complemented
228#103—231no—
229#103—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102—231no—
235#102—231no—
236C22⋊C8C2×D2311yescharacteristic
237C22⋊C8C2×D2311yescharacteristic
238#97C2×D2311yescharacteristic, complemented
239C4×C8C2×D2311yescharacteristic, complemented
240C23#311811yescharacteristic, complemented, Sylow
241C24—461no—
242C2×Q8—231no—
243C2×Q8—461no—
244C2×D4—231no—
245C2×D4—231no—
246C2×D4—231no—
247C2×D4—462no—
248C2×D4—462no—
249C2×D4—461no—
250C2×D4—461no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4C22×D2311yescharacteristic
257SD16—462no—
258SD16—462no—
259D8—462no—
260D8—462no—
261C2×C8C22×D2311yescharacteristic
262C2×C8C22×D2311yescharacteristic
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4D9211yescharacteristic
273C4⋊C4D9211yescharacteristic
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4D9211yescharacteristic
285C22⋊C4D9211yescharacteristic
286C42—461no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C42C22×D2311yescharacteristic
290C23—464no—
291C23—461no—
292C23—461no—
293C23—461no—
294C23—1841no—
295C23—1841no—
296C23C2×D9211yescharacteristic
297Q8—461no—
298Q8—461no—
299Q8—1841no—
300D4—232no—
301D4—232no—
302D4—464no—
303D4—461no—
304D4—461no—
305D4—461no—
306D4—461no—
307D4—1841no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—461no—
311C2×C4—461no—
312C2×C4—461no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—1841no—
316C2×C4—1841no—
317C2×C4—1841no—
318C2×C4—1841no—
319C2×C4—1841no—
320C2×C4C2×D9211yescharacteristic
321C2×C4C2×D9211yescharacteristic
322C2×C4C2×D9211yescharacteristic
323C2×C4C2×D9211yescharacteristic
324C2×C4C2×D9211yescharacteristic
325C2×C4C23×D2311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—462no—
334C22—462no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22—921no—
342C22—1844no—
343C22C22×D9211yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—921no—
350C4—921no—
351C4—921no—
352C4—921no—
353C4—921no—
354C4#41×D2311yescharacteristic
355C4#41×D2311yescharacteristic
356C2—41no—
357C2—922no—
358C2—922no—
359C2—1841no—
360C2#1309292911yescharacteristic
361C2#1309322211yescharacteristic
362C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#433C2
socleC22×C23C22×D4
prime radical#13092553C2
hypercenter#433D23
hypocenterC23#3118
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #13093038C2semidirect
2. #13092891C2semidirect
3. #13092759C2semidirect
4. #13092742C2semidirect
5. #13092708C2semidirect
6. #13092698C2semidirect
7. #13092633C2semidirect
8. #13092633C2semidirect
9. #13092570C2semidirect
11. #13092530C2semidirect
12. #13092519C2semidirect
13. C4×#67263C2semidirect
14. C4×D184C2semidirect
15. C23×#433C2semidirect
33. #10625046C22semidirect
38. C4×D92C22semidirect
39. #10625040C22semidirect
40. C4×Dic46C22semidirect
41. C23×C4⋊C8C22semidirect
42. C23×C4⋊C8C22semidirect
45. C23×#97C22semidirect
46. C4×C8×C23C22semidirect
51. #10625003C22semidirect
52. #10625003C22semidirect
53. #10625000C22semidirect
54. #10625000C22semidirect
55. #10624999C22semidirect
56. #10624999C22semidirect
57. #10624998C22semidirect
58. #10624998C22semidirect
189. #433D23semidirect
226. C4⋊C8C2×D23semidirect
227. C4⋊C8C2×D23semidirect
238. #97C2×D23semidirect
239. C4×C8C2×D23semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130930382
#130928912
#130927592
#130927422
#130927082
#130926982
#130926332
#130925702
#130925532
#130925302
#130925192
C4×#672632
C4×D1842
C23×#4332
#311823