Finite Group Databasebeta

← #15683581

Subgroups — #15683581

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#13092758C211yesmaximal, characteristic, complemented
3#13092741C211yesmaximal, characteristic, complemented
4#13092707C211yesmaximal, characteristic, complemented
5#13092697C211yesmaximal, characteristic, complemented
6#13092632C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092568C211yesmaximal, characteristic, complemented
9#13092551C211yesmaximal, characteristic
10#13092527C211yesmaximal, characteristic, complemented
11#13092517C211yesmaximal, characteristic, complemented
12C4×#67273C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14#13092478C211yesmaximal, characteristic, complemented
15C23×#518C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C4×D4×C23—21no—
18C4×D4×C23—21no—
19C4×D4×C23C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic
21C4×D4×C23C2211yescharacteristic
22C4×D4×C23C2211yescharacteristic
23C23×#117C2211yescharacteristic
24C23×#117C2211yescharacteristic
25C2×C22⋊C4×C23—21no—
26C2×C22⋊C4×C23—21no—
27C2×#67273C2211yescharacteristic
28C2×#67273C2211yescharacteristic
29C2×#67272C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625095C2211yescharacteristic
33#10625069—21no—
34#10625067—21no—
35#10625056—21no—
36#10625054—21no—
37#10625046C2211yescharacteristic, complemented
38C4×D92C2211yescharacteristic, complemented
39#10625040C2211yescharacteristic, complemented
40C4×Dic46C2211yescharacteristic, complemented
41#10625014C2211yescharacteristic
42#10625014C2211yescharacteristic
43#10625014C2211yescharacteristic
44#10625014C2211yescharacteristic
45C22⋊(C23⋊C8)C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic
47#10624992C2211yescharacteristic, complemented
48#10624992C2211yescharacteristic, complemented
49#10624991C2211yescharacteristic, complemented
50#10624991C2211yescharacteristic, complemented
51#10624990C2211yescharacteristic, complemented
52#10624990C2211yescharacteristic, complemented
53#10624989C2211yescharacteristic, complemented
54#10624989C2211yescharacteristic, complemented
55C4⋊(C23⋊C8)C2211yescharacteristic, complemented
56C4⋊(C23⋊C8)C2211yescharacteristic, complemented
57#10624985C2211yescharacteristic, complemented
58C4×C23⋊C8C2211yescharacteristic, complemented
59C24×C23—21no—
60C2×D4×C23—22no—
61C2×D4×C23—22no—
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C22×C4×C23—21no—
68C22×C4×C23—21no—
69C22×C4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×Dic46—21no—
74C2×Dic46C2311yescharacteristic
75C4⋊C4×C23D411yescharacteristic
76C4⋊C4×C23D411yescharacteristic
77C4⋊C4×C23C2311yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C22⋊C4×C23—21no—
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C22⋊C4×C23—21no—
84C22⋊C4×C23D411yescharacteristic
85C22⋊C4×C23D411yescharacteristic
86C42×C23—21no—
87C42×C23C2311yescharacteristic
88C42×C23C2311yescharacteristic
89C22⋊Dic23—21no—
90#67273—22no—
91#67273—22no—
92#67272—22no—
93#67272—22no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103C4×Dic23—21no—
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—24no—
109C23×C23—21no—
110C23×C23—21no—
111C23×C23—81no—
112C23×C23—81no—
113C23×C23C2×D411yescharacteristic
114C22×D23—21no—
115D4×C23—24no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23#4112yes—
119D4×C23#4112yes—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—81no—
125C2×C4×C23—81no—
126C2×C4×C23—81no—
127C2×C4×C23—81no—
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2×D411yescharacteristic
132C2×C4×C23C2×D411yescharacteristic
133C2×C4×C23C2411yescharacteristic
134C22⋊D23—81no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138D92—21no—
139D92—21no—
140C4×D23—81no—
141Dic46—21no—
142Dic46—21no—
143Dic46—81no—
144C23⋊C8—21no—
145C23⋊C8—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—84no—
