Finite Group Databasebeta

← #15684888

Subgroups — #15684888

Order 2944.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625103C211yesmaximal, characteristic, complemented
2C22×#67273C211yesmaximal, characteristic, complemented
3#13093076C211yesmaximal, characteristic, complemented
4#13092804C211yesmaximal, characteristic, complemented
5#13092661C211yesmaximal, characteristic, complemented
6#13092651C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092614C211yesmaximal, characteristic, complemented
9#13092568C211yesmaximal, characteristic, complemented
10#13092560C211yesmaximal, characteristic, complemented
11#13092555C211yesmaximal, characteristic, complemented
12#13092551C211yesmaximal, characteristic, complemented
13#13092517C211yesmaximal, characteristic, complemented
14#13092489C211yesmaximal, characteristic, complemented
15D42×C23C211yesmaximal, characteristic, complemented
16C22×D4×C23—21no—
17C22×D4×C23C2211yescharacteristic
18C22×D4×C23C2211yescharacteristic
19C2×#67288C2211yescharacteristic, complemented
20C22×Dic46C2211yescharacteristic, complemented
21C23×#127C2211yescharacteristic
22C23×#121—21no—
23C23×#121C2211yescharacteristic
24C23×#121C2211yescharacteristic
25C23×#120—21no—
26C23×#120—21no—
27C4×D4×C23C2211yescharacteristic
28C4×D4×C23C2211yescharacteristic
29#10625110—21no—
30C2×#67273—24no—
31C2×#67273C2211yescharacteristic
32C2×#67273C2211yescharacteristic
33C2×#67273C2211yescharacteristic, complemented
34C2×#67273C2211yescharacteristic, complemented
35C2×#67273C2211yescharacteristic, complemented
36C2×#67273C2211yescharacteristic, complemented
37#10625103—24no—
38C2×#67272C2211yescharacteristic
39C2×#67272C2211yescharacteristic, complemented
40C2×#67272C2211yescharacteristic, complemented
41#10625101C2211yescharacteristic, complemented
42#10625095C2211yescharacteristic, complemented
43C2×#67267C2211yescharacteristic, complemented
44C22×C23⋊C8C2211yescharacteristic, complemented
45#10625067—21no—
46#10625056—21no—
47(C22⋊D23)⋊C4—21no—
48#10625046C2211yescharacteristic, complemented
49C4×Dic46C2211yescharacteristic, complemented
50#10625014C2211yescharacteristic
51#10625014C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic, complemented
53C22⋊(C23⋊C8)C2211yescharacteristic, complemented
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C4⋊(C23⋊C8)C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C24×C23—21no—
62C24×C23—21no—
63C2×D4×C23—22no—
64C2×D4×C23—22no—
65C2×D4×C23—21no—
66C2×D4×C23—21no—
67C2×D4×C23—21no—
68C2×D4×C23—21no—
69C2×D4×C23—21no—
70C2×D4×C23—21no—
71C2×D4×C23—41no—
72C2×D4×C23—41no—
73C2×D4×C23—44no—
74C2×D4×C23D411yescharacteristic
75C2×D4×C23C2311yescharacteristic
76C2×D4×C23C2311yescharacteristic
77C2×D4×C23C2311yescharacteristic
78C22×C4×C23—21no—
79C22×C4×C23C2311yescharacteristic
80C22×C4×C23C2311yescharacteristic
81C2×C22⋊D23—21no—
82C2×C22⋊D23—21no—
83C22×Dic23—21no—
84#67288—22no—
85#67288—41no—
86C2×D92C2311yescharacteristic
87C2×C4×D23—21no—
88C2×Dic46—22no—
89C2×Dic46—21no—
90C2×Dic46—41no—
91C2×Dic46C2311yescharacteristic
92C2×Dic46C2311yescharacteristic
93C4⋊C4×C23D411yescharacteristic
94C4⋊C4×C23C2311yescharacteristic
95C22⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊C4×C23—21no—
98C22⋊C4×C23D411yescharacteristic
99C22⋊C4×C23D411yescharacteristic
100C42×C23C2311yescharacteristic
101C22⋊Dic23—21no—
102#67273—22no—
103#67273—22no—
104#67273—22no—
105#67273—22no—
106#67273—41no—
107#67273D414yescomplemented
108#67272—22no—
109#67272—22no—
