Finite Group Databasebeta

← #15683584

Subgroups — #15683584

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#13093040C211yesmaximal, characteristic, complemented
2#13092891C211yesmaximal, characteristic, complemented
3#13092741C211yesmaximal, characteristic, complemented
4#13092706C211yesmaximal, characteristic, complemented
5#13092696C211yesmaximal, characteristic, complemented
6#13092635C211yesmaximal, characteristic, complemented
7#13092635C211yesmaximal, characteristic, complemented
8#13092567C211yesmaximal, characteristic, complemented
9#13092553C211yesmaximal, characteristic
10#13092528C211yesmaximal, characteristic, complemented
11#13092520C211yesmaximal, characteristic, complemented
12#13092502C211yesmaximal, characteristic, complemented
13#13092499C211yesmaximal, characteristic, complemented
14#13092475C211yesmaximal, characteristic, complemented
15C23×#485C211yesmaximal, characteristic, complemented
16C22×D92C2211yescharacteristic
17C23×C22⋊Q8C2211yescharacteristic
18C23×#117C2211yescharacteristic
19#10625118C2211yescharacteristic, complemented
20Q8×Dic23C2211yescharacteristic, complemented
21C2×#67274C2211yescharacteristic
22C2×#67274C2211yescharacteristic
23#10625101C2211yescharacteristic
24#10625097C2211yescharacteristic
25C2×D184C2211yescharacteristic
26C2×D184C2211yescharacteristic
27#10625069—21no—
28#10625068—21no—
29#10625064C2211yescharacteristic
30#10625064C2211yescharacteristic
31#10625064C2211yescharacteristic
32#10625064C2211yescharacteristic
33#10625064C2211yescharacteristic, complemented
34#10625059C2211yescharacteristic, complemented
35#10625056—21no—
36#10625054—21no—
37C22⋊C4×D23—21no—
38C22⋊C4×D23—21no—
39C4×D92—21no—
40C4×D92—21no—
41C23×#107C2211yescharacteristic, complemented
42C23×#106C2211yescharacteristic, complemented
43C23×#103C2211yescharacteristic, complemented
44C23×#103C2211yescharacteristic, complemented
45C23×C22⋊C8C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10624997C2211yescharacteristic, complemented
50Dic23⋊C8C2211yescharacteristic, complemented
51Dic23⋊C8C2211yescharacteristic, complemented
52C8×Dic23C2211yescharacteristic, complemented
53#10624991C2211yescharacteristic
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic, complemented
56#10624991C2211yescharacteristic, complemented
57#10624990C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C2×C22⋊D23—21no—
63C2×D92—21no—
64C2×D92—22no—
65C2×D92—22no—
66C2×D92C2311yescharacteristic
67C2×D92C2311yescharacteristic
68C2×D92C2311yescharacteristic
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×Dic46—21no—
75C2×C8×C23C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C4⋊C4×C23—21no—
78C4⋊C4×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C22⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C42×C23—21no—
84C22⋊Dic23D411yescharacteristic
85C22⋊Dic23D411yescharacteristic
86#67274—22no—
87#67274—22no—
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—
95(C2×D23)⋊C4—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23D411yescharacteristic
98C4⋊Dic23D411yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101C4×Dic23—21no—
102C4×Dic23C2311yescharacteristic
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106D184—22no—
107D184—22no—
108C23×C23C2×D411yescharacteristic
109C22×D23—21no—
110C22×D23—21no—
111C22×D23—24no—
112C22×D23—21no—
113C22×D23—81no—
114C22×D23—81no—
115Q8×C23—21no—
116Q8×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23—81no—
126C2×Dic23—21no—
127C2×Dic23C2×D411yescharacteristic
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131D92—24no—
132D92—21no—
133D92—21no—
134D92—21no—
135D92—21no—
136D92#4112yes—
137D92#4112yes—
138C4×D23—81no—
139C4×D23—81no—
140C4×D23—81no—
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—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—41no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23—41no—
168C4×C23C2×#4111yescharacteristic
169C4×C23C2×#4111yescharacteristic
170Dic23—21no—
171Dic23—21no—
172Dic23—21no—
173Dic23—21no—
174Dic23—41no—
175#542—231no—
176#518—231no—
177#485D2311yescharacteristic, complemented
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#433—231no—
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—461no—
208C22⋊Q8C2×D2311yescharacteristic
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#107C2×D2311yescharacteristic, complemented
224#106—231no—
225#106C2×D2311yescharacteristic, complemented
226C4⋊C8—231no—
227C4⋊C8—231no—
228#103C2×D2311yescharacteristic, complemented
229#103C2×D2311yescharacteristic, complemented
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102—231no—
235#102—231no—
236C22⋊C8—231no—
237C22⋊C8C2×D2311yescharacteristic
238#97—231no—
239C4×C8—231no—
240C23#311811yescharacteristic, complemented, Sylow
241C24—461no—
242C2×Q8—461no—
243C2×Q8C22×D2311yescharacteristic
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×C8—231no—
262C2×C8—231no—
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4C22×D2311yescharacteristic
272C4⋊C4C22×D2311yescharacteristic
273C4⋊C4C22×D2311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—231no—
277C22⋊C4—231no—
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—21no—
287C42—231no—
288C42—231no—
289C42—461no—
290C23—464no—
291C23—461no—
292C23—461no—
293C23—461no—
294C23—1841no—
295C23—1841no—
296C23D4×D2311yescharacteristic
297Q8—21no—
298Q8—21no—
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—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—231no—
315C2×C4—231no—
316C2×C4—231no—
317C2×C4—231no—
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—21no—
332C22—21no—
333C22—462no—
334C22—462no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22—921no—
342C22—1844no—
343C22C2×D4×D2311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—461no—
350C4—461no—
351C4—461no—
352C4—461no—
353C4—921no—
354C4#41×D2311yescharacteristic
355C4#41×D2311yescharacteristic
356C2—41no—
357C2—922no—
358C2—922no—
359C2—1841no—
360C2#1309292511yescharacteristic
361C2#1309321911yescharacteristic
362C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#485C2
socleC22×C23C22×D4
prime radical#13092553C2
hypercenter#485D23
hypocenterC23#3118
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #13093040C2semidirect
2. #13092891C2semidirect
3. #13092741C2semidirect
4. #13092706C2semidirect
5. #13092696C2semidirect
6. #13092635C2semidirect
7. #13092635C2semidirect
8. #13092567C2semidirect
10. #13092528C2semidirect
11. #13092520C2semidirect
12. #13092502C2semidirect
13. #13092499C2semidirect
14. #13092475C2semidirect
15. C23×#485C2semidirect
19. #10625118C22semidirect
20. Q8×Dic23C22semidirect
33. #10625064C22semidirect
34. #10625059C22semidirect
41. C23×#107C22semidirect
42. C23×#106C22semidirect
43. C23×#103C22semidirect
44. C23×#103C22semidirect
49. #10624997C22semidirect
50. Dic23⋊C8C22semidirect
51. Dic23⋊C8C22semidirect
52. C8×Dic23C22semidirect
55. #10624991C22semidirect
56. #10624991C22semidirect
57. #10624990C22semidirect
58. #10624989C22semidirect
177. #485D23semidirect
223. #107C2×D23semidirect
225. #106C2×D23semidirect
228. #103C2×D23semidirect
229. #103C2×D23semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130930402
#130928912
#130927412
#130927062
#130926962
#130926352
#130925672
#130925532
#130925282
#130925202
#130925022
#130924992
#130924752
C23×#4852
#311823