159C22×C23C22×D411yescharacteristic
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23C2×#4111yescharacteristic
171C4×C23C2×#4111yescharacteristic
172Dic23—41no—
173Dic23—41no—
174Dic23—41no—
175#542—231no—
176#518D2311yescharacteristic, complemented
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#433—231no—
190C2×C23—41no—
191C2×C23—42no—
192C2×C23—42no—
193C2×C23#52511yescharacteristic
194C2×C23#57611yescharacteristic
195C2×C23#57711yescharacteristic
196D23—81no—
197C22×D4C2×D2311yescharacteristic
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—21no—
212C4×D4—21no—
213C4×D4—231no—
214C4×D4C2×D2311yescharacteristic
215C4×D4C2×D2311yescharacteristic
216C4×D4C2×D2311yescharacteristic
217C4×D4C2×D2311yescharacteristic
218#117C2×D2311yescharacteristic
219#117C2×D2311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
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#102—231no—
235#102—231no—
236C22⋊C8—231no—
237C22⋊C8—231no—
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—231no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—461no—
256C22×C4C22×D2311yescharacteristic
257SD16—462no—
258SD16—462no—
259D8—462no—
260D8—462no—
261C2×C8—231no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8—231no—
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—461no—
268C4⋊C4—461no—
269C4⋊C4—461no—
270C4⋊C4C22⋊D2311yescharacteristic
271C4⋊C4C22⋊D2311yescharacteristic
272C4⋊C4C22×D2311yescharacteristic
273C4⋊C4C22×D2311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4C22⋊D2311yescharacteristic
285C22⋊C4C22⋊D2311yescharacteristic
286C42—21no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C42C22×D2311yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—461no—
296C23C2×C22⋊D2311yescharacteristic
297Q8—461no—
298Q8—461no—
299Q8—1841no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—461no—
304D4—461no—
305D4—1841no—
306D4#6728812yes—
307D4#6728812yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—461no—
319C2×C4—1841no—
320C2×C4C2×C22⋊D2311yescharacteristic
321C2×C4C2×C22⋊D2311yescharacteristic
322C2×C4C2×C22⋊D2311yescharacteristic
323C2×C4C2×C22⋊D2311yescharacteristic
324C2×C4C2×C22⋊D2311yescharacteristic
325C2×C4C23×D2311yescharacteristic
326C8—461no—
327C8—461no—
328C8—461no—
329C8—461no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—921no—
341C22—921no—
342C22—921no—
343C22C22×C22⋊D2311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—921no—
352C4—921no—
353C4—921no—
354C4C2×#6728811yescharacteristic
355C4C2×#6728811yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—1841no—
360C2#1309292811yescharacteristic
361C2#1309322011yescharacteristic
362C2#1309322811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#518C2
socleC22×C23C22×D4
prime radical#13092551C2
hypercenter#518D23
hypocenterC23#3118
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #13093038C2semidirect
2. #13092758C2semidirect
3. #13092741C2semidirect
4. #13092707C2semidirect
5. #13092697C2semidirect
6. #13092632C2semidirect
7. #13092632C2semidirect
8. #13092568C2semidirect
10. #13092527C2semidirect
11. #13092517C2semidirect
12. C4×#67273C2semidirect
13. C4×#67272C2semidirect
14. #13092478C2semidirect
15. C23×#518C2semidirect
37. #10625046C22semidirect
38. C4×D92C22semidirect
39. #10625040C22semidirect
40. C4×Dic46C22semidirect
47. #10624992C22semidirect
48. #10624992C22semidirect
49. #10624991C22semidirect
50. #10624991C22semidirect
51. #10624990C22semidirect
52. #10624990C22semidirect
53. #10624989C22semidirect
54. #10624989C22semidirect
55. C4⋊(C23⋊C8)C22semidirect
56. C4⋊(C23⋊C8)C22semidirect
57. #10624985C22semidirect
58. C4×C23⋊C8C22semidirect
176. #518D23semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130930382
#130927582
#130927412
#130927072
#130926972
#130926322
#130925682
#130925512
#130925272
#130925172
C4×#672732
C4×#672722
#130924782
C23×#5182
#311823