110#67272—41no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4—21no—
113(C2×D23)⋊C4—21no—
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116Dic23⋊C4—21no—
117C4×Dic23—21no—
118#67267—22no—
119C2×C23⋊C8—22no—
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122C2×C23⋊C8C2311yescharacteristic
123C2×C23⋊C8C2311yescharacteristic
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—21no—
127C23×C23—42no—
128C23×C23—42no—
129C23×C23—42no—
130C23×C23—42no—
131C23×C23—81no—
132C23×C23—81no—
133C23×C23C2×D411yescharacteristic
134C23×C23C2×D411yescharacteristic
135C22×D23—21no—
136D4×C23—22no—
137D4×C23—21no—
138D4×C23—21no—
139D4×C23—21no—
140D4×C23—21no—
141D4×C23—21no—
142D4×C23—42no—
143D4×C23—42no—
144D4×C23—42no—
145D4×C23—42no—
146D4×C23—42no—
147D4×C23—81no—
148D4×C23C2×D412yes—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23—42no—
155C2×C4×C23C2×D411yescharacteristic
156C2×C4×C23C2×D411yescharacteristic
157C2×C4×C23C2×D411yescharacteristic
158C2×C4×C23C2×D411yescharacteristic
159C2×C4×C23C2411yescharacteristic
160C22⋊D23—42no—
161C22⋊D23—42no—
162C2×Dic23—21no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—42no—
166D92—21no—
167D92—21no—
168C4×D23—42no—
169Dic46—21no—
170Dic46—21no—
171Dic46—21no—
172Dic46—42no—
173Dic46C2×D412yescomplemented
174C23⋊C8—21no—
175C23⋊C8—21no—
176C23⋊C8—21no—
177C23⋊C8C2×D412yescomplemented
178#3265—231nomaximal, Sylow
179C22×C23—21no—
180C22×C23—21no—
181C22×C23—21no—
182C22×C23—22no—
183C22×C23—21no—
184C22×C23—21no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23—41no—
192C22×C23—41no—
193C22×C23—84no—
194C22×C23—84no—
195C22×C23AGL(1,ℤ/8)12yescomplemented
196C22×C23C22×D411yescharacteristic
197C2×D23—41no—
198C2×D23—41no—
199C2×D23—41no—
200C4×C23—21no—
201C4×C23—21no—
202C4×C23—21no—
203C4×C23—21no—
204C4×C23—41no—
205C4×C23C22×D411yescharacteristic
206C4×C23H(5,𝔽2)11yescharacteristic
207Dic23—22no—
208Dic23—41no—
209Dic23—41no—
210C2×AGL(1,ℤ/8)—231no—
211C22×SD16—231no—
212#548—231no—
213D42D2311yescharacteristic, complemented
214#496—231no—
215#468—231no—
216#466—231no—
217#463—231no—
218#460—231no—
219#450—231no—
220#449—231no—
221#448—231no—
222#447—231no—
223#440—231no—
224#435—231no—
225C2×C23—22no—
226C2×C23—41no—
227C2×C23—42no—
228C2×C23—81no—
229C2×C23—81no—
230C2×C23D4211yescharacteristic
231C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
232C2×C23#57711yescharacteristic
233D23—81no—
234C2×#41—231no—
235C22×Q8—231no—
236C22×D4—21no—
237C22×D4C2×D2311yescharacteristic
238C22×D4C2×D2311yescharacteristic
239AGL(1,ℤ/8)—464no—
240C2×SD16—231no—
241C2×SD16—231no—
242C2×SD16—231no—
243C2×SD16—231no—
244C2×SD16—231no—
245C2×SD16—231no—
246C2×SD16—464no—
247C2×D8—231no—
248C2×D8—231no—
249C2×D8—231no—
250C2×M16—231no—
251C22×C8—231no—
252#127C2×D2311yescharacteristic
253#124—231no—
254#124—461no—
255C22⋊Q8—231no—
256C22⋊Q8—461no—
257#121—21no—
258#121—231no—
259#121—461no—
260#121C2×D2311yescharacteristic
261#121C2×D2311yescharacteristic
262#120—21no—
263#120—21no—
264C4×Q8—231no—
265C4×D4—461no—
266C4×D4C2×D2311yescharacteristic
267C4×D4C2×D2311yescharacteristic
268#107—231no—
269C4⋊C8—231no—
270#103—231no—
271#103—231no—
272#102—231no—
273#102—231no—
274#102—231no—
275#102—231no—
276C22⋊C8—231no—
277C22⋊C8—231no—
278#97—231no—
279C23#326511yescharacteristic, complemented, Sylow
280C24—21no—
281C24—21no—
282#41—462no—
283#41—921no—
284C2×Q8—231no—
285C2×Q8—231no—
286C2×Q8—462no—
287C2×Q8—461no—
288C2×Q8—921no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—231no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4C22⋊D2311yescharacteristic
304C2×D4C22×D2311yescharacteristic
305C2×D4C22×D2311yescharacteristic
306C2×D4C22×D2311yescharacteristic
307C22×C4—21no—
308C22×C4—461no—
309C22×C4—461no—
310C22×C4C22×D2311yescharacteristic
311C22×C4C22×D2311yescharacteristic
312SD16—234no—
313SD16—462no—
314SD16—462no—
315SD16—462no—
316SD16—462no—
317SD16—921no—
318D8—462no—
319D8—462no—
320D8—921no—
321M16—462no—
322C2×C8—231no—
323C2×C8—231no—
324C2×C8—231no—
325C2×C8—231no—
326C2×C8—462no—
327C4⋊C4—231no—
328C4⋊C4—461no—
329C4⋊C4—461no—
330C4⋊C4C22⋊D2311yescharacteristic
331C4⋊C4C22×D2311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—461no—
336C22⋊C4—461no—
337C22⋊C4—461no—
338C22⋊C4—461no—
339C22⋊C4C22⋊D2311yescharacteristic
340C22⋊C4C22⋊D2311yescharacteristic
341C42—461no—
342C42C22×D2311yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—461no—
353C23C2×C22⋊D2311yescharacteristic
354C23C2×C22⋊D2311yescharacteristic
355Q8—232no—
356Q8—461no—
357Q8—461no—
358Q8—461no—
359Q8—922no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—461no—
373D4—461no—
374D4—922no—
375D4—922no—
376D4D4×D2312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—461no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—922no—
387C2×C4—922no—
388C2×C4C2×C22⋊D2311yescharacteristic
389C2×C4C2×C22⋊D2311yescharacteristic
390C2×C4C2×C22⋊D2311yescharacteristic
391C2×C4C2×C22⋊D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—232no—
394C8—461no—
395C8—461no—
396C8—461no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—921no—
414C22—921no—
415C22—921no—
416C22#1062510312yescomplemented
417C22C22×C22⋊D2311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—462no—
424C4—921no—
425C4—921no—
426C4C2×D4×D2311yescharacteristic
427C4#1062515511yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—1841no—
434C2D4×C22⋊D2311yescharacteristic
435C2C2×#1062510311yescharacteristic
436C2#1309322811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingD42×C23C2
socleC22×C23C22×D4
hypercenterD42D23
hypocenterC23#3265
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. C22×#67273C2semidirect
3. #13093076C2semidirect
4. #13092804C2semidirect
5. #13092661C2semidirect
6. #13092651C2semidirect
7. #13092632C2semidirect
8. #13092614C2semidirect
9. #13092568C2semidirect
10. #13092560C2semidirect
11. #13092555C2semidirect
12. #13092551C2semidirect
13. #13092517C2semidirect
14. #13092489C2semidirect
15. D42×C23C2semidirect
19. C2×#67288C22semidirect
20. C22×Dic46C22semidirect
33. C2×#67273C22semidirect
34. C2×#67273C22semidirect
35. C2×#67273C22semidirect
36. C2×#67273C22semidirect
39. C2×#67272C22semidirect
40. C2×#67272C22semidirect
41. #10625101C22semidirect
42. #10625095C22semidirect
43. C2×#67267C22semidirect
44. C22×C23⋊C8C22semidirect
48. #10625046C22semidirect
49. C4×Dic46C22semidirect
51. #10625014C22semidirect
52. #10625014C22semidirect
53. C22⋊(C23⋊C8)C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
55. #10624992C22semidirect
56. #10624992C22semidirect
57. #10624991C22semidirect
58. #10624989C22semidirect
59. C4⋊(C23⋊C8)C22semidirect
60. #10624985C22semidirect
107. #67273D4semidirect
173. Dic46C2×D4semidirect
177. C23⋊C8C2×D4semidirect
195. C22×C23AGL(1,ℤ/8)semidirect
213. D42D23semidirect
279. C23#3265semidirect
416. C22#10625103semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
C22×#672732
#130930762
#130928042
#130926612
#130926512
#130926322
#130926142
#130925682
#130925602
#130925552
#130925512
#130925172
#130924892
D42×C232
#